bluuebunny/crossref_metadata_2025 huggingface dataset:
SEQUENTIAL WIENER DECONVOLUTION TO IMPROVE SEISMIC RESOLUTION1
Authors: FERBER R.‐G. , KOITKA H.
Published: April 2006

Abstract

Two different techniques for performing time‐variable Wiener deconvolution are compared using stacked seismic data. The conventional technique involves the empirical division of the data into a number of gates and the determination of time‐invariant deconvolution filters for each gate. In the second technique, the deconvolution filter is recomputed after each time increment from a fixed‐length data gate sliding along the trace. This scheme has the advantage that no a priori segmentation of the data is needed.
INTEGRATED INTERPRETATION, 3D MAP MIGRATION AND VSP MODELLING PROJECT, NORTHERN U.K. SOUTHERN GAS BASIN1
Authors: REILLY J. M.
Published: April 2006

Abstract

Depth conversion in the northern part of the U.K. Southern Gas Basin is complicated by the presence of Zechstein (Permian) salt swells and diapirs. In addition, the post‐Zechstein (post‐Permian) section displays large lateral velocity variations. The primary agents which control the velocity of this stratigraphic section are: (1) depth of burial, (2) lithological variation within individual formations, and (3) the effects of subsequent tectonic inversion. An integrated approach which combines well velocity, seismic velocity and seismic interpretation is required for accurate depth estimation.

In 1988 Mobil and partners drilled an exploratory well in the northern part of the U.K. Southern Gas Basin. This well was located near the crest of a Zechstein salt diapir. Over 2000 m of Zechstein was encountered in the well. The Permian Rotliegendes objective was penetrated at a depth of over 3700 m.

The initial delineation of the objective structure was based on the results of 3D map migration of the seismic time interpretation. Spatially‐variant interval velocity functions were used to depth convert through five of the six mapped horizons. Both well and model‐based seismic interval velocity analysis information was used to construct these functions.

A moving‐source well seismic survey was conducted. The survey was run in two critical directions. In conjunction with presurvey modelling, it was possible to confirm immediately the structural configuration as mapped to a distance of 7 km from the well. Post‐survey 3D map migration and modelling was employed to further refine the structural interpretation. Although the question of stratigraphic anisotropy was considered in the evaluation of the long offset modelling, no evidence was found in the field data to support a significant effect.

Finally, comparisons were made of: curved‐ray versus straight‐ray migration/modelling, midpoint‐depth velocity versus (depth‐dependant instantaneous velocity functions, and Hubral‐ versus Fermat‐based map depth migration algorithms. Significant differences in the results were observed for structural dips exceeding 15o and/or offsets exceeding 6 km. Map depth migration algorithms which employed both curved rays and spatially‐variant instantaneous velocity functions were found to best approximate the ‘true’ geological velocity field in the study area.
PRESTACK INVERSION OF GROUP‐FILTERED SEISMIC DATA1
Authors: HELGESEN JAN
Published: April 2006

Abstract

Three methods for least‐squares inversion of receiver array‐filtered seismic data are investigated: (1) point receiver inversion where array effects are neglected; (2) preprocessing of the data with an inverse array filter, followed by point receiver inversion; (3) array inversion, where the array effects are included in the forward modelling.

The methods are tested on synthetic data generated using the acoustic wave equation and a horizontally stratified earth model. It is assumed that the group length and the group interval are identical. For arrays that are shorter than the minimum wavelength of the emitted wavefield, and when the data are appropriately muted, point receiver inversion (first method) gives satisfactory results. For longer arrays, array inversion (third method) should be used.

The failure of the inverse array filter (second method) is due to aliasing problems in the data.
AUTOMATIC INTERPRETATION OF GRAVITY GRADIOMETRIC DATA IN TWO DIMENSIONS: VERTICAL GRADIENT1
Authors: KLINGELÉ E. E. , MARSON I. , KAHLE H.‐G.
Published: April 2006

Abstract

The magnetic and gravity field produced by a given homogeneous source are related through Poisson's equation. Starting from this consideration, it is shown that some 2D interpretation tools, widely applied in the analysis of aeromagnetic data, can also be used for the interpretation of gravity gradiometric data (vertical gradient). This paper deals specifically with the Werner deconvolution, analytic signal and Euler's equation methods. After a short outline of the mathematical development, synthesized examples have been used to discuss the efficiency and limits of these interpretation methods. These tools could be applied directly to airborne gravity gradiometric data as well as ground gravity surveys after transformation of the Bouguer anomalies into vertical gradient anomalies. An example is given of the application of the Werner deconvolution and Euler's equation methods to a microgravity survey.
GRAVITY GRADIENT TENSORS DUE TO A POLYHEDRON WITH POLYGONAL FACETS1
Authors: KWOK YUE‐KUEN
Published: April 2006

Abstract

Using the conjugate complex variables formulation, closed‐form formulae for the gravity gradient tensors of the gravitational potential due to a homogeneous polyhedral body composed of polygonal facets are derived. The treatise considers the cases of the observation point being inside the polyhedron, on the surface of a facet, or outside the polyhedron.
MEASURED REFLECTION STRENGTHS OF UNDERWATER PIPES IRRADIATED BY A PULSED HORIZONTAL DIPOLE IN AIR: COMPARISON WITH CONTINUOUS PLANE‐WAVE SCATTERING THEORY1
Authors: WENSINK W. A. , HOFMAN J. , VAN DEEN J. K.
Published: April 2006

Abstract

At Delft Geotechnics the technique of ground‐penetrating radar is in use for the detection of buried objects such as pipes. In order to give our ‘measurements in the field’ a more quantitative interpretation, a series of experiments has been started under well‐defined conditions.

A cylindrical vessel contains water, simulating wet soil. A pulsed transmitting antenna (TA) is mounted above the water‐surface irradiating horizontal underwater pipes. The reflected pulses are detected by a horizontal receiving dipole (AP, i.e. ‘air‐probe’) in the air. The reflecting objects used in the experiments are steel pipes, PVC rods and hollow PVC pipes filled with air or water. The depth of the pipes varies from 0.25 to 2 m. The strength of the reflected pulse depends on the type of pipe, its diameter, its depth, the electromagnetic properties of the water and also on the strength and polarization of the incident E‐field. The latter is (mainly) parallel to the axis of the pipe in the present experiments.

The experimental results have been compared with calculated results using the theory of a continuous plane wave, incident on an infinitely long cylinder in a homogeneous dielectric medium with the same dielectric constant as water. In a previous paper an experiment was described in which a movable receiving dipole in the water measured the transverse, mutually orthogonal Eø‐ and Eθ‐components of the pulses emitted by the TA. The amplitudes of Eθ versus depth, measured in that paper, are used in the calculations as amplitudes of the incident field. The attenuation of the scattered field is accounted for by assuming exponential damping. The relative amplitudes of the scattered field for different pipes lying at the same depth are reproduced very well by this simple theory. Also the relative values of the scattered amplitudes for a given pipe lying at different depths are described neatly, provided the refraction of the scattered field at the water‐air interface is accounted for.
A SEARCH FOR DIRECT HYDROCARBON INDICATORS IN THE FORMBY AREA1
Authors: BUSBY J. P. , PEART R. J. , GREEN C. A. , OGILVY R. D. , WILLIAMSON J. P.
Published: April 2006

Abstract

It has been proposed that the high‐frequency, low‐amplitude magnetic anomalies found over some hydrocarbon deposits are due to long‐term microseepage of hydrocarbons into iron‐rich sedimentary roof rocks, with subsequent precipitation of diagenetic magnetite or pyrrhotite at or near the water‐table. Aerogeophysical data sets, comprising both magnetic and gamma‐ray spectrometer measurements, over the Formby oil‐field, Lancashire, U.K., have been analysed for hydrocarbon‐related anomalies. Detailed ground magnetic traverses were also made to investigate some of the aeromagnetic anomalies.

No hydrocarbon‐induced magnetic anomalies were detected. The majority of the high‐frequency events occurring in the aeromagnetic data correlated with cultural features, others were attributed to artefacts of the data processing. In particular there were no extensive areas of high‐frequency, low‐amplitude anomalies as might be expected from authigenic magnetic minerals.

Borehole chippings from inside and outside the oil‐field were examined. High magnetic susceptibilities were due to contamination during drilling. Magnetite, which was identified by mineralogical analysis, was found to be of detrital origin. If any diagenetic magnetic material was present it was in such small quantities as to be insignificant.

The oil‐field did not possess a characteristic gamma‐ray spectrometric signature. Anomalies were found to be related to hydrological conditions and to the distribution of surficial deposits. Attempts to suppress the influence of the drift geology had only limited success.

It is concluded that the effectiveness of high‐resolution aeromagnetic onshore surveys for direct hydrocarbon detection has yet to be established. In particular, the anomaly found over the Formby oil‐field was caused by the cumulative effect of borehole casing. Similar cultural contamination by oil‐field equipment may explain some of the anomalies discovered over hydrocarbon deposits in North America. It is also unlikely that the spectrometric method can be applied diagnostically in any but the most simple and drift‐free geological environments.
CHEBYSHEV EXPANSIONS FOR THE SOLUTION OF THE FORWARD GRAVITY PROBLEM1
Authors: ZHAO S. K. , YEDLIN M. J.
Published: April 2006

Abstract

Chebyshev expansions are used to solve the 3D forward gravity problem. Since the matrix factorization method is used to solve the coefficient equation system and the fast Fourier transform (FFT) technique is used to compute the forward and backward Chebyshev expansions, this method is very fast. Multipole expansions are used to calculate approximate boundary conditions (BCs) for realistic problems. When the length of any source‐body dimension is less than 70% of the minimum dimension of the computational domain, the relative error caused by the approximate BCs is about 1%. A cell‐average discretization method is suggested. The accuracy obtained by the cell‐average discretization is much better than that obtained by the traditional point‐injection discretization. The Chebyshev expansion technique was applied to four density models including a complex geological structure consisting of two normally faulted layers. Models which were finely sampled had a maximum relative error of about 1%.
ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS1
Authors: LI YAOGUO , OLDENBURG DOUGLAS W.
Published: April 2006

Abstract

When an electric current is introduced to the earth, it sets up a distribution of charges both on and beneath the earth's surface. These charges give rise to the anomalous potential measured in the d. c. resistivity experiment. We investigate different aspects of charge accumulation and its fundamental role in d. c. experiments. The basic equations and boundary conditions for the d. c. problem are first presented with emphasis on the terms involving accumulated charges which occur wherever there is a non‐zero component of electric field parallel to the gradient of conductivity. In the case of a polarizable medium, the polarization charges are also present due to the applied electric field, yet they do not change the final field distribution. We investigate the precise role of the permittivity of the medium. The charge buildup alters the electric fields and causes the refraction of current lines; this results in the well‐known phenomenon of current channelling. We demonstrate this by using charge density to derive the refraction formula at a boundary. An integral equation for charge density is presented for whole‐space models where the upper half‐space is treated as an in‐homogeneity with zero conductivity. The integral equation provides a tool with which the charge accumulation can be examined quantitatively and employed in the practical forward modelling. With the aid of this equation, we investigate the effect of accumulated charges on the earth's surface and show the equivalence between the half‐space and whole‐space formulations of the problem. Two analytic examples are presented to illustrate the charge accumulation and its role in the d. c. problem. We investigate the relationship between the solution for the potential via the image method and via the charge density. We show that the essence of the image method solution to the potential problem is to derive a set of fictitious sources which produce the same potential as does the true charge distribution. It follows that the image method is viable only when the conductivity structure is such that the effect of the accumulated charge can be represented by a set of point images. As numerical examples, we evaluate quantitatively the charge density on the earth's surface that arises because of topography and the charge density on a buried conductive prism. By these means, we demonstrate the use of the boundary element technique and charge density in d. c. forward modelling problems.
AMPLITUDE, PHASE AND FREQUENCY VERSUS OFFSET APPLICATIONS1
Authors: MAZZOTTI A.
Published: April 2006

Abstract

In a layered earth the seismic reflection response for incidence at non‐normal angles is dependent upon the elastic constants and thicknesses of the layers.

The possibility is investigated of increasing the diagnostic value of seismic data by using the phase and the frequency v. offset information in addition to that from the amplitude v. offset.

The combined amplitude, phase and frequency versus offset (APF.VO) analysis is carried out through the computation of amplitude, phase and frequency indicators based on the analytical description of seismic traces.

Both synthetic and actual data are examined.

From the analyses of synthetic seismograms, it is shown that modifying the velocities and thicknesses of a given target layer, by introducing different pore fluids or lithological conditions, produces changes in APF.VO plots. In particular, the effects related to interference among reflections and to critical angle phenomena are clearly detected by both the phase and amplitude v. offset indicators in terms of phase shifts and amplitude variations. The frequency indicator is mainly controlled by the spectrum of the propagating wavelet.

Since the basic synthetic model is derived from an existing well, located close to a seismic line, some actual CDP gathers are analysed. Features related to interference and critical angle are again evident in the APF.VO plots of the actual data. The amplitude indicator appears to be reasonably stable while the phase shows a higher spatial variability and a stronger sensitivity to noise.

Differential interference with offset often occurs in actual layered structures and distorts seismic data significantly. Therefore AVO interpretation and AVO inversion procedures must also tackle this problem. Knowledge of phase and frequency variations v. offset may help classical AVO interpretation and yield further information for use in inversion techniques.
SOME REMARKS ON NOISE STABILITY IN DYNAMIC INVERSION OF REFLECTION SEISMIC DATA1
Authors: MEYER H. G.
Published: April 2006

Abstract

The dynamic inversion of reflection seismic data is investigated with reference to the influence of noise on pseudo‐impedance logs. Model traces are calculated with 0, 5, 15 and 50% noise, respectively. In solving the inversion problem, the algorithm of Marquardt and Levenberg is used in connection with singular value decomposition (SVD). The results are within a 1% error range so that there was no visible change in the logs. Further signal analysis show that there is no dependence on the phase content of the wavelet used if all other parameters of the model are known.
RESISTIVITY OF ROCK‐SALT IN ASSE (GERMANY) AND PETROPHYSICAL ASPECTS1
Authors: YARAMANCI U. , FLACH D.
Published: April 2006

In the Asse salt‐mine (Germany), where extensive research is carried out on various aspects of nuclear waste disposal in rock‐salt formations, the resistivity of a future construction site for a test seal at a depth of 945 m has been investigated. Measurements have been conducted, using various types of the four‐point electrode configuration, on a network of 180 electrodes permanently installed in boreholes. A fully computer‐controlled measurement system has been built consisting of a resistivity meter, a switchbox for electrodes and a computer with special control software. The system has interactive and programmable automatic working modes with an extensive capability for documentation and processing including the immediate evaluation of apparent resistivities and is suitable for long‐term continuous observations.

The average resistivity at the site which consists of almost homogeneous Stassfurt rock‐salt, is approximately 0.6 × 106Ωm with little variation. There is a small anomaly due to a conductive inclusion, probably a local anhydrite band. There is no indication of anisotropy so far and no significant change with time. The specific amount of water in the effective pores and its change can be estimated from the observed resistivities using the extended form of Archie's equation with pore saturation included. In this case data for the specific internal surface from samples are available and the order of permeability may be estimated using the formation factor derived from resistivities.
BOREHOLE RADAR APPLIED TO THE CHARACTERIZATION OF HYDRAULICALLY CONDUCTIVE FRACTURE ZONES IN CRYSTALLINE ROCK1
Authors: OLSSON OLLE , FALK LARS , FORSLUND OLOF , LUNDMARK LARS , SANDBERG ERIC
Published: April 2006

Abstract

The borehole radar system, RAMAC, developed within the framework of the International Stripa Project, can be used in three different measuring modes; single‐hole reflection, cross‐hole reflection and cross‐hole tomography. The reflection modes basically provide geometrical data on features located at some distance from the borehole. In addition the strength of the reflections indicate the contrast in electrical properties. Single‐hole reflection data are cylindrically symmetrical with respect to the borehole, which means that a unique fracture orientation cannot be obtained. A method has been devised where absolute orientation of fracture zones is obtained by combining single‐hole reflection data from adjacent holes. Similar methods for the analysis of cross‐hole reflection data have also been developed and found to be efficient. The radar operates in the frequency range 20‐‐60 MHz which gives a resolution of 1–3 m in crystalline rock. The investigation range obtained in the Stripa granite is approximately 100 m in the single‐hole mode and 200‐‐300 m in the cross‐hole mode.

Variations in the arrival time and amplitude of the direct wave between transmitter and receiver have been used for cross‐hole tomographic imaging to yield maps of radar velocity and attenuation. The cross‐hole measurement configuration coupled with tomographic inversion has less resolution than the reflection methods but provides better quantitative estimates of the values of measured properties.

The analysis of the radar data has provided a consistent description of the fracture zones at the Stripa Cross‐hole site in agreement with both geological and geophysical observations. Comparison of the radar results with seismic cross‐hole data showed excellent agreement with respect to shape and location of the fracture zones in space. Comparison with hydraulic data shows that the features identified by radar are of hydrogeological significance.
INVERSION OF GRAVITY AND MAGNETIC DATA FOR THE LOWER SURFACE OF A 2.5 DIMENSIONAL SEDIMENTARY BASIN1
Authors: MICKUS KEVIN L. , PEEPLES WAYNE J.
Published: April 2006

Abstract

Gravity and magnetic data have been inverted to obtain the continuous lower surface of a 2.5 dimensional sedimentary basin. The non‐linear problem is linearized and a solution is calculated through a recursive process until the predicted data matches the observed data. An average model is then calculated and a resolution analysis shows which features are uniquely determined. The results of individual inversion indicate that a final solution is initial model dependent but the average models are independent of the initial model except at the margins. The average model for the magnetic solutions have uniformly smaller spreads than the gravity solutions.

The algorithms were applied to data from the Sanford Basin in North Carolina. The results indicate that the basin is asymmetrical in shape with a maximum depth of 3.2 km. Comparing these results with those obtained from a generalized linear inverse (GLI) algorithm indicate that the higher‐frequency features determined from the GLI algorithm are not resolved.
SHEAR‐WAVE VELOCITY ESTIMATION IN POROUS ROCKS: THEORETICAL FORMULATION, PRELIMINARY VERIFICATION AND APPLICATIONS1
Authors: GREENBERG M. L. , CASTAGNA J. P.
Published: April 2006

Abstract

Shear‐wave velocity logs are useful for various seismic interpretation applications, including bright spot analyses, amplitude‐versus‐offset analyses and multicomponent seismic interpretations. Measured shear‐wave velocity logs are, however, often unavailable.

We developed a general method to predict shear‐wave velocity in porous rocks. If reliable compressional‐wave velocity, lithology, porosity and water saturation data are available, the precision and accuracy of shear‐wave velocity prediction are 9% and 3%, respectively. The success of our method depends on: (1) robust relationships between compressional‐ and shear‐wave velocities for water‐saturated, pure, porous lithologies; (2) nearly linear mixing laws for solid rock constituents; (3) first‐order applicability of the Biot–Gassmann theory to real rocks.

We verified these concepts with laboratory measurements and full waveform sonic logs. Shear‐wave velocities estimated by our method can improve formation evaluation. Our method has been successfully tested with data from several locations.
PLANE‐WAVE CONSTRAINTS IN 2D FILTER DESIGN1
Authors: WALTHAM D.
Published: April 2006

Abstract

A method is presented for developing and/or evaluating 2D filters applied to seismic data. The approach used is to express linear 2D filtering operations in the space‐frequency (x–ω) domain. Correction filters are then determined using plane‐wave constraints. For example, requiring a vertically propagating plane wave to be unaffected by migration necessitates application of a half‐derivative correction in Kirchhoff migration. The same approach allows determination of the region of time‐offset space where half‐derivative corrections are correct in x–t domain dip moveout. Finally, an x–ω domain dip filter is derived using the constraint that a plane wave be attenuated as its dip increases. This filter has the advantage that it is significantly faster than f–k domain dip filtering and can be used on irregularly spaced data. This latter property also allows the filter to be used for interpolation of irregular data onto a regular grid.
MODELLING CHANNEL WAVES WITH SYNTHETIC SEISMOGRAMS IN AN ANISOTROPIC IN‐SEAM SEISMIC SURVEY1
Authors: LIU ENRU , CRAMPIN STUART , ROTH BRUCE
Published: April 2006

Abstract

In‐seam seismic surveys with channel waves have been widely used in the United Kingdom and elsewhere to map coal‐seams and to detect anomalous features such as dirt bands, seam thinning and thickening, and particularly in‐seam faulting. Although the presence of cleat‐induced anisotropy has been recognized in the past, almost all previous analyses have assumed homogeneous isotropic or transversely isotropic coal‐seams. Channel waves, however, exhibit properties which cannot be fully explained without introducing anisotropy into the coal‐seam. In particular, Love‐type channel waves are observed for recording geometries where, in a homogeneous isotropic or transversely isotropic structure, the source would not be expected to excite transverse motion. Similarly, modes of channel‐wave propagation display the coupled three‐component motion of generalized modes in anisotropic substrates, which would not be expected for Rayleigh and Love wave motion in isotropy or in transversely isotropic media with azimuthal isotropy.

We model the observed in‐seam seismic channel waves with synthetic seismograms to gain an understanding of the effects of cleat‐induced anisotropy on the behaviour of channel waves. The results show a reasonable good match with the observations in traveltime, relative amplitudes, dispersion characteristics and particle motions. We demonstrate that anisotropy in the surrounding country rocks contributes significantly to the coupling of channel wave particle motion, although its effect is not as strong as the anisotropy in the coal‐seam. We conclude that the effects of cleat‐ and stress‐induced anisotropy are observed and can be modelled with synthetic seismograms, and that anisotropy must be taken into account for the detailed interpretation of channel waves.
FREQUENCY‐SELECTIVE DESIGN OF THE KIRCHHOFF MIGRATION OPERATOR1
Authors: GRAY SAMUEL H.
Published: April 2006

Abstract

Integral migration techniques perform a sum over an aperture of input traces to obtain output at a single point. The length of the aperture is limited by a spatial Nyquist criterion, which typically prohibits imaging very steep dips at very high frequencies without generating severe migration artifacts (migration operator aliasing). For time‐domain Kirchhoff migration, this can be a fatal shortcoming. The standard way to address this problem is to interpolate traces spatially before migration. This reduces the trace spacing, thereby increasing the frequency content which can be migrated without aliasing at steep dips.

An alternative remedy to the operator aliasing problem is to modify the phase response of the Kirchhoff migration operator. This operator is frequency‐selective across the migration aperture: it passes all temporal frequencies of the input traces in the innermost portion of the aperture (referring to the shallow dips), and gradually cuts out the higher frequencies as it approaches the outer portion of the aperture. Thus, while all frequencies of the input data contribute to the shallow‐dip portion of the migrated image, only the permissible low frequencies of the input data contribute to imaging the steepest dips.

Using a simple realization of a frequency‐selective Kirchhoff migration operator, this technique is illustrated on a synthetic data set involving greater than vertical dips.
REFLECTION AND POLARIZATION OF TUBE WAVES AS SEEN IN VSP DATA1
Authors: MJELDE R.
Published: April 2006

Abstract

P‐wave and S‐wave data acquired with vertical seismic profiling (VSP) often include tube waves propagating in the borehole, although considerable efforts are generally made to ensure that these waves are not recorded. However, several theoretical studies have indicated that tube waves could provide important information about the rock formation and thus should not be considered as pure noise.

In order to study some of these aspects experimentally, tube waves were acquired by VSP in a well in the Paris Basin both before and after casing. A sparker was used as source inside the borehole, which ensured that the data recorded contained high‐amplitude tube waves.

It is shown that the casing is an obstacle which prevents the study of formation parameters, and thus further tube‐wave acquisitions should be carried out in open holes only.

The before‐casing tube‐wave reflection log is compared to a synthetic log computed from the sonic log. The high resolution of the tube waves is of particular interest, revealing layers that are too thin to be detected in body‐wave surveys.

It has recently been suggested that the projection of the tube‐wave polarization in the horizontal plane can be used to determine directions of stress‐induced anisotropy in the rock formation. Strong polarization anomalies are observed in the data sets but are attributed to tool problems rather than any rock‐formation feature.
MODELLING OF GI GUN SIGNATURES1
Authors: LANDRØ MARTIN
Published: April 2006

Abstract

In 1989 a new type of marine seismic source was introduced. This new air‐gun, which consists of two air chambers instead of one, is called the GI gun. The main feature of this gun is that the bubble created by the gun is stabilized by an injection of extra air from the second chamber at a later time. This injection mechanism reduces the amplitude of the bubble oscillations, which also means that the acoustic signal from a GI gun shot is characterized by a very clean primary pulse followed by very small bubble oscillations. A method for calculating the acoustic signal generated by a GI gun is presented. Based on the solution of a damped Kirkwood–Bethe equation, the far‐field pressure of single GI guns and of arrays of GI guns is calculated.

It is shown that the optimal values for injection start time and injection period vary with injector volume and gun depth. It is also shown that the precision in the firing time for the injector should be of the order of 4 ms, while the precision of the injection period should be of the order of 8 ms. Modelled and measured far‐field signatures have been compared, and the relative error energy is found to be less than 3.5% for all examples.
ANISOTROPIC Q AND VELOCITY DISPERSION OF FINELY LAYERED MEDIA1
Authors: CARCIONE JOSÉ M.
Published: April 2006

Abstract

When a seismic signal propagates through a finely layered medium, there is anisotropy if the wavelengths are long enough compared to the layer thicknesses. It is well known that in this situation, the medium is equivalent to a transversely isotropic material. In addition to anisotropy, the layers may show intrinsic anelastic behaviour. Under these circumstances, the layered medium exhibits Q anisotropy and anisotropic velocity dispersion.

The present work investigates the anelastic effect in the long‐wavelength approximation. Backus's theory and the standard linear solid rheology are used as models to obtain the directional properties of anelasticity corresponding to the quasi‐compressional mode qP, the quasi‐shear mode qSV, and the pure shear mode SH, respectively. The medium is described by a complex and frequency‐dependent stiffness matrix. The complex and phase velocities for homogeneous viscoelastic waves are calculated from the Christoffel equation, while the wave‐fronts (energy velocities) and quality factor surfaces are obtained from energy considerations by invoking Poynting's theorem.

We consider two‐constituent stationary layered media, and study the wave characteristics for different material compositions and proportions. Analyses on sequences of sandstone‐limestone and shale‐limestone with different degrees of anisotropy indicate that the quality factors of the shear modes are more anisotropic than the corresponding phase velocities, cusps of the qSV mode are more pronounced for low frequencies and midrange proportions, and in general, attenuation is higher in the direction perpendicular to layering or close to it, provided that the material with lower velocity is the more dissipative. A numerical simulation experiment verifies the attenuation properties of finely layered media through comparison of elastic and anelastic snapshots.
COMMENT ON ‘ASPECTS OF CHARGE‐ACCUMULATION IN D.C. RESISTIVITY EXPERIMENTS’ BY Y. LI AND D. W. OLDENBURG1
Authors: SZARKA L.
Published: April 2006

Abstract

The paper by Li and Oldenburg (1991) gives an important insight into d.c. charge accumulation problems. Nevertheless, their derivation concerning the role of the permittivity of the medium is not as straightforward as it could be. Another question, worth discussing, is the problem of double layers, which is missing from the authors’ paper.
REFLECTION AMPLITUDES AND MIGRATION AMPLITUDES (ZERO‐OFFSET SITUATION)1
Authors: BORTFELD R. , KIEHN M.
Published: April 2006

Abstract

The effect of wave‐equation migration on amplitudes is determined. This effect is derived for zero‐offset traces and for second‐order approximations of the traveltimes. Three steps are followed: firstly, the amplitudes of zero‐offset traces are established; secondly minus half the traveltimes are used as input for downward continuation in migration (forward in space and time); thirdly, the amplitudes of the migrated events are determined by downward continuation (at zero‐traveltimes).

Layered models (piles of homogeneous layers) with smooth interfaces are used. The determinants of the 2 × 2 matrices B0 obtained for these models are responsible for the main effect on migration. The migration result primarily depends on the overburden as the inverse of det (B0). Drastic effects can occur over small distances. For weakly reflecting media, it is confirmed that wave‐equation migration gives “correct” results (but the input data must be multiplied by V0T0), i.e. amplitudes proportional to the reflection coefficient. For any velocity changes, the inverse of det (B0) will, in general, give inaccurate migration amplitudes and inaccurate lithological interpretations. In a simple step, true amplitude migration, or exact migration, is derived from our results.

It is assumed that no focus phenomena are present. The effect of buried foci is discussed briefly.
FIXED LOOP SOURCE EM MODELLING RESULTS USING 2D FINITE ELEMENTS1
Authors: VALLA PIERRE
Published: April 2006

Abstract

Among electromagnetic sounding techniques, the Mélos method possesses the specific feature of including an apparent resistivity computation. This acts as a normalizing scheme so that 2D modelling results can be obtained without accounting for a true 3D source. However, in order to get reliable numerical modelling results for a 2D magnetic dipole source, improved algorithms are required in order to apply the standard finite‐element technique: quadratic basis functions must be used in place of linear basis functions, and a more sophisticated method than conventional ones is necessary for properly solving the resulting system of linear equations.

Such modelling results have been used to study theoretical responses for the Mélos method in the search for conductive bodies in mineral exploration. Two sets of models are presented and discussed. They show that the typical Mélos response to a conductive target is a bipolar anomaly on the apparent resistivity pseudo‐section, with a conductive pole at low frequency which is centred above the target.
COMMENT ON ‘THE RESOLUTION OF NARROW LOW‐VELOCITY ZONES WITH THE GENERALIZED RECIPROCAL METHOD’ BY DERECKE PALMER1
Authors: WHITELEY R. J.
Published: April 2006

Abstract

The following discussion concentrates on one of the synthetic examples used by Palmer (1991) to justify his method of seismic refraction interpretation (Fig. 2, p. 1035) and on his field data and interpretation of the first field example (a collapsed doline) which appeared on pp. 1050–1053.
ASPECTS OF 1D SEISMIC MODELLING USING THE GOUPILLAUD PRINCIPLE1
Authors: SLOB EVERT , ZIOLKOWSK1 ANTON
Published: April 2006

Abstract

A reflection response function for a 1D discretized earth model can be obtained using ray‐theory and Z‐transforms with the Goupillaud model. This is usually done by taking the source function as a plane wave impinging normally on the layered earth. Two important problems have been tackled with this basic idea. The first, extraction of the source wavelet, and the second, a description of the free‐surface related problems.

In the Goupillaud model, the one‐way traveltime in each layer is taken to be the same time interval At, which is also the time unit for the Z‐transform. The two‐way traveltime in any layer is 2Δt, corresponding to a multiplication by Z2. The reflection impulse response therefore contains only even powers of Z. The convolution of the reflection response with the wavelet yields a seismogram whose Z‐transform contains both odd and even powers of Z. However, even though the seismogram contains more coefficients than unknowns, the wavelet cannot be extracted, because the coefficients are not independent: later coefficients are functions of earlier ones, which does not make sense physically. To overcome this physical problem for the reflection seismogram, the two‐way traveltime through the layer should be Δt. It is then impossible to extract the wavelet, as there are fewer coefficients in the seismogram than unknowns.

Szaraniec has proposed a modification to the Goupillaud model, known as the odd‐depth model, that includes the free surface and a top layer whose two‐way traveltime Δt is half the two‐way traveltime 2Δt of all the other layers. Using what Szaraniec calls the fundamental identity of the odd‐depth model, it is possible to extract the source wavelet from the seismogram. We show that this fundamental identity holds only if reflection coefficients of deeper interfaces are functions of the reflection coefficients of shallower interfaces; that is, for extremely improbable geologies.

Neither of these approaches offers a solution to the deconvolution problem. It is better to obtain the source signature from measurements in the field. Only Szaraniec's model offers the possibility of tackling the problem of the free surface but because of an inherent flaw in the model, it fails to address the problem.
DETERMINATION OF ELECTRICAL PROPERTIES OF THE GROUND AT SHALLOW DEPTH WITH AN ELECTROSTATIC QUADRUPOLE: FIELD TRIALS ON ARCHAEOLOGICAL SITES1
Authors: TABBAGH ALAIN , HESSE ALBERT , GRARD RÉJEAN
Published: April 2006

Abstract

Knowledge of both the electrical resistivity ρ and the dielectric permittivity ɛ of the ground is important for the determination of characteristics such as granularity, porosity, moisture and salt content. Whereas the measurement of ρ is very common and can be achieved using either the d.c. resistivity method or a wide variety of EM devices, ɛ remains practically unknown in the low‐frequency domain between the IP domain and the high‐frequency domain. Following the principle of the quadrupole technique used in d.c. prospecting and of the quadrupolar probe for measuring the complex permittivity of the ionosphere, we propose a new approach which does not require any galvanic contact between the poles and the ground. The transfer impedance can be evaluated using the quasi‐static approximation for low frequency or the full EM theory for higher frequencies. The conditions under which both calculations apply are discussed. At low frequencies and for low resistivity ground, the electrostatic quadrupole measures ρ exactly as with the d.c. technique; for higher resistivities or frequencies the simultaneous measurement of both properties becomes possible. Examples in archaeological prospecting are presented and checked against independent d.c. resistivity measurements or excavation analyses.
DIELECTRIC PROPERTIES OF WET SOILS IN THE FREQUENCY RANGE 1–3000 MHz1
Authors: WENSINK W.A.
Published: April 2006

Abstract

The effective relative dielectric constant ɛe, r and the effective conductivity σe have each been determined as a function of frequency in the range 1–3000 MHz at volumetric water contents of up to approximately 0.74 for clays, 0.83 for a peat and 0.56 for a silt.

At frequencies above about 25 MHz (depending on soil type), ɛe, rincreases with water content for all samples. However, at lower frequencies, ɛe, ronly increases with water content as long as the wet density also increases, which is the case for water contents up to a critical value lying between 0.35 and 0.48. At higher water contents, ɛe, rand the wet density decrease with increasing water content. Consequently, curves of ɛe, rversus frequency for two wet samples with different water contents, at least one of them higher than the critical value, are seen to cross at about 25 MHz. Below the critical value the curve of the sample with the lower water content is below the other curve at all freqencies applied. At a given frequency, σe has a maximum as a function of water content. This is tentatively explained by assuming that σe is the sum of pore water conductivity (increasing with water content until all salts in the soil are dissolved into the water and then decreasing) and surface water conductivity (increasing with wet density and therefore increasing with water content up to the critical value and then decreasing).

At frequencies higher than 1000 MHz, ɛe, rdepends only weakly on salinity (which is represented by the measured conductivity). It shows an increasing dependence if the frequency is decreased towards 1 MHz.

The highest values of ɛe, rand σe, measured in this work, occur for a sample of wet, nearly saturated silt originating from a location below sea‐level near to the Dead Sea, Israel: ɛe, rdecreases continuously from a value of about 104 at 3 MHz to about 102 at 200 MHz, while σe rises from about 4 S/m to 5 S/m at these respective frequencies. The dependence of the wavelength on the loss‐tangent is strong and the wavelength is considerably smaller than it would be in a dielectric. This is the only sample for which σe increases with water content, even if the latter is above its critical value. Therefore it is assumed that the pore water conductivity is greater than the surface water conductivity if the volumetric water content is lower than 0.564, the maximum value applied. The measurements give evidence for the presence of a relaxation at about 3 MHz for all samples examined.
A RECONCILIATION OF MATHEMATICAL MODELS FOR SPONTANEOUS MINERALIZATION POTENTIALS1
Authors: FURNESS PETER
Published: April 2006

Abstract

Two methods for computing spontaneous mineralization potentials in the region external to the source body are reviewed. The first of these is a long‐established technique in which the causation is assumed to be a distribution of simple current source on the boundary of the mineralization. The second is a more recent technique which assumes a surface distribution of current dipole moment (double layer) along the boundary of the source body.

The former technique is a special case of a more general spontaneous potential (SP) model in which the source is a density of current dipole moment (current polarization) distributed throughout the mineralization. As far as the potentials in the region external to the source body are concerned this current polarization can be simply related to an equivalent double layer source function, i.e. the potential discontinuity produced over the boundary of the mineralization by an equivalent double layer model.

This simple relationship suggests an integral equation technique for the exact numerical solution of boundary value problems appropriate to the polarization model for spontaneous mineralization potentials. The technique is applied to exploring the justification of interpreting mineralization self‐potentials by the traditional approach.
DIFFRACTION BY A WEDGE IN AN ACOUSTIC CONSTANT DENSITY MEDIUM1
Authors: BERG PER , IF FLEMMING , NIELSEN PER , SKOVGAARD OVE
Published: April 2006

Abstract

A new method is presented for solving the 2D problem of diffraction of a plane wave by a wedge of arbitrary angle in a purely acoustic, constant‐density medium with different constant compressional wave speeds inside and outside the wedge. The diffraction problem is formulated as integral equations, and a wavenumber–frequency representation of the scattered field is obtained. With the aid of the Cagniard–de Hoop method, exact analytical expressions in the space–time domain are obtained for the different wave constituents, i.e. geometric optical scattered waves and edge diffracted waves including head waves. These expressions can be computed to any degree of accuracy within reasonable computation times on a computer, and the semi‐analytical method of solution presented thus constitutes a means of constructing reference solutions for wedge configurations. Such highly accurate reference solutions are of importance for verification of results that include diffraction phenomena modelled by general numerical approximate methods, e.g. finite differences, finite elements and spectral methods. Examples of such applications of the method of solution are given.
Relation of in situ resistivity to water content in salt rocks1
Authors: Yaramanci U.
Published: April 2006

The investigation of water in salt‐rock formations is of particular relevance to underground nuclear waste repositories. In the Asse salt‐mine (Germany) a study into the relationship of in situ resistivity to water content has been made. Measurements were carried out in older rock‐salt using an electrode array in boreholes, an electrode profile in a drift and small resistivity sensors in and around a drift seal. Further measurements were made on moist zones in a contact area of younger rock‐salt and carnallitite and also in older rock‐salt with anhydrite bands using electrode profiles in the drifts. The resistivities range from 102Ωm to 106Ωm. Corresponding probes have water contents from 0.01% to 1.3%. A definite relationship between resistivity and water content is revealed which can be described by Archie's law using a cementation factor m of 1.9. Porosities are between 0.08% and 1.4% and the saturations vary considerably. An explicit influence of saturation on resistivity cannot be discovered using the present data. The results enable us to estimate the in situ water content and the order of the in situ porosity using resistivity surveys at different scales. This increases significantly the safety of a nuclear repository site.
Shallow fault location in coal measures using offset Wenner resistivity profiling1
Authors: Hobbs B.A. , Reading A.M.
Published: April 2006

The five‐electrode resistivity configuration of Barker, who introduced the concept of offset resistivity measurements, is used in a profiling mode in the search for lateral variations of resistivity down to depths of a few tens of metres. Theoretical computations show that plotting simple pseudosections of offset measurements over faults is sufficient to reveal the fault position. The method is subsequently applied in the field for locating a buried fault in coal measures. Although offset pseudosections are often all that is required, apparent resistivity pseudosections are examined and compared to collations of 1D inversions of the sounding profile data and to computations over 2D models. It is shown that apparent restivity pseudosections may present a rather misleading picture.
A physical approach to computing magnetic fields1
Authors: Furness Peter
Published: April 2006

The superposition integral expressing the field due to a magnetic source body is relatively simple to evaluate in the case of a homogeneous magnetization. In practice this generally requires that any remnant component is uniform and the susceptibility of the body is sufficiently low to permit the assumption of a uniform induced magnetization. Under these conditions the anomalous magnetic field due to a polyhedral body can be represented in an intuitive and physically appealing manner. It is demonstrated that the components of the magnetic field H can be expressed as a simple combination of the potentials due to two elementary source distributions. These are, firstly, a uniform double layer (normally directed dipole moment density) located on the planar polygonal faces of the body and, secondly, a uniform line source located along its edges. In practice both of these potentials (and thus the required magnetic field components) are easily computed. The technique is applicable to polyhedra with arbitrarily shaped faces and the relevant expressions for the magnetic field components are suitable for numerical evaluation everywhere except along the edges of the body where they display a logarithmic singularity.