ALBERT

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: 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.

Notes: A new time-domain method is introduced for the calculation of theoretical seismograms which include frequency dependent effects like absorption. To incorporate these effects the reflection and transmission coefficients become convolutionary operators. The method is based on the communication theory approach and is applicable to non-normal incidence plane waves in flat layered elastic media. Wave propagation is simulated by tracking the wave amplitudes through a storage vector inside the computer memory representing a Goupillaud earth model discretized by equal vertical transit times. Arbitrary numbers of sources and receivers can be placed at arbitrary depth positions, while the computational effort is independent of that number. Therefore, the computation of a whole plane-wave vertical seismic profile is possible with no extra effort compared to the computation of the surface seismogram. The new method can be used as an aid to the interpretation of plane-wave decomposed reflection data where the whole synthetic vertical seismic profile readily gives the interpreter the correct depth position of reflection events.

Notes: A parameter estimation or inversion procedure is incomplete without an analysis of uncertainties in the results. In the fundamental approach of Bayesian parameter estimation, discussed in Part I of this paper, the a posteriori probability density function (pdf) is the solution to the inverse problem. It is the product of the a priori pdf, containing a priori information on the parameters, and the likelihood function, which represents the information from the data. The maximum of the a posteriori pdf is usually taken as a point estimate of the parameters. The shape of this pdf, however, gives the full picture of uncertainty in the parameters. Uncertainty analysis is strictly a problem of information reduction. This can be achieved in several stages. Standard deviations can be computed as overall uncertainty measures of the parameters, when the shape of the a posteriori pdf is not too far from Gaussian. Covariance and related matrices give more detailed information. An eigenvalue or principle component analysis allows the inspection of essential linear combinations of the parameters.The relative contributions of a priori information and data to the solution can be elegantly studied. Results in this paper are especially worked out for the non-linear Gaussian case. Comparisons with other approaches are given. The procedures are illustrated with a simple two-parameter inverse problem.

Notes: For converted waves stacking requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. We consider converted waves of the PS- and SP-type in a stack of horizontal layers.The coordinates of the conversion points for waves of PS- or SP-type, respectively, in a single homogeneous layer are calculated as a function of the offset, the reflector depth and the velocity ratio vp/vs. Knowledge of the conversion points enables us to gather the seismic traces in a common conversion point (CCP) record. Numerical tests show that the CCP coordinates in a multilayered medium can be approximated by the equations given for a single layer. In practical applications, an a priori estimate of vp/vs is required to obtain the CCP for a given reflector depth.A series expansion for the traveltime of converted waves as a function of the offset is presented. Numerical examples have been calculated for several truncations. For small offsets, a hyperbolic approximation can be used. For this, the rms velocity of converted waves is defined. A Dix-type formula, relating the product of the interval velocities of compressional and shear waves to the rms velocity of the converted waves, is presented.

Notes: An increase in the grain/pore size can cause the received echo signal to be distorted due to the preferential attenuation of the high-frequency components of the transmitted acoustic signal. Therefore, a rock acts as a low-pass filter and the property of the filter has a linear relation to the grain/pore size. The results have shown that P- and S-wave attenuations can be used to characterize selected internal characteristics of a rock. For example, an increase in the differential stress can cause an increase in the attenuation, due to the sensitivity of the S-wave to microcracks.

Notes: Three-component recordings permit the construction of particle trajectories. These three-dimensional pictures of particle motion show successive predominant directions of polarization and allow wave modes with distinct polarization directions to be recognized. A polarization selection, called ‘spatial directional filtering’, can be accomplished by several methods; four techniques are described. The application of these polarization filters to a noise shot, offset VSPs and CDP stack are also presented. This type of filtering is shown to cancel waves with undue polarization and to enhance the signal-to-noise ratio.

Notes: Gold, as a trace element, is not directly detectable by geophysical borehole logging techniques. Geophysical logging methods have therefore been used to infer the presence of structural features and alteration processes associated with gold. Since these features and processes differ with the style of gold mineralization, a unique relation between geophysical anomalies and gold cannot be established. However, in a particular environment, such an association can be established. We examined geophysical log data (self potential, induced polarization, resistivity, gamma, temperature, and temperature gradient) and drill core from the Barber-Larder property in NE Ontario. The geophysically detectable alteration processes associated with gold were identified as sericitization and pyritization, by means of factor analysis. A linear discriminant function was constructed which allowed the zones of economic mineralization (nominally 0.05 oz/ton or 1.5 ppm) to be identified with a 75% success rate based on geophysical log data alone. This rate was achieved without sophisticated non-linear data transformations.

Notes: A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.

Notes: Ray theories are a class of methods often chosen to compute synthetic seismograms due to their efficiency and ability to deal with complex, three-dimensional inhomogeneous media. To deal with the large number of rays needed to compute synthetic seismograms, a ray generation algorithm is given which is capable of generating a numerical code describing each ray. The code describes a subset of all possible rays by considering only pre-critical reflections. In a horizontally plane-layered medium the generation of rays and computation of amplitudes and traveltimes can be efficiently accomplished by grouping the rays into reflection order and dynamic analogue groups. Expressions summing all unconverted rays and rays with a single mode conversion are given for source and receiver located at arbitrary positions within the medium. Examples of zero-offset synthetic VSPs obtained by this method are given.

Notes: The cross-correlation technique for increasing the anomaly-to-noise ratio is applied to the interpretation of resistivity profiles.To verify the method theoretically, resistivity profiles above a body having the shape of a parallelepiped were simulated with correlated and uncorrelated noise. Seven different electrode geometries are discussed. As a practical test, we considered profiles of a geoelectrical survey to locate tombs at a site of archaeological interest.When the shape and dimensions of the anomaly can be foreseen, the cross-correlation method can be applied and it gives a substantial improvement in the signal-to-noise ratio.

Notes: In the quantitative data interpretation for HLEM induction prospecting, a vertical half-plane model in an insulating medium is widely employed. For this assumption to be valid, the steeply dipping massive sulphide dykes must have large strike lengths and depth extents, but small thickness.We report investigations, using the laboratory scale-modelling method, on the response variation of large vertical conductors as the thickness is varied. We conclude that a steeply dipping large dyke can be approximated by a half-plane model only if its thickness is less than half the skin depth. An inductively thick conductor produces larger amplitudes and relatively higher quadrature compared to a thin conductor, even if both have the same induction number.

Notes: A model has been developed to relate the velocities of acoustic waves Vp and Vs in unconsolidated permafrost to the porosity and extent of freezing of the interstitial water. The permafrost is idealized as an assemblage of spherical quartz grains embedded in a matrix composed of spherical inclusions of water in ice. The wave-scattering theory of Kuster and Toksoz is used to determine the effective elastic moduli, and hence the acoustic velocities. The model predicts Vp and Vs to be decreasing functions of both the porosity and the water-to-ice ratio. The theory has been applied to laboratory measurements of Vp and Vs in 31 permafrost samples from the North American Arctic. Although no direct measurements were made of the extent of freezing in these samples, the data are consistent with the predictions of the model. Electrical resistivity measurements on the permafrost samples have demonstrated their essentially resistive behaviour. The ratio of resistivity of permafrost in its frozen state to that in its unfrozen state has been related to the extent of freezing in the samples.Electromagnetic and seismic reflection surveys can be used together in areas of permafrost: firstly an EM survey to determine the extent of freezing and then the acoustic velocity model to predict the velocities in the permafrost. The necessary transit time corrections can thus be made on seismic reflection records to compensate for the presence of permafrost.

Notes: The classical aim of non-linear inversion of seismograms is to obtain the earth model which, for null initial conditions and given sources, best predicts the observed seismograms. This problem is currently solved by an iterative method: each iteration involves the resolution of the wave equation with the actual sources in the current medium, the resolution of the wave equation, backwards in time, with the current residuals as sources; and the correlation, at each point of space, of the two wavefields thus obtained.Our view of inversion is more general: we want to obtain a whole set of earth model, initial conditions, source functions, and predicted seismograms, which are the closest to some a priori values, and which are related through the wave equation. It allows us to justify the previous method, but it also allows us to set the same inverse problem in a different way: what is now searched for is the best fit between calculated and a priori initial conditions, for given sources and observed surface displacements. This leads to a completely different iterative method, in which each iteration involves the downward extrapolation of given surface displacements and tractions, down to a given depth (the‘bottom’), the upward extrapolation of null displacements and tractions at the bottom, using as sources the initial time conditions of the previous field, and a correlation, at each point of the space, of the two wavefields thus obtained. Besides the theoretical interest of the result, it opens the way to alternative numerical methods of resolution of the inverse problem. If the non-linear inversion using forward-backward time propagations now works, this non-linear inversion using downward-upward extrapolations will give the same results but more economically, because of some tricks which may be used in depth extrapolation (calculation frequency by frequency, inversion of the top layers before the bottom layers, etc.).

Notes: Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated.Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data.Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi-ray rather than straight-ray inversion techniques, despite the occurrence of pronounced ray bending.

Notes: The WKB-method is used for the derivation of both the complex dispersion relation and displacement functions for Love channel-waves that propagate in a coal seam of varying thickness. The constant Q-model is used to describe the anelastic friction. With numerical solutions of the absorption-dispersion relation, the influence of thickness changes on the phase velocity and absorption coefficient of Love seam-waves is analysed at various frequencies. It is shown that the changes in the seam thickness can be optimally detected around the average Airy-phase frequency. An equivalence is pointed out between the wave guide structures: homogeneous with varying seam thickness and horizontally inhomogeneous with constant seam thickness.

Notes: Methods of minimum entropy deconvolution (MED) try to take advantage of the non-Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band-pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band-limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters.The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal-dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data.Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full-band, noise-free data.

Notes: The Offset Wenner resistivity sounding system provides for the extrapolation of the Wenner resistivity curve. The extrapolation technique was applied to data measured in the Solomon Islands and it is shown to be unreliable. An accurate method of predicting the reliability of extrapolation using measured resistances could not be found.

Notes: The concept of multifrequency induction logging simulations in the frequency range of 10 kHz to 1 MHz, applied to two-dimensional, axial symmetric model geometries, is presented. The scalar Helmholtz equation has been solved by a finite-element procedure. The model domain has been discretisized under the condition that the discontinuities in conductivity are represented by the nodes of the adjacent triangular elements. The modification of the signal distribution by the skin effect is illustrated for several models. Several sets of induction logs have been calculated with particular consideration of the frequency-dependent conductivities and permittivities.The improvement of a multifrequency inversion technique, based on standard least-squares methods, is shown for a two-layer model including borehole and invasion zones. Using this improved inversion technique we can state, as an additional inversion parameter, the frequency dependence of each inverted rock conductivity.

Notes: The wavefield in, and at the surface of, a homogeneous, isotropic, perfectly elastic half-space, excited by a traction distribution at the surface of the medium is investigated. The emitted wavefield is a spatial convolution of the surface tractions and the spatial impulse response. The properties of the wavefield in the far-field of the medium are derived and it is shown that the far-field particle velocity is essentially equal to a weighted sum of the time derivative of the integrated surface tractions, that is, of the components of the ‘ground force’. The theory is valid for an arbitrary geometry and orientation of the surface tractions, and is independent of the boundary conditions at the surface of the medium.The surface tractions are related to a source that consists of a mass distribution with an arbitrary force distribution imposed upon it. A boundary condition is introduced that accounts for the mass load and the forces applied to it but neglects vibrations within the mass. The boundary condition follows from the equation of motion of the surface mass load.The theory is applied to the Vibroseis configuration, using a P-wave vibrator model with a uniformly distributed force imposed on top of the baseplate, and assuming that horizontal surface traction components are absent. The distribution of displacement and stress directly underneath the baseplate of a single vibrator and an array of vibrators is investigated. Three different boundary conditions are used: (1) assuming uniform pressure, (2) assuming uniform displacement, (3) using the equation of motion of the baseplate as a boundary condition. The calculations of the distribution of stress and displacement over the plate for different elastic media and several frequencies of operation show that only the results obtained with the mixed boundary condition agree with measurements made in the field.The accuracy of three different phase-feedback signals is compared using synthetic data. Baseplate velocity phase-feedback leads to huge deviations in the determination of the far-field wavelet; reaction mass acceleration phase-feedback looks stable but neglects the differentiating earth filter; and phase-feedback to a weighted sum of baseplate and reaction mass accelerations becomes unstable with increasing frequency. The instability can be overcome using measurements over the whole baseplate.The model can be extended to a lossy layered earth.

Notes: This paper describes a method of generating pseudovelocity logs using measurements of electrical resistivity. A theoretical relation between electrical resistivity and transit time, which is applicable to a wide range of lithologies, has been developed. The application of this relation using a method which defines lithoresistivity zones as lithological intervals related to the same formation and showing small resistivity variations, has been tested in the Recôncavo sedimentary basin in Bahia, Brazil. A comparison of derived pseudovelocity logs with actual sonic logs for five wells whows the validity of the present approach.

Notes: Determination of petrography and pore fluid content is an ultimate goal of an integrated seismic-petrophysical study. For lack of a general inversion technique, forward modelling is useful in studying the relations between lithology, stratigraphy, pore fluid content and the seismic response. This report describes a study of two clastic sequences in Utah, from which 32 rock samples were analysed. A detailed petrographic study was done. Laboratory measurements were made of ultrasonic compressional- and shear-wave velocity as a function of pressure. We computed the velocities at seismic frequencies for the samples when dry, over-pressured, brine saturated, and oil saturated. The velocities were sensitive to the porosity, carbonate cementation and the depositional facies. We generated velocity profiles for hypothetical reservoirs for a range of saturation states. The velocity profiles were used to generate synthetic seismic shot gathers to study the seismic response of these clastic reservoirs. The fluid-saturation strongly affects the seismic respone, as does the presence of a coal seam. An amplitude change with offset is often observed. However, stratigraphy appears to have a stronger effect on the seismic response.

Notes: Two-dimensional VSP surveys are often conducted to provide structural illumination of the subsurface away from the borehole. The illumination is achieved through offsetting the source with respect to the downhole geophone. This inevitably gives rise to mode-conversions in both downgoing and upgoing wavefields.Migration of mixed-mode wavefields is complex because the velocity profile used for wavefield extrapolation is valid only for a particular propagation mode; the other mode always propagates at a different velocity. It is therefore advisable to separate the wave-types (P-wave and SV-wave) prior to migration. This may be achieved through wavemode filtering, a multichannel process which exploits the relation between propagation velocity, slowness of events at the recording array and particle motion. The necessary information about particle motion is available only if the VSP data are acquired with a three-component downhole geophone assembly.The wavemode filter partitions wave-types at the recording array; it provides no information about the various changes of propagation mode experienced by the energy as it travels from source to geophone. For the purpose of migration, the intermediate modes of propagation must be deduced.Much of the energy arriving at the receivers is P-wave which has followed the P-wave velocity profile from the source. It can therefore be imaged by conventional (Kirchhoff) migration. As an example of SV-wave imaging, a common mode-code is P-wave from source to reflector and SV-wave from reflector to geophone. Migration of such data calls for back-propagation of the geophone array wavefield, at SV-wave velocity, to the point in the subsurface where it is time-coincident with the forward propagated downwave, at P-wave velocity.

Notes: This paper gives a review of Bayesian parameter estimation. The Bayesian approach is fundamental and applicable to all kinds of inverse problems. Its basic formulation is probabilistic. Information from data is combined with a priori information on model parameters. The result is called the a posteriori probability density function and it is the solution to the inverse problem. In practice an estimate of the parameters is obtained by taking its maximum. Well-known estimation procedures like least-squares inversion or l1 norm inversion result, depending on the type of noise and a priori information given. Due to the a priori information the maximum will be unique and the estimation procedures will be stable except (in theory) for the most pathological problems which are very unlikely to occur in practice. The approach of Tarantola and Valette can be derived within classical probability theory.The Bayesian approach allows a full resolution and uncertainty analysis which is discussed in Part II of the paper.

Notes: A triple axis borehole magnetometer is described that consists of a Förster-probe (fluxgate) triplet (sensitivity 1 n T), a Förster-probe gradiometer (sensitivity 2 nT/40 cm), a gyro unit (mean angular drift approx. 0.5°/h) which is equipped with accelerometers (sensitivity 1/100°), and a data transmission unit (with multiplexer and 16-bit AD converter). The sensitive fluxgate-magnetometer can detect weakly magnetic or small source bodies. Data from the gyro and the accelerometers allow the 3-component magnetic field values to be transformed to north, east and vertical components. Since they do not rely on magnetically-determined directional data, the results are not disturbed by local anomalies of the magnetic declination. Furthermore, the magnetometer can also be used in vertical boreholes. 3-component measurements are carried out at discrete points in the neighbourhood of a source body to locate its position, and within the source body to determine the direction of magnetization. The strength of magnetization and information on magnetic classification are obtained by continuous measurement of one or more components within the source body. Calculation algorithms and computer programs are available to simplify data processing and interpretation. Survey examples are discussed.

Notes: Resistivity measurements were carried out in a survey area in the south of Germany. This area is characterized by complicated subsurface geology. Schlumberger full-arrays and their respective half-arrays were recorded simultaneously. The results obtained by the one-dimensional (1D) interpretation of the full-array measurements were incorrect because of a resistivity discontinuity. This discontinuity, under a relatively thick overburden, could only be located by the half-array soundings. Its exact location and the resistivity distribution in the subsurface were ascertained by comparing the sounding curves with 2D model curves, which are calculated by a finite-difference method.

Notes: A novel process is used to coat glass spheres with a polymerizing thermo-setting resin, only microns thick. Synthetic rocks of known grain size distribution and pore space characteristics are then made by heating the resin-coated glass spheres under compression in a special mould. The dynamic Young's moduli of these rocks are found to be affected by the percentage of resin content (cement) and the synthetic diagenesis rather than the grain size and permeability.

Notes: Broad-band ultrasonic impulses and the attenuation spectral ratio technique have been used to investigate the characteristics of synthetic rocks for different saturants, by obtaining the attenuation coefficients in the frequency range of 0.1-1.0 MHz.The general trend of the data indicates that the experimental attenuation coefficient increases with an increase in the grain/pore size. Results show that large grains/pores can increase the attenuation coefficient in all mechanisms, and water-saturated synthetic sandstone rocks result in a higher attenuation coefficient than similar oil-saturated rocks.

Notes: It is now believed that the negative transients observed in coincident-loop transient electromagnetic (TEM) measurements are caused by polarizable bodies (bodies whose conductivity increases as a function of frequency). Ordinarily the TEM response of polarizable bodies is obtained by calculating the frequency-domain response at many frequencies and transforming it to the time domain via Fourier, Laplace or Hankel transforms. This is normally a computationally laborious task. However, for some simple non-polarizable bodies the time-domain response is analytical and can be computed easily. When these simple bodies are weakly polarizable an approximate response can be obtained by convolving the easily-calculated, non-polarizable response with the impulse response of the polarization. The approximate response is found to be very similar to the exact response for the polarizabilities normally seen in geological materials.

Notes: Migration of zero-offset data from a point diffractor gives an elliptic or hyperbolic ‘smile’ when the velocity is too high or too low, respectively (over- and undermigration).The phase-shift within the smile is positive (approximately +π/4) when the velocity is too high, and negative (approximately –π/4) when the velocity is too low. The phase-shift is calculated from the stationary phase approximation of the Kirchhoff integral.

Notes: Media containing aligned cracks show anisotropy with respect to elastic wave propagation. There are several models describing the wave propagation in cracked media, most of them only valid for cracks with small aspect ratios. One of these models (Crampin's model) is compared with a model valid for all aspect ratios (Nishizawa's model). The elastic constants and the group velocities are compared for both dry and liquid-filled inclusions with aspect ratios ranging from 0.0001 (flat cracks) up to 1 (spheres). The difference between both models is small for small aspect ratios but becomes larger for increasing aspect ratios. At a crack density of 0.05 both models give-within an error of 5%–the same results for aspect ratios up to 0.3. Therefore Crampin's model can be applied to a large range of cracked media even if the aspect ratio of the inclusions is not small. The variation of the anisotropy as a function of the aspect ratio can be studied using Thomsen's dimensionless parameters δ, E and y. They show how inclusions with large aspect ratios result in elliptical anisotropy.

Notes: The theory by which the Surface Integral Equation method may be applied to the solution of electromagnetic transmission boundary value problems is presented. For a 3D target of arbitrary electrical property contrast with its host medium excited by an arbitrary time-harmonic source, two integral equations are derived which need to be simultaneously solved for tangential electric and magnetic source density on the target's surface. If the target is 2D, though still excited by an arbitrary source (the 2½ D case), the problem is best solved in the transform domain for a number of different wavenumbers in the target's strike direction. Then a set of four simultaneous scalar integral equations needs to be solved for the components of the surface source density transforms in the target's strike direction and in the direction of the tangent vector to the target's cross-sectional contour.Examples are presented in which the 2½D problem is solved numerically using the method of moments with piecewise linear basis functions. Although the results generally compare well with analytical solutions, or solutions obtained numerically by other means, errors appear in the calculation of the real response of these targets to excitation by a magnetic dipole source at low frequencies. This is attributed to ill-conditioning of the system resulting from a non-unique solution at zero frequency.

Notes: A plasma gun source has been successfully used to obtain sub-bottom profiles. The profiles show better penetration than with a 3-5 kHz source and more resolution than with an air gun. The plasma gun source is compact, self-contained, and requires no complex auxiliary equipment. The device was deployed from large research vessels and a small boat. The plasma gun produces sufficient acoustic energy and with its characteristically short pulse length and broad bandwidth it is an attractive sub-bottom profiler, especially in shallow fresh or salt water.

Notes: Electromagnetic scale modelling for most conductors encountered in prospecting requires models of conductivity in the range 10-1000 S/m. A polyester composite filled with aluminium fillers is used to design the required materials. The fillers are chosen with a high aspect ratio to achieve the desired conductivities without altering mechanical properties. The design process, consisting of a chemical reaction, is simple, repeatable and easy to realize in a geophysical laboratory.The conductivity of the designed material is estimated by an inductive method based upon the variation of the quality factor of a coil in which the samples are inserted. This method is much less influenced by the distribution and orientation of fillers in the resin matrix than a galvanic method.The conductivities obtained fill the major part of the interval 10-1000 S/m without requiring unreasonable mixing ratios. The homogeneity of the material was tested and the anisotropy was low at high conductivities. The electrical properties do not vary with time in free air or when immersed in salt water.We propose standard curves giving conductivities of composites filled with aluminium fibres and flakes. A large cylindrical model of fixed resin-to-filler ratio was made to show the capability of the technique to produce models of useful size. Its measured conductivity agrees well with the expected conductivity from the established standard curves. A scale modelling experiment with the horizontal loop technique was carried out over a horizontal thin sheet made of the material, and again the conductivity obtained from the results agrees reasonably well with the expected value.The noted difference between the inductively and galvanically measured conductivities of the proposed material presently restricts the use of the technique to EM scale experiments for which the host rock is considered very resistive.

Notes: Determination of impedance or velocity from a stacked seismic trace generally suffers from noise and the fact that seismic data are bandlimited. These deficiencies can frequently be alleviated by ancillary information which is often expressed more naturally in terms of probabilities than in the form of equations or inequalities.In such a situation information theory can be used to include ‘soft’information in the inversion process. The vehicle used for this purpose is the Maximum Entropy (ME) principle. The basic idea is that a prior probability distribution (pd) of the unknown parameter(s) or function(s) is converted into a posterior pd which has a larger entropy than any other pd which also accounts for the information. Since providing new information generally lowers the entropy, this means that the ME pd is as non-committal as possible with regard to information which is not (yet) available. If the information used is correct, then the ME pd cannot be contradicted by new, also correct, data and thus represents a conservative solution to the inverse problem.In the actual implementation, the final result is, generally, not the pd itself (which may be quite broad) but rather the expectation values of the desired parameter(s) or function(s).A general problem of the ME approach is the need for a prior pd for the parameter(s) to be estimated. The approach used here for the velocity is based on an invariance criterion, which ensures that the result is the same whether velocity or slowness is estimated. Unfortunately, this criterion does not provide a unique prior pd but rather a class of functions from which a suitable one must be selected with the help of other considerations.

Notes: Moving source profiling is a modification of walk-away vertical seismic profiling in which the source is moved along a line across a well while the signal is recorded in the well at a certain depth. The method was designed to better predict the target horizon below the drill bit and away from the well location. The method has several advantages in areas of complicated overburden.In overthrust regions, the receiver is placed below much of the complicated structure to minimize distortion of the reflected signal. The final seismic image is a depth presentation of the subsurface structure and stratigraphy based on wavefront calculations. This depth estimation is obtained without extensive processing of the recorded data. The final result is available within a few days and can help interpreters to decide if and where to sidetrack the well. The method is demonstrated using an example from the overthrust zone of the Lower Saxonian Basin and the Pompeckj's well in Northern Germany.

Notes: Most seismic data is processed using a sample interval of 4 ms two-way time (twt). The study of the statistical properties of primary reflection coefficients showed that the power spectrum of primaries can change noticeably when the logs are averaged over blocks of 0.5, 1 and 2 ms twt (block-averaging). What is a suitable block-averaging interval for producing broadband synthetics, and in particular how should the power spectrum of primaries be constructed when it is to be used to correct 4 ms sampled deconvolved seismic data for the effects of coloured primary reflectivity?In this paper we show that for a typical sonic log, a block-averaging interval of 1 ms twt should satisfy some important requirements. Firstly, it is demonstrated that if the reflection coefficients in an interval are not too large the effect of all the reflection impulses can be represented by another much sparser set at intervals of Δt twt, The coefficient amplitudes are given by the differences in the logarithmic acoustic impedances, thus justifying block-averaging. However, a condition for this to hold up to the aliasing (Nyquist) frequency is that Δt takes a maximum value of about 1 ms twt. Secondly, an event on a log should be represented in the seismic data. For this the acoustic impedance contrast must have sufficient lateral extent or continuity. By making some tentative suggestions on the relation between continuity and bed-thickness, a bed-thickness requirement of 0.15 m or more is obtained. Combining this requirement with the maximum number of beds allowable in an interval in order that multiple reflections do not contribute significantly to the reflections in the interval, again suggests a value of about 1 ms for the block-averaging interval.With this in mind an experiment was performed on three sonic logs. The logs were block-averaged at 1 ms, and primary reflection coefficients calculated. These primaries were then anti-alias filtered and resampled to get a series of primaries at 4 ms, followed by ARMA spectrum fitting. The same logs were also block-averaged at 4 ms directly and primaries computed, followed by ARMA spectrum fitting. In all three cases the first approach gave the ARM A model spectrum with greatest dynamic range, which strongly suggests that direct 4 ms block-averaging introduces significant aliased energy into low frequencies of the primaries spectrum.The conclusion is that routine computation of broadband synthetics (primaries only or primaries plus multiples) should be carried out using a block-averaging interval of 1 ms twt, followed by anti-alias filtering and thinning to the desired final sample interval. In theory it would be advantageous to go to even finer intervals-say 0.5 ms-but in practice at this level the averaging of slowness imposed by the somic logging tool appears to attenuate high-wave number fluctuations, i.e. it interferes with the‘real’data. The 1ms choice is thus a reasonable compromise which will help minimize non-trivial aliasing effects and should give better matches to the seismic data.

Notes: A novel fixed-source electromagnetic system has been developed. The transmitter is a large rectangular loop or grounded dipole. The transmitted waveform consists of up to five superimposed pure sinusoids at well-separated frequencies. The receiver measures the amplitude and phase at two frequencies from a single receiver coil. The amplitude ratio is routinely calculated. Field trials with both surface and downhole configurations show that the method has advantages over the more traditional frequency-domain Turam type and downhole electromagnetic (DHEM) systems. Among such advantages are the use of a single receiver coil and the removal of noise due to free-space variations in transmitter-receiver geometry. The latter is important for DHEM surveys. In terms of field procedures and quantities measured, the system is similar to time-domain methods.

Notes: Expressions are derived for the acoustic pressure in a fluid-filled borehole due to the passage of plane compressional or shear waves propagating in a porous and permeable medium. The derivation is based on a quasistatic description, yielding results applicable at low frequencies. Computations for a plausible sandstone (with porosity of 0.21 and permeability of 300 millidarcies) show accoustic pressure to be a surprisingly distortion-free version of the stress waveform in a plane compressional wave. For a plane shear wave, the pressure waveform is visibly distorted.

Notes: The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity-depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots.The process input consists of unstacked seismic data and an initial velocity-depth model. This model is often based on nearby well information and an interpretation of the stacked section.Inversion is performed iteratively layer after layer; during each iteration synthetic travel-time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non-linear programming.The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data.

Notes: The detection and resolution of a thin layer closely situated above a high-impedance basement are predominantly determined by both the frequency content of the incident seismic wavelet and the existence of the nearby high-impedance bedrock.The separation of the thin layer and the basement arrivals is investigated depending on the low-frequency content of the wavelet. The high-frequency content of the wavelet is kept constant. The initial wavelet spectrum with low frequencies has a rectangular shape. All wavelets used have zero-phase characteristics. Numerical and analogue seismic modelling techniques are used. The study is based on the geology of the Pachangchi Sandstone in West Taiwan.Firstly the resolution of a thin layer between two half-spaces is examined by applying the Ricker and De Voogd-Den Rooijen criteria. The lack of low-frequency components of the incident seismic wavelet reduces the shortest true two-way traveltime by about 20%. In addition, low-frequency components of the wavelet diminish the deviation between true and apparent two-way traveltime by about 65% for layer thicknesses in the transition from a thick to a thin layer.The second step deals with the influence of a high-impedance basement just below a thin layer on the detection and resolution of that thin layer. Reflected signal energies and apparent two-way traveltimes are considered. The reflected signal energy depends on the low-frequency content of the incident wavelet, the layer's thickness and the distance between the basement and the layer. This applies only to layers with thicknesses less than or equal to one-third of the mean wavelength in the layer, and a distance to basement in the range of one to one-half of the mean wavelength in the rock material between layer and basement.The minimum thin-layer thickness resolvable decreases with increasing distance to the basement; i.e. for a layer thickness of one-third of the mean wavelength in the layer the relative error of the two-way traveltime increases from 5% to 30%, if the distance is reduced from one to one-half of the mean wavelength in the material between the basement and the thin layer.Finally, a combination of vertical seismic profiling and downward-continuation techniques is presented as a preprocessing procedure to prepare realistic data for the detection and resolution investigation.

Notes: Numerical wavefield extrapolation represents the backbone of any algorithm for depth migration pre- or post-stack. For such depth imaging techniques to yield reliable and interpretable results, the underlying wavefield extrapolation algorithm must propagate the waves through inhomogeneous media with a minimum of numerically induced distortion, over a range of frequencies and angles of propagation.A review of finite-difference (FD) approximations to the acoustic one-way wave equation in the space-frequency domain is presented. A straightforward generalization of the conventional FD formulation leads to an algorithm where the wavefield is continued downwards with space-variant symmetric convolutional operators. The operators can be precomputed and made accessible in tables such that the ratio between the temporal frequency and the local velocity is used to determine the correct operator at each grid point during the downward continuation.Convolutional operators are designed to fit the desired dispersion relation over a range of frequencies and angles of propagation such that the resulting numerical distortion is minimized. The optimization is constrained to ensure that evanescent energy and waves propagating at angles higher than the maximum design angle are attenuated in each extrapolation step. The resulting operators may be viewed as optimally truncated and bandlimited spatial versions of the familiar phase shift operator. They are unconditionally stable and can be applied explicitly. This results in a simple wave propagation algorithm, eminently suited for implementation on pipelined computers and on large parallel computing systems.

Notes: The attenuation in the vicinity of the geothermal anomaly at Urach was determined by means of two near-vertical reflection profiles. The attenuation in the sediments and in the upper crust (3-4 km depth) was estimated by interpretation of the first (refracted) arrivals. For calculating the attenuation, the amplitude decay with respect to distance was used. Corrections for the spread factor, i.e. the geometric amplitude divergence was deduced from the traveltime curves. Below the anomaly, higher attenuation values (Q−1∼ 0.008) were observed compared with those in the undisturbed crust (Q−1∼ 0.002). This effect is probably due to the cracks and fissures in the upper part of the crystalline basement.The attenuation in the middle and lower crust was determined using near-vertical reflections from this depth interval. The use of the spectral ratio method leads to higher values of the effective attenuation Q−1eff below the heat flow anomaly compared to those of the‘ normal’crust. This zone of high Q−1eff coincides with the low velocity body below the heat flow anomaly. Both effects, the higher attenuation and the lower velocities, could be caused by high temperatures, cracks and fissures in the crust.

Notes: A method is proposed to detect buried magnetite concentrations within river sediments. Model studies show that relatively small (thickness 1 m, width 10 m) plate-shaped volumes with magnetite contents of 0.5% within a non-magnetic matrix can be detected by a detailed ground magnetic survey using a sensitive (0.1 nT) magnetometer. Tests along lines perpendicular to the river but at a different angle to the bedrock trend (or the aeromagnetic anomaly trend) reveal that essentially all total field and vertical’gradient’anomalies detected in the profiles are elongated in the river and/or valley direction. This shows that the anomaly sources are (buried) volumes of higher magnetite content within the river sediments. Further evidence for this is (1) that higher intensity total field and vertical’gradient’anomalies occur in an area where the river cuts through strongly magnetic serpentinites, (2) the absence of high frequency anomalies over unsorted glacial till, and (3) some features on power spectra. Relatively large volumes of high magnetite concentrations within the river sediments may well contain the highest concentration of heavy economic minerals such as gold. Consequently, the areas of greatest interest in the exploitation of buried placers may be selected from maps obtained by detailed magnetic surveys either on the ground or at low altitude by helicopter.