ALBERT

Description: ABSTRACT There is no meta‐heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta‐heuristic algorithms. Out of all meta‐heuristic algorithms swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves (GW) considered as apex predators, motivated us to simulate GW in the optimization of geophysical data sets. The GW Optimizer (GWO) is a swarm‐based meta‐heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behavior of GW. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolf. The three main phases of hunting i.e., searching, encircling, and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the GWO, we performed inversion on the total gradient of magnetic, gravity and self‐potential (SP) anomalies. The results have been compared with the Particle Swarm Optimization (PSO) technique. Global minimum for all the examples from GWO was obtained with 7 wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise free and noise corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that compared to PSO, GWO is less sensitive to search space variations. Inversion of noise corrupted data shows that GWO has a better capability in handling noisy data as compared to PSO. Practical applicability of the GWO has been demonstrated by adopting four profiles (i.e., surface magnetic, airborne magnetic, gravity and SP) from the published literature. The GWO results show better data fit than the PSO results and match well with borehole data. This article is protected by copyright. All rights reserved

Description: ABSTRACT Seismic facies analysis is a well-established technique in the workflow followed by seismic interpreters. Typically, huge volumes of seismic data are scanned to derive maps of interesting features and find particular patterns, correlating them with the subsurface lithology and the lateral changes in the reservoir. In this paper, we show how seismic facies analysis can be accomplished in an effective and complementary way to the usual one. Our idea is to translate the seismic data in the musical domain through a process called sonification , mainly based on a very accurate time–frequency analysis of the original seismic signals. From these sonified seismic data, we extract several original musical attributes for seismic facies analysis, and we show that they can capture and explain underlying stratigraphic and structural features. Moreover, we introduce a complete workflow for seismic facies analysis starting exclusively from musical attributes, based on state-of-the-art machine learning computational techniques applied to the classification of the aforementioned musical attributes. We apply this workflow to two case studies: a sub-salt two-dimensional seismic section and a three-dimensional seismic cube. Seismic facies analysis through musical attributes proves to be very useful in enhancing the interpretation of complicated structural features and in anticipating the presence of hydrocarbon-bearing layers. This article is protected by copyright. All rights reserved

Description: ABSTRACT Average elastic properties of a fluid-saturated fractured rock are discussed in association with the extremely slow and dispersive Krauklis wave propagation within individual fractures. The presence of the Krauklis wave increases P-wave velocity dispersion and attenuation with decreasing frequency. Different laws (exponential, power, fractal and gamma laws) of distribution of the fracture length within the rock show more velocity dispersion and attenuation of the P-wave for greater fracture density, in particular, at low seismic frequencies. The results exhibit a remarkable difference in the P-wave reflection coefficient for frequency and angular dependency from the fractured layer in comparison with the homogeneous layer. The biggest variation in behavior of the reflection coefficient versus incident angle is observed at low seismic frequencies. The proposed approach and results of calculations allow an interpretation of abnormal velocity dispersion, high attenuation, and special behavior of reflection coefficients vs. frequency and angle of incidence as the indicators of fractures. This article is protected by copyright. All rights reserved

Description: ABSTRACT Radio-frequency electromagnetic tomography (or radio imaging method) employs radio-frequency (typically 0.1–10 MHz) electromagnetic wave propagation to delineate the distribution of electric properties between two boreholes. Currently, the straight-ray imaging method is the primary imaging method for the radio imaging method data acquired for mineral exploration. We carried out synthetic studies using three-dimensional finite-element modelling implemented in COMSOL Multiphysics to study the electromagnetic field characteristics and to assess the capability of the straight-ray imaging method using amplitude and phase data separately. We studied four sets of experiments with models of interest in the mining setting. In the first two experiments, we studied models with perfect conductors in homogeneous backgrounds, which show that the characteristics of the electromagnetic fields depend mainly on the wavelength. When the borehole separations are less than one wavelength, induction effects occur; conductors with simple geometries can be recovered acceptably with amplitude data but are incorrectly imaged on the phase tomogram. When the borehole separations are longer than two wavelengths, radiation effects play a major role. In this case, phase tomography provides images with acceptable quality, whereas amplitude tomography does not provide satisfactory results. The third experiment shows that imaging with both original and reciprocal datasets is somewhat helpful in improving the imaging quality by reducing the impact of noise. In the last experiment, we studied models with conductive zones extended into the borehole plane with different lengths, which were not accurately recovered with amplitude tomography. The experiment implies that it is difficult to determine the extent of a mineralised zone that has been intersected by one of the boreholes. Due to the large variation of the wavelength in the radio-frequency range, we suggest investigating the local electric properties to select an operating frequency prior to a survey. We conclude that straight-ray tomography with either amplitude or phase data cannot provide high-quality imaging results. We suggest using more general methods based on full electromagnetic modelling to interpret the data. In circumstances when computational time is critical, we suggest saving time by using either induction methods for borehole separations less than one wavelength or wave-based methods (only radiation fields are considered) for borehole separation larger than two wavelengths. This article is protected by copyright. All rights reserved

Description: ABSTRACT A focusing acoustic wave field, emitted into a medium from its boundary, converges to a focal spot around the designated focal point. Subsequently, the focused field acts as a virtual source which emits a field propagating away from the focal point, mimicking the response to a real source at the position of the focal point. In this first part of a two-part review paper on virtual sources and their responses, we define the focusing wave field as the time-reversal of an observed point-source response. This approach underlies time-reversal acoustics as well as seismic interferometry. We analyse the propagation of a time-reversed point-source response through an inhomogeneous medium, paying particular attention to the effect of internal multiples. We investigate the differences between emitting the focusing field from a closed boundary and from an open boundary and we analyse in detail the properties of the virtual source. Whereas emitting the time-reversed field from a closed boundary yields an accurate isotropic virtual source, emitting the field from an open boundary leads to a highly directional virtual source and significant artefacts related to multiple scattering. The latter problems are addressed in Part II, where we define the focusing wave field as an inverse filter which accounts for primaries and multiples. This article is protected by copyright. All rights reserved

Description: ABSTRACT The well-known asymptotic fractional four-parameter traveltime approximation and the five-parameter generalised traveltime approximation in stratified multi-layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure-mode and converted waves. The first three parameters of these traveltime expansions are zero-offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four-parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above-mentioned five-parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five-parameter traveltime approximations, which can be considered extensions of the four-parameter approximation and an alternative to the five-parameter approximation previously mentioned. The first three short-offset parameters are the same as before, but the two additional long-offset parameters are different and have specific physical meaning. One of them describes the propagation in the high-velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above-mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi-compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above-mentioned approximations are used, such as reflection and diffraction analysis and imaging.

Description: ABSTRACT Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high-frequency components, such as noise, and create undesirable imaging artifacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant- Q wave equation with decoupled fractional Laplacians, and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse-time migration (RTM). A time-dependent imaging condition is derived by applying Q -compensation in the frequency domain, while a time-independent imaging condition is formed in the image space by calculating image normalization weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high-frequency noise in the data. This article is protected by copyright. All rights reserved

Description: ABSTRACT Although seismic sources typically consist of identical broadband units alone, no physical constraint dictates the use of only one kind of device. We propose an acquisition method that involves the simultaneous exploitation of multiple types of sources during seismic surveys. It is suggested to replace (or support) traditional broadband sources with several devices individually transmitting diverse and reduced frequency bands and covering together the entire temporal and spatial bandwidth of interest. Together these devices represent a so-called Dispersed Source Array. As a consequence, the use of simpler sources becomes a practical proposition for seismic acquisition. In fact, the devices dedicated to the generation of the higher frequencies may be smaller and less powerful than the conventional sources, providing the acquisition system with an increased operational exibility and decreasing its environmental impact. Offshore we can think of more manageable boats carrying airguns of different volumes or marine vibrators generating sweeps with different frequency ranges. On land vibrator trucks of 1 different sizes, specifically designed for the emission of particular frequency bands, are pre- ferred. From a manufacturing point of view, such source units guarantee a more effcient acoustic energy transmission than today's complex broadband alternatives, relaxing the low versus high frequencies compromise. Furthermore, specific attention can be addressed to choose shot densities that are optimum for the different devices according to their emitted bandwidth. In fact, since the sampling requirements depend on the maximum transmit-ted frequencies, the appropriate number of sources dedicated to the lower frequencies is relatively small, provided the signal-to-noise ratio requirements are met. Additionally, the method allows to rethink the way to address the ghost problem in marine seismic acquisi-tion, permitting to tow different sources at different depths based on the devices individual central frequencies. As a consequence, the destructive interference of the ghost notches, including the one at 0 Hz, is largely mitigated. Furthermore, blended acquisition (also known as simultaneous source acquisition) is part of the Dispersed Source Array concept, improving the operational exibility, the cost effciency and the signal to noise ratio. Based on theoretical considerations and numerical data examples, the advantages of this approach and its feasibility are demonstrated. This article is protected by copyright. All rights reserved

Description: ABSTRACT Prestack image volumes may be decomposed into specular and non-specular parts by filters defined in the dip-angle domain. For space-shift extended image volumes, the dip-angle decomposition is derived via local Radon transform in depth and midpoint coordinates, followed by an averaging over space-shifts. We propose to employ prestack space-shift extended reverse-time migration and dip-angle decomposition for imaging small-scale structural elements, considered as seismic diffractors, in models with arbitrary complexity. A suitable design of a specularity filter in the dip-angle domain rejects the dominant reflectors and enhances diffractors and other non-specular image content. The filter exploits a clear discrimination in dip between specular reflections and diffractions. The former are stationary at the specular dip, whereas the latter are non-stationary without a preferred dip direction. While the filtered image volume features other than the diffractor images (for example, noise and truncation artifacts are also present), synthetic and field data examples suggest that diffractors tend to dominate, and are readily recognizable. Averaging over space-shifts in the filter construction makes the reflectors rejection robust against migration velocity errors. Another consequence of the space-shift extension and its angle-domain transforms is the possibility of exploring the image in a multiple set of common-image gathers. The filtered diffractions may be analyzed simultaneously in space-shift, scattering-angle, and dip-angle image-gathers, by means of a single migration job. The deliverables of our method obviously enrich the processed material on the interpreter's desk. We expect them to further supplement our understanding of the earth's interior. This article is protected by copyright. All rights reserved

Description: ABSTRACT In this paper, we propose a workflow based on SalSi for the detection and delineation of geological structures such as salt domes. SalSi is a seismic attribute designed based on the modeling of human visual system that detects the salient features and captures the spatial correlation within seismic volumes for delineating seismic structures. Using SalSi , we can not only highlight the neighboring regions of salt domes to assist a seismic interpreter but also delineate such structures using a region growing method and post-processing. The proposed delineation workflow detects the salt-dome boundary with very good precision and accuracy. Experimental results show the effectiveness of the proposed workflow on a real seismic dataset acquired from the North Sea, F3 block. For the subjective evaluation of the results of different salt-dome delineation algorithms, we have used a reference salt-dome boundary interpreted by a geophysicist. For the objective evaluation of results, we have used five different metrics based on pixels, shape, and curvedness to establish the effectiveness of the proposed workflow. The proposed workflow is not only fast but also yields better results as compared to other salt-dome delineation algorithms and shows a promising potential in seismic interpretation. This article is protected by copyright. All rights reserved

Description: High Resolution Aeromagnetic Data over the Bida Basin, North Central Nigeria has been analyzed to investigate the possible continuity of Ifewara fault zone, through the Bida Basin, to Zungeru fault zone. Analytic Signal Magnitude, Horizontal Gradient Magnitude and Euler Deconvolution methods were applied to the aeromagnetic data to delineate the subsurface structures. The results showed that a prominent NNE-SSW trending fault associated with the Ifewara fault zone extends through the study area. Other faults trending in the ENE-WSW, NE-SW, NW-SE, E-W and WNW-ESE directions were also mapped. Interpreted models revealed the presence of intrusives and a possible mineralized zone within the study area. We therefore concluded that the inferred faults zone within the basin have affinity with the trend of Ifewara fault zone; an indication of possible extension and linkage with Zungeru fault zone through the Bida Basin. This article is protected by copyright. All rights reserved

Description: The existence of strong random noise in surface microseismic data may decrease the utility of these data. Non-subsampled shearlet transform (NSST) can effectively suppress noise by properly setting a threshold to the NSST coefficients. However, when the signal-to-noise ratio (SNR) of data is low, the coefficients related to the noise are so close to the coefficients associated with signals in the NSST domain that the coefficients related to the noise will be treated as signals and retained. Therefore, we need to minimize the overlapping coefficients before thresholding. In this paper, a singular value decomposition (SVD) algorithm is introduced to the NSST coefficients, and the low-rank approximation reconstructs each NSST coefficient matrix in SVD domain. The NSST coefficients of signals have bigger singular values than those of the random noise, which implies that the NSST coefficients can be well estimated by taking only a few largest singular values. Therefore, those proprieties of SVD may significantly help to minimize the overlapping of noise and signals coefficients in NSST domain. Finally, the denoised microseismic data are obtained easily by giving a simple threshold to the reconstructed coefficients matrix. The performance of the proposed method is evaluated on both synthetic and field microseismic data. The experimental results illustrate that the proposed method can more effectively eliminate the random noise and preserve signals of interest. This article is protected by copyright. All rights reserved

Description: ABSTRACT Reverse-time migration (RTM) has become an industry standard imaging method for complex geological areas. We present an approach for increasing its imaging resolution by employing time-shift gathers. The method consists of two steps: 1) migrating seismic data with the extended imaging condition to get time-shift gathers; 2) accumulating the information from time-shift gathers after they are transformed to zero-lag time-shift by a post-stack depth migration on a finer grid. The final image is generated on a grid which is denser than that of the original image thus increasing its resolution. The proposed method is based on the observation that non-zero-lag time-shift images recorded by the regular computing grid contain the information of zero-lag time-shift image of a denser grid, and such information can be continued to zero-lag time-shift and refocused at the correct locations on the denser grid. The extra computational cost of the proposed method amounts to the computational cost of zero-offset migration, and is almost negligible compared to the cost of prestack shot-record RTM. Numerical tests on synthetic models demonstrate that the method can effectively improve RTM resolution. It can also be regarded as an approach to improve the effciency of RTM by performing wavefield extrapolation on a coarse grid and generating the final image on the desired fine grid. This article is protected by copyright. All rights reserved

Description: ABSTRACT There is no meta-heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta-heuristic algorithms. Out of all meta-heuristic algorithms swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves (GW) considered as apex predators, motivated us to simulate GW in the optimization of geophysical data sets. The GW Optimizer (GWO) is a swarm-based meta-heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behavior of GW. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolf. The three main phases of hunting i.e., searching, encircling, and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the GWO, we performed inversion on the total gradient of magnetic, gravity and self-potential (SP) anomalies. The results have been compared with the Particle Swarm Optimization (PSO) technique. Global minimum for all the examples from GWO was obtained with 7 wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise free and noise corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that compared to PSO, GWO is less sensitive to search space variations. Inversion of noise corrupted data shows that GWO has a better capability in handling noisy data as compared to PSO. Practical applicability of the GWO has been demonstrated by adopting four profiles (i.e., surface magnetic, airborne magnetic, gravity and SP) from the published literature. The GWO results show better data fit than the PSO results and match well with borehole data. This article is protected by copyright. All rights reserved

Description: ABSTRACT We propose a robust approach for joint inversion of PP- and PSV-wave angle gathers along different azimuths for the elastic properties of the homogeneous isotropic host rock and excess compliances due to the presence of fractures. Motivated by the expression of fluid content indicator in fractured reservoirs and the sensitivity of Lamé impedances to fluid type, we derive PP- and PSV-wave reflection coefficients in terms of Lamé impedances, density, and fracture compliances for an interface separating two horizontal transversely isotropic media. Following a Bayesian framework, we construct an objective function that includes initial models. We employ the iteratively reweighted least-squares algorithm to solve the inversion problem to estimate unknown parameters (i.e., Lamé impedances, density, and fracture compliances) from PP- and PSV-wave angle gathers along different azimuths. Synthetic tests reveal that the unknown parameters estimated by the joint inversion approach match true values better than those estimated by a PP-wave amplitude inversion only. A real data test indicates that reasonable results for subsurface fracture detection are obtained from the joint inversion approach. This article is protected by copyright. All rights reserved

Description: ABSTRACT Data interpolation is an important step for seismic data analysis because many processing tasks, such as multiple attenuation and migration, are based on regularly sampled seismic data. Failed interpolations may introduce artifacts and eventually lead to inaccurate final processing results. In this paper, we generalize seismic data interpolation as a basis pursuit problem and propose an iteration framework for recovering missing data. The method is based on nonlinear iteration and sparse transform. A modified Bregman iteration is used for solving the constrained minimization problem based on compressed sensing. The new iterative strategy guarantees fast convergence by using a fixed threshold value. We also propose a generalized velocity-dependent (VD) formulation of the seislet transform as an effective sparse transform, in which the nonhyperbolic normal moveout equation serves as a bridge between local slope patterns and moveout parameters in the common midpoint domain. It can also be reduced to the traditional VD-seislet if special heterogeneity parameter is selected. The generalized VD-seislet transform predicts prestack reection data in offset coordinates, which provides a high compression of reection events. The method was applied to synthetic and field data examples and the results show that the generalized VD-seislet transform can reconstruct missing data with the help of the modified Bregman iteration even for nonhyperbolic reections under complex conditions, such as VTI media or aliasing. This article is protected by copyright. All rights reserved

Description: An improved iteratively re-weighted factor analysis procedure is presented to interpret engineering geophysical sounding logs in shallow unsaturated sediments. We simultaneously process cone resistance, electric resistivity and nuclear data acquired by direct-push tools to give robust estimates of factor variables and water content in unconsolidated heterogeneous formations. The statistical procedure is based on the iterative re-weighting of the deviations between the measured and calculated data using the Most Frequent Value method famous for its robustness and high statistical efficiency. The iterative approach improves the result of factor analysis for not normally distributed data and extremely noisy measurements. By detecting a strong regression relation between one of the extracted factors and the fractional volume of water, we establish an independent method for water content estimation along the penetration hole. We verify the estimated values of water volume by using a highly overdetermined quality checked interval inversion procedure. The multidimensional extension of the statistical method allows the estimation of water content distribution along both the vertical and horizontal coordinates. Numerical tests using engineering geophysical sounding data measured in a Hungarian loessy-sandy formation demonstrate the feasibility of the Most Frequent Value based factor analysis, which can be efficiently used for a more reliable hydrogeophysical characterization of the unsaturated zone. This article is protected by copyright. All rights reserved

Description: The reflectivity method plays an important role in seismic modeling. It has been used to model different types of waves propagating in elastic and anelastic media. The diffusive-viscous wave equation was proposed to investigate the relationship between frequency dependence of reflections and fluid saturation. It is also used to describe the attenuation property of seismic wave in a fluid-saturated medium. The attenuation of diffusive-viscous wave is mainly characterized by the effective attenuation parameters in the equation. Thus, it is essential to obtain those parameters and further to characterize the features of the diffusive-viscous wave. In this work, we use inversion method to obtain the effective attenuation parameters through Quality Factor Q p to investigate the characteristics of diffusive-viscous wave by comparing with those of viscoacoustic wave. Then, the reflection/transmission coefficients in a dip plane layered medium are studied through coordinate transform and plane wave theory. Consequently, the reflectivity method is extended to compute seismograms of diffusive-viscous wave in a dip plane multi-layered medium. Finally, we present two models to simulate the propagation of diffusive-viscous wave in a dip plane multi-layered medium by comparing the results with those in a viscoacoustic medium. The numerical results demonstrate the validity of our extension of reflectivity method to the diffusive-viscous medium. The numerical examples in both time domain and time-frequency domain show that the reflections from a dip plane interface have significant phase shift and amplitude change compared with the results of horizontal plane interface due to the differences in reflection/transmission coefficients. Moreover, the modeling results show strong attenuation and phase shift in the diffusive-viscous wave compared with those of viscoacoustic wave. This article is protected by copyright. All rights reserved

Description: ABSTRACT The classical finite-difference methods for seismic wave modeling are very accurate at low wavenumbers, but suffer from inaccuracies at high wavenumbers, particularly at Nyquist wavenumber. In contrast, the optimization finite-difference methods reduce inaccuracies at high wavenumbers, but suffer from inaccuracies at low wavenumbers, particularly at zero wavenumber when the operator length is not long and the whole range of wavenumbers is considered. Inaccuracy at zero wavenumber means that the optimization methods only have a zeroth-order accuracy of truncation, and thus are not rigorously convergent. To guarantee the rigorous convergence of the optimization methods, we have developed accuracy-constrained optimization methods. Different-order accuracy-constrained optimization methods are presented. These methods not only guarantee the rigorous convergence but also reduce inaccuracies at low wavenumbers. Accuracy-constrained optimization methods are applied to staggered-grid elastic wave modeling. This article is protected by copyright. All rights reserved

Description: We have applied a wavelet-based spectral decomposition scheme and a multilayered feed-forward neural network to interpret turbidite depositional systems from 3D reflection seismic data and well logs for a prospective hydrocarbon zone in the outer fold and thrust belt of the Niger Delta. The goal was to overcome difficulties in interpreting depositional systems from deep sections of the Field, occasioned by loss of seismic resolution with depth and the sparse distribution of wells. The decomposition scheme allowed us to delineate multiple depositional systems not apparent on the conventional seismic amplitude display. These systems include linear channels systems with terminal splay lobes, a sinuous channel system and its abandoned meander loops, and sediment wave features in over-bank areas. Delineated channel morphologies and transport directions varied both laterally and vertically and were possibly dependent upon the disposition of the pre-thrusting paleo-seafloor. Terminal splay lobes are fragmented and coincident with the locations of topographic lows which are possibly related to the initial configurations of the oceanic basement below. Predicted porosity and resistivity distributions have morphologies which correlate well with the mapping provided by the spectral decomposition scheme. The property distributions indicate that reservoir prone systems in the Field, and possibly within the outer fold and thrust belt, comprise primarily of channel systems, both linear and sinuous, and their associated splay lobes. The channel systems appear vertically stacked and this situation possibly increases the potential success rate for exploration wells in the region. Beyond channel limits, re-distributive bottom currents varying rapidly in speed and direction apparently encouraged the dispersal of sand rich sediments to form sediment waves. Despite the limited well control, the methodology significantly aided our interpretation. It proved effective at revealing the distribution of reservoir prone facies within the Field and provided insight into the dominant factors which controlled deposition within the Field. This article is protected by copyright. All rights reserved

Description: In recent years, the necessity of constructing new geomagnetic observatories in Iran has been discussed from various aspects. Improper site selection of such important data centers can significantly affect the quality of their recorded data. In this research, site selection studies were performed to find the most favorable location to construct a geomagnetic observatory in Kerman province, southeast of Iran. Having defined eleven site selection criteria for geomagnetic observatories, all the data layers were prepared for the whole province. After detection of seven promising regions using Analytical Hierarchy Process and Fuzzy Logic method in Geographical Information System (GIS), Technique for Order of Preference by Similarity to Ideal Solution was used for ranking of the suitable areas. The most favorable region was finally detected in the southwest of Kerman Province, located between the cities of Baft and Sirjan. Detailed land surveys can be focused in this region to decide on the optimum area for the construction of the geomagnetic observatory. This article is protected by copyright. All rights reserved

Description: ABSTRACT The topography-dependent eikonal equation formulated in a curvilinear coordinate system has recently been established, and has been revealed as effective for calculating first-arrival traveltimes of seismic waves in an Earth model with an irregular free surface. The Lax-Friedrichs sweeping scheme, widely used in the previous studies to approximate the topography-dependent eikonal equation viscosity solutions, is more dissipative and needs a much higher number of iterations to converge. Furthermore, the required number of iterations grows with the grid refinement and results in heavy computation in dense grids, which hampers the application of the Lax-Friedrichs sweeping scheme to seismic wave traveltime calculation and high-resolution imaging. In this paper, we introduce a new upwind fast sweeping solver by discretizing the Legendre transform of the numerical Hamiltonian of the topography-dependent eikonal equation using an explicit formula. The minimization related to the Legendre transform in the sweeping scheme is solved analytically, which proved to be much more efficient than the Lax-Friedrichs algorithm in solving the topography-dependent eikonal equation. Several numerical experiments demonstrate that the new upwind fast sweeping method converges and achieves much better accuracy after a finite number of iterations, independently of the mesh size, which makes it an efficient and robust tool for calculating traveltimes in the presence of a non-flat free surface. This article is protected by copyright. All rights reserved

Description: ABSTRACT We develop a new time-domain reverse-time migration method called double plane-wave reverse-time migration that uses plane-wave transformed gathers. Original shot gathers with appropriate data acquisition geometry are double slant stacked into the double plane-wave domain with minimal slant stacking artefacts. The range of plane-wave components needed for migration can be determined by estimating the maximum time dips present in shot gathers. This reduces the total number of input traces for migration and increases migration efficiency. Unlike the pre-stack shot-profile reverse-time migration where the number of forward propagations is proportional to the number of shots, the number of forward propagations needed for the proposed method remains constant and is relatively small even for large seismic datasets. Therefore, the proposed method can improve the efficiency of the migration and be suitable for migrating large datasets. Double plane-wave reverse-time migration can be performed for selected plane-wave components to obtain subsurface interfaces with different dips, which makes the migration method target oriented. This feature also makes the method a useful tool for migration velocity analysis. For example, we are able to promptly obtain trial images with nearly horizontal interfaces and adjust velocity models according to common image gathers. Seismic signal coming from steeply dipping interfaces can be included into the migration to build images with more detailed structures and higher spatial resolution as better velocity models become available. Illumination compensation imaging conditions for the proposed method are also introduced to obtain images with balanced amplitudes.

Description: ABSTRACT Clays and clay-bearing rocks like shale are extremely water sensitive. This is partly due to the interaction between water and mineral surfaces, strengthened by the presence of nanometer-size pores and related large specific surface areas. Molecular-scale numerical simulations, using a discrete-element model, show that shear rigidity can be associated with structurally ordered (bound or adsorbed) water near charged surfaces. Building on these and other molecular dynamics simulations plus nanoscale experiments from the literature, the water monolayer adjacent to hydrophilic solid surfaces appears to be characterised by shear stiffness and/or enhanced viscosity. In both cases, elastic wave propagation will be affected by the bound or adsorbed water. Using a simple rock physics model, bound water properties were adjusted to match laboratory measured P- and S-wave velocities on pure water-saturated kaolinite and smectite. To fit the measured stress sensitivity, particularly for kaolinite, the contribution from solid-grain contact stiffness needs to be added. The model predicts, particularly for S-waves, that viscoelastic bound water could be a source of dispersion in clay and clay-rich rocks. The bound-water-based rock physics model is found to represent a lower bound to laboratory-measured velocities obtained with shales of different mineralogy and porosity levels.

Description: ABSTRACT The oil shale exploration program in Jordan is undertaking great activity in the domain of applied geophysical methods to evaluate bitumen-bearing rock. In the study area, the bituminous marl or oil shale exhibits a rock type dominated by lithofacies layers composed of chalky limestone, marls, clayey marls and phosphatic marls. The study aims to present enhancements for oil shale seam detection using progressive interpretation from a one-dimensional inversion to a three-dimensional modelling and inversion of ground-based transient electromagnetic data at an area of stressed geological layers. The geophysical survey combined 58 transient electromagnetic sites to produce geoelectrical structures at different depth slices, and cross-sections were used to characterise the horizon of the most likely sites for mining oil shale. The results show valuable information on the thickness of the oil shale seam at 3.7 Ωm, which is correlated to the geoelectrical layer between 2 ms and 4 ms transient time delays, and at depths ranging between 85 m and 105 m. The 300 m penetrated depth of the transient electromagnetic soundings allows the resolution of the main geological units at narrow resistivity contrast and the distinction of the main geological structures that constrain the detection of the oil shale seam. This geoelectrical layer at different depth slices illustrates a localised oil shale setting and can be spatially correlated with an area bounded by fold and fault systems. Also, three-dimensional modelling and inversion for synthetic and experimental data are introduced at the faulted area. The results show the limitations of oil shale imaging at a depth exceeding 130 m, which depends on the near surface resistivity layer, the low resistivity contrast of the main lithological units, and the degree of geological detail achieved at a suitable model's misfit value. This article is protected by copyright. All rights reserved

Description: We propose a sparsity enhanced (time-invariant) wavelet deconvolution process, in which the sparse-spike deconvolution of the residual wavelet i.e.; the Wiener deconvolved wavelet (which usually is not a spike due to band-limitations of the original wavelet), is being gradually added to the data after Wiener deconvolution. The contribution of the sparse-spike deconvolution result is proportional to the deviation of the amplitude spectrum of the residual wavelet from unity, i.e.; it is stronger the closer the amplitude spectrum of the residual wavelet is to zero, but very small the closer it is to unity. We demonstrate the proposed technique on real data with the deconvolution of the (normal-incidence) source side sea-surface ghost of marine towed streamer data. We also present the extension of the proposed technique to time-variant wavelet deconvolution. This article is protected by copyright. All rights reserved

Description: Damage characterization in solid media is studied in this work through ultrasonic measurements. A synthetic 3D printed sample including a system of horizontally aligned microcracks is used. In contrast to other manual fabrication methods presented in the literature, the construction process considered here ensures a better control and accuracy of size, shape and spatial distribution of the microcracks network in the synthetic sample. The acoustic measure-ments were conducted through a specific device using triple acoustic sensors, which allows to capturing at each incident direction three wave-modes. The evolution of the ultrasonic velocities with respect to incident angle accounted for the damage-induced anisotropy. The experimental results are then compared with some well-known effective media theories in order to discuss their potential use for following studies. Finally, we highlighted and compared the accuracy of these theories used for inversion procedure to quantify damage in the medium. This article is protected by copyright. All rights reserved

Description: ABSTRACT We develop a 2D full waveform inversion approach for the simultaneous determination of S-wave velocity and density models from SH- and Love wave data. We illustrate the advantages of the SH/Love full waveform inversion with a simple synthetic example and demonstrate the method's applicability to a near-surface data set, recorded in the village Cˇ achtice in Northwestern Slovakia. Goal of the survey was to map remains of historical building foundations in a highly heterogeneous subsurface. The seismic survey comprises two parallel SH-profiles with maximum offsets of 24 m and covers a frequency range from 5 Hz to 80 Hz with high signalto-noise ratio well suited for full waveform inversion. Using the Wiechert-Herglotz method we determined a 1D gradient velocity model as a starting model for FWI. The 2D waveform inversion approach uses the global correlation norm as objective function in combination with a sequential inversion of low-pass filtered field data. This mitigates the non-linearity of the multi-parameter inverse problem. Test computations show that the influence of visco-elastic effects on the waveform inversion result is rather small. Further tests using a mono-parameter shear modulus inversion reveal that the inversion of the density model has no significant impact on the final data fit. The final full waveform inversion S-wave velocity and density models show a prominent low-velocity weathering layer. Below this layer the subsurface is highly heterogeneous. Minimum anomaly sizes correspond to approximately half of the dominant Love-wavelength. The results demonstrate the ability of 2D SH waveform inversion to image shallow small scale soil structure. However, they do not show any evidence of foundation walls. This article is protected by copyright. All rights reserved

Description: In this paper we present a methodology to perform geophysical inversion of large scale linear systems via a covariance-free orthogonal transformation: the Discrete Cosine Transform (DCT). The methodology consists in compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore-Penrose pseudo-inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions, and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic 2D gravimetric problem for different dimensionalities and different levels of white Gaussian noise, and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the DCT pseudoinverse outperforms the classical least-squares techniques, mainly in presence of noise, since the solutions that are obtained are more stable and fit the observed data with a lowest RMS error. Besides, we show that the model reduction is a very effective way of parameter regularization when the conditioning of the reduced DCT matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this nonlinear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and nonlinear inverse problems (through linearization) arising in technology and particularly in geophysics, independently of the geophysical model discretization and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill-conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations. This article is protected by copyright. All rights reserved

Description: ABSTRACT Z-axis tipper electromagnetic (ZTEM) and broadband magnetotelluric (MT) data were used to determine three-dimensional (3-D) electrical resistivity models of the Morrison porphyry Cu-Au-Mo deposit in British Columbia. ZTEM data are collected with a helicopter, thus allowing rapid surveys with uniform spatial sampling. Ground-based MT surveys can achieve a greater exploration depth than ZTEM, but data collection is slower and can be limited by difficult terrain. The airborne ZTEM tipper data and the ground MT tipper data show good agreement at the Morrison deposit despite differences in the data collection method, spatial sampling and collection date. Resistivity models derived from individual inversions of the ZTEM tipper data and MT impedance data contain some similar features, but the ZTEM model appears to lack resolution below a depth of 1 km and the MT model suffers from non-uniform and relatively sparse spatial sampling. The joint ZTEM-MT inversion solves these issues by combining the dense spatial sampling of the airborne ZTEM technique and the deeper penetration of the lower frequency MT data. The resulting joint resistivity model correlates well with the known geology and distribution of alteration at the Morrison deposit. Higher resistivity is associated with the potassic alteration zone and volcanic country rocks, whereas areas of lower resistivity agree with known faults and sedimentary units. The pyrite halo and ≥0.3 % Cu zone have the moderate resistivity that is expected of disseminated sulfides. The joint ZTEM-MT inversion provides an improved resistivity model by enhancing the lateral and depth resolution of resistivity features compared to the individual ZTEM and MT inversions. This case study shows that a joint ZTEM-MT approach effectively images the interpreted mineralized zone at the Morrison deposit and could be beneficial in exploration for disseminated sulfides at other porphyry deposits. This article is protected by copyright. All rights reserved

Description: ABSTRACT Multiparameter inversion for pre-stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem, due to the non-unique results and unstable nature of the processing; the pre-stack seismic inversion problem is ill-posed and band-limited. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge-preserving regularization and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimization problem. The method directly obtains reflectivity R PP values using the full Zoeppritz equation instead of its approximations, and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S- and P-wave velocity ratio and using the generalized Gardner equation. We substituted the inverted parameters, i.e., the P-wave velocity, the fitting deviation of S-wave velocity, and the density were inverted instead of the P-wave velocity, the S-wave velocity, and the density, and the generalized Gardner equation was applied as a constraint. Test results on 2-D synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilizing high-order anisotropic Markov random field neighbourhoods at early stages and low-order anisotropic Markov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves. This article is protected by copyright. All rights reserved

Description: ABSTRACT The electromagnetic response of a horizontal electric dipole transmitter in the presence of a conductive, layered earth is important in a number of geophysical applications, ranging from controlled-source audio-frequency magnetotellurics to borehole geophysics to marine electromagnetics. The problem has been thoroughly studied for more than a century, starting from a dipole resting on the surface of a halfspace and subsequently advancing all the way to a transmitter buried within a stack of anisotropic layers. The solution is still relevant today. For example, it is useful for one-dimensional modelling and interpretation, as well as to provide background fields for two- and three-dimensional modelling methods such as integral equation or primary-secondary field formulations. This tutorial borrows elements from the many texts and papers on the topic and combines them into what we believe is a helpful guide to performing layered earth electromagnetic field calculations. It is not intended to replace any of the existing work on the subject. However, we have found that this combination of elements is particularly effective in teaching electromagnetic theory and providing a basis for algorithmic development. Readers will be able to calculate electric and magnetic fields at any point in or above the earth, produced by a transmitter at any location. As an illustrative example, we calculate the fields of a dipole buried in a multilayered anisotropic earth to demonstrate how the theory developed in this tutorial can be implemented in practice; we then use the example to examine the diffusion of volume charge density within anisotropic media – a rarely visualized process. The algorithm is internally validated by comparing the response of many thin layers with alternating high and low conductivity to the theoretically equivalent (yet algorithmically simpler) anisotropic solution, as well as externally validated against an independent algorithm. This article is protected by copyright. All rights reserved

Description: ABSTRACT We investigate fracture induced attenuation anisotropy in a cluster of events from a microseismic dataset acquired during hydraulic fracture stimulation. The dataset contains 888 events of magnitude −3.0 to 0.0. We use a log-spectral-amplitude-ratio method to estimate change in t * over a half hour time period where fluid is being injected and an increase in fracturing from S-wave splitting analysis has been previously inferred. A Pearson's correlation analysis is used to assess whether or not changes in attenuation with time are statistically significant. P-waves show no systematic change in t * during this time. In contrast, S-waves polarised perpendicular to the fractures show a clear and statistically significant increase with time, whilst S-waves polarised parallel to the fractures show a weak negative trend. We also compare t * between the two S-waves, finding an increase in Δ t * with time. A poroelastic rock physics model of fracture-induced attenuation anisotropy is used to interpret the results. This model suggests that the observed changes in t* are related to an increase in fracture density of up to 0:04. This is much higher than previous estimates of 0:025 ± 0:002 based on S-wave velocity anisotropy, but there is considerably more scatter in the attenuation measurements. This could be due to the added sensitivity of attenuation measurement to non-aligned fractures, fracture shape, and fluid properties. Nevertheless, this pilot study shows that attenuation measurements are sensitive to fracture properties such as fracture density and aspect ratio. This article is protected by copyright. All rights reserved

Description: SUMMARY When modelling the propagation of 3-D non-axisymmetric viscoelastic waves in cylindrical coordinates using the finite-difference time-domain (FDTD) method, one encounters a mathematical singularity due to the presence of 1 /r terms in the viscoelastic wave equations. For many years this issue has been impeding the accurate numerical solution near the axis. In this paper, we propose a simple but effective method for the treatment of this numerical singularity problem. By rotating the Cartesian coordinate (RCC) system around the z -axis in cylindrical coordinates, the numerical singularity problems in both 2-D and 3-D cylindrical coordinates can be removed. This algorithm has three advantages over the conventional treatment techniques: 1) the excitation source can be directly loaded at r = 0; 2) the central difference scheme with second-order accuracy is maintained; 3) the stability condition at the axis is consistent with the FDTD in Cartesian coordinates. This method is verified by several 3-D numerical examples. Results show that the method is accurate and stable at the singularity point. The improved FDTD algorithm is also applied to sonic logging simulations in non-axisymmetric formations and sources. This article is protected by copyright. All rights reserved

Description: Our objective was to discover the effect of variations in fluid properties and fracture geometry on the velocity of seismic wave propagation in fluid-saturated media with parallel planar fractures. We used numerical models calculated by analytical solutions to examine the behaviour of P-wave phase velocity dispersion in the normal direction to layering, in non-porous and porous media with planar fractures. We also examined the anisotropy of low frequency phase and group velocities of fast and slow P-waves and angular dependent reflection coefficients in media with planar fractures, under conditions of saturation by fluids with varying bulk moduli, densities, and fracture apertures. We defined several parameters: rHL , rhl , and Ic characterising dispersion, ϵ′ characterising anisotropy, rFS characterising the difference between fast and slow modes, R 0 and G′ characterising reflection. Our results show that the behaviour of dispersion shows wider stopbands in the case of gas saturation. Concavity indicator of dispersion Ic for gas saturation was greater than that for liquid saturation, and is usually greater than 1. Anisotropy is more sensitive to bulk modulus contrast than to density contrast between the solid and fluid, and rFS is more sensitive to density contrast than to bulk modulus contrast. The case of gas saturation usually had a greater negative R 0 and a greater value of G′ compared with those of brine, heavy and light oil saturations. Our results are helpful in distinguishing fluid types saturating geophysical fractures and estimating the aperture and spacing of planar fractures. In seismic exploration, bulk modulus and fluid density can provide useful information in distinguishing among brine, oil, and gas; fracture geometry is important to estimate the permeability of reservoirs. This article is protected by copyright. All rights reserved

Description: This paper develops the generalized effective-medium theory of induced polarization (GEMTIP) for the rock models with elliptical grains and applies this theory to studying the complex resistivity of typical mineral rocks. We first demonstrate that the developed GEMTIP model can correctly represent the induced polarization (IP) phenomenon in multiphase artificial rock samples manufactured using pyrite and magnetite particles. We have also collected representative rock samples from the Cu-Au deposit in Mongolia, and subjected them to the mineralogical analysis using Quantitative Evaluation of Minerals by Scanning Electron Microscopy (QEMSCan) technology. The electrical properties of the same samples were determined using the laboratory complex resistivity measurements. As a result, we have established relationships between the mineral composition of the rocks, determined using QEMSCan analysis, and the parameters of the GEMTIP model defined from the lab measurements of the electrical properties of the rocks. These relationships open the possibility for remote estimation of types of mineralization and for mineral discrimination using spectral IP data. This article is protected by copyright. All rights reserved

Description: Seismic monitoring of reservoir and overburden performance during subsurface CO 2 storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock-stiffness and elastic-velocity changes of a shale overburden formation caused by both reservoir-inflation induced stress changes, and leakage of CO 2 into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in-situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of: (i) ultrasonic velocities; (ii) quasi-static rock deformations, (iii) dynamic elastic stiffnesses at seismic frequencies within single test; which allowed to quantify effects of seismic dispersion. In addition fluid-substitution effects connected with possible CO 2 leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that: (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in-situ stress changes mostly affects the P-wave velocities; (iv) small leakage of the CO 2 into the overburden may lead to the velocity changes which are comparable with one associated with geomechanical influence; (v) non-elastic effects increase stress sensitivity of an acoustic waves; (iv) both geomechanical and fluid substitution effects would create significant time shifts which should be detectable by time-lapse seismic. This article is protected by copyright. All rights reserved

Description: Analysis of pre-stack seismic data is important for seismic interpretation and geological features classification. However, most classification analyses are based on post-stack data, which ignores pre-stack information and it may be disadvantageous for complex geological description. In this work we propose a method to address the classification of pre-stack seismic data decomposed using the wavelet transform to spread the amplitude and frequency seismic attributes at the same time, which are then classified by a self-organizing map. The resulting classes constitute an attribute constructed by the joint amplitude-frequency components of the transformed pre-stack seismic gathers, which create a multidimensional set defined through a given metric. Tests on a real seismic cube revealed that the method can identify patterns observed on the seismic images, which agree with our current knowledge of the seismic data. The method can be used as a complementary tool to identify features and structures in seismic signals. This article is protected by copyright. All rights reserved

Description: We present a 2D inversion scheme for magnetotelluric data, where the conductivity structure is parameterized with different wavelet functions that are collected in a wavelet-based dictionary. The inversion model estimate is regularized in terms of wavelet coefficient sparsity following the compressive sensing approach. However, when the model is expressed in the basis of a single wavelet family only, the geometrical appearance of model features reflects the shape of the wavelet functions. Combining two or more wavelet families in a dictionary provides greater flexibility to represent model structure, permitting for example for the simultaneous occurrence of smooth and sharp anomalies within the same model. We show that the application of the sparsity regularization scheme with wavelet dictionaries provides the user with a number of different model classes that may explain the data to the same extent. For a real data example from the Dead Sea Transform, we show that the use of such a scheme can be beneficial to evaluate the geometries of conductivity anomalies and to understand the effect of regularization on the model estimate. This article is protected by copyright. All rights reserved

Description: ABSTRACT We investigate the influence of source wavelet errors on inversion-based surface-related multiple attenuation, in order to address how the inverted primary impulse response, estimated primaries and predicted multiples are affected by the estimated wavelet. In theory, errors in estimated wavelet can lead to errors in the upgoing waves. Because of smoothness and band-limitedness characteristics of the estimated wavelet, errors in the upgoing waves are usually not white and random. Theoretical analysis and two synthetic examples demonstrate that (1) when the overall amplitude scalar of the estimated wavelet is under-estimated, the inversion of the primary impulse response suffers from instability which will distort the estimation of primaries, and (2) when wavelet is over-estimated, the estimated primaries will simply mimic the recorded upgoing waves. Nevertheless, the quality of the estimated primaries in the region above the first-order water-bottom multiples is independent of the estimated wavelet. Synthetic results illustrate that inversion-based surface-related multiple attenuation with a known wavelet is stable, since slight inaccuracy in amplitude spectrum and/or phase spectrum of the given wavelet or the corresponding upgoing waves will not lead to considerable deviation in the waveforms of the inverted results from those of the references. Furthermore, shot-to-shot wavelet variations, with maximum amplitude difference of 5% and maximum phase difference of 10 degrees, create just slight artifacts in both the inverted primary impulse response and estimated primaries. Moreover, the sensitivity test of estimation of primaries by sparse inversion method involving wavelet estimation shows that this method can stably and alternately update the wavelet and the primary impulse response, however, different choices of the initial wavelet can lead to different final inverted results. This article is protected by copyright. All rights reserved

Description: ABSTRACT We present a nonlinear method to invert potential fields data, based on inverting the scaling function (τ) of the potential fields, a quantity that is independent on the source property, that is the mass density in the gravity case or the magnetic susceptibility in the magnetic case. So, no a priori prescription of the density contrast is needed and the source model geometry is determined independently on it. We assume Talwani's formula and generalize the Multi-HOmogeneity Depth Estimation (MHODE) method to the case of the inhomogeneous field generated by a general 2D source. The scaling function is calculated at different altitudes along the lines defined by the extreme points of the potential fields and the inversion of the scaling function yields the coordinates of the vertices of a multiple source body. Once the geometry is estimated, the source density is automatically computed from a simple regression of the scaling function of the gravity data vs. that generated from the estimated source body with a unit-density. We solve the above nonlinear problem by the Very Fast Simulated Annealing algorithm. The best performance is obtained when some vertices are constrained by either reasonable bounds or exact knowledge. In the salt-dome case we assumed that the top of the body is known from seismic observations and we solved for the lateral and bottom parts of the body. We applied the technique on three synthetic cases of complex sources and on the gravity anomalies over the Mors salt-dome (Denmark) and the Godavari Basin (India). In all these cases the method performed very well in terms of both geometrical and source-property definition. This article is protected by copyright. All rights reserved

Description: ABSTRACT The quantitative explanation of the potential field data of 3-D geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a 3D petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasi-norm on model parameters. To solve the representation problem, a L0 quasi-norm minimization model with different smooth approximations is proposed. Hence, the data space ( N ) method, which is much smaller than model space ( M ), combined with the gradient projected method and the model space combined with the modified Newton method for L0 quasi-norm sparse constraints leads to a computationally efficient method by using an N × N system versus an M × M one, because N 〈〈 M . Tests on synthetic data and real data sets demonstrate the stability and validity of the L0 quasi-norm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasi-norm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularization). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the Salt Dome, offshore Louisiana is considered as a real case study. The real inversion result shows that the inclusion the L0 quasi-norm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasi-norm sparse constraint method and indicate its application for other potential field data inversions and the exploration of geological structures. This article is protected by copyright. All rights reserved

Description: ABSTRACT The theory and practice of multisource full waveform inversion of marine supergathers are described with a frequency-selection strategy. The key enabling property of frequency selection is that it eliminates the crosstalk among sources, thus overcoming the aperture mismatch of marine multisource inversion. Tests on multisource full waveform inversion of synthetic marine data and Gulf of Mexico data show speedups of 4× and 8×, respectively, compared to conventional full waveform inversion. This article is protected by copyright. All rights reserved

Description: ABSTRACT Streaming potential is the result of a coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz-Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge the fractal geometry theory is not yet applied to analyze the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz-Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz-Smoluchowski equation, in particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analyzed. This article is protected by copyright. All rights reserved

Description: ABSTRACT Hydraulic fractures generated by fluid injection in rock formations are often mapped by seismic monitoring. In many cases the microseismicity is asymmetric relative to the injection well, which has been interpreted by stress gradient along the direction of the hydraulic fracture. We present a mathematical model of asymmetric hydrofracture growth based on relations between the solid-phase stress and the fracture hydraulics. For single fracture and single injection point, the model has three parameters, hydraulic conductivities of the fracture wings and normalized stress gradient and predicts the positions of the fracture tips as functions of time. The model is applied to a set of microseismic event locations occurred during and after an injection process. Two different methods are suggested that make it possible to delineate the fracture tips from the set of microseismic events. This makes it possible to determine the model parameters and to check the agreement between the model prediction and the measured data. The comparison of the measured and modeled growth of fracture wings supports both the assumption of the nonzero stress gradient and the existence of the post-injection unilateral growth. This article is protected by copyright. All rights reserved

Description: SUMMARY A robust metric of data misfit like ℓ 1 -norm is required for geophysical parameter estimation when the data are contaminated by erratic noise. Recently the iteratively re-weighted and refined least squares ( IRRLS or RR for short) algorithm was introduced for efficient solution of geophysical inverse problems in the presence of additive Gaussian noise in the data. We extend the algorithm in two practically important directions to make it applicable to data with non-Gaussian noise and to make its regularization parameter tuning more efficient and automatic. The regularization parameter in RR algorithm varies with iteration allowing efficient solution of constrained problems. A technique is proposed based on the secant method for root finding to concentrate on finding a solution that satisfies the constraint, either fitting to a target misfit (if a bound on the noise is available) or having a target size (if a bound on the solution is available). This technique leads to an automatic update of the regularization parameter at each and every iteration. We further propose a simple and efficient scheme that tunes the regularization parameter without requiring the target bounds. This is of great importance for the field data inversion where there is no information about the size of the noise and the solution. Numerical examples from non-stationary seismic deconvolution and velocity-stack inversion show that the proposed algorithm is efficient, stable and robust, and outperforms the conventional and state-of-the art methods. This article is protected by copyright. All rights reserved

Description: ABSTRACT Unlike conventional sensors that measure the passage of seismic waves at a single position, distributed vibration sensing systems, also known as distributed acoustic sensing systems, detect the passage of seismic waves by averaging a measurement of strain over a section of fibre-optic cable. Distributed vibration sensing systems work by transmitting pulses of light down the fibre and measuring the phase of the Rayleigh backscatter. At random positions along the fibre, however, fading occurs; this is where the amplitude of the backscattered signal is very small due to cancellation of the scattered electric fields, resulting in anomalously noisy traces in a common source gather. This paper addresses the problem of fading in a particular form of distributed vibration sensors: a new optical arrangement of the instrumentation is described that allows the measurement to be carried out quasi-simultaneously at multiple optical interrogation frequencies. The interrogation frequencies are chosen to be sufficiently different that their fading properties are distinct and the diversity thus obtained is used to aggregate the data obtained to substantially reduce the noise caused by fading. As well as reducing the effects of fading, the aggregation of the independent results can also help to reduce the overall noise of the measurement and improve the linearity of the distributed vibration sensing system. This article is protected by copyright. All rights reserved

Description: In marine acquisition, reflections of sound energy from the water-air interface result in ghosts in the seismic data, both in the source side and receiver side. Ghosts limit the bandwidth of the useful signal and blur the final image. The process to separate the ghost and primary signals, called the deghosting process, can fill the ghost notch, broaden the frequency band, and help to achieve high-resolution images. Low signal to noise ratio near the notch frequencies and 3D effects are two challenges that the deghosting process has to face. In this paper, starting from an introduction to the deghosting process, we present and compare two strategies to solve the latter. The first is an adaptive mechanism which adjusts the deghosting operator to compensate for 3D effects or errors in source/receiver depth measurement. This method does not include explicitly the crossline slowness component and is not affected by the sparse sampling in the same direction. The second method is an inversion type approach which does include the crossline slowness component in the algorithm and handles the 3D effects explicitly. Both synthetic and field data examples in wide azimuth (WAZ) acquisition settings are shown to compare the two strategies. Both methods provide satisfactory results. This article is protected by copyright. All rights reserved

Description: ABSTRACT Borehole guided waves that are excited by explosive sources outside of the borehole are important for interpreting borehole seismic surveys and for rock property inversion workflows. The borehole seismograms are typically modeled using numerical methods of wave propagation. In order to benchmark such numerical algorithms and partially to interpret the results of modeling, I present here an analytical methodology to compute synthetic seismograms. The specific setup is a wavefield emanating from a monopole point source embedded within a homogeneous elastic medium that interacts with a fluid-filled borehole and a free surface. The methodology assumes that the wavelength of the seismic signal is much larger than the borehole radius. I suppose in this paper that there is no poroelastic coupling between the formation and the borehole. The total wavefield solution consists of P, PP, PS body waves, the surface Rayleigh wave and the low-frequency guided Stoneley wave (often referred as the tube wave) within the borehole. In its turn, the tube wave consists of the partial responses generated by the incident P wave and the reflected PP and PS body waves at the borehole mouth and by the Rayleigh wave as well as the Stoneley wave eigenmode. The Mach tube wave, which is a conic tube wave, additionally appears in the Mach cone in a slow formation with the tube-wave velocity greater than the shear one. The conditions of appearance of the Mach wave in a slow formation are formulated. It is shown that the amplitude of the Mach tube wave strongly depends on Poisson's ratio of the slow surrounding formation. The amplitude of the Mach tube wave exponentially decreases when the source depth grows for weakly compressible elastic media with Poisson's ratio close to 0.5 (i.e., saturated clays and saturated clay soils). I also provide asymptotic expressions to compute the wavefield amplitudes for different combinations of source depth and source-well offset. These expressions allow an approximate solution of the wavefield to be computed much faster (within several seconds) than directly computing the implicit integrals arising from the analytical formulation. This article is protected by copyright. All rights reserved

Description: Extracting true amplitude versus angle common image gathers (GIG) is one of the key objectives in seismic processing and imaging. This is achievable to different degrees using different migration techniques (e.g. Kirchhoff, wavefield extrapolation techniques, RTM) and is a common tool in exploration but the costs can vary depending on the selected migration algorithm and the desired accuracy. Here, we investigate the possibility of combining the local-shift imaging condition, specifically the time-shift extended imaging condition, for angle gathers with a Kirchhoff migration. The aims are not to replace the more accurate full wavefield migration but to offer a cheaper alternative where ray-based methods are applicable; to use Kirchhoff time-lag CIGs to help bridge the gap between the traditional offset CIGs and RTM angle gathers; and finally, given the higher level of summation inside the extended imaging migration, we wish to understand the impact on the amplitude versus angle response. The implementation of the time-shift imaging condition along with the computational cost is discussed and results of four different datasets are presented. The four example datasets, two synthetic, one land acquisition and a marine dataset, have been migrated using a Kirchhoff offset method, a Kirchhoff time-shift method and for comparison a RTM algorithm. The results show that the time-shift imaging condition at zero time-lag is equivalent to the full offset stack as expected. The output gathers are cleaner and more consistent in the time-lag derived angle gathers but the conversion from time-lag to angle can be considered a post-processing step. The main difference arises in the amplitude versus offset/angle distribution where the responses are different and dramatically so for the land data. The results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers. The same disadvantages with a ray-based approach will apply using the extended imaging condition relative to a wave equation angle gather solution. Nevertheless, using this approach allows one to explore the relationship between the velocity model and focusing of the reflected energy, to use the Radon transformation to remove noise and multiples and to generate consistent products from a ray based migration and a full wave equation migration which can then be interchanged depending on the process under study. This article is protected by copyright. All rights reserved

Description: Adverse geologies are often encountered during tunnel construction, which could seriously endanger the construction. To ensure the safety, it's essential to detect adverse geologies and their water-bearing situation ahead the tunnel face. Ground penetrating radar (GPR) is a suitable instrument, but the accurate interpretation of its detection results is difficult. In this paper, at first an improved back projection imaging algorithm is proposed, which can make reflection waves closer to the real geological boundaries with few artificial clutters. And then forward modeling of GPR is carried out for typical adverse geologies such as karst caves, faults, fractured rock masses, fracture network and water-bearing body. Their corresponding response features are obtained, accumulating experience for geological interpretation. The above two methods provide the basis for target identification and geological interpretation. In the last part, the application of the above two methods in several engineering cases are given and their effectiveness is verified. This article is protected by copyright. All rights reserved

Description: We propose a new approach for calculating the dynamic range of an accelerometer based on an Allan deviation analysis of production seismic data. This test is intended as a field audit technique and does not require an unconditioned dataset from a low-noise environment. We first show that Allan deviation can measure white noise levels using two commercial accelerometers. The analysis accurately captures the manufacturing noise density specifications as well as known relationships between white noise, preamplifier gain, and group forming. We then show that a production seismic dataset is suitable for an Allan deviation analysis because the results are not critically affected by a recording filter. Finally, we illustrate the proposed technique by calculating the dynamic range of an accelerometer channel in a seismic streamer using a production dataset. This article is protected by copyright. All rights reserved

Description: ABSTRACT Classical least-squares techniques (Moore-Penrose pseudoinverse) are covariance-based and are therefore unsuitable for the solution of very large-scale linear systems in geophysical inversion due to the need of diagonalization. In this paper we present a methodology to perform the geophysical inversion of large-scale linear systems via the Discrete Wavelet Transform. The methodology consists of compressing the linear system matrix using the interesting properties of covariance-free orthogonal transformations, to design an approximation of the Moore-Penrose pseudoinverse. We show the application of the Discrete Wavelet Transform pseudoinverse to well-conditioned and ill-conditioned linear systems. We show the application to a general-purpose linear problem where the system matrix has been generated using geostatistical simulation techniques, and also to a synthetic 2D gravimetric problem with two different geological set-ups, in the noise-free and noisy cases. In both cases the Discrete Wavelet Transform pseudoinverse can be applied to the original linear system and also to the linear systems of normal equations and minimum norm. The results are compared to those obtained via the Moore-Penrose and the Discrete Cosine Transform pseudoinverses. The Discrete Wavelet Transform and the Discrete Cosine Transform pseudoinverses provide similar results and outperform the Moore-Penrose pseudoinverse, mainly in the presence of noise. In the case of well-conditioned linear systems this methodology is more efficient when applied to the least squares and minimum norm systems due to their higher condition number that allows for a more efficient compression of the system matrix. Also in the case of ill-conditioned systems with very high underdetermined character the application of the Discrete Cosine Transform to the minimum norm solution provides very good results. Both solutions might differ on their regularity, depending on the wavelet family that is adopted. These methods have a general character and can be applied to solve any linear inverse problem arising in technology and particularly in geophysics, and also to nonlinear inversion by linearization of the forward operator. This article is protected by copyright. All rights reserved

Description: ABSTRACT The Tobago Basin, which is located offshore northern Venezuela with a southern margin close to Trinidad and Tobago, has an area of approximately 59,600 km 2 . The Tobago Basin has relatively favorable hydrocarbon prospects, and to date, exploration work has mainly concentrated on small areas of the southwestern portion of the basin. To conduct a comprehensive study of the structural framework of the basin and the characteristics of the basement in order to identify prospective zones for hydrocarbon exploration, shipborne- and satellite-measured gravity data, shipborne-measured magnetic data, and aeromagnetic survey data provided by GETECH were analyzed. A regularization filtering method was used to separate and obtain regional and residual gravity and magnetic anomalies. Directional gradients of gravity and magnetic anomalies and the total horizontal gradient and vertical second derivative of gravity anomalies were employed to extract information about fault structures. Regression analysis methods were used to determine the basement depth. The geological significance of the gravity and magnetic fields was examined, the structural framework of the basin was assessed, the basement depth was estimated, and favorable hydrocarbon exploration prospects within the basin were identified. The results show that the Tobago Basin contains complex structures consisting mainly of two groups of faults trending in northeasterly (NE) and northwesterly (NW) directions, and that the major NE-trending faults control the main structural configuration and depositional system within the basin. The basement of the Tobago Basin has deep rises and falls. It can be divided into the following four secondary tectonic units: the western sub-basin, central uplift area, southern sub-basin, and northeastern sub-basin. The central uplift area and northeastern sub-basin are most likely to have developed hydrocarbon accumulations and should be targeted for further exploration. This article is protected by copyright. All rights reserved

Description: ABSTRACT Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artifacts in the pseudo-spectral solution of the first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic, or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid based pseudo-spectral method possesses the best balance between the mitigation of artifacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artifacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations. This article is protected by copyright. All rights reserved

Description: ABSTRACT Physical modelling of cracked/fractured media using downscaled laboratory experiments has been used with great success as a useful alternative for understanding the effect of anisotropy in the hydrocarbon reservoir characterization, and in the crustal and mantle seismology. The main goal of this work was to experimentally verify the predictions of effective elastic parameters in anisotropic cracked media by Hudson and Eshelby-Cheng's effective medium models. For this purpose, we carried out ultrasonic measurements on synthetic anisotropic samples with low crack densities and different aspect ratios. Twelve samples were prepared with two different crack densities, 5% and 8%. Three samples for each crack density presented cracks with only one crack aspect ratio, while other three samples for each crack density presented cracks with three different aspect ratios in their composition. It results in samples with aspect ratio values varying from 0.13 to 0.26. All the cracked samples were simulated by penny-shape rubber inclusions in a homogeneous isotropic matrix made with epoxy resin. Moreover, an isotropic sample for reference was constructed with epoxy resin only. Regarding velocity predictions performed by the theoretical models, Eshelby-Cheng shows a better fit when compared to the experimental results for samples with single and mix crack aspect ratio (for both crack densities). From velocity values, our comparisons were also performed in terms of the ε, γ and δ parameters (Thomsen parameters). The results show that Eshelby-Cheng effective medium model fits better the measurements of ε and γ parameters for crack samples with only type of crack aspect ratio. This article is protected by copyright. All rights reserved

Description: ABSTRACT The Central Indian region is having complex geology covering the Godavari Graben, the Bastar Craton (including the Chhattisgarh Basin), the Eastern Ghat Mobile Belt, the Mahanadi Graban and some part of the Deccan Trap, the Northern Singhbhum Orogen and the Eastern Dharwar Craton. The region is well covered by reconnaissance scale aeromagnetic data, analyzed for the estimation of basement and shallow anomalous magnetic sources depth using scaling spectral method. The shallow magnetic anomalies are found to vary from 1 to 3 km whereas magnetic basement depth values are found to vary from 2 to 7 km. The shallowest basement depth of 2 km corresponds to the Kanker granites, a part of the Bastar Craton, whereas deepest basement depth of 7 km is for the Godavari Basin and the southeastern part of the Eastern Ghat Mobile Belts near the Parvatipuram Bobbili fault. The estimated basement depth values correlate well with the values found from earlier geophysical studies. The earlier geophysical studies are limited to few tectonic units whereas our estimation provides detailed magnetic basement mapping in the region. The magnetic basement and shallow depth values in the region indicate complex tectonic, heterogeneity and intrusive bodies at different depth which can be attributed to different thermo-tectonic processes since Precambrian. This article is protected by copyright. All rights reserved

Description: ABSTRACT In this paper we study the possibilities of the use of microtremor records in the detection and delineation of near-surface underground cavities. Three-dimensional physical modelling data showed that the averaging amplitude spectra of a large number of microtremor records makes it possible to evaluate the frequencies and amplitudes of compressional standing waves generated by microtremor in the space between the ground surface and underground cavities. We illustrate how these parameters can be used to estimate the shape of the underground cavity horizontal projection. If the compressional wave velocity in the enclosing rock is known, it is possible to evaluate the depth to the cavity top using the frequencies of the standing waves. The results of the field experiment confirmed the possibility of underground cavities detection using microtremor data. This article is protected by copyright. All rights reserved

Description: The present paper is concerned with reflection and transmission of a plane, elastic, inhomogeneous wave striking obliquely at some discontinuity inside a porous medium composed of two distinct solids and saturated by two immiscible fluids. It is found that four P and two SV -waves are reflected, while four P and two SV -waves are transmitted at the interface. All reflected and transmitted waves are inhomogeneous in nature and specified with different directions of propagation and attenuation vectors. Expression for Umov-Poynting energy flux vector is derived for the system. Continuity of energy flux along normal to the interface gives twelve required boundary conditions. Expressions of amplitude and energy ratios of various reflected and transmitted waves are derived. Variations in amplitude and energy coefficients of reflected and transmitted waves with angle of incidence are studied numerically for a porous matrix composed of shaley sandstone and clay, saturated with water and oil. The effects of change in oil saturation and volume fraction of clay are also observed on amplitude ratios. Numerical simulation reveals that the change in sign in the difference of capillary pressure across the interface causes jump in the values of amplitude ratios of all waves. This article is protected by copyright. All rights reserved

Description: ABSTRACT The Generalised Derivative Operator is an image processing tool for the enhancement of potential field data. It produces an amplitude balanced image of the derivative of a potential field in any direction in three dimensional space. This paper shows how, by using the correct inclination angle ϕ , the Generalised Derivative Operator can be used to produce images where its maxima/minima lie directly over dipping contacts and thin dykes with arbitrary magnetisation vectors. The dip of contacts and dykes can be found by varying ϕ until a symmetrical result is obtained (in the absence of unknown remanent magnetisation). Furthermore, the width of the peak of the Generalised Derivative Operator can then be used to determine the depth of the contact or dyke. This article is protected by copyright. All rights reserved

Description: ABSTRACT Commonly, geomagnetic prospection is performed via scalar magnetometers which measure values of the total magnetic intensity (TMI). Recent developments of Superconducting Quantum Interference Devices (SQUIDs) lead to their integration in Full Tensor Magnetic Gradiometry (FTMG) systems consisting in planar-type first-order gradiometers and magnetometers fabricated in thin-film technology. With these systems measuring directly the magnetic gradient tensor and field vector, a significantly higher magnetic and spatial resolution of the magnetic maps is yield than for those produced via conventional magnetometers. In order to preserve the high data-quality in this work we develop a workflow containing all necessary steps for generating the gradient tensor and field vector quantities from the raw measurement data up to their integration into high­resolution, low­noise and artefact­less 2D maps of the magnetic field vector. The gradient tensor components are processed by superposition of the balanced gradiometer signals and rotation into an Earth-centered Earth-fixed coordinate frame. As the magnetometers have sensitivity lower than the gradiometers and the TMI is not directly recorded we employ Hilbert-like transforms, e.g. integration of the gradient tensor components or the conversion of the TMI derived by calibrated magnetometer readings to obtain these values. This can lead to a better interpretation of the measured magnetic anomalies of the Earth's magnetic field that is possible from scalar TMI measurements. Our conclusions are drawn from the application of these algorithms on a survey acquired in South Africa containing FTMG data. This article is protected by copyright. All rights reserved

Description: ABSTRACT The article discusses excitation of transient IP responses using current and voltage sources. The first method has found a wide application in IP surveys, and - directly or indirectly - in the theory of the IP method. Typically, rectangular current pulses are injected into the earth via grounding electrodes, and decaying IP voltage is measured during the pauses between pulses. In this case, only the secondary field is recorded in the absence of the primary one, which is an important advantage of this method. On the other hand, since the current injected into the ground is fully controlled by the source, this method does not allow studying IP by measuring the current in the transmitter line or associated magnetic field. When energizing the earth with voltage pulses, the measured quantity is the transient IP current. In principle, this method allows IP studies to be done by recording the transmitter line current, the associated magnetic field, or its rate of change. The decay of current in a grounded transmitter line depends not only on the IP of the earth, but on the polarization of the grounding electrodes as well. This problem does not occur when IP transients in the earth are exited inductively. Grounded transmitter line is a mixed type source, so for purely inductive excitation of IP transients one should use an ungrounded loop, which is coupled to the earth solely by electromagnetic induction. This article is protected by copyright. All rights reserved

Description: ABSTRACT Acoustic impedance (AI) is one of the best attributes for seismic interpretation and reservoir characterization. We present an approach for estimating AI accurately from a band-limited and noisy seismic data. The approach is composed of two stages: inverting for reflectivity from seismic data and then estimating impedance from the reflectivity inverted in the first stage. For the first stage we achieve a two-step spectral inversion (TSSI) that locates the positions of reflection coefficients in the first step and determines the amplitudes of the reflection coefficients in the second step under the constraints of the positions located in the first step. For the second stage we construct an iterative impedance estimation algorithm (IIEA) base on reflectivity. In each iteration, the IIEA estimates the absolute AI based on an initial AI model that is given by summing the high-frequency component of AI estimated at the last iteration and a low-frequency component determined in advance using other data. The known low-frequency component is used to restrict the AI variation tendency in each iteration. Examples using 1D and 2D synthetic and field seismic data show that the approach is flexible and superior to the conventional spectral inversion and recursive inversion methods for generating more accurate AI models. This article is protected by copyright. All rights reserved

Description: ABSTRACT We apply interferometric theory to solve a 3D seismic residual statics problem to improve reflection imaging. The approach calculates the static solutions without picking the first arrivals from the shot or receiver gathers. The static correction accuracy can be significantly improved by utilizing stacked virtual refraction gathers in the calculations. Shots and receivers may be placed at any position in a 3D seismic land survey. Therefore, it is difficult to determine stationary shots and receivers to form the virtual refraction traces which have identical arrival times, as in a 2D scenario. To overcome this problem, we use a 3D super-virtual interferometry method for residual static calculations. The virtual refraction for a stationary shot/receiver pair is obtained via an integral along the receiver/shot lines, which does not require knowledge of the stationary locations. We pick the max-energy times on the interferometric stacks and solve a set of linear equations to derive reliable residual static solutions. We further apply the approach to both synthetic and real data. This article is protected by copyright. All rights reserved

Description: ABSTRACT Geologically constrained inversion of gravity and magnetic field data of the Victoria property (located in Sudbury, Canada) was undertaken in order to update the present three-dimensional geological model. The initial and reference model was constructed based on geological information from over 950 drillholes to constrain the inversion. In addition, downhole density and magnetic susceptibility measured in six holes were statistically analysed to derive lower and upper bounds on the physical properties attributed to the lithological units in the reference model. Constrained inversion of the ground gravity and the airborne magnetic data collected at the Victoria property were performed using GRAV3D and MAG3D, respectively. A neural network was trained to predict lithological units from the physical properties measured in six holes. Then, the trained network was applied on the three-dimensional distribution of physical properties derived from the inversion models to produce a three-dimensional litho-prediction model. Some of the features evident in the lithological model are remnants of the constraints, where the data did not demand a significant change in the model from the initial constraining model (e.g., the thin pair of diabase dykes). However, some important changes away from the initial model are evident; for example, a larger body was predicted for quartz diorite, which may be related to the prospective offset dykes; a new zone was predicted as sulfide, which may represent potential mineralisation; and a geophysical subcategory of metabasalt was identified with high magnetic susceptibility and high density. The litho-prediction model agrees with the geological expectation for the three-dimensional structure at Victoria and is consistent with the geophysical data, which results in a more holistic understanding of the subsurface lithology.

Description: ABSTRACT A method for interpolation of multicomponent streamer data based on using the local directionality structure is presented. The derivative components are used to estimate a vector field that locally describes the direction with the least variability. Given this vector field, the interpolation can be phrased in terms of the solution of a partial differential equation that describes how energy is transported between regions of missing data. The approach can be efficiently implemented using readily available routines for computer graphics. The method is robust to noise in the measurements and particularly towards high levels of low-frequent noise that is present in the derivative components of the multicomponent streamer data.

Description: High-resolution 3D images are used in Digital Rock Physics (DRP) to numerically compute rock physical properties such as permeability and elastic moduli. These images are not widely available and their preparation is both expensive and time consuming. All of these issues highlight the importance of alternative DRP methods that are based on 2D images and use different approaches to compute effective properties of 3D samples. In addition, the scale of study in both standard and alternative DRP is very small, which applications of its results are questionable at wells or reservoir scale. The aim of this study is to use 2D images and alternative DRP techniques for computing seismic wave velocity and permeability, which are compared with well and laboratory data. For this purpose, data from one well in a reservoir located in southwestern part of Iran is used. First, two clean (carbonate) and two cemented (limy-sandstone) samples were collected from well cores at different depths. Then, 2D images by Scanning Electron Microscope (SEM) and conventional microscope were captured. In the next step, two alternative DRP methods, namely empirical relations and conditional reconstruction, have been employed to compute P-wave velocity and permeability of 3D medium. Results showed that, in clean (mono-mineral) samples, velocity values were reasonably close to well data. However, permeability values are may underestimated comparing with laboratory data because laboratory data were obtained at ambient pressure, whereas alternative DRP results are more representative of reservoir pressure conditions. Nevertheless, permeability-porosity trends are valid for both samples. In the case of cemented samples, a two-scale procedure along with a method for two-scale computation and grain-cement segmentation are presented and developed. Results showed that P-wave velocity are overestimated probably due to random sampling in this method. However,velocity-porosity trends are in agreement with well data. Moreover, permeability results obtained for cemented samples were also similar to those obtained for the clean samples. This article is protected by copyright. All rights reserved

Description: ABSTRACT The broadband capabilities of marine, seabed and land seismic equipment are reviewed with respect to both the source and the receiver sides. In marine acquisition, the main issue at both ends of the spectrum relates to ghosts occurring at the sea surface. Broadband deghosting requires towing at variable depth to introduce notch diversity or using new equipment like multi-component and/or low noise streamers. As a result a doubling of the bandwidth from about 3 to 6 octaves (2.5-200 Hz) has been achieved. Such improvement is not yet observed for seabed surveys in spite of deghosting being a standard process on the receiver side. One issue may be related to the coupling of the particle motion sensor, particularly at high frequencies. For land acquisition, progress came from the vibrators. New shakers and control electronics using broadband sweeps made it possible to add two more octaves to the low frequency signal (from 8 to 2 Hz). While conventional 10-Hz geophones are still able to record such low frequencies, 5-Hz high gain geophones or digital accelerometrers enhance them to keep the signal above the noise floor. On the high end of the bandwidth, progress is not limited by equipment specifications. Here the issue is related to a low signal-to-noise ratio due to the strong absorption that occurs during signal propagation. To succeed in enlarging the bandwidth, these improved equipment and sweeps must be complemented by a denser spatial sampling of the wavefield by point-source and point-receiver acquisition. This article is protected by copyright. All rights reserved

Description: ABSTRACT Extrapolating wavefields and imaging at each depth during 3D recursive wave-equation migration is a time-consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier-transform-related wavefield extrapolation method. First, we formulate a 3D first-order separation-of-variables screen propagator (SVSP1) for large-step wavefield extrapolation, which allows for wide-angle propagations in high-contrasting media. This propagator significantly improves the performance of the split-step Fourier (SSF) method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform (FFT) in each thick slab. We then extend the 2D Kirchhoff (KKF) and Born-Kirchhoff (BK) local wavefield interpolators to 3D cases for each slab. The 3D KKF interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, while the 3D BK interpolator is derived from the Lippmann-Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the 3D SEG/EAGE salt model demonstrate that 3D SVSP1-BK depth migration using thick-slab wavefield extrapolation plus thin-slab interpolation tolerates a considerable depth-step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed 3D interpolators are presented with one-way Fourier extrapolation methods, they can be extended for applications to general migration methods. This article is protected by copyright. All rights reserved

Description: ABSTRACT Most seismic processing algorithms generally consider the sea surface as a flat reflector. However, acquisition of marine seismic data often takes place in weather conditions where this approximation is inaccurate. The distortion in the seismic wavelet introduced by the rough sea may influence (for example) deghosting results, as deghosting operators are typically recursive and sensitive to the changes in the seismic signal. In this paper we study the effect of sea surface roughness on conventional (5-160 Hz) and ultra-high resolution (200-3500 Hz) single-component towed-streamer data. To this end, we numerically simulate reflections from a rough sea surface using the Kirchhoff approximation. Our modeling demonstrates that for conventional seismic frequency band sea roughness can distort results of standard 1D and 2D deterministic deghosting. To mitigate this effect we introduce regularization and optimization based on the minimum-energy criterion and show that this improves the processing output significantly. Analysis of ultra-high resolution field data in conjunction with modeling shows that even relatively calm sea state (i.e. 15 cm wave height) introduces significant changes in the seismic signal for ultra-high frequency band. These changes in amplitude and arrival time may degrade the results of deghosting. Using the field dataset, we show how the minimum-energy optimization of deghosting parameters improves the processing result. This article is protected by copyright. All rights reserved

Description: ABSTRACT Based on knowledge of a commutative group calculation of the rock stiffness and on some geophysical assumptions, the simplest fractured medium may be regarded as a fracture embedded in an isotropic background medium, and the fracture interface can be simulated as a linear slip interface that satisfies nonwelded contact boundary conditions: the kinematic displacements are discontinuous across the interface, whereas the dynamic stresses are continuous across the interface. The finite-difference method with boundary conditions explicitly imposed is advantageous for modelling wave propagation in fractured discontinuous media that are described by the elastic equation of motion and nonwelded contact boundary conditions. In this paper, finite-difference schemes for horizontally, vertically and orthogonally fractured media are derived when the fracture interfaces are aligned with the boundaries of the finite-difference grid. The new finite-difference schemes explicitly have an additional part that is different from the conventional second-order finite-difference scheme and that directly describes the contributions of the fracture to the wave equation of motion in the fractured medium. The numerical seismograms presented, to first order, show that the new finite-difference scheme is accurate and stable and agrees well with the results of previously published finite-difference schemes (the Coates and Schoenberg method). The results of the new finite-difference schemes show how the amplitude of the reflection produced by the fracture varies with the fracture compliances. Later, comparisons with the reflection coefficients indicate that the reflection coefficients of the fracture are frequency dependent, whereas the reflection coefficients of the impedance contrast interface are frequency independent. In addition, the numerical seismograms show that the reflections of the fractured medium are equal to the reflections of the background medium plus the reflections of the fracture in the elastic fractured medium. This article is protected by copyright. All rights reserved

Description: ABSTRACT Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness-constrained least-squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint-equation method is used to calculate the Jacobian matrices required by the least-squares method to reduce the calculation time. In areas with large near-surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrodes displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time-lapse data set (with accurately known electrode positions) is used as the starting model for the inversion of the later-time data set. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half-space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine. This article is protected by copyright. All rights reserved

Description: ABSTRACT Diffractions carry valuable information about local discontinuities and small scale objects in the subsurface. They are still not commonly used in the process of geological interpretation. Many diffraction imaging techniques have been developed and applied for isotropic media while relatively few techniques have been developed for anisotropic media. Ignoring anisotropy can result in low-resolution images with wrongly positioned or spurious diffrators. In this article, we suggest taking anisotropy into account in 2D poststack domain by considering P-wave non-hyperbolic diffraction traveltime approximations for vertical transverse isotropy media, previously developed for reflection seismology. The accuracy of final images is directly connected to the accuracy of the diffraction traveltime approximations. We quantified the accuracy of six different approximations, including hyperbolic moveout approximation, by the application of a poststack diffraction imaging technique on 2D synthetic data examples. This article is protected by copyright. All rights reserved

Description: ABSTRACT We have developed a novel method for missing seismic data interpolation using f-x domain regularized nonstationary autoregression. f-x regularized nonstationary autoregression interpolation can deal with the events which have space-varying dips. We assume that the coefficients of f-x regularized nonstationary autoregression are smoothly varying along the space axis. This method includes two steps: the estimation of the coefficients and the interpolation of missing traces using estimated coefficients. We estimate the f-x regularized nonstationary autoregression coefficients for the completed data using weighted nonstationary autoregression equations with smoothing constraints. For regularly missing data, similar to Spitz f-x interpolation, we use autoregression coefficients estimated from low frequency components without aliasing to obtain autoregression coefficients of high frequency components with aliasing. For irregularly missing or gapped data, we use known traces to establish nonstationary autoregression equations with regularization to estimate the f-x autoregression coefficients of the complete data. We implement the algorithm by iterated scheme using frequency domain conjugate gradient method with shaping regularization. The proposed method improves the calculation efficiency by applying shaping regularization and implementation in frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples. This article is protected by copyright. All rights reserved

Description: ABSTRACT We study the interaction of a seismic wave-field with a spherical acoustic gas or fluid-filled cavity. The intention of this study is to clarify whether seismic resonances can be expected, a characteristic feature, which may help detecting cavities in the subsurface. This is important for many applications, as in particular the detection of underground nuclear explosions which are to be prohibited by the Comprehensive-Test-Ban-Treaty. In order to calculate the full seismic wave-field from an incident plane wave that interacts with the cavity, we considered an analytic formulation of the problem. The wave-field interaction consists of elastic scattering and the wave-field interaction between the acoustic and elastic media. Acoustic resonant modes, caused by internal reections in the acoustic cavity, show up as spectral peaks in the frequency domain. The resonant peaks coincide with the eigenfrequencies of the undamped system described by the particular acoustic medium bounded in a sphere with stiff walls. The filling of the cavity could thus be determined by the observation of spectral peaks from acoustic resonances. By energy transmission from the internal oscillations back into the elastic domain, the oscillations experience damping, resulting in a frequency shift and a limitation of the resonance amplitudes. In case of a gas-filled cavity the impedance contrast is still high, which means low damping of the internal oscillations resulting in very narrow resonances of high amplitude. In synthetic seismograms calculated in the surrounding elastic domain, the acoustic resonances of gas-filled cavities show up as persisting oscillations. However, due to the weak acoustic-elastic coupling in this case the amplitudes of the oscillations are very low. Due to a lower impedance contrast, a fluid-filled cavity has a stronger acoustic-elastic coupling, which results in wide spectral peaks of lower amplitudes. In the synthetic seismograms derived in the surrounding medium of fluid-filled cavities, acoustic resonances show up as strong but fast decaying reverberations. This article is protected by copyright. All rights reserved

Description: ABSTRACT The empirical mode decomposition aims to decompose the input signal into a small number of components named intrinsic mode functions with slowly varying amplitudes and frequencies. In spite of its simplicity and usefulness, however, the empirical mode decomposition lack solid mathematical foundation. In this paper, we describe a method to extract the intrinsic mode functions of the input signal using non-stationary Prony method. The proposed method captures the philosophy of the empirical mode decomposition, but use a different method to compute the intrinsic mode functions. Having the intrinsic mode functions obtained, we then compute the spectrum of the input signal using Hilbert transform. Synthetic and field data validate the proposed method can correctly compute the spectrum of the input signal, and could be used in seismic data analysis to facilitate interpretation. This article is protected by copyright. All rights reserved

Description: ABSTRACT Rock fractures are of great practical importance to petroleum reservoir engineering because they provide pathways for fluid flow, especially in reservoirs with low matrix permeability, where they constitute the primary flow conduits. Understanding the spatial distribution of natural fracture networks is thus key to optimizing production. The impact of fracture systems on fluid flow patterns can be predicted using discrete fracture network models, which allow not only the 6 independent components of the second-rank permeability tensor to be estimated, but also the 21 independent components of the fully anisotropic fourth-rank elastic stiffness tensor, from which the elastic and seismic properties of the fractured rock medium can be predicted. As they are stochastically generated, discrete fracture network realizations are inherently non-unique. It is thus important to constrain their construction, so as to reduce their range of variability and hence the uncertainty of fractured rock properties derived from them. This paper presents the underlying theory and implementation of a method for constructing a geologically realistic discrete fracture network, constrained by seismic amplitude variation with offset and azimuth data. Several different formulations are described, depending on the type of seismic data and prior geologic information available, and the relative strengths and weaknesses of each approach are compared. Potential applications of the method are numerous, including the prediction of fluid flow, elastic and seismic properties of fractured reservoirs, model-based inversion of seismic amplitude variation with offset and azimuth data, and the optimal placement and orientation of infill wells to maximize production. This article is protected by copyright. All rights reserved

Description: ABSTRACT Measurement of the electric field (E-field) data due to an inductive loop source in a controlled source electromagnetic (CSEM) survey is not common, because E-field data, usually involving grounded electrodes, are expensive to acquire and difficult to interpret. With the recently developed capability of versatile 3D inversion, we revisit the idea of measuring E-field in a large ground loop survey for mineral exploration. 3D modeling and inversion approach helps us quantitatively understand the detectability and recoverability of the proposed survey configuration. Our detectability study using forward modeling shows that the relative anomaly (percentage difference) in E-field does not decay with a lower induction number, but the conventional magnetic field data (dB/dt) does. Our recoverability study examines how much and what kind of information can be extracted from Efield data for the reconstruction of a 3D model. Synthetic inversions show that: (1) E-field data are good at locating the lateral discontinuity, whereas dB/dt has better depth resolution. (2) E-field is less sensitive to the background conductivity, and thus is prone to misinterpretation because of bad initial model in inversion. We recommend warm-start the E-field inversion with an initial model from a separate dB/dt inversion. (3) E-field data may be severely contaminated by near-surface heterogeneity, but an inversion can recover the deep target concealed by the geologic noise. (4) Even one line of single-component E-field data can greatly improve the horizontal resolution in a dB/dt inversion. Finally, we investigate a field data set of both E-field and dB/dt measurements at a uranium deposit. The field example confirms that the E-field and magnetic field data contain independent information that is both crucial in the accurate recovery of subsurface conductivity. Our synthetic and field examples demonstrate the benefit of acquiring E-field data along with magnetic field data in an inductive source survey. This article is protected by copyright. All rights reserved

Description: Improved estimates of the amount of subsurface gas hydrates are needed for natural resource, geohazard and climate impact assessments. To evaluate gas hydrate saturation from seismic methods, the properties of pure gas hydrates need to be known. While the properties of sediments, specifically sands, and hydrate-bearing sediments are well studied, the properties of pure hydrates are largely unknown. Hence, we present laboratory ultrasonic P-wave velocity and attenuation measurements on pure tetrahydrofuran (THF) hydrates as they form with reducing temperatures from 25°C to 1°C under atmospheric pressure conditions. THF hydrates, with structure II symmetry, are considered as proxies for the structure I methane hydrates because both have similar effects on elastic properties of hydrate-bearing sediments. We find that although velocity increased, the waveform frequency content and amplitude decreased after the hydrate formation reaction was complete, indicating an increase in P-wave attenuation after hydrate formation. When the THF hydrate was cooled below the freezing point of water, velocity and quality factor increased. Nuclear Magnetic Resonance results indicate the presence of water in the “pure hydrate” samples above the water freezing point, but none below. The presence of liquid water between hydrate grains most likely causes heightened attenuation in THF hydrates above the freezing point of water. In naturally occurring hydrates, a similarly high attenuation might relate to the presence of water. This article is protected by copyright. All rights reserved

Description: We compare the performances of four different stochastic optimisation methods using four analytic objective functions and two highly non-linear geophysical optimisation problems: 1D elastic full-waveform inversion (FWI) and residual static computation. The four methods we consider, namely, adaptive simulated annealing (ASA), genetic algorithm (GA), neighbourhood algorithm (NA), and particle swarm optimisation (PSO), are frequently employed for solving geophysical inverse problems. Because geophysical optimisations typically involve many unknown model parameters, we are particularly interested in comparing the performances of these stochastic methods as the number of unknown parameters increases. The four analytic functions we choose simulate common types of objective functions encountered in solving geophysical optimisations: a convex function, two multi-minima functions that differ in the distribution of minima, and a nearly flat function. Similar to the analytic tests, the two seismic optimisation problems we analyse are characterized by very different objective functions. The first problem is a 1D elastic FWI, which is strongly ill-conditioned and exhibits a nearly flat objective function, with a valley of minima extended along the density direction. The second problem is the residual static computation, which is characterized by a multi-minima objective function produced by the so-called cycle-skipping phenomenon. According to the tests on the analytic functions and on the seismic data, GA generally displays the best scaling with the number of parameters. It encounters problems only in the case of irregular distribution of minima, that is, when the global minimum is at the border of the search space and a number of important local minima are distant from the global minimum. The ASA method is often the best-performing method for low-dimensional model spaces, but its performance worsens as the number of unknowns increases. The PSO is effective in finding the global minimum in the case of low-dimensional model spaces with few local minima or in the case of a narrow flat valley. Finally, the NA method is competitive with the other methods only for low-dimensional model spaces; its performance stability sensibly worsens in the case of multi-minima objective functions. This article is protected by copyright. All rights reserved

Description: Planar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real-world seismic events usually have curvature or amplitude variability that means their Fourier transforms are no longer strictly linear, but rather occupy conic regions of the Fourier domain that are narrow at low frequencies, but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised “signal cones". In this work, we consider a space-time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting and translation of the kernel for cone-limited (C-limited) functions (functions whose Fourier transform lives within a cone) or C-Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency) which constitutes our dictionary. We find a discrete number of scaling, slanting and translation parameters from a continuum by optimally matching the data. This is a nonlinear optimization problem which we address by a fixed point method which utilizes a variable projection method with e 1 constraints on the linear parameters and bound constraints on the nonlinear parameters. We observe that slow decay and oscillatory behavior of the kernel for C- limited functions constitute bottlenecks for the optimization problem which we partially overcome by the C-Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity promoting curvelet decomposition, matching pursuit Fourier interpolation and sparsity promoting plane wave decomposition methods. This article is protected by copyright. All rights reserved

Description: ABSTRACT A thorough and complete understanding of the structural geology and evolution of the Cooper-Eromanga Basin has been hampered by low resolution seismic data that becomes particularly difficult to interpret below the thick Permian coal measures. As a result, researchers are tentative to interpret the basement fault architecture within the basin, which is largely undefined. To provide a better understanding of the basement fault geometry, all available two-dimensional seismic lines together with 12 three-dimensional seismic surveys were structurally interpreted with assistance from seismic attribute analysis. The Upper Cretaceous, Cadna-owie Formation, and top Permian reflectors were analysed using a common seismic attribute technique (incoherency) that was used to infer the presence of faults that may have otherwise been overlooked. Detailed basement fault maps for each seismic survey were constructed and used in conjunction with two-dimensional seismic data interpretation to produce a regional basement fault map. Large NNE-SSW striking sinistral strike-slip faults were identified within the Patchawarra Trough appearing to splay from the main NE-SW striking ridge. These sinistral NNE-SSW striking faults, together with field scale SE-NW striking dextral strike-slip faults, are optimally oriented to have potentially developed as a conjugated fault set under a SSE-NNW oriented strike-slip stress regime. Geomechanical modelling for a regionally extensive system of Cretaceous polygonal faults was performed to calculate the Leakage Factor and Dilation Tendency of individual faults. Faults that extend into Lower Cretaceous oil-rich reservoirs with strikes of between 060ᵒN and 140ᵒN and a high to near vertical dip angle were identified to be most likely to act as conduits for the tertiary migration of hydrocarbons from known Lower Cretaceous hydrocarbon reservoirs into shallow Cretaceous sediments. This research provides valuable information on the regional basement fault architecture and a more detailed exploration target for the Cooper-Eromanga Basin, which were previously not available in literature. This article is protected by copyright. All rights reserved

Description: ABSTRACT We present a new workflow for imaging damped three-dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short-offset and low-frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine-scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite-difference frequency-domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full-waveform inversion workflow is applied to the 3D Marmousi-2 and SEG/EAGE Salt models with long-offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one-third of the maximum offset length at a resolution consistent with the inverted frequencies.

Description: ABSTRACT Shales comprise more than 60% of sedimentary rocks and form natural seals above hydrocarbon reservoirs. Their sealing capacity is also used for storage of nuclear wastes. The world's most important conventional oil and gas reservoirs have their corresponding source rocks in shale. Furthermore, shale oil and shale gas are the most rapidly expanding trends in unconventional oil and gas. Shales are notorious for their strong elastic anisotropy, i.e., so-called vertical transverse isotropy. This vertical transverse isotropy, characterised by a vertical axis of invariance, is of practical importance as it is required for correct surface seismic data interpretation, seismic to well tie, and amplitude versus offset analysis. A rather classical paradigm makes a clear link between compaction in shales and the alignment of the clay platelets (main constituent of shales). This would imply increasing anisotropy strength with increasing compaction. Our main purpose is to check this prediction on two large databases in shaly formations (more than 800 samples from depths of 0–6 km) by extracting the major trends in the relation between seismic anisotropy and compaction. The statistical analysis of the database shows that the simultaneous increase in density and velocity, a classical compaction signature, is quite weakly correlated with the anisotropy strength. As a consequence, compaction can be excluded as a major cause of seismic anisotropy, at least in shaly formations. Also, the alignment of the clay platelets can explain most of the anisotropy measurements of both databases. Finally, a method for estimating the orientation distribution function of the clay platelets from the measurement of the anisotropy parameters is suggested.

Description: ABSTRACT Geostatistical seismic inversion methods are routinely used in reservoir characterization studies because of their potential to infer the spatial distribution of the petro-elastic properties of interest (e.g., density, elastic and acoustic impedances) along with the associated spatial uncertainty. Within the geostatistical seismic inversion framework, the retrieved inverse elastic models are conditioned by a global probability distribution function and global spatial continuity model as estimated from the available well-log data for the entire inversion grid. However, the spatial distribution of the real subsurface elastic properties is complex, heterogeneous and in many cases non-stationary since they directly depend on the subsurface geology, i.e., the spatial distribution of the facies of interest. In these complex geological settings, application of a single distribution function and spatial continuity model is not enough to properly model the natural variability of the elastic properties of interest. In this study, we propose a 3D geostatistical inversion technique that is able to incorporate the reservoir's heterogeneities. This method uses a traditional geostatistical seismic inversion conditioned by local multi-distribution functions and spatial continuity models under non-stationary conditions. The procedure of the proposed methodology is based on a zonation criterion along the vertical direction of the reservoir grid. Each zone can be defined by conventional seismic interpretation, with the identification of the main seismic units and significant variations of seismic amplitudes. The proposed method was applied to a highly non-stationary synthetic seismic dataset with different levels of noise. The results of this work clearly show the advantages of the proposed method against conventional geostatistical seismic inversion procedures. It is important to highlight the impact of this technique in terms of a higher convergence between real and inverted reflection seismic data and the more realistic approximation towards the real subsurface geology comparing with traditional techniques. This article is protected by copyright. All rights reserved

Description: ABSTRACT Depth from extreme points method is an important tool to estimate the depth of sources of gravity and magnetic data. In order to interpret gravity gradient tensor data conveniently, formulas for the tensor data form regarding depth from extreme points method were calculated in this paper. Then all of the gradient tensor components were directly used to interpret the causative source. Beyond the g zz component, also the g xx and g yy components can be used to obtain depth information. In addition, the total horizontal derivative of the depth from extreme points of the gradient tensor can be used to describe the edge information of geologic sources. In this paper, we investigated the consistency of the homogeneity degree calculated by using the different components, which leads to the calculated depth being confirmed. Therefore, a more integrated interpretation can be obtained by using the gradient tensor components. Different synthetic models were used with and without noise to test the new approach, showing stability, accuracy and speed. The proposed method proved to be a useful tool for gradient tensor data interpretation. Finally, the proposed method was applied to full tensor gradient data acquired over the Vinton Salt Dome, Louisiana, USA, and the results are in agreement with those obtained by previous researches. This article is protected by copyright. All rights reserved

Description: ABSTRACT We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2 N refraction travel times, which can be spawned into refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

Description: ABSTRACT We present a new inversion method to estimate, from prestack seismic data, blocky P- and S-wave velocity and density images and the associated sparse reflectivity levels. The method uses the three-term Aki and Richards approximation to linearise the seismic inversion problem. To this end, we adopt a weighted mixed l 2, 1 -norm that promotes structured forms of sparsity, thus leading to blocky solutions in time. In addition, our algorithm incorporates a covariance or scale matrix to simultaneously constrain P- and S-wave velocities and density. This a priori information is obtained by nearby well-log data. We also include a term containing a low-frequency background model. The l 2, 1 mixed norm leads to a convex objective function that can be minimised using proximal algorithms. In particular, we use the fast iterative shrinkage-thresholding algorithm. A key advantage of this algorithm is that it only requires matrix–vector multiplications and no direct matrix inversion. The latter makes our algorithm numerically stable, easy to apply, and economical in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional l 2 - or l 1 -norm regularised solutions, is able to provide consistent blocky and/or sparse estimators of P- and S-wave velocities and density from a noisy and limited number of observations.

Description: ABSTRACT We examine the problem of localization of a single microseismic event and determination of its seismic moment tensor in the presence of strongly correlated noise. This is a typical problem occurring in monitoring of microseismic events from a daylight surface during producing or surface monitoring of hydraulic fracturing. We propose a solution to this problem based on the method of maximum likelihood. We discuss mathematical aspects of the problem, some features and weak points of the proposed approach, estimate the required computing resources, and present the results of numerical experiments. We show that the proposed approach is much more resistant to correlated noises than diffraction stacking methods and time reverse modeling.

Description: ABSTRACT Passive microseismic data are commonly buried in noise, which presents a significant challenge for signal detection and recovery. For recordings from a surface sensor array where each trace contains a time-delayed arrival from the event, we propose an autocorrelation-based stacking method that designs a denoising filter from all the traces, as well as a multi-channel detection scheme. This approach circumvents the issue of time aligning the traces prior to stacking because every trace's autocorrelation is centred at zero in the lag domain. The effect of white noise is concentrated near zero lag; thus, the filter design requires a predictable adjustment of the zero-lag value. Truncation of the autocorrelation is employed to smooth the impulse response of the denoising filter. In order to extend the applicability of the algorithm, we also propose a noise prewhitening scheme that addresses cases with coloured noise. The simplicity and robustness of this method are validated with synthetic and real seismic traces.

Description: ABSTRACT The applied potential, or mise-à-la-masse, method is used in mineral exploration and environmental applications to constrain the shape and extent of conductive anomalies. However, few simple calculations exist to help gain understanding and intuition regarding the pattern of measured electrical potential at the ground surface. While it makes intuitive sense that the conductor must come close to the ground surface in order for the lateral extent of the potential anomaly to be affected by the dimensions of the conductor rather than simply by the depth, no simple calculation exists to quantify this effect. In this contribution, a simple method of images solution for the case of a sphere of constant electrical potential in a conducting half-space is presented. The solution consists of an infinite series where the first term is the same as the method of images solution for a point current source in an infinite half-space. The higher order terms result from the interaction of the constant potential sphere with the no-flux boundary condition representing the ground surface and cause the change in the shape of the potential anomaly that is of interest in the applied potential method. The calculation is relevant to applied potentials when the conductive anomaly is limited in all three space dimensions and is highly conductive. Using the derived formula, it is shown that, while the electrical potential at the ground surface caused by the sphere is affected even when the sphere is quite deep, the ratio of the potential to the current, a quantity that is more relevant to the applied potential method, is not affected until the centre of the sphere is within two radii of the ground surface. An expression for the contact resistance of the sphere as a function of depth is also given, and the contact resistance is shown to increase by roughly 45% as the sphere is moved from great depth to the ground surface.

Description: ABSTRACT Local seismic event slopes contain subsurface velocity information, and can be used to estimate seismic stacking velocity. In this paper, we propose a novel approach to estimate the stacking velocity automatically from seismic reflection data using similarity-weighted k- means clustering, in which the weights are local similarity between each trace in common midpoint gather and a reference trace. Local similarity reflects the local signal-to-noise ratio in common midpoint gather. We select the data points with high signal-to-noise ratio to be used in the velocity estimation with large weights in mapped traveltime and velocity domain by similarity-weighted k- means clustering with thresholding. By using weighted k- means clustering, we make clustering centroids closer to those data points with large weights which are more reliable and have higher signal-to-noise ratio. The interpolation is used to obtain the whole velocity volume after we have got velocity points calculated by weighted k- means clustering. Using the proposed method, one obtains a more accurate estimate of the stacking velocity because the similarity based weighting in clustering takes into account the signal-to-noise ratio and reliability of different data points in mapped traveltime and velocity domain. In order to demonstrate that, we apply the proposed method to synthetic and field data examples and the resulting images are of higher quality when compared to the ones obtained using existing methods. This article is protected by copyright. All rights reserved

Description: ABSTRACT Noise suppression or signal-to-noise ratio (S/N) enhancement is often desired for better processing results from a microseismic dataset. In this paper, a polarization-linearity and time-frequency thresholding based approach is used for denoising waveforms. A polarization-linearity filter is initially applied to preserve the signal intervals and suppress the noise amplitudes. This is followed by time-frequency thresholding for further S/N enhancement in the S transform domain. The parameterization for both polarization filter and time-frequency thresholding is also discussed. Finally, real microseismic data examples are shown to demonstrate the improvements in processing results when denoised waveforms are considered in the workflow. The results indicate that current denoising approach effectively suppresses the background noise and preserves the vector fidelity of signal waveform. Consequently, the quality of event detection, arrival-time picking and hypocenter location improves. This article is protected by copyright. All rights reserved

Description: A prediction model for frequency spectrum of blast-induced seismic waves is established. The effect of explosive sources is considered in this model. Our model implies that the frequency spectrum of blast-induced seismic wave is mainly influenced by the initial pressure and the adiabatic exponent of explosives. The dominant frequency increases with the decreasing of initial pressure or the increasing of adiabatic exponent. In addition, this prediction model is verified by the experiment. The error of the dominant frequency is 4%-6%. It is indicate that the proposed model in this paper can reasonably predict the frequency spectrum of blast-induced seismic waves, and then we can provide a better frequency spectrum by optimizing the explosion source. This article is protected by copyright. All rights reserved