ALBERT

Notizen: Acoustic reverse-time finite-difference migration for zero-offset data is extended from two- to three-dimensional media. The formulation is based on the full three-dimensional acoustic wave equation and so has no dip restrictions and it involves extrapolation in a velocity distribution variable in three dimensions. The algorithm is demonstrated by successful migration of synthetic data sets for three models: a point diffractor, an oblique pinch-out, and a dome overlying a planar reflector.

Notizen: Seismic attenuation introduces modifications in the wavelet shape in vertical seismic profiles. These modifications can be quantified by measuring particular signal attributes such as rise-time, period and shape index. Use of signal attributes leads to estimations of a seismic-attenuation log (Q-log).To obtain accurate signal attributes it is important to minimize noise influence and eliminate local interference between upgoing and downgoing waves at each probe location. When tube waves are present it is necessary to eliminate them before performing separation of upgoing and downgoing events. We used a trace-by-trace Wiener filter to minimize the influence of tube waves. The separation of upgoing and downgoing waves was then performed in the frequency domain using a trace-pair filter.We used three possible methods based on signal attribute measurements to obtain g-log from the extracted downgoing wavefield. The first one uses a minimum phasing filter and the arrival time of the first extremum. The two other methods determine the Q-factor from simple relations between the amplitudes of the first extrema and the pseudo-periods of the down-going wavelet.The relations determined between a signal attribute and traveltime over quality factor were then calibrated using field source signature and constant-Q models computed by Ganley's method. Q-logs thus obtained from real data are discussed and compared with geological information, specifically at reservoir level.Analysis of the tube wave arrivals at the level of the reservoir showed a tube wave attenuation that could not be explained by simple transmission effects. There was also a loss of signal coherence. This could be interpreted as tube wave diffusion in the porous reservoir, followed by dispersion. If this interpretation can be verified, tube wave analysis could lead to further characterization of porous permeable zones.

Notizen: During the last couple of years there has been much research in the area of wavefield separation of borehole seismic data, and several articles have been published on various separation techniques. Methods involving the application of two-dimensional Fourier transformation, the Radon transformation, multi-level median filters or optimal filters, are all suggested as possible approaches to the wavefield separation problem.This paper compares some of these methods commonly used in the industry.The theories of the chosen methods are described to see how they are related. Using the different methods on synthetic and real data, we show how this theoretical relation is reflected in the relatively similar results obtained. We also show how the different filters treat coherent and random noise.

Notizen: Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions.Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable interpretation.

Notizen: Underground gravity observations in deep coal mines using the conventional gravity meters Worden (type Master) and LaCoste-Romberg (model D), both of which have been adapted to the fire damp regulations, can be accurate to ± 10 and ± 3 μgal, respectively. For underground determination of the vertical gradient of gravity the LaCoste-Romberg meter is used together with a specially designed measuring tower. Using this euipment an accuracy in tower gradient observations of ± 30 E was obtained.To apply the equipment to precision gravity observations in underground situations an additional correction, i.e. a gallery correction, is needed. High accuracy in correction is achieved by a new method of three-dimensional modelling. The gravity effect is computed for bodies with a surface approximated by triangular elements, which are generated from corner points of the body. The combination of gallery correction with tower gradient data leads to a new method for in situ density determination. It offers the possibility of horizontal instead of vertical density profiling.To demonstrate the effectiveness of the developments in underground observations the localization of a pump room is presented. Microgravity and tower gradient observations were carried out to detect the cavity. The horizontal gradient was also calculated to give a more reliable location.

Notizen: Power spectrum analysis of the Bouger gravity values in the Eastern Alps suggests that the gravity field may be separated into long and short wavelength components. The long wavelength component is assumed to be caused by Alpine crustal thickening. This long wavelength component was subjected to a gravimetric single density-interface inversion procedure, giving a gravimetric Mohorovičić model which is generally in good agreement with Moho-depths derived by refraction and reflection seismology.The residual high-frequency gravity component correlates well with the main surface geological units in the Eastern Alps.Apparent density mapping by applying an inverse density deconvolution filter to the short wavelength gravity component gives density values for the upper crust which correspond well with averaged density values from rock samples.

Notizen: Hydrogeological problems which involve the determination of lateral variations in structures or physical properties may be solved with electrical resistivity gradient profiling if there are significant variations in electrical resistivity, spatially or temporally. The method is explained, evaluated for sensitivity, compared with other methods, and applied to the location of volcanic dike zones that are impounding an anomalous water body near Schofield, Oahu, Hawaii. From the electrical soundings and other independent data, the lateral positions of the boundaries have been refined and their nature estimated.

Notizen: 3D Kirchhoff migration and acoustic Born inversion of zero-offset seismic data in a constant-velocity medium can be uniformly factored as a cascade of two 2D diffraction integrals. The formal argument is based on a straightforward implementation of the original time-domain approach of Gibson, Larner and Levin. The factorization differs from the factorization described by Jakubowicz and Levin in omitting all time-dependent filters from the 2D operators in favour of ID filtrations performed as a preprocess and a postprocess.

Notizen: Effective noise reduction of single-sweep recorded data is achieved by application of a velocity filter process on a decomposed vibrator pattern. This technique promises high resolution results with a minimum effect on signal characteristic. A comparison of the stacked section of records vertically stacked in the field with the stacked section of velocity-filtered receiver gathers shows a significant increase in resolution and signal-to-noise ratio.

Notizen: In recent years, the use of wide source arrays in marine seismic surveys has been a topic of interest in the seismic industry. Although one motivation for wide arrays is to get more guns in a source array without increasing the in-line array dimension, wide arrays can also provide the benefit of suppressing side-scattered energy. Comparisons of common midpoint (CMP) stacks of data acquired offshore Washington and Alaska with wide and conventional-width source arrays, however, show only small and sometimes inconsistent differences. These data were acquired in areas where side-scattered energy is a problem. Comparisons of pre-stack data, however, show substantial differences between the wide and conventional source array data.The disparity between the stacked and prestack data is explained by analysing the effective suppression of back-scattered energy by CMP stacking. Energy reflected from scatterer positions broadside to a given CMP location has a lower stacking velocity than that of the primary reflection events. Thus, CMP stacking attenuates the side-scattered energy. In both survey areas the action of CMP stacking was so powerful in suppressing the broadside energy that the additional action of the wide array was inconsequential in the final stacked sections. In other areas, where the scattering velocity is comparable to the primary stacking velocity, wide arrays could provide considerable advantage.Even though CMP stacked data from wide and conventional-width arrays may appear similar, the reduced amount of side-scattered energy in wide-array prestack data may provide a benefit for data dependent processes such as predictive deconvolution and velocity analysis. However, wide arrays cannot be used indiscriminately because they can degrade cross-dipping primary events. They should be considered primarily as a special tool for attacking severe source-generated noise from back-scattered waves in areas where the action of CMP stacking is insufficient.

Notizen: A new approximate method to calculate the space-time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration is presented. The configuration consists of a stack of fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. A distorted-wave Born approximation is introduced; the important feature of the method is the assumption of a background medium with vertical varying root-mean-square acoustic wave speed. A closed-form expression for the scattered field in space and time as a function of the contrast parameters is deduced. The result agrees closely with rigorously calculated synthetic seismograms. In the inverse scheme the wave speed and mass density can be reconstructed within a single trace. Results of the inversion scheme applied to synthetic data are shown.

Notizen: A particular methodology adapted to crystalline formations with a thin weathered zone was developed for a village hydrological project, in Benin. A combination of electrical profiles, Schlumberger and square arrays, was able to locate the most fractured zones in the basement. We present some results obtained from theoretical models as well as from field data.The suggested methodology uses both measurements of resistivity and anisotropy. Strong anisotropy and low resistivity indicate the most productive hydrogeological areas.

Notizen: Seismic data often contain traces that are dominated by noise; these traces should be removed (edited) before multichannel filtering or stacking. Noise bursts and spikes should be edited before single channel filtering. Spikes can be edited using a running median filter with a threshold; noise bursts can be edited by comparing the amplitudes of each trace to those of traces that are nearby in offset-common midpoint space. Relative amplitude decay rates of traces are diagnostic of their signal-to-noise (S/N) ratios and can be used to define trace editing criteria. The relative amplitude decay rate is calculated by comparing the time-gated trace amplitudes to a control function that is the median trace amplitude as a function of time, offset, and common midpoint. The editing threshold is set using a data-adaptive procedure that analyses a histogram of the amplitude decay rates.A performance evaluation shows that the algorithm makes slightly fewer incorrect trace editing decisions than human editors. The procedure for threshold setting achieves a good balance between preserving the fold of the data and removing the noisiest traces. Tests using a synthetic seismic line show that the relative amplitude decay rates are diagnostic of the traces’S/N ratios. However, the S/N ratios cannot be accurately usefully estimated at the start of processing, where noisy-trace editing is most needed; this is the fundamental limit to the accuracy of noisy trace editing.When trace equalization is omitted from the processing flow (as in amplitude-versus-offset analysis), precise noisy-trace editing is critical. The S/N ratio of the stack is more sensitive to type 2 errors (failing to reject noisy traces) than it is to type 1 errors (rejecting good traces). However, as the fold of the data decreases, the S/N ratio of the stack becomes increasingly sensitive to type 1 errors.

Notizen: This paper presents results of testing an efficient ray generation scheme needed whenever ray synthetic seismograms are to be computed for layered models with more than 10‘ thick’layers. Our ray generation algorithm is based on the concept of kinematically equivalent waves (the kinematic analogs) having identical traveltimes along different ray-paths between the source and the receiver, both located on the surface of the model. These waves, existing in any medium composed of laterally homogeneous parallel layers, interfere at any location along the recording surface, thereby producing a composite wavelet whose amplitude and shape depend directly on the number of kinematic analogs (the multiplicity factor). Hence, explicit knowledge of the multiplicity factor is crucial for any analysis based on the amplitude and shape of individual wavelets, such as wavelet shaping, Q estimation, or linearized wavelet inversion.For unconverted waves, such as those discussed in this paper, the multiplicity factor can be computed analytically using formulae given in the Appendix; for converted waves, the multiplicity factor should be computed numerically, using the algorithm employed for the computation of the seismograms presented in a previous paper by one of the authors.

Notizen: Data from offshore Norway is used to study applications of elastic VSP modelling in detecting shear waves and observing the effects of successive mode conversion in field-recorded VSP data. The shear-wave velocities and densities from log data are used in conjunction with compressional wave velocities determined from surface seismic and log data in the VSP modelling.The time domain non-normal incidence elastic VSP modelling technique of Aminzadeh and Mendel is used as the modelling algorithm. Two surface seismograms are computed first. One is the vertical component and the other is the horizontal component for plane waves that have specified incident angles. A downward continuation method is then applied to generate seismograms at different depth points. The collection of these seismograms constitutes non-normal incidence VSPs. Both vertical and horizontal components of VSP data can be obtained by this procedure.In this paper non-normal incidence VSPs are generated for a 12.5° incident plane wave. The modelling results of layered earth systems of thin layers and thick layers are both compared with field data, and the effect of mode conversions in thin layers is observed. Several events in the field data can be explained by this elastic VSP modelling.Comparison of the model data and field data enabled a probable tube wave or out-of-plane event to be identified, the removal of which significantly improved the final VSP section. This study also shows how the VSP data helped the interpretation of the surface 3D data.

Notizen: An efficient full 3D wavefield extrapolation technique is presented. The method can be used for any type of subsurface structure and the degree of accuracy and dip-angle performance are user-defined. The extrapolation is performed in the space-frequency domain as a space-dependent spatial convolution with recursive Kirchhoff extrapolation operators.To get a high level of efficiency the operators are optimized such that they have the smallest possible size for a specified accuracy and dip-angle performance. As both accuracy and maximum dip-angle are input parameters for the operator calculation, the method offers the possibility of a trade-off between these quantities and efficiency. The operators are calculated in advance and stored in a table for a range of wavenumbers. Once they have been calculated they can be used many times.At the basis of the operator design is the well-known phase-shift operator. Although this operator is exact for homogeneous media only, it is assumed that it may be applied locally in case of inhomogeneities. Lateral velocity variations can then be handled by choosing the extrapolation operator according to the local value of the velocity. Optionally the operators can be designed such that they act as spatially variant high-cut filters. This means that the evanescent field can be suppressed in one pass with the extrapolation. The extrapolation method can be used both in prestack and post-stack applications. In this paper we use it in zero-offset migration. Tests on 2D and 3D synthetic and 2D real data show the excellent quality of the method. The full 3D result is much better then the result of two-pass migration, which has been applied to the same data.The implementation yields a code that is fully vectorizable, which makes the method very suitable for vector computers.

Notizen: A method for estimating the degree of polynomial fitted to gravity anomalies to evaluate the regional anomaly is presented. The anomaly can be fitted by polynomials of different degrees with the least-squares method and the optimum degree of the polynomial evaluating this anomaly can be estimated from the point of discontinuity of the gradient on a graph of variance against the polynomial degree. The Bouguer gravity is initially separated by upward continuation to a proper height and then the degree of regional polynomial to fit the Bouguer anomaly can be estimated. Theoretical and field examples show the effectiveness of the method.

Notizen: The copper sulphide exploration programme in Albania involves a number of geophysical methods. The most important ones are the Induced Polarization (IP) and the Turam methods. This paper reports some recent achievements in increasing the depth of investigation and in discriminating sulphide ore textures by the IP, spectral IP and Turam methods.

Notizen: Seismic anisotropy is an unfamiliar concept to many geophysicists and the use of misleading and ambiguous terminology has made it more difficult to understand. I suggest here a consistent terminology in which simple expressions have specific meanings similar to their colloquial meanings. It is hoped that use of such language will help to make the increasing number of papers reporting seismic anisotropy more readily comprehensible to the non-specialist. This not a manual of anisotropy, and it is not intended for theoreticians. It is a list of terms which may make anisotropy a little easier to understand for those more familiar with wave propagation in isotropic solids.

Notizen: The possibilities for reconstructing seismic velocity distributions containing low-velocity anomalies by iterative tomographic methods are examined studying numerical and analogue 2D model data. The geometrical conditions of the model series were designed to generalize the geometrical characteristics of a typical cross-hole tomographic field case. Models with high (30%) and low (8%) velocity contrasts were realized. Traveltimes of 2D ultrasonic P-waves, determined for a dense net of raypaths across each model, form the analogue data set. The numerical data consists of traveltimes calculated along straight raypaths. Additionally, a set of curved-ray traveltimes was calculated for a smoothed version of the high-contrast model.The Simultaneous Iterative Reconstruction Technique (SIRT) was chosen from the various tomographic inversion methods. The abilities of this standard procedure are studied using the low-contrast model data. The investigations concentrate on the resolving power concerning geometry and velocity, and on the effects caused by erroneous data due to noise or a finite time precision. The grid spacing and the source and receiver patterns are modified. Smoothing and slowness constraints were tested. The inversion of high-contrast analogue model data shows that curved raypaths have to be considered. Hence, a ray-tracing algorithm using velocity gradients was developed, based on the grid structure of the tomographic inversion. This algorithm is included in the SIRT-process and the improvements concerning anomaly localization, resolution and velocity reconstruction are demonstrated. Since curved-ray tomography is time-consuming compared with straight-ray SIRT, it is necessary to consider the effects of grid spacing, ray density, slowness constraints and the

Notizen: Residual migration can correct for migration done with the wrong velocity. The initial migration can be done with a less accurate, fast time-migration algorithm followed by a residual depth-migration operator. This combines the speed and accuracy of different migration schemes.The residual depth-migration equation can be obtained by an appropriate transformation of a typical finite-difference, depth-migration equation. Since the cheaper, initial time-migration has already partially migrated the data, the residual depth-migration has less work to do than if the depth-migration were done in a single step. As a result, the overall process has increased the speed and reduced the dip limitations associated with typical depth-migration operators. Results on a steeply dipping model demonstrate the validity and usefulness of residual depth-migration.

Notizen: A method for transforming Normal Moveout corrected CMP-gathers is proposed. The method is based upon the availability of a model of the CMP-gather. However, the transformation can be performed with any degree of accuracy in the model. Ideally the employed model should be a synthesis of all available a priori information about the particular data set.Mathematically the transformation is performed as follows. The CMP-gather is considered to be a matrix. This matrix is first decomposed into a set of submatrices of the same dimensions. Each submatrix consists of non-zero elements or samples with the same relative amount of noise. By reducing each of these submatrices to a vector (a trace) we get a new set of traces. This set then represents the transformed CMP-gather.The purpose of the transformation is to organize the CMP data in a form which makes it easier both to analyse the noise distribution and to take the necessary steps to improve the signal-to-noise ratio at the stacking stage. In principle the method incorporates the exploitation of multichannel recordings with the use of models. Several examples of transformed gathers and their applications to the improvement of real seismic data are shown.

Notizen: The techniques of downward continuation and imaging invented for seismic waves can be applied to other types of waves. We show how they can be applied to electromagnetic surveys conducted with Synthetic Aperture Radar (SAR). The algorithms used closely follow those used for seismic waves. Differences are induced by alternate wavelengths, wave velocities, distances between sources and reflectors, etc. We analyse in detail a survey carried out using a satellite; difficulties arise from because the orbit of the satellite cannot be approximated by a simple straight line if the spatial resolution of the survey is high. We determine appropriate techniques for the correction of the distortion induced by the latter and we delimit the resolution of the observed data, as seen from a satellite. Finally we show examples of the application of the technique of seismic migration to satellite data that were irradiated to Earth during the short but productive life of Seasat.

Notizen: Media containing aligned cracks or ellipsoidal inclusions as well as media consisting of sequences of isotropic layers show transverse isotropy with respect to elastic wave propagation. However, the transversely isotropic media which are equivalent to media containing aligned inclusions do not necessarily have to be representable by sequences of stable isotropic layers. These transversely isotropic media can be modelled by such sequences if - and only if - several stability conditions are satisfied. Important parameters determining whether these conditions are satisfied are the aspect ratio of the inclusions and the material filling the inclusions, the‘fluid’. An analytical expression describing the range of aspect ratios for which the constraints are satisfied can be derived. This expression (which is a good approximation for several crack models) and numerical calculations show that media containing water-filled inclusions can be represented by sequences of stable isotropic layers if the inclusions have aspect ratios less than 0.1. The limiting aspect ratio decreases for a decreasing ratio of the bulk modulus of the fluid to the shear modulus of the matrix material. Finally, media containing dry inclusions of any aspect ratio cannot be modelled by thin isotropic layering. These results depend only weakly on the crack density and on the matrix material. The representation of crack-induced anisotropy by layer-induced anisotropy can be used to classify crack-induced anisotropy and might be useful in the separation of the cause of anisotropy and the determination of the nature of the fluid.

Notizen: High resolution seismic reflection exploration for minerals places severe demands on field practice so as to maximize the signal-to-noise bandwidth. In particular, all horizontally propagating coherent noise, especially ground roll, must be attenuated.The blocking effect of a trench between source and receiver has been investigated by means of two-dimensional physical seismic model experiments. Rectangular, circular and wedge-shaped saw-cuts of various dimensions were studied. The results show that thin rectangular cuts of depth equal to one-quarter of the Rayleigh wave noise wavelength produce a 12 dB or better improvement in the signal-to-noise ratio. Rayleigh wave attenuation is greater than 30 dB at a cut depth of one wavelength. In the field applications envisaged, this corresponds to trenches up to a few metres deep. The trenches should be filled with foam or loose sand to dampen out mode conversion and diffraction noise. There are obvious practical difficulties of implementing such a technique in routine CMP operations.The technical effectiveness of the saw-cut is illustrated by imaging a deeply-buried small hole (diffractor) in an aluminium plate. Without the saw-cut between source and receiver, the seismic record is dominated by Rayleigh wave noise, masking P-wave arrivals from the target diffractor. However, with a saw-cut of depth three-quarters of a Rayleigh wave wavelength, the improvement is dramatic, making it easy to detect and identify the hole. When scaled to the field situation, this is equivalent to imaging a 6 m tunnel at a depth of 400 m, using a surface trench of depth 2 m to block ground roll.

Notizen: The quality of Vibroseis survey data can be improved by continuously monitoring the vibrator's baseplate and reaction mass accelerations. Equipment failures can be detected as they occur, rather than relying on similarity trials at the beginning and end of the day's production. Equipment faults can then be corrected as they happen and thus would not have a detrimental effect on the quality of the survey data. Source efficiency can be optimized by monitoring the amount of harmonic distortion generated by the vibrator at different drive levels on the different surfaces which may be encountered during a survey. Phase problems introduced by poor coupling of the baseplate to the ground can also be identified and addressed in the field.Rapid analysis of vibrator signals is required if continuous monitoring is to be useful. Frequency-time (f-t) analyses of vibrator signals are often used in processing centres, but are slow and require a large storage capacity which makes the technique unsuitable for a field analysis system.The two methods proposed to analyse vibrator signals entail the use of hodograms and time-varying notch filters. Hodograms provide a qualitative analysis of harmonic distortion and vibrator performance. A fast, time-varying notch filter gives quantitative and qualitative information about the harmonic distortion present in the signal and can be used to identify problems with vibrator behaviour. Both the hodogram and fast, time-varying notch filter methods can analyse the vibrator's reaction mass and baseplate accelerations as it progresses through its sweep and can present automatically interpreted results to the operator before moving to the next vibrator point.

Notizen: The use of cables with a large number of closely spaced receivers has become increasingly common in marine seismic acquisition; this gives geophysicists the opportunity to improve data quality in processing centres. In particular, arrays need not be fixed in the field, but instead can be flexibly simulated in the computer.The paper defines a strategy to optimize the application of receiver-array simulation, based on the requirement that signal resolution should not be compromised. The approach consists in the design of k-domain filters through the use of Chebyshev polynomials that define the spatial response of the desired array, with array length that varies with time according to spatial and vertical resolution constraints set by the interpreter.An example, taken from a marine 240-channel seismic line, ties the underlying ideas to practical application and shows that appropriate array processes can contribute to improving the quality of seismic data, especially in areas with complex geology and strong coherent noise.

Notizen: DEKORP 2-S is the first profile carried out in the German continental reflection seismic programme. Besides numerous reflections in the lower crust, the seismic section is characterized by strongly curved events that are interpreted as diffractions. These diffractions occur as clusters, mainly in two areas of the profile: the Dinkelsbühl and the Spessart area. This paper deals with the Dinkelsbühl diffractions where three-dimensional control is available. The control is provided by two additional profiles P-1 and Q-40 which run parallel and perpendicular to the main line, DEKORP 2-S. The type and the location of the diffractors are determined by traveltime-modelling using crustal velocity functions derived from in-line wide-angle observations. A model with inclined line diffractors provides the best fit to the data for all three profiles. Projections of these line diffractors to the surface show that they are aligned parallel to the strike direction of the Variscides. This suggests that the diffractions are associated with the suture zone between the Saxothuringian and Moldanubian geological provinces.

Notizen: An accurate, fast, and simple algorithm for 3D modelling of seismic edge diffractions is presented. It is based on a generalized Kirchhoff theory that applies also to inhomogeneous (non-uniform) media. Both the boundary values and the Green functions in the Kirchhoff diffraction integral are determined by dynamic ray tracing, and each ray event is treated separately to obtain a description with clear physical interpretation. For each event the resulting Kirchhoff diffraction integral is evaluated by means of a uniform asymptotic technique that remains valid for receiver points near shadow boundaries. Since all parameters needed in the computations are obtained from dynamic ray tracing, the algorithm can readily be incorporated in existing software packages for 3D seismic ray modelling.

Notizen: The inverse problem of magnetotellurics over a horizontally stratified earth is described, with emphasis on practical application. The inversion is divided into basically two steps. The construction of some best solution, and the analysis of that solution with regard to uncertainty and complexity. For the construction of best solutions a robust non-linear solver was developed, and for the estimation of parameter errors a modified eigenvalue-eigenvector analysis is performed to better describe non-linear effects. The choice of the number of layers is shown to be intimately connected with the structure of data errors and the misfit between model and data. An example from the Siljan impact structure in Sweden illustrates the power of the technique.

Notizen: Two geophysical methods [resistivity soundings and spontaneous potentials (SP)] are used to investigate aquifers in the Quaternary volcanic formations of the Chaîne des Puys (France). The interpretation of the resistivity soundings required a specific work of determination of the resistivity of the formations concerned. The basement topography, characterized by axial horst and graben structures and perpendicular palaeovalleys, was revealed. SP was developed experimentally in the field and theoretically. It is shown that the SP anomalies can be considered as double-layer potentials, with their source on the aquifers' interfaces. The most significant of them is the water table, which creates an SP anomaly of similar but inverted form. SP anomalies due to flows in unconfined aquifers, in palaeovalleys, and in volcanic ranges are computed and compared with the observed ones. These two methods have determined the extent and the boundary conditions of the different hydrogeological basins and have determined the major drainage axes and the groundwater flow pattern.

Notizen: The analytical solution, for the H-polarization magnetotelluric impedance, of a series of multiple, vertical, conducting slabs (dikes) embedded in a host medium is extended to an infinite array in order to model an anisotropic layer. The solution is used to study the effects of such strongly anisotropic media on the surface impedance. At low frequencies such vertically laminated structures behave as a bulk material. It is shown that the effective bulk parameters are those expected from d.c. theory. However, practical electrode separations may not be long enough or adequately positioned to correctly obtain these bulk parameters from the measured impedance. Thus, such structures can masquerade as quite different one-dimensional structures. A haphazard use of long electrode spacings will not necessarily produce correct results.

Notizen: Multiple coverage reflection seismic data provide an important source of information concerning the subsurface. However, due to the stacking and migration techniques used in the processing, the first arrivals are muted and details about the upper part of the sections are generally lost.This paper describes a computerized method for the inverse modelling of laterally varying velocities and shallow depths which are not sufficiently resolved in the reflection seismic processing. The method minimizes, in a least-squares manner, the difference between the observed first arrivals, picked from the reflection traces, and a set of synthetic traveltimes, calculated by ray tracing in a cell model. An initial model, e.g. from a priori knowledge or the application of a conventional interpretation method, is refined iteratively until no further essential improvement can be achieved. Traditional first-arrival inversion methods cannot, in general, provide such flexible modelling. The technique is successfully tested on synthetic data as well as on first arrivals picked automatically from the records of a reflection seismic survey in North Jutland, Denmark.

Notizen: Static corrections for reflection seismic data shot on high velocity crystalline rock can be calculated directly from the data using a global, iterative stackpower optimization. The reflections consist of several peaks, creating the possibility of aligning the wrong peak in the signals. Due to misalignments a large number of local maxima in the stackpower exist in a cyclic manner, only slightly smaller than thes stackpower of the‘best’stack. Therefore the search must be of a global nature. A Monte Carlo search requires long run times. A global search method is presented using a varying sequence of parameters within each iteration. The ability for a set of static corrections and the associated stackpower to move from a local maximum to a larger maximum is enhanced. The performance of the iterative process is improved, so a relatively small number (about 20) of iterations is needed to obtain the optimum set of corrections. The risk of misalignment of traces by using the wrong peak in a signal consisting of several peaks is diminished, and it is less important that the initial set of corrections is close to the final set. The method is illustrated by a synthetic example and on a data set shot on the granites of Dalarna, Sweden.

Notizen: We analyse the stacking process within the framework of imaging techniques. Our results show how the NMO stretch, traditionally looked upon as giving a negative contribution, can be utilized to improve the vertical resolution of the stacked data from a source deficient in low frequencies. The added bandwidth is provided by the spatial coherency of the energy emitted by a point source.

Notizen: In order to make 3D prestack depth migration feasible on modern computers it is necessary to use a target-oriented migration scheme. By limiting the output of the migration to a specific depth interval (target zone), the efficiency of the scheme is improved considerably. The first step in such a target-oriented approach is redatuming of the shot records at the surface to the upper boundary of the target zone. For this purpose, efficient non-recursive wavefield extrapolation operators should be generated. We propose a ray tracing method or the Gaussian beam method. With both methods operators can be efficiently generated for any irregular shooting geometry at the surface. As expected, the amplitude behaviour of the Gaussian beam method is better than that of the ray tracing based operators.The redatuming algorithm is performed per shot record, which makes the data handling very efficient. From the shot records at the surface‘genuine zero-offset data’are generated at the upper boundary of the target zone. Particularly in situations with a complicated overburden, the quality of target-oriented zero-offset data is much better than can be reached with a CMP stacking method at the surface. The target-oriented zero-offset data can be used as input to a full 3D zero-offset depth migration scheme, in order to obtain a depth section of the target zone.

Notizen: Ground-penetrating radar is a technique which offers a new way of viewing shallow soil and rock conditions. The need to better understanding overburden conditions for activities such as geochemical sampling, geotechnical investigations, and placer exploration, as well as the factors controlling groundwater flow, has generated an increasing demand for techniques which can image the subsurface with higher resolution than previously possible.The areas of application for ground-penetrating radar are diverse. The method has been used successfully to map ice thickness, water depth in lakes, bedrock depth, soil stratigraphy, and water table depth. It is also used to delineate rock fabric, detect voids and identify karst features. The effective application of the radar for the high-resolution definition of soil stratigraphy and fractures in bedrock is highlighted.The basic principles and practices involved in acquiring high quality radar data in the field are illustrated by selected case histories. One example demonstrates how radar has been used to map the bedrock and delineate soil horizons to a depth of more than 20 m. Two case histories show how radar has been used to map fractures and changes of rock type to 40 m range from inside a mine. Another case history demonstrates how radar has also been used to detect and map the extent of groundwater contamination. The corroboration of the radar results by borehole investigations demonstrates the power and utility of the high-resolution radar method as an aid for interpolation and extrapolation of the information obtained with conventional coring programmes. With the advent of new instrumentation and field procedures, the routine application of the radar method is becoming economically viable and the method will see expanded use in the future.

Notizen: The conventional tomographic inversion consists in minimizing residuals between measured and modelled traveltimes. The process tends to be unstable and some additional constraints are required to stabilize it. The stochastic formulation generalizes the technique and sets it on firmer theoretical bases.The Stochastic Inversion by Ray Continuation (Sirc) is a probabilistic approach, which takes a priori geological information into account and uses probability distributions to characterize data correlations and errors. It makes it possible to tie uncertainties to the results.The estimated parameters are interval velocities and B-spline coefficients used to represent smoothed interfaces. Ray tracing is done by a continuation technique between source and receivers. The ray coordinates are computed from one path to the next by solving a linear system derived from Fermat's principle. The main advantages are fast computations, accurate traveltimes and derivatives.The seismic traces are gathered in CMPs. For a particular CMP, several reflecting elements are characterized by their time gradient measured on the stacked section, and related to a mean emergence direction.The program capabilities are tested on a synthetic example as well as on a field example. The strategy consists in inverting the parameters for one layer, then for the next one down. An inversion step is divided in two parts. First the parameters for the layer concerned are inverted, while the parameters for the upper layers remain fixed. Then all the parameters are reinverted.The velocity-depth section computed by the program together with the corresponding errors can be used directly for the interpretation, as an initial model for depth migration or for the complete inversion program under development.

Notizen: The magnetometric resistivity (MMR) method uses a sensitive magnetometer to measure the low-level, low-frequency magnetic fields associated with the galvanic current flow between a pair of electrodes. While the MMR anomalies of simple structures such as dikes and vertical contacts have been determined analytically, there is a lack of systematic information on the expected responses from simple three-dimensional bodies. We determine the characteristic anomalies associated with square, plate-like conductors, which are excellent models of many base metal mineral deposits.The anomalies of plates of finite size are determined numerically using an integral equation method. A plate is subdivided into many sections and the current flow within each section is solved by equating the electrical field within each section to the tangential electrical field just outside it. When the plate size is small in relation to either the depth or the transmitter spacing, the shape and amplitude of the anomaly produced is closely approximated by a current dipole model of the same length and depth. At the other extreme, a large plate is represented by a half-plane. The dipole and half-plane models are used to bracket the behaviour of plates of finite size.The form of a plate anomaly is principally dependent on the shape, depth and orientation of the plate. A large, dipping plate near the surface produces a skewed anomaly highly indicative of its dip, but the amount of skew rapidly diminishes with increased depth or decreased size. Changes in plate conductivity affect the amplitude of the anomaly, but have little effect on anomaly shape. A current channelling parameter, determined from the conductivity contrast, can thus be used to scale the amplitude of an anomaly whose basic shape has been determined from geometrical considerations.The separation into geometrical and electrical factors greatly simplifies both the interpretation and modelling of MMR anomalies, particularly in situations with multiple plates. An empirical formula, using this separation, predicts the anomaly of two or more parallel plates with different conductances. In addition, the relation between the resolution of two vertical, parallel plates of equal conductance and their separation is determined.The ability of the integral equation method to model plate-like structures is demonstrated with the interpretation of an MMR anomaly in a survey conducted at Cork Tree Well in Western Australia. The buried conductor, a mineralized graphitic zone, is modelled with a vertical, bent plate. The depth to the top of the plate, and the plate conductance, is adjusted to fit the anomaly amplitude as closely as possible. From the modelling it would appear that this zone is not solely responsible for the observed anomaly.

Notizen: We present a new rapid expansion method (REM) for the time integration of the acoustic wave equation and the equations of dynamic elasticity in two spatial dimensions. The method is applicable to spatial grid methods such as finite differences, finite elements or the Fourier method. It is based on a Chebyshev expansion of the formal solution to the appropriate wave equation written in operator form. The method yields machine accuracy yet it is faster than methods based on temporal differencing. Its disadvantages are that it does not apply to all types of material rheology, and it can also require much storage when many snapshots and time sections are desired. Comparisons between numerical and analytical solutions for simple acoustic and elastic problems demonstrate the high accuracy of the REM.

Notizen: A conventional velocity-stack gather consists of constant-velocity CMP-stacked traces. It emphasizes the energy associated with the events that follow hyperbolic traveltime trajectories in the CMP gather. Amplitudes along a hyperbola on a CMP gather ideally map onto a point on a velocity-stack gather. Because a CMP gather only includes a cable-length portion of a hyperbolic traveltime trajectory, this mapping is not exact. The finite cable length, discrete sampling along the offset axis and the closeness of hyperbolic summation paths at near-offsets cause smearing of the stacked amplitudes along the velocity axis. Unless this smearing is removed, inverse mapping from velocity space (the plane of stacking velocity versus two-way zero-offset time) back to offset space (the plane of offset versus two-way traveltime) does not reproduce the amplitudes in the original CMP gather. The gather resulting from the inverse mapping can be considered as the model CMP gather that contains only the hyperbolic events from the actual CMP gather. A least-squares minimization of the energy contained in the difference between the actual CMP gather and the model CMP gather removes smearing of amplitudes on the velocity-stack gather and increases velocity resolution. A practical application of this procedure is in separation of multiples from primaries.A method is described to obtain proper velocity-stack gathers with reduced amplitude smearing. The method involves a t2-stretching in the offset space. This stretching maps reflection amplitudes along hyperbolic moveout curves to those along parabolic moveout curves. The CMP gather is Fourier transformed along the stretched axis. Each Fourier component is then used in the least-squares minimization to compute the corresponding Fourier component of the proper velocity-stack gather. Finally, inverse transforming and undoing the stretching yield the proper velocity-stack gather, which can then be inverse mapped back to the offset space. During this inverse mapping, multiples, primaries or all of the hyperbolic events can be modelled. An application of velocity-stack processing to multiple suppression is demonstrated with a field data example.

Notizen: The relation between the horizontal profiles of the subsurface resistivity and surface magnetotelluric data can be described by the input and output of a moving-average filter. The impulse response of this spatial filter, which characterizes the averaging process of the magnetotelluric measurements, is given by the sensitivity profile. Thus, the sensitivity analysis can provide insight into the characteristics of the measurements and hence the mechanism of the static effects. The sensitivity analysis presented here consists of constructing the vertical section of the sensitivity distribution using the finite-element method and then Fourier transforming the selected horizontal profiles. When the dipole is assumed for measuring the electric field, the static effects can be explained by the high-pass filter characteristics for the near-surface. When the electrode separation is taken into account, the sensitivity can be obtained by averaging the sensitivities for the dipoles over the horizontal distance equal to the electrode separation. Therefore, the higher-frequency components at each depth decrease with increasing electrode separation. Thus, although the static effects can be reduced simply by increasing the electrode separation, information on the resistivity variation at depth is also lost. However, such an adverse effect can be reduced by making the EMAP-type measurements followed by the spatial filtering of the profile data using the tapered weighting function.

Notizen: Utilizing electromagnetic data in geophysical exploration work is difficult when measured responses are complicated by the effects of 3D structures. 1D and 2D models may not be capable of accurately simulating the physical processes that contribute to a measured response. 3D conductive-host modelling is difficult, costly and time-consuming. Using a 3D inverse procedure it is possible to automate the interpretation of controlled-source electromagnetic data. This procedure uses an inverse formulation based on frequency-domain, volume integral equations and a pulse-basis representation for the internal electrical field and anomalous conductivity. Beginning with an initial model composed of a 3D inhomogeneous region residing in a laterally homogeneous (layered-earth) geoelectrical section, iterative least-squares algorithms are used to refine the geometry and the conductivity of the inhomogeneity. This novel approach for 3D electromagnetic interpretation yields a reliable and stable inverse solution provided constraints on how much the variable can change at each iteration are incorporated. Integral-equation-based inverse formulations that do not correctly address the non-linearity of this inverse problem may have poor convergence properties, particularly when dealing with the high conductivity contrasts that are typical of many exploration problems.While problems associated with contamination of the data by random noise and non-uniqueness of solutions do not usually influence the inverse solution in an adverse manner, problems associated with model inadequacy and errors in an assumed background conductivity structure can produce undesirable effects.

Notizen: The measurement of wavetilt is diagnostic for determining the electrical characteristics of the upper layers of the ground at VLF and LF frequency ranges. Theoretical and field studies have indicated that electric wavetilt using the transverse magnetic (TM) waves detects lateral inhomogeneities virtually instantly as abrupt changes in electrical properties are encountered. Theoretical studies have also indicated that magnetic wavetilt measurements using transverse electric (TE) waves are superior to electric wavetilts for such purposes.An experimental survey was conducted at two locations near Atikokan, Ontario, to verify the theoretical predictions. The survey area, forming a part of a large granitic pluton, was mapped earlier by various geophysical techniques, including the ground VLF-EM method, to detect weak conductors formed either by the presence of fractures in the bedrock filled with water and/or clay, or overburden filling bedrock depressions.A small, multi-turn, horizontal loop was used during the survey as the transmitter to generate TE waves at eleven frequencies from 10.7 to 58.5 kHz. The magnetic wavetilt measurements detected all previously known conductors at the two locations. In addition, the survey detected several weak conductors that were missed by the VLF survey. Thus, the survey indicated the usefulness of magnetic wavetilt results for detection of weak conductors at shallow depths, which may have application in engineering geophysical surveys. The multi-frequency wavetilt data also provided some indications of the depth and depth extent of such conductors.

Notizen: Different types of median-based methods can be used to improve multichannel seismic data, particularly at the stacking stage in processing. Different applications of the median concept are described and discussed. The most direct application is the Simple Median Stack (SMS), i.e. to use as output the median value of the input amplitudes at each reflection time. By the Alpha-Trimmed Mean (ATM) method it is possible to exclude an optional amount of the input amplitudes that differ most from the median value. A more novel use of the median concept is the Weighted Median Stack (WMS). This method is based on a long-gapped median filter. The implicit weighting, which is purely statistical in nature, is due to the edge effects that occur when the gapped filter is applied. By shifting the traces around before filtering, the maximum weight may be given to, for example, the far-offset traces. The fourth method is the Iterative Median Stack (IMS). This method, which also includes a strong element of weighting, consists of a repeated use of a gapped median filter combined with a gradual shortening of the filter after each pass. Examples show how the seismic data can benefit from the application of these methods.

Notizen: Bispherical coordinates are used to derive an exact mathematical solution for the potential field generated by direct current electric conduction in an earth model consisting of two spherical inclusions in a uniform whole-space. The solution takes the form of a spherical harmonic expansion in bispherical coordinates; coefficients in the expansion are obtained by solving sets of linear equations. Rapid forward modelling of numerous interesting situations in d.c. resistivity prospecting is facilitated by the generality and computational efficiency inherent to this new solution. For example, the accuracy of image (or superposition) methods for calculating potential solutions can be quantified. Similarly, the ability of d.c. conduction methods to resolve two distinct bounded bodies in three-dimensional space can be examined by repeatedly calculating the secondary potential or apparent resistivity response of an earth model as a selected parameter is varied. Synthetic mise à la masse, crosshole, or areal potential data sets can be generated for subsequent use in inversion studies. Improvements in solution technique derived here also apply to a simpler model consisting of a single sphere buried in a half-space.

Notizen: The study of wave propagation in media with elliptical velocity anisotropy shows that seismic energy is focused according to the horizontal component of the velocity field while the vertical component controls the time-to-depth relation. This implies that the vertical component cannot be determined from surface seismic velocity analysis but must be obtained using borehole or regional geological information. Both components of the velocity field are required to produce a correctly focused depth image. A paraxial wave equation is developed for elliptical anisotropic wave propagation which can be used for modelling or migration. This equation is then transformed by a change of variable to a second paraxial equation which only depends on one effective velocity field. A complete anisotropic depth migration using this transformed equation involves an imaging step followed by a depth stretching operation. This allows an approximate separation or splitting of the focusing and depth conversion steps of depth migration allowing a different velocity model to be used for each step. This split anisotropic depth migration produces a more accurate result than that obtained by a time migration using the horizontal velocity field followed by an image-ray depth conversion using the vertical velocity field. The results are also more accurate than isotropic depth migration and yield accurate imaging in depth as long as the lateral variations in the anisotropy are slow.

Notizen: A borehole sparker seismic source enclosed in a semi-flexible tube has been developed to produce a short compressional seismic pulse with a frequency content in the range 250 Hz to 3.5 kHz with a peak power at 570 Hz. The pulse shape and frequency content are shown to be a function of the input power, the diameter of the spark chamber, the salinity of the electrolyte, the material of the spark chamber and the electrode configuration. When in a borehole, the source produces a vertically polarized shear wave but, being similar to a small explosive charge does not allow phase reversal as a means of identifying the shear wave in the received pulse train. The source is shown to be ideal for tomographic imaging surveys because of its repetitive nature, high frequency content and reliability. Very high resolution seismic reflection surveys are also shown to be possible under favourable circumstances.

Notizen: For the correct interpretation of data gathered in the seismic prospecting of complex heterogeneous structures, elastic effects must often be taken into consideration. The use of the elastic wave equations to model the seismic response of an hypothesized geological structure is a valuable tool for relating observed seismic data to the earth's inhomogeneities and verify an interpretation.Several methods may be used to integrate numerically the partial differential equations describing elastic wave propagation. Pseudospectral (Fourier) methods represent the leading numerical integration technique. Their main advantage is high accuracy and suitability to vector and parallel computer architectures, while their main drawback is high computational cost. However, for a given accuracy, the required grid size with pseudospectral methods is smaller than that required by finite-difference schemes, thus balancing the computational cost. We describe a two-dimensional pseudospectral elastic model implemented on the vector multiprocessor IBM 3090 VF. The algorithm has been suitably adapted to fully exploit the computer architecture and thereby maximize the performance.The elastic model has been validated in a variety of problems in geophysics and, in particular, in the amplitude-versus-offset analysis which has proved to be an effective technique to extract additional information from the recorded (prestack) data. With proper conditioning and processing of seismic data, and separating amplitude variations due to changes in reflectivity from variations due to other effects, the resulting offset signatures have been successfully used, for instance, to distinguish true bright spots due to gas-bearing sands, from false ones associated with lithological changes. To interpret the observed amplitude-versus-offset signatures, it is necessary to know the reflection coefficients as a function of angle and frequency for planar interfaces, as well as for other structures of geological interest.The modelling is first validated by computing the reflection coefficients for planar interfaces, and then used to analyse the reflection signatures of thin beds, corrugated interfaces and multilayers. Their implications, as well as impact on amplitude-versus-offset analysis, are discussed. We conclude that elastic modelling is an effective and valuable tool to further our understanding of the amplitude anomalies observed in field data.