ALBERT

Notes: A method is presented for the prediction and attenuation of long-period water-layer multiples based on an adaptive multichannel lattice algorithm. The multichannel approach can be viewed as a generalization of two-dimensional linear prediction. The multichannel linear least-squares prediction problem is reviewed briefly and the performance and limitations of the algorithm are demonstrated on two different marine data sets with different properties of the simple and peg-leg multiple system. The algorithm works well even on problematic data sets and is very easy to apply.

Notes: Gravity observations made over the Groningen gasfield from 1978 onwards are available. The existing gravity data were reanalysed and a new survey was carried out. The observed gravity changes obtained during four surveys, spanning an 18-year period, were compared with the gravity effect due to natural gas extraction computed from the reservoir model and the production data. The random error in the gravity values is small enough to detect the effect of gas extraction after a few years (up to 2 μgal/year). The trends obtained from observed and calculated gravity changes agree well within their expected error margins after statistical data snooping. Due to the inadequate measurement set-up of the previous surveys, systematic errors present in the gravity data hampered the use of this data for refinement of the reservoir and the production models. However, with improved gravity monitoring, in particular a very systematic network set-up and well-calibrated instruments, this should now be feasible. By using the network analysis from the 1996 measurements for the planning of a network in space and time, most of the current problems can be avoided.

Notes: We analyse the geophone orientation and coupling in a data set from the North Sea. Based on the polarization of the water-break on the sea-floor, we have derived processing algorithms for determining the receiver orientation for gimballed and non-gimballed geophone systems. For a gimballed system, the problem reduces to a simple horizontal rotation. However, for a non-gimballed system, where all three geophone axes may vary due to varying acquisition conditions such as dipping sea-floor, twisting of recording cable, etc., the three orientation angles cannot be found directly from the recorded displacement vectors. Using the data redundancy within a common-receiver gather, a robust two-stage method is derived for the non-gimballed system in which all three orientations can initially be unknown. Testing on the North Sea data set acquired with a gimballed system shows that the three-component geophones in the data set are orientated satisfactorily within an error of 5°. However, there are some undesirable cross-couplings between the vertical and horizontal geophones, which results in leakage of shear-wave energy from the horizontal components to the vertical components.

Notes: The great majority of data processing methods for magnetotelluric measurements are based on an average Fourier spectral analysis to estimate either the transfer function or the coherence function. This assumes that the time-series data are stationary. The aim of this paper is to present a preprocessing method able to extract the stationary and coherent part of the original signals. The practitioner can then apply the magnetotelluric method of his choice to these new data. This preliminary data sorting is done in four steps: (i) slow drifts are eliminated using a high-pass filter whose cut-off frequency is determined by an iterative procedure. Based on run tests, this procedure is also able to remove segments with non-independent samples in the time series; (ii) non-stationary segments are eliminated after band-pass filtering; (iii) non-coherent segments are eliminated before spectral analysis; (iv) the impedance tensor value is then retained, at a given frequency, only if the signals are coherent. This preprocessing method was tested on the simplest, but still used, magnetotelluric method which uses only two field components, and it was found that the average resistivity standard deviation decreased significantly from 14.6 Ωm without sorting to 8.6 Ωm after sorting.

Notes: Prestack depth migrations based on wavefield extrapolation may be computationally expensive, especially in 3D. They are also very dependent on the acquisition geometry and are not flexible regarding the geometry of the imaging zone. Moreover, they do not deal with all types of wave, considering only primary reflection events through the model. Integral approaches using precalculated Green's functions, such as Kirchhoff migration and Born-based imaging, may overcome these problems. In the present paper, both finite-difference traveltimes and wavefront construction are used to obtain asymptotic Green's functions, and a generalized diffraction tomography is applied as an example of Born-based acoustic imaging. Target-orientated imaging is easy to perform, from any type of survey and subselection of shot/receiver pairs. Multifield imaging is possible using Green's functions that take into account, for instance, reflections at model boundaries. This may help to recover parts of complex structures which would be missing using a paraxial wave equation approach. Finally, a numerical evaluation of the resolution, or point-spread, function at any point of the depth-migrated section provides valuable information, either at the survey planning stage or for the interpretation.

Notes: We propose a new method for removing sea-surface multiples from marine seismic reflection data in which, in essence, the reflection response of the earth, referred to a plane just above the sea-floor, is computed as the ratio of the plane-wave components of the upgoing wave and the downgoing wave. Using source measurements of the wavefield made during data acquisition, three problems associated with earlier work are solved: (i) the method accommodates source arrays, rather than point sources; (ii) the incident field is removed without simultaneously removing part of the scattered field; and (iii) the minimum-energy criterion to find a wavelet is eliminated.Pressure measurements are made in a horizontal plane in the water. The source can be a conventional array of airguns, but must have both in-line and cross-line symmetry, and its wavefield must be measured and be repeatable from shot to shot. The problem is formulated for multiple shots in a two-dimensional configuration for each receiver, and for multiple receivers in a two-dimensional configuration for each shot. The scattered field is obtained from the measurements by subtracting the incident field, known from measurements at the source. The scattered field response to a single incident plane wave at a single receiver is obtained by transforming the common-receiver gather to the frequency–wavenumber domain, and a single component of this response is obtained by Fourier transforming over all receiver coordinates. Each scattered field component is separated into an upgoing wave and a downgoing wave using the zero-pressure condition at the water-surface. The upgoing wave may then be expressed as a reflection coefficient multiplied by the incident downgoing wave plus a sum of scattered downgoing plane waves, each multiplied by the corresponding reflection coefficient. Keeping the upgoing scattered wave fixed, and using all possible incident plane waves for a given frequency, yields a set of linear simultaneous equations for the reflection coefficients which are solved for each plane wave and for each frequency. To create the shot records that would have been measured if the sea-surface had been absent, each reflection coefficient is multiplied by complex amplitude and phase factors, for source and receiver terms, before the five-dimensional Fourier transformation back to the space–time domain.

Notes: A new algorithm for tomographic inversion of traveltimes of reflected and refracted seismic waves is developed. The inversion gives interface configurations and velocity distributions in layers. The important features of the algorithm are: (a) the inclusion of shot time delays in the list of unknown parameters; (b) the regularization is applied in such a way that the most probable model is characterized by the similarity of neighbouring interfaces. As the problem under consideration is non-linear, several iterations are necessary in order to obtain the final model. In the case of a very inexact initial model, a ‘layer-by-layer’ inversion strategy is recommended as a first inversion step. The inversion program is supplied with a user interface, thanks to which one can: (a) pick interactively and identify seismic traveltimes; (b) build and edit depth/velocity models; and (c) display calculated traveltime curves and compare them with picked traveltimes as well as with the original seismic sections. The efficiency of the inversion software developed is illustrated by a numerical example and a field example in which shallow seismic data are considered. Application to wide-aperture reflection/refraction profiling (WARRP) data is also possible.

Notes: Non-aliased integral (Kirchhoff-type) transformations for forward and downward wavefield extrapolations in inhomogeneous media with interfaces are described. Special weights are computed to compensate for operator aliasing and finite-aperture effects, even when the data are spatially aliased and irregularly sampled. Basic components of the algorithm, such as Green's function computation, can be replaced by alternative solutions in conjunction with ray-tracing methods. Applications of this algorithm to model and real data in both two and three dimensions are discussed in terms of its impact on seismic modelling, multiple prediction and prestack imaging.

Notes: Attenuation of seismic waves, quantified by the seismic quality factor Q, holds important information for seismic interpretation, due to its sensitivity to rock and fluid properties. A recently published study of Q, based on surface seismic reflection data, used a modified spectral ratio approach (QVO), but both source and receiver responses were treated as isotropic, based on simple raypath arguments. Here, this assumption has been tested by computing apparent attenuation generated by frequency-dependent directivity of typical marine source and receiver arrays and acquisition geometries. Synthetic wavelet spectra were computed for reflected rays, summed over the first Fresnel zone, from the base of a single interval, 50–3000 m thick and velocity 2000 m/s, overlying a 2200 m/s half-space, and for offsets of 71–2071 m. The source and receiver geometry were those of an actual survey.The modelled spectra are clearly affected by directivity, most strongly because of surface ghosts. In general, the strong high-frequency component, produced by the array design, leads to apparently negative attenuation in individual reflection events, though this is dependent on offset and target depth. For shallow targets (less than 400–500 ms two-way traveltime (TWT) depth), apparent Q-values as extreme as −50 to −100 were obtained. For deeper target depths, the directivity effect is far smaller. The implications of the model study were tested on real data. QVO was applied to 20 true-spectrum-processed CMPs, in a shallow (405–730 ms TWT) and a deeper (1000–1300 ms TWT) interval, firstly using a measured far-field source signature (effectively isotropic), and secondly using computed directivity effects instead. Mean interval Q−1-values for the deeper interval, 0.029 ± 0.011 and 0.027 ± 0.018 for conventional and directional processing, respectively, suggested no directivity influence on attenuation estimation. For the shallow interval (despite poor spectral signal-to-noise ratios and hence scattered attenuation estimates), directional processing removed directivity-generated irregularities from the spectral ratios, resulting in an improvement from Q−1int = −0.036 ± 0.130 to a realistic Q−1int = 0.012 ± 0.030: different at 94% confidence level. Equivalent Q-values are: for the deeper interval, 35 and 37 for conventional and directional processing, respectively, and −28 and 86 for the shallow interval.These results support the conclusions of the model studies, i.e. that source/receiver directivity has a negligible effect except for shallow targets (e.g. TWT depth ≤ 500 ms) imaged with conventional acquisition geometry. In such cases directivity corrections to spectra are strongly recommended.

Notes: Modelling of AVO signatures for reservoir characterization requires VS estimation from other available logs when shear-wave data are not available. We tested various models for predicting VS from P-wave velocity, porosity and shale volume measured in well logs. Effective medium models which characterize the pore space in terms of ellipsoidal inclusions were compared with statistical VP–VS regressions. The inclusion models were calibrated by non-linear minimization of the difference between model-predicted velocities and actual measured velocities. The quality of the VS prediction was quantified in terms of the rms error by comparison with shear-wave data in wells where both VP and VS were measured. The linear regressions were found to be more robust and the rms error in the prediction was comparable to effective medium model-based predictions.

Notes: Multichannel filtering to obtain wavefield separation has been used in seismic processing for decades and has become an essential component in VSP and cross-well reflection imaging. The need for good multichannel wavefield separation filters is acute in borehole seismic imaging techniques such as VSP and cross-well reflection imaging, where strong interfering arrivals such as tube waves, shear conversions, multiples, direct arrivals and guided waves can overlap temporally with desired arrivals. We investigate the effects of preprocessing (alignment and equalization) on the quality of cross-well reflection imaging wavefield separation and we show that the choice of the multichannel filter and filter parameters is critical to the wavefield separation of cross-well data (median filters, f–k pie-slice filters, eigenvector filters). We show that spatial aliasing creates situations where the application of purely spatial filters (median filters) will create notches in the frequency spectrum of the desired reflection arrival. Eigenvector filters allow us to work past the limits of aliasing, but these kinds of filter are strongly dependent on the ratio of undesired to desired signal amplitude. On the basis of these observations, we developed a new type of multichannel filter that combined the best characteristics of spatial filters and eigenvector filters. We call this filter a ‘constrained eigenvector filter’. We use two real data sets of cross-well seismic experiments with small and large well spacing to evaluate the effects of these factors on the quality of cross-well wavefield separation. We apply median filters, f–k pie-slice filters and constrained eigenvector filters in multiple domains available for these data sets (common-source, common-receiver, common-offset and common-midpoint gathers). We show that the results of applying the constrained eigenvector filter to the entire cross-well data set are superior to both the spatial and standard eigenvector filter results.

Notes: For many geophysical and astrophysical applications the relationship between physical bulk properties and porosity is needed. As part of the preparation for the ‘Rosetta’ comet rendezvous mission, a simple model for the porosity dependence of the elastic properties of granular media, i.e. the elastic moduli and the propagation velocities of elastic waves, has been developed based on textural properties and the contact stiffness of the constituent particles. It is shown that the derived relationships fit very well with sandstone data. The model is also consistent with data for snow and ice and is in agreement with the transformation mechanisms from snow to ice. A short review shows the relevance to another physical bulk property, the thermal conductivity.

Notes: Seismic velocities (Vp and Vs) of compressional (P-) and shear (S-) waves are important parameters for the characterization of marine sediments with respect to their sedimentological and geotechnical properties. P- and S-wave velocity data of near-surface marine sediments (upper 9 m) of the continental slope of the Barents Sea are analysed and correlated to sedimentological and geotechnical properties. The results show that the S-wave velocity is much more sensitive to changes in lithology and mechanical properties than the P-wave velocity, which is characterized by a narrow range of values. The correlation coefficients between S-wave velocity and silt and clay content, wet bulk density, porosity, water content and shear strength are higher than 0.5 while the correlation coefficients of P-wave velocity and the same parameters are always lower than 0.4. Although the relationship between Vs and clay content has been widely described, the data show that Vs is better correlated with silt content than with clay content for the sediments of the area investigated. However, they show different trends. While Vs increases with increasing clay content, it decreases with increasing silt content.

Notes: In order to perform resistivity imaging, seismic waveform tomography or sensitivity analysis of geophysical data, the Fréchet derivatives, and even the second derivatives of the data with respect to the model parameters, may be required. We develop a practical method to compute the relevant derivatives for 2.5D resistivity and 2.5D frequency-domain acoustic velocity inversion. Both geophysical inversions entail the solution of a 2.5D Helmholtz equation. First, using differential calculus and the Green's functions of the 2.5D Helmholtz equation, we strictly formulate the explicit expressions for the Fréchet and second derivatives, then apply the finite-element method to approximate the Green's functions of an arbitrary medium. Finally, we calculate the derivatives using the expressions and the numerical solutions of the Green's functions. Two model parametrization approaches, constant-point and constant-block, are suggested and the computational efficiencies are compared. Numerical examples of the derivatives for various electrode arrays in cross-hole resistivity imaging and for cross-hole seismic surveying are demonstrated. Two synthetic experiments of resistivity and acoustic velocity imaging are used to illustrate the method.

Notes: Seismic exploration in mountainous areas imposes serious compromises on both acquisition and processing. Access restrictions usually result in profiles that are not straight and are not recorded along the true dip direction (if there is a true dip direction!). Processing constraints often result in very poor approximate corrections for elevations and for deviations from a straight line. Most fundamentally, 2D acquisition and processing assumes that the earth is 2D; this assumption is often seriously violated in mountainous areas. While we cannot efficiently correct 2D seismic data for the effects of a fully 3D subsurface, we can improve the data quality in thrust areas where the assumption of 2D subsurface variation is reasonable. We do this in a series of small steps, which improves the accuracy of several approximations made in processing 2D land data.

Notes: During processing of magnetotelluric (MT) data, acquired in a survey carried out in southern Italy, a problem was encountered, connected with the so-called ‘dead band’ of the MT signal (around 1 Hz). In the apparent resistivity curves of some MT soundings, a V-shaped minimum appeared, centred on the dead-band frequency. This phenomenon turned out to originate from a strong artificial source and was not due to a downward bias of the robust processing techniques adopted. The source distance from the MT sounding locations was such that the V-shaped minimum fell precisely in the dead-band frequency range. Theoretical considerations about fields generated by an electric dipole led us to the probable identification of the source as the d.c.-powered railway between Naples and Bari.

Notes: Analysis of prestack P-wave seismic data yields information about both the P- and S wave properties of the earth. An anticipated advantage of having two measurements (P and S) is that they can be combined into a new measurement that is less sensitive to lithology variations and more sensitive to fluid effects. The amplitude-variation-with-offset (AVO) gradient is one such measure that is often used qualitatively as a fluid indicator. The gradient always becomes softer (more negative) when hydrocarbon replaces brine in the pore spaces but the overall AVO response is dominated by the lithology. Fluid effects are expressed primarily by the normal-incidence P-wave response and only secondarily by the offset dependence. The gradient often does not function as an effective fluid indicator. This is partially due to the fact that the gradient is roughly twice as sensitive to S- than to P-wave properties. More importantly, effective random noise in the CMP gathers introduces a strong correlation between the AVO intercept and gradient and, hence, between the measured P- and S-wave properties. This correlation in the AVO attributes corresponds to a significant error in the estimation of the S-wave properties and can dominate the measurements from many of the popular AVO techniques. A simple method to minimize the effect of this noise-induced correlation is to stack the data. The stack corresponds to a coordinate rotation in elastic space with the stack amplitudes measured along one of the new axes and the other (unmeasured) axis naturally tending to line up with the noise and thus suppressing it. Fluid effects cause the data to move roughly perpendicular to this noise trend. The stack axis is then in the direction of the fluid effect. The stack thus combines both the P- and S-wave (normal and oblique incidence) information into a single measurement which can be made to optimally suppress background noise and highlight fluid effects. A major consequence of this interpretation is the simplicity of both prospect identification and quantitative amplitude analysis.

Notes: This paper describes a large-scale reservoir characterization experiment carried out in Oman in 1991 which comprised the acquisition, processing and interpretation of a 28.4 km2 3D multicomponent seismic experiment over the Natih field. The objective of the survey was to obtain information on the fracture network present in the Natih carbonates from shear-wave anisotropy. Shear-wave anisotropy in excess of 20% time splitting was encountered over a large part of the survey. The seismic results are confirmed by geological and well data but provide additional qualitative information on fracturing where this was not available before. Regions of stronger and weaker shear-wave anisotropy appear to be fault-bounded. The average well flow rates (which are fracture-dominated) within such blocks correlate with the average anisotropy of the blocks. The further observation that the anisotropy is largest in the fracture gas cap of the reservoir suggests that shear waves can provide a direct hydrocarbon indicator for fractured rock.

Notes: It is shown that the electromagnetic (EM) spectrum is characterized by strong amplitude-modulated transmitters operating in the target bandwidth of transient electromagnetic (TEM) measurements. As these transmitters cause significant noise in TEM soundings, it is mandatory to band-limit the input signals to improve the signal-to-noise ratio and thereby the depth of exploration. Band-limitation will distort the TEM responses, which leads to erroneous inversion results if the applied low-pass filters are not accounted for in the inversion scheme. We incorporate the low-pass filters in the inversion scheme and test the inversion approach on theoretical and field data. Inversion of band-limited theoretical responses results in recovery of erroneous resistivity models if the filters are not included in the inversion scheme. By contrast, inversion of band-limited theoretical and field data, for which the applied low-pass filters are included in the inversion scheme, leads to recovery of similar resistivity models, independent of the applied cut-off frequencies.

Notes: Non-linear least-squares inversion operates iteratively by updating the model parameters in each step by a correction vector which is the solution of a set of normal equations. Inversion of geoelectrical data is an ill-posed problem. This and the ensuing suboptimality restrict the initial model to being in the near vicinity of the true model. The problem may be reduced by introducing damping into the system of equations. It is shown that an appropriate choice of the damping parameter obtained adaptively and the use of a conjugate-gradient algorithm to solve the normal equations make the 1D inversion scheme efficient and robust. The scheme uses an optimal damping parameter that is dependent on the noise in the data, in each iterative step. The changes in the damping and relative residual error with iteration number are illustrated. A comparison of its efficacy over the conventional Marquardt and simulated annealing methods, tested on Inman's model, is made. Inversion of induced polarization (IP) sounding is obtained by inverting twice (true and modified) DC apparent resistivity data. The inversion of IP data presented here is generic and can be applied to any of the IP observables, such as chargeability, frequency effect, phase, etc., as long as these observables are explicitly related to the DC apparent resistivity. The scheme is used successfully in inverting noise-free and noisy synthetic data and field data taken from the published literature.

Notes: We improve two aspects of the modelling scheme for the simulation of electromagnetic radio waves, based on the Fourier pseudospectral method.When there are large contrasts in the material properties, use of the standard algorithm (regular grid) causes a series of artefacts, as, for instance, ringing and acausal events. These problems, due to the non-locality of the differential operator, are solved by using the staggered Fourier method (staggered grid).Realistic radiation patterns can be obtained from simple combinations of magnetic and electric sources. If the directivity pattern of the antenna is known, from either a finite-difference simulation or an analytic evaluation or an experimental characterization, it can then be simulated by a composite-source concept. This effective source is implemented in the modelling algorithm by means of a perturbation technique, which first computes the intensity and directional spectra of the single electromagnetic sources. Their location is optimized to obtain the best fit with a minimum number of sources. The approach is, in principle, valid for the far-field radiation pattern of the antenna.

Notes: It is well known that the migrated image given by a Kirchhoff-type (diffraction-stack) migration with limited aperture is always accompanied by some events which depend on the migration aperture. Although these events may severely affect the quality of migration, they have been studied only in 2D cases. Here, the events due to the migration aperture in 3D situations are investigated using a new method of analysing the reconstructed wavefield. It is found that a finite migration aperture results in a reconstructed wavefield with two components. One comes from the tangent points and curves between the traveltime surfaces of reflected and point-diffracted rays and is independent of the migration aperture, and the other is from the boundary of the migration aperture and depends strongly on the location and size as well as on the shape of the migration aperture. It is this last component that describes the aperture effect in migration. If the migration aperture is not sufficiently large, and if the input for migration is not zero on the boundary of the migration aperture, the boundary component may partially or totally cancel the migration signal. Furthermore, for synthetic data, the aperture effect cannot be eliminated by enlarging the migration aperture because, except for the common-shotpoint data, the aperture effect always exists however large the migration aperture becomes. This leads to the conclusion that the published Kirchhoff-type operators are not the exact inverse operators of the Fresnel–Kirchhoff integral if the input data are synthetic.

Notes: Borehole-wall imaging is currently the most reliable means of mapping discontinuities within boreholes. As these imaging techniques are expensive and thus not always included in a logging run, a method of predicting fracture frequency directly from traditional logging tool responses would be very useful and cost effective. Artificial neural networks (ANNs) show great potential in this area. ANNs are computational systems that attempt to mimic natural biological neural networks. They have the ability to recognize patterns and develop their own generalizations about a given data set. Neural networks are trained on data sets for which the solution is known and tested on data not previously seen in order to validate the network result. We show that artificial neural networks, due to their pattern recognition capabilities, are able to assess the signal strength of fracture-related heterogeneity in a borehole log and thus fracture frequency within a borehole. A combination of wireline logs (neutron porosity, bulk density, P-sonic, S-sonic, deep resistivity and shallow resistivity) were used as input parameters to the ANN. Fracture frequency calculated from borehole televiewer data was used as the single output parameter. The ANN was trained using a back-propagation algorithm with a momentum learning function. In addition to fracture frequency within a single borehole, an ANN trained on a subset of boreholes in an area could be used for prediction over the entire set of boreholes, thus allowing the lateral correlation of fracture zones.

Notes: Long-offset transient electromagnetics (LOTEM) is now regarded as a suitable electrical method for deep exploration along with magnetotellurics (MT). In this method, the vertical magnetic-field impulse response and, occasionally, the horizontal electric-field step response of a grounded-wire source on the surface of the earth are measured. Here, these two responses are computed for 3D models of three deep resistivity structures of interest in hydrocarbon exploration: (i) a faulted graben in a resistive basement rock at a depth of 4 km beneath a conductive overburden; (ii) a facies change in a resistive layer buried at a depth of 2 km in the conductive overburden above a resistive basement; and (iii) an anticlinal uplift of a resistive layer at a depth of 1 km in the conductive overburden above a resistive basement. The results show that the sensitivity of the electric-field response to model perturbation is generally greater than that of the magnetic-voltage response. Further, the electric-field sensitivity is confined to early and intermediate times while that of the magnetic-voltage response is confined to intermediate and late times. Hence it is recommended that both electric and magnetic recordings are made in a LOTEM survey so that the final results can be presented as apparent-resistivity curves derived from the two responses jointly as well as separately.

Notes: The surface nuclear magnetic resonance (SNMR) method has been tested at a site in Haldensleben, northern Germany, to assess the suitability of this new method for groundwater exploration and environmental investigations. More information is obtained by SNMR, particularly with respect to aquifer parameters, than with other geophysical techniques. SNMR measurements were carried out at three borehole locations, together with 2D and 1D direct current geoelectrics, as well as ground-penetrating radar, and well logging (induction log, gamma-ray log and pulsed neutron-gamma log). Permeabilities were calculated from the grain-size distributions of core material determined in the laboratory. It is demonstrated that the SNMR method is able to detect groundwater and the results are in good agreement with other geophysical and hydrogeological data. Using the SNMR method, the water content of the unsaturated and saturated zones (i.e. porosity of an aquifer) can be reliably determined. This information and resistivity data permit in situ determination of other aquifer parameters. Comparison of the SNMR results with borehole data clearly shows that the water content determined by SNMR is the free or mobile water in the pores. The permeabilities estimated from the SNMR decay times are similar to those derived from sieve analysis of core material. Thus, the combination of SNMR with geoelectric methods promises to be a powerful tool for studying aquifer properties.

Notes: Since the work of Postma and Backus, much has been learned about elastic constants in vertical transversely isotropic (VTI) media when the anisotropy is due to fine layering of isotropic elastic materials. Nevertheless, there has continued to be some uncertainty about the possible range of Thomsen's anisotropy parameters ε and δ for such media. We use both Monte Carlo studies and detailed analysis of Backus' equations for both two- and three-component layered media to establish the results presented. We show that ε lies in the range −3/8 〈inlineGraphic alt="leqslant R: less-than-or-eq, slant" extraInfo="nonStandardEntity" href="urn:x-wiley:00168025:GPR163:les" location="les.gif"/〉 ε 〈inlineGraphic alt="leqslant R: less-than-or-eq, slant" extraInfo="nonStandardEntity" href="urn:x-wiley:00168025:GPR163:les" location="les.gif"/〉 ½[〈v2p〉〈v−2p〉−1], for finely layered media; smaller positive and all negative values of ε occur for media with large fluctuations in the Lamé parameter λ in the component layers. We show that δ can also be either positive or negative, and that for constant density media, sign (δ) = sign (〈v−2p〉 − 〈v−2s〉〈v2s/v2p〉). Monte Carlo simulations show that among all theoretically possible random media, positive and negative δ are equally likely in finely layered media. (Of course, the δs associated with real earth materials may span some smaller subset of those that are theoretically possible, but answering this important question is beyond our present scope.) Layered media having large fluctuations in λ are those most likely to have positive δ. This is somewhat surprising since ε is often negative or a small positive number for such media, and we have the general constraint that ε − δ 〉 0 for layered VTI media. Since Gassmann's results for fluid-saturated porous media show that the mechanical effects of fluids influence only the Lamé parameter λ, not the shear modulus μ, these results suggest that small positive δ occurring together with small positive ε (but somewhat larger than δ) may be indicative of changing fluid content in a layered earth.

Notes: The multifold acquisition principle was applied to a borehole radar survey, performed in a granitic site (Grimsel Test Site, Switzerland). Two multifold coverage acquisitions (40-fold and 20-fold) were carried out in a subhorizontal borehole. Instrumental drifts (transmission time and sampling frequency fluctuations) were corrected in order to remove shifts observed on CMP gathers and to optimize velocity analysis and trace stacking. Computation of velocity spectra was adapted in order to take into account the features of the medium investigated (homogeneous velocity, various reflector orientations). The NMO velocities were then interpreted as angles between reflectors and the survey line. The processing, based on the computation of several constant velocity stacked sections performed with different NMO velocities, leads to better results than the standard DMO + NMO processing. The signal-to-noise ratio of the stacked profile is improved in comparison with the single-fold section, which results from a standard acquisition. From a practical point of view, the implementation of a multifold radar survey within a borehole is difficult but a greater investigation range is obtained, more reflectors are detected and the mapping of geological discontinuities is improved.

Notes: Electromagnetic (EM) fields radiated from the transmission lines of the New Zealand electricity grid have been digitally recorded at test sites near the Tokaanu geothermal field. Amplitudes and phases of the 50 Hz signals (and the odd harmonics up to 450 Hz) were determined using a software implementation of a phase-locked filter. These data were then analysed to determine the components of the magnetotelluric impedance tensor and the corresponding apparent resistivities and phases. At most sites, there was sufficient variation in the elliptical polarization of the EM fields to enable the impedance tensors to be determined in full. Sites where the EM data had been affected by near-source effects were identified by having large vertical magnetic field components and by being closer to a power line source than about 3–5 skin depths. With the test measurements, the north-eastern part of the Tokaanu geothermal field was successfully delineated giving low resistivities (〈 5 Ωm) on the inside and higher resistivities on the outside, in agreement with the Schlumberger array DC apparent resistivities. The small size of the 50 Hz magnetotelluric equipment and its portable nature make this method of resistivity measurement suitable for reconnaissance resistivity mapping in places with difficult access.

Notes: Parameter estimation from the elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently, the source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of an NMO ellipse, in particular the parameter α, is also sensitive to the magnitude of anisotropy. On the other hand, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any magnitude of anisotropy.  To invert for the NMO ellipse parameters at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60° apart. Having more than three distinct source-to-receiver azimuths (e.g. full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates.  In order to maximize quality in the inversion process, it is recommended to design the seismic data acquisition such that it contains small sectors (≤10°) with adequate fold and offset distribution.  Using three NMO-velocity measurements, 60° apart, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might occur for fractured reservoirs) should have a relative thickness (in time) with respect to the total thickness at least equal to the ratio of the error in the NMO (stacking) velocity to the interval anisotropy of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50%, depending on the number of observations (NMO velocities) that enter the inversion procedure.

Notes: Obtaining high-resolution images of the geology and hydrogeology of the subsurface in the depth range from ground level to 50 m is one of the major challenges of modern geophysics. The methods which are commonly used (such as compressional-wave surveys and ground-penetrating radar) often suffer from adverse effects caused by the near-surface conditions, changes in water saturation and various sources of noise. This paper demonstrates some of the advantages offered by the use of shear-wave seismology and by the combination of shear- and compressional-wave seismic methods in shallow subsurface investigations.Multicomponent shallow seismic tests were carried out at four different sites to examine the effectiveness of different acquisition geometries under a variety of near-surface geological conditions. Near-surface conditions encountered at the sites included thick clays, clay/sand sequences overlying Chalk, mudstone overlying granodiorite bedrock and landfill material.Under all conditions, shear-wave data acquisition was found to have advantages over compressional-wave acquisition for the investigation of the shallow subsurface. Shear head waves, being unaffected by water saturation, achieved penetration to greater depths at a site in Crewkerne, Dorset where compressional head-wave penetration was limited to the near-surface layers. Better vertical resolution was achieved at shallow depths using shear-wave reflection energy at a landfill site. Shear-wave reflections from shallow interfaces were in some cases less affected by noise compared with the equivalent compressional-wave reflections. Combinations of shear- and compressional-wave data recording allowed the measurement of a Poisson's ratio log and gave indications of seismic anisotropy at two sites where dipping clay layers were present.

Notes: A laboratory study was carried out to investigate the influence of confining stress on compressional- and shear-wave velocities for a set of rock samples from gas-producing sandstone reservoirs in the Cooper Basin, South Australia. The suite of samples consists of 22 consolidated sublitharenites with helium porosity ranging from 2.6% to 16.6%. We used a pulse-echo technique to measure compressional- and shear-wave velocities on dry samples (cylindrical 4.6 × 2 cm) at room temperature and at elevated confining stress (≤ 60 MPa). Compressional- and shear-wave velocities in samples increase non-linearly with confining stress. A regression equation of the form V = A − Be−DP gives a good fit to the measured velocities with improved prediction of velocities at high confining stresses compared with equations suggested by other studies. The predicted microcrack-closure stresses of the samples show values ranging from 70 MPa to 95 MPa and insignificant correlation with porosity, permeability or clay content. There is a positive correlation between change in velocity with core porosity and permeability, but this association is weak and diminishes with increasing confining stress. Experimental results show that pore geometry, grain-contact type, and distribution and location of clay particles may be more significant than total porosity and clay content in describing the stress sensitivity of sandstones at in situ reservoir effective stress. The stress dependence of Cooper Basin sandstones is very large compared with data from other studies. The implication of our study for hydrocarbon exploration is that where the in situ reservoir effective stress is much less than the microcrack-closure stress of the reservoir rocks, the variation of reservoir effective stress could cause significant changes in velocity of the reservoir rocks. The velocity changes induced by effective stress in highly stress-sensitive rocks can be detected at sonic-log and probably surface-seismic frequencies.

Notes: The applicability of seismic refraction profiling for the detection of velocity inversion, which is also known as a low-velocity layer (LVL), is investigated with the aid of synthetic seismogram computations for a range of models. Our computational models focus on the inherent ambiguities in the interpretation of first-arrival time delays or ‘skips’ in terms of LVL model parameters. The present modelling results reveal that neither the measure nor even the existence of a shadow zone and/or a time shift (skip) in first arrivals is necessarily indicative of an LVL. Besides attenuation effects, the cap-layer velocity gradient is a critical parameter, determining the termination point of the cap-layer diving wave and thus the time skip.We suggest that shallow LVLs can be delineated more reliably by traveltime and amplitude modelling of coherent phases reflected from their top and bottom boundaries, often clearly observed in the pre- and near-critical ranges in seismogram sections of refraction profiling experiments with a close receiver spacing. We demonstrate the applicability of this approach for a field data set of a refraction profile in the West Bengal Basin, India. The inferred LVL corresponds to the Gondwana sediments underlying the higher-velocity layer of the Rajmahal Traps. This interpretation is consistent with the data from a nearby well in the region.

Notes: The determination of small-scale velocity anomalies (from tens to a few hundreds of metres) is a major problem in seismic exploration. The impact of such anomalies on a structural interpretation can be dramatic and conventional techniques such as tomographic inversion or migration velocity analysis are powerless to resolve the ambiguity between structural and velocity origins of anomalies. We propose an alternative approach based on stochastic modelling of numerous anomalies until a set of models is found which can explain the real data. This technique attempts to include as much a priori geological information as possible. It aims at providing the interpreter with a set of velocity anomalies which could possibly be responsible for the structural response. The interpreter can then choose one or several preferred models and pursue a more sophisticated analysis. The class of retained models are all equivalent in terms of data and therefore represent the uncertainty in the model space.The procedure emulates the real processing sequence using a simplified scheme. Essentially, the technique consists of five steps: 1 Interpretation of a structural anomaly in terms of a velocity anomaly with its possible variations in terms of position, size and amplitude. 2 Drawing a model by choosing the parameters of the anomaly within the acceptable range. 3 Modelling the traveltimes in this model and producing the imaging of the reflected interface. 4 Comparing the synthetic data with the real data and keeping the model if it lies within the data uncertainty range. 5 Iterate from step 2.In order to avoid the high computational cost inherent in using statistical determinations, simplistic assumptions have been made:• The anomaly is embedded in a homogeneous medium: we assume that the refraction and the time shift due to the anomaly have a first-order effect compared with ray bending in the intermediate layers.• We model only the zero-offset rays and therefore we restrict ourselves to structural problems.• We simulate time migration and so address only models of limited structural complexity.These approximations are justified in a synthetic model which includes strong lateral velocity variations, by comparing the result of a full processing sequence (prestack modelling, stack and depth migration) with the simplified processing. This model is then used in a blind test on the inversion scheme.

Notes: The relative merits of a 48-gun, 9324 cu. in. (153 litre) airgun array and a 200 kg explosive source are considered for the purposes of long-range (0–400 km) refraction seismic work, with particular reference to traveltime modelling. Theoretical source calculations indicate that in the frequency range 2.5–12.0 Hz, the airgun source will produce an RMS pressure ∼ 8% of that produced by the explosive source and an initial burst pressure ∼17% of that produced by the explosive source. Observed data support these calculations at short ranges and illustrate the greater attenuation of the airgun signal with range due to its lack of very low frequency (〈 5 Hz) content. At short offsets, the airgun array provides a preferable seismic source to the explosives, due to densely spaced shots and a consistent waveform resulting in excellent trace-to-trace coherence. With increasing offsets, it may be necessary to stack the airgun data to enhance its signal-to-noise ratio: here we use a 4-fold stack. Large explosive shots, although more powerful, produce a less consistent waveform and are more widely spaced due to operational constraints. The offset at which airguns provide a preferable source is dependent on the ambient noise. This practical comparison of real sources demonstrates that, even without advanced processing, a well-tuned airgun array may provide a preferable source to explosives at offsets up to 160 km, under favourable experimental conditions.

Notes: Probability tomography is a new concept reflecting the inherently uncertain nature of any geophysical interpretation. The rationale of the new procedure is based on the fact that a measurable anomalous field, representing the response of a buried feature to a physical stimulation, can be approximated by a set of partial anomaly source contributions. These may be given a multiplicity of configurations to generate cumulative responses, which are all compatible with the observed data within the accuracy of measurement. The purpose of the new imaging procedure is the design of an occurrence probability space of elementary anomaly sources, located anywhere inside an explored underground volume. In geoelectrics, the decomposition is made within a regular resistivity lattice, using the Frechet derivatives of the electric potential weighted by resistivity difference coefficients. The typical tomography is a diffuse image of the resistivity difference probability pattern, that is quite different from the usual modelled geometry derived from standard inversion.

Notes: Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry.For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions.Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces.The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.

Notes: The current inverse scattering solution used for multiple attenuation of marine seismic reflection data assumes that sources and receivers are located in the water. To adapt this solution to the ocean-bottom cable (OBC) experiment where receivers are located on the sea-floor, we have proposed combining the conventional marine surface seismic reflection data (streamer data) with OBC data. The streamer data add to the OBC data some of the wave paths needed for multiple attenuation. This combination has allowed us to develop a multiple attenuation method for OBC data which does not require any knowledge of the subsurface and which takes into account all free-surface multiples, including receiver ghosts. A non-linear synthetic data example consisting of pressure and particle velocity fields is used to illustrate the procedure.

Notes: The history of subsidence, fires, flooding and other kinds of environmental hazards related to shallow coal workings in India goes back to colonial times some 300 years ago. As coal production accelerated in modern times, so did the environmental and socio-economic drawbacks related to exploitation. In the mid-1980s, a hydropneumatic sand-stowing method was developed to fill in abandoned galleries but their exact location had to be known. Unfortunately, most of these old workings are uncharted and consequently large tracts of land cannot be stabilized. A research programme making use of integrated surface, borehole and cross-hole geophysical methods was undertaken over a five-year span to try to solve this problem. Surface geophysical methods, being cheaper and faster than their cross- and downhole counterparts, were used to cover larger areas on an exploratory basis, while cross-hole methods were employed to locate more accurately one or a network of galleries to be perforated by drillhole(s) and used as a conduit for sand stowing.We report the results of one of the cross-hole geophysical methods: electrical resistivity tomography (ERT). A pole–dipole configuration is used and both cross-hole and surface-borehole methodologies are tested. Forward modelling and inversion of synthetic data making use of downhole and surface physical and geometrical parameters are presented first. This phase is followed by the inversion of real data. It is concluded that ERT is not applicable for the detection of dry voids, but is effective in a waterlogged environment which is estimated to represent 85–90% of the cases. In waterlogged galleries, ERT is applicable in both cross-hole and surface-downhole modes, the latter allowing a larger surface coverage at low cost. ERT is thus a reliable geophysical tool to image water-filled voids and an adequate technique to address environmental and geotechnical problems.

Notes: The Yurihara oil and gas field is located on the southern edge of Akita Prefecture, northeastern Japan. In this area, drilling, surface geological surveys and many seismic surveys have been used to investigate the geological structure. Wells drilled into the Nishikurosawa Basalt Group (NBG) of Miocene age found oil and gas reservoirs at depths of 1.5–2 km. Oil and gas are now being produced commercially and further exploration is required in the surrounding areas. However, since the neighbouring areas are covered with young volcanic products from the Chokai volcano, and have a rough topography, the subsurface distribution of the NBG must be investigated using other methods in addition to seismic reflection. According to the well data, the resistivity of the NBG is comparatively higher than that of the overlying sedimentary formations, and therefore the magnetotelluric (MT) method is expected to be useful for the estimation of the distribution of the NBG.An MT survey was conducted along three survey lines in this area. Each line trended east–west, perpendicular to the regional geological strike, and was composed of about 25 measurement sites. Induction vectors evaluated from the magnetic field show that this area has a two-dimensional structure. The evaluated resistivity sections are in agreement with the log data. In conclusion, we were able to detect resistive layers (the NBG) below conductive layers. The results indicate that the NBG becomes gradually less resistive from north to south. In the centre of the northern line, an uplifted resistive area is interpreted as corresponding to the reservoir. By comparison with a seismic section, we prove the effectiveness of the integration of seismic and MT surveys for the investigation of the morphology and internal structure of the NBG. On other survey lines, the resistive uplifted zones are interpreted as possible prospective areas.

Notes: Magnetic methods are used in detection of environmental, engineering and military objects fabricated of thin ferromagnetic sheets having volume susceptibilities higher than 100 SI units. Magnetic modelling of such objects would be advantageous, but it requires knowledge of the susceptibility and remanence values of sheet materials, which is scarce. We introduce a magnetometer method for the determination of susceptibility and remanence on thin steel samples. The area of the sample must be so large that its within-sheet magnetization remains below the saturation state. The measurements are made in normal office surroundings in the Earth's magnetic field with an ordinary fluxgate magnetometer.The square-shaped sheet samples measured in this work have an edge length of 17.5 cm and a thickness in the range 0.5–1.0 mm. During the measuring procedure the sample is placed in four positions on a subvertical measurement board. For each position, the magnetic field in the dip direction of the board plane is measured on the opposite sides of the sample. The secondary field values are averaged for each sample position in order to reduce the effect of sample inhomogeneities. With these data, the susceptibility and remanence of the sample in its edge directions are then determined, based on a model curve which is calculated numerically using thin-sheet integral equations.The susceptibilities measured for different steel types (cold rolled and hot-dip zinc-coated steel sheets) varied in the range 200–500 SI units, and the remanence varied in the range 1000–20 000 A/m. No systematic differences were observed between the magnetic properties of various steel types. The repeatability of the susceptibility measurements was good (variations 〈 5%) but the remanence could be changed by 50% between repeated determinations.The measured susceptibility range signifies that pieces of steel with a typical thickness of 0.5 mm remain below magnetic saturation when their edge dimension is larger than 5 cm. Therefore magnetic modelling of larger steel pieces must be made using the thin-sheet theory with known magnetic properties, whereas smaller saturated pieces can be alternatively modelled as an equipotential system.

Notes: We consider 2D earth models consisting of laterally variable layers. Boundaries between layers are described by their depths at a set of nodes and interpolated laterally between nodes. Conductivity within each layer is described by values at a set of nodes fixed within each layer, and is interpolated laterally within each layer. Within the set of possible models of this sort, we iteratively invert magnetotelluric data for models minimizing the lateral roughness of the layer boundaries, and the lateral roughness of conductivities within layers, for a given level of data misfit. This stabilizes the inverse problem and avoids superfluous detail. This approach allows the determination of boundary positions between geological units with sharp discontinuities in properties across boundaries, while sharing the stability features of recent smooth conductivity distribution inversions.We compare sharp boundary inversion results with smooth conductivity distribution inversion results on a numerical example, and on inversion of field data from the Columbia River flood basalts of Washington State. In the synthetic example, where true positions and resistivities are known, sharp boundary inversion results determine both layer boundary locations and layer resistivities accurately. In inversion of Columbia flood basalt data, sharp boundary inversion recovers a model with substantially less internal variation within units, and less ambiguity in both the depth to base of the basalts and depth to resistive basement.

Notes: We study six different methods for the calculation of seismic traveltimes. All methods yield traveltimes at all points of a regular grid.The methods examined comprise three different variants of finite-difference (FD) eikonal solvers, the graph method, wavefront construction and a combined FD and Runge–Kutta method.The main points of investigation are computational time, accuracy and memory requirements. We took measures to obtain a high level of both general validity and clear understanding of the results. We used a profiling program to be able to measure the time that the actual core algorithm needs, thus avoiding any overhead of highly system-dependent in-/output operations.The comparison shows that no single method is the most appropriate but that the choice depends on the task to be fulfilled. The FD eikonal solver that uses expanding squares proves to be best suited for models which are not too complicated because it offers the best compromise between speed and accuracy, whereas wavefront construction should be applied to complex media because of its superior reliability which then justifies the much higher computational times.

Notes: A useful analysis of the mise-à-la-masse problem can be made by considering a perfectly conducting orebody in a piecewise uniform conducting earth. While the use of a perfect conductor is clearly an idealization of the true geological conditions it provides several advantages for the present purpose.The electric field associated with the above model can be expressed in terms of a surface integral of the normal potential gradient over the boundary of the conductor, where the normal gradient satisfies a well-posed Fredholm integral equation of the first kind. This integral equation formulation remains unchanged when the conductor is arbitrarily located in the conducting earth, including the important case when it crosses surfaces of conductivity discontinuity. Moreover, it is readily specialized to the important case of a thin, perfectly conductive lamina.Consideration of the boundary value problem relevant to a conductive body fed by a stationary current source suggests that under certain circumstances, equivalent mise-à-la-masse responses will result from any perfect conductor confined by the equipotential surfaces of the original problem. This type of equivalence can only be reduced by extending the potential measurements into or on to the conductor itself.This ambiguity in the interpretation of mise-à-la-masse surveys suggests a simple if approximate integral solution to the mise-à-la-masse problem. The solution is suitable for modelling the responses of perfect conductors and could possibly be used as the basis of a direct inversion scheme for mise-à-la-masse data.

Notes: Using a lightweight portable vibrator, we have evaluated the accuracy of the ‘weighted sum’ method for calculating ground force. Experiments in which the vibrator was suspended elastically have shown that, contrary to expectations based on standard theory, the amplitude of the weighted sum ground force was significantly above zero at high frequencies (〉 500 Hz). Complementary investigations with load cells confirmed these results. If not accounted for, these deviations may introduce significant ‘vibroseis-correlation noise’ in processed records. Furthermore, we have demonstrated that ground force and base-plate velocity can be used to estimate the radiation impedance, which describes the interaction of (vibratory) sources with the ground. Using the mechanical characteristics of the system (i.e. maximum displacement, maximum velocity and maximum acceleration of the base-plate) and the radiation impedance, the behaviour of the portable vibrator on typical Dutch soil types was evaluated. We found that for the same sweep, more high-frequency energy could be generated on hard grounds (e.g. concrete) characterized by a higher radiation impedance than on softer grounds (e.g. clay or sand). Knowledge of this behaviour may provide important information for use in data interpretation.

Notes: Ultrasonic compressional- and shear-wave attenuation measurements have been made on 40, centimetre-sized samples of water- and oil-saturated oolitic limestones at 50 MPa effective hydrostatic pressure (confining pressure minus pore-fluid pressure) at frequencies of about 0.85 MHz and 0.7 MHz respectively, using the pulse-echo method. The mineralogy, porosity, permeability and the distribution of the pore types of each sample were determined using a combination of optical and scanning electron microscopy, a helium porosimeter and a nitrogen permeameter. The limestones contain a complex porosity system consisting of interparticle macropores (dimensions up to 300 microns) and micropores (dimensions 5–10 microns) within the ooids, the calcite cement and the mud matrix. Ultrasonic attenuation reaches a maximum value in those limestones in which the dual porosity system is most fully developed, indicating that the squirt-flow mechanism, which has previously been shown to occur in shaley sandstones, also operates in the limestones. It is argued that the larger-scale dual porosity systems present in limestones in situ could similarly cause seismic attenuation at the frequencies of field seismic surveys through the operation of the squirt-flow mechanism.

Notes: Global optimization with very fast simulated annealing (VFSA) in association with joint inversion is performed for 1D earth structures. The inherent problems of equivalence and suppression in electromagnetic (EM) and direct current (DC) resistivity methods are studied. Synthetic phase data from multifrequency sounding using a horizontal coplanar coil system and synthetic apparent resistivity data from Schlumberger DC resistivity measurements are inverted individually and jointly over different types of layered earth structures. Noisy data are also inverted. The study reveals that global optimization of individual data sets cannot solve inherent equivalence or suppression problems. Joint inversion of EM and DC measurements can overcome the problem of equivalence very well. However, a suppression problem cannot be solved even after combination of data sets. This study reveals that the K-type earth structure is easiest to resolve while the A-type is the most difficult. We also conclude that the equivalence associated with a thin resistive layer can be resolved better than that for a thin conducting layer.

Notes: Near-surface inhomogeneities (NSIs) can lead to severe problems in the interpretation of apparent resistivity pseudosections because their effects significantly complicate the image aspect. In order to carry out a more efficient and reliable interpretation process, these problematic features should be removed from field data. We describe a filtering scheme using two-sided half-Schlumberger array data. The scheme was tested on synthetic data, generated from a simple 2D resistivity model contaminated by NSIs, and is shown to be suitable for eliminating such contaminations from apparent resistivity data. Furthermore, the original model without NSIs can be recovered satisfactorily from the inversion of filtered apparent resistivity data. The algorithm is also applied efficiently to a real data set collected at Nsimi, in southern Cameroon, along a 200-m shallow depth profile crossing a complex transitional zone. For this case, the filtering scheme provides accurate structural and behavioural interpretations of both the geometry of the major soil constituents and the groundwater partitioning.

Notes: Noise contamination of measured data greatly affects the final results of inversion. Three types of noise source — random and systematic errors and the uncertainties due to the inadequacy of the mathematical model in representing the actual physical conditions — are discussed in the framework of resistivity sounding data. Two methods are proposed for describing these uncertainties. The first possibility is to smooth the measured data by a combination of simple fitting functions that satisfies the ‘1D smoothness’ criteria and consequently simulates the behaviour of a 1D Schlumberger apparent resistivity curve. The second method is to derive weight coefficients from the differences between the measured and the smoothed data sets. Both methods are carried out under the control of the interpreter.The relative merits and drawbacks of the direct and iterative interpretation methods used for the estimation of the parameters of the layered earth model are summarized. Two variants of the combination of these methods are presented to obtain more powerful and automatic interpretation schemes. In the sequential interpretation, an initial guess supplied by the direct method is improved by the iterative method to obtain a reasonable fit between the measured data and the model response. In the simultaneous interpretation, the successive application of the direct and iterative methods is carried out, starting from the first branch of the apparent resistivity curve. The operation is then shifted to subsequent branches that represent the deeper parts of the geoelectric section. This is similar to the data acquisition applied in direct current sounding in which the depth penetration is increased by expanding the current electrode spacings. The proposed sequential and simultaneous interpretation algorithms require minimum aids and efforts of the interpreter.

Notes: The reliability and ruggedness of LaCoste-and-Romberg gravity meters has meant that their use has extended over recent years from gravity mapping to the investigation of small gravity changes (〉 10 μGal) with time. When using the instrument at the limit of its capability, limitations become apparent. Some instruments drift more than others and some are prone to excessive tares. However, with regular servicing these problems are minimized. Here we demonstrate clear evidence for calibration changes of the order of 1000 ppm for LaCoste-and-Romberg meter G513, which, for gravity differences of over 50 mGal, represents a highly significant induced error of over 50 μGal. Data collected over 15 years using nearly 4000 mGal of the 7000 mGal range of the instrument illustrates that long periods of stability may be interspersed with periods lasting several months while the calibration changes by up to 0.1%. This is comparable with the calibration drift of a new Scintrex CG-3M instrument, although the process causing the change may not be the same.