bluuebunny/crossref_metadata_2025 huggingface dataset:
USE OF ELECTRICAL RESISTIVITY METHODS FOR THE STUDY OF COAL SEAMS IN PARTS OF THE RANIGANJ COALFIELD (INDIA)*
Authors: VERMA R. K. , BANDOPADHYAY T. K. , BHUIN N. C.
Published: April 2006

Abstract

The surface resistivity method has been used to study a few exposed coal seams located in the northwestern part of the Raniganj Coalfield (belonging to the Damodar Valley Gondwana basin), India. Different electrode configurations, viz., Wenner, two‐electrode and half‐Schlumberger, have been used with different electrode spacings in horizontal profiling. The vertical distribution of resistivity has been studied using Schlumberger configuration at different locations along the profile.

Laboratory studies of resistivity (at partial to full water saturation conditions) and porosity of different coal, shaly sandstone and sandstone samples of the survey area had already been carried out before the field survey. The results indicated the presence of a good resistivity contrast between the coal seams and the surrounding formations.

The field results did not bear this out: the resistivity responses of the coal formations on the profiles and sounding curves are not as clear as one would expect for such high contents. The Wenner profiles show a broad resistivity anomaly over the coal seams. Two‐electrode profiles are less noisy than Wenner profiles. Sharp peaks have been observed over the coal seams. The half‐Schlumberger configuration seems the best: all the coal seams and their edges can be accurately outlined on the resistivity curves.

Borehole data close to the profile have been used for correlating the field results. There is good agreement with vertical electrical soundings.
UNCERTAIN RESISTIVITY SOUNDING AND EQUIVALENT MODELS*
Authors: SZARANIEC E.
Published: April 2006

Abstract

Problems of the resistivity sounding method may be reparametrized by means of Dar Zarrouk—or generalized D.Z.—transformations.

A complete set of equivalent models is subdivided into three classes: initial models, intermediate models, and all other models. Equivalent reparametrized models are subdivided into three analogous classes. There is no one‐to‐one mapping of intermediate primary and intermediate reparametrized models. Non‐trivial equivalent models are generated from initial models via intermediate reparametrized models. A method is developed to find equivalent models relative to the uncertainty of resistivity soundings.

There are different forms of approximate equivalence laws, apart from those commonly accepted. The equivalence depends considerably on the “flatness” of the sounding curve. For mean flatness, the electric models exhibit the (hp±2)‐equivalence rather than the (hp±1)‐equivalence.
TIME‐TO‐DEPTH MIGRATION USING WAVEFRONT CURVATURE*
Authors: URSIN B.
Published: April 2006

Abstract

A well‐known technique for the migration of normal‐incidence two‐way travel‐time maps is extended to common‐source‐point travel‐time data. The travel time and the travel‐time gradient are used to compute the parameters defining the tangent plane of the reflecting interface. It is also shown how the curvature matrix of the received wavefront can be used to compute the curvature of the reflecting interface. The method is initially derived for common‐source‐point data and then extended to common‐midpoint data.

In a three‐dimensional medium the wavefront curvature matrix is computed by solving a 2 × 2 symmetric matrix Riccati equation. In a two‐dimensional medium and in a medium with constant velocity gradient, the wavefront curvature matrix is computed by solving a scalar Riccati equation and two linear equations. The migration procedures are also simplified.

When the velocity function is unknown, the migration procedures cannot be used. An inverse modeling algorithm which simultaneously performs the migration and estimates the velocity function must then be applied. Two different inversion schemes are discussed briefly.
BIPOLE‐DIPOLE FIELD DIFFERENCE—A NEW RESISTIVITY SOUNDING TECHNIQUE*
Authors: DAS U. C. , SINGH R. D.
Published: April 2006

Abstract

The method of field differences using two parallel bipole sources is described. The system possesses much greater resolving power and investigating depth than the conventional Schlumberger configuration. Of the two variations, the longitudinal field difference has about two and half times greater depth of investigation than the transverse one. Practical advantage of the present technique over the Schlumberger system in reducing the ambiguity in interpretation due to equivalent layered structures is demonstrated on a theoretical example.
APPLICATION OF THE GENERAL COMPLEX COMPLIANCE MODEL TO THE DIRECT‐DETECTION PROBLEM*
Authors: STRICK E.
Published: April 2006

Abstract

A methodology is outlined for using general complex compliance functions—which contain the constant‐Q case and any kind of fluid saturant as special cases—to determine the nature of that saturant from seismic reflections observed on seismic records. The important attribute of such a formulation based upon complex compliance functions is that the presence of any kind of saturant is indicated by the values of the parameters contained within the complex compliance function, the latter having the same mathematical form for all rocks under any conditions as long as it remains a crystalline solid.
QUANTITATIVE INTERPRETATION OF HORIZONTAL‐LOOP EM MEASUREMENTS USING A PERMEABLE SPHERE MODEL*
Authors: RAI S. S. , VERMA S. K.
Published: April 2006

Abstract

An interpretation scheme for horizontal‐loop EM measurements is presented for a permeable sphere model. The induced multipole moments are found to contribute significantly even at very low frequencies for a permeable conductor. The anomaly profiles are computed considering multipole excitation (up to 20) to study the effect of depth of burial and permeability of conductor. The anomaly half‐width along with the inphase and quadrature anomaly amplitudes allow direct interpretation of the parameters of the sphere. The above scheme is suitable for results of Dighem II (coplanar configuration), Slingram and Max Min II measurements.
COMPARISON OF FIVE LEAST‐SQUARES INVERSION TECHNIQUES IN RESISTIVITY SOUNDING*
Authors: HOVERSTEN G. M. , DEY A. , MORRISON H. F.
Published: April 2006

Abstract

A brief history of the development of the inverse problem in resistivity sounding is presented with the development of the equations governing the least‐squares inverse. Five algorithms for finding the minimum of the least‐square problem are described and their speed of convergence is compared on data from two planar earth models. Of the five algorithms studied, the ridge‐regression algorithm required the fewest numbers of forward problem evaluations to reach a desired minimum.

Solution space statistics, including (1) parameter‐standard errors, (2) parameter correlation coefficients, (3) model parameter eigenvectors, and (4) data eigenvectors are discussed. The type of weighting applied to the data affects these statistical parameters. Weighting the data by taking log10 of the observed and calculated values is comparable to weighting by the inverse of a constant data error. The most reliable parameter standard errors are obtained by weighting by the inverse of observed data errors. All other solution statistics, such as dataparameter eigenvector pairs, have more physical significance when inverse data error weighting is used.
A CONTRIBUTION TO THE INVESTIGATION OF AMPLITUDE CHARACTERISTICS OF VIBRATOR SIGNALS*
Authors: EDELMANN H. A. K.
Published: April 2006

Abstract

The characteristic and information content of a seismic signal depends considerably on the bandwidth of the signal. The Vibroseis system gives the possibility of selecting a certain frequency range. This selection is mostly done in the field by visual comparison, mainly taking into account the characteristic of the signal and the signal/noise ratio. A signal with a good characteristic has, in some cases, an arbitrary amplitude and phase characteristic which is not by itself optimum for the transmission of the desired stratigraphic information. The different factors which influence the amplitude characteristic of a Vibroseis signal are discussed. The present situation is illustrated by some results of measurements of vibrators in different areas. An outlook of how the characteristic of vibrators may be improved is given.
COMBINED SWEEP SIGNALS FOR CORRELATION NOISE SUPPRESSION*
Authors: EDELMANN H. A. K. , WERNER H.
Published: April 2006

Abstract

Comparison of both synthetic and field data shows that considerable suppression of correlation noise can be achieved with the Combisweep technique and with the Encoded Sweep Technique. In the first technique, the spectrum is shaped by superposition of linear sweeps with different frequency range; in the second technique, short sweeps of different polarity are combined to form the “alphabet” of a code.
OFFSET CONTINUATION FOR SEISMIC STACKING*
Authors: SALVADOR L. , SAVELLI S.
Published: April 2006

Abstract

Wave equation migration techniques have shown the limits of traditional stacking methods with data from tectonically complicated areas. An improved stack can be obtained utilizing the dip‐moveout correction technique based on offset continuation. The properties and the limits of the algorithms used are summarized briefly.

Several synthetic and real data examples are shown and compared with the results obtained using conventional processing in order to show the focusing effects and the strong improvement in signal‐to‐noise ratios, both at the stacked and migrated section level. The possibility of exploiting this technique to transform multiple coverage into increased spatial resolution is illustrated with examples.
USE OF THE SEISMIC DYNAMIC DECONVOLUTION ALGORITHM IN DIRECT RESISTIVITY INTERPRETATION*
Authors: SZARANIEC E.
Published: April 2006

Abstract

Seismic dynamic deconvolution is the mathematical basis on which a degree of unification in different prospecting methods is possible, relative to the parameter identification in horizontally stratified media. There is a basic structure which has some immediate applications to the inversion of resistivity data and possibly to other problems. For resistivity soundings there exists a key equation which is parallel to the energy conservation law in the theory of synthetic seismograms.
MAGNETOTELLURIC RESPONSE ON VERTICALLY INHOMOGENEOUS EARTH HAVING CONDUCTIVITY VARYING LINEARLY WITH DEPTH*
Authors: KAO D.
Published: April 2006

Abstract

Magnetotelluric response is studied for an inhomogeneous medium having conductivity varying linearly with depth as σ(z) =σ1+αz. For a medium having conductivity increasing linearly with depth, the phase of the impedance approaches 60° at long periods and the apparent resistivity becomes log (ρa) = 2 log (1.36/α1/3) — 1/3 log (T'). The asymptote of log (ρa, T'→∞) when plotted against log (T') has a constant gradient —1/3 and has an intercept on the log (T') axis, which equals 6 log (1.36/α1/3). When a homogeneous layer with a moderate thickness overlies an inhomogeneous half‐space, this layer does not affect the asymptote, but it affects the cut‐off period and pushes this toward the long period direction. For a medium having conductivity decreasing linearly with depth, the impedance is equivalent to that of a Cagniard two‐layer model; the intercept period related to the thickness is T'0=σ1(h2/2)2. Homogeneous multilayer approximations to an inhomogeneous layer are also investigated, and it is shown that the fit to the model variation depends on the number of layers and the layer parameters chosen.
A NUMERICAL METHOD TO COMPUTE THE RESISTIVITY TRANSFORM FROM WENNER SOUNDING DATA*
Authors: KUMAR RAKESH , CHOWDARY M. V. RAMANAIAH
Published: April 2006

Abstract

A numerical technique to compute the resistivity transform directly from the observed Wenner sounding data has been developed. In principle, the procedure is based on a decomposition method and consists of two steps: the first step determines a function that approximates the apparent resistivity data and the second step transforms this function into the corresponding kernel by an analytical operation. The proposed method is tested on some theoretical master curves. A high degree of precision is achieved with very little computer time. The applicability is shown on two field examples.
EFFICIENT 3‐D MIGRATION IN TWO STEPS*
Authors: GIBSON B. , LARNER K. , LEVIN S.
Published: April 2006

Abstract

The addition of a third dimension to seismic data acquisition offers significant improvement of our reflection images of geologic structures, but potentially at a substantial increase in data processing cost. Here we study an approach to migration of three‐dimensional (3‐D) stacked data that can considerably reduce the burden of computation and data manipulation. Cascading two‐dimensional (2‐D) migrations in orthogonal lateral directions, we obtain an efficient 3‐D scheme that is exact for homogeneous media. As applied to examples of synthetic data from inhomogeneous media, the scheme introduces errors well below those attributable, in practice, to uncertainties in migration velocity. Application of this two‐step approach, using both Kirchhoff‐summation and finite‐difference algorithms, to a 3‐D seismic land survey over an area of known hydrocarbon traps additionally proves the importance of 3‐D migration in stratigraphic imaging.
A SIMPLE EXACT METHOD OF 3‐D MIGRATION—THEORY*
Authors: JAKUBOWICZ H. , LEVIN S.
Published: April 2006

Abstract

Recently, a heuristic and empirical analysis of a method of three‐dimensional (3‐D) migration has been presented by Gibson, Larner, and Levin. It consists of sets of two‐dimensional (2‐D) migrations in orthogonal directions. In this paper, we examine this two‐pass method using scalar wave theory and show its action to be identical to that of so‐called full 3‐D migration for constant‐velocity media. The demonstration of equivalence is carried out in both the frequency‐space and frequency‐wavenumber domains, the latter providing a particularly transparent view of the mechanism of the two‐pass approach. We then extend our analysis to consider how various approximate algorithms used in practical implementations affect the validity of our conclusion.
SIGNATURES FROM SINGLE AIRGUNS*
Authors: VAAGE S. , HAUGLAND K. , UTHEIM T.
Published: April 2006

Abstract

The far‐field signatures from a comprehensive and systematic airgun pulse test have been analyzed. Empirical relations between the characteristic signature parameters and depth (5–12 m), pressure (100–137 bar = 10–13.7 MPa) and total chamber volume (0.65–9.5 l) have been derived. Also, the influence of using waveshape kits in different positions within the chamber has been tested.

The results indicate that:

 The amplitude is proportional to chamber pressure to the power 3/4.

 The bubble period is nearly independent of the position of the waveshape plate.

 The increase in primary/bubble amplitude ratio is inversely proportional to the chamber volume above the waveshape plate.

 The amplitude is independent of airgun depth.

Suggestions and comments regarding this work from Dr B. Ursin and Dr A. Ziolkowski are appreciated. The field work was supported by the Norwegian Petroleum Directorate through the Continental Shelf Project at the Seismological Observatory, University of Bergen.

An airgun allowing for continuous variation of the chamber volumes was supplied by GECO (Geophysical Company of Norway). The purchase of two airguns was financed by Norske Getty Exploration A/S.
ON THE APPLICATION OF INVERSE THEORY TO GRAVITY INTERPRETATION*
Authors: CHAVEZ R. E. , GARLAND G. D.
Published: April 2006

Abstract

Numerical investigations have been carried out on suitable interpretation schemes for gravity, based upon Backus‐Gilbert inverse theory. A two‐dimensional linear model consisting of horizontal prisms (grid shape) has been adopted for interpretation of gravity profiles. An inversion technique, which uses a linear approach suitable for rapid computation, and studies with synthetic bodies have led to improvements in the method, mainly by applying weighting factors, which improve the solution in the final stages of computational work. Gravity data from the well‐known Cyprus island positive anomaly were inverted to demonstrate the feasibility of the method.
REMOTE‐REFERENCE MAGNETOTELLURICS: EQUIPMENT AND PROCEDURES*
Authors: CLARKE J. , GAMBLE T. D. , GOUBAU W. M. , KOCH R. H. , MIRACKY R. F.
Published: April 2006

Abstract

During the past 3 years, major advances in the magnetotelluric technique have improved the quality of magnetotelluric data to the point where random errors in the impedance tensor and tipper are generally smaller than the uncertainty in their interpretation. The major factor in this improvement has been the introduction of the remote‐reference technique, although the use of ultrasensitive magnetometers and minicomputers for in‐field data processing has also been important. After a review of the remote‐reference technique, this paper describes the equipment and procedures used for remote‐reference magnetotellurics by the authors. Magnetometers using d.c. Superconducting Quantum Interference Devices typically have a sensitivity of 10−14 T Hz−1/2, a dynamic range of 107 in a 1 Hz bandwidth, and a slewing rate of 3 × 10−5.T s−1 at 10 kHz. The electric field measurements use conventional Cu‐CuSO4 electrodes. The remote magnetic reference signals are transmitted to the base station using FM analog telemetry. The data are collected and processed by a minicomputer based on an LSI‐11 microprocessor; the essential results—for example, the apparent resistivities and the tipper components, with their probable errors—are available in the field. Practical details are given of the handling of superconducting devices, low temperature cryostats and liquid helium in the field. Various spurious noise sources are mentioned, and techniques for minimizing their effects are described.
TEST RESULTS OF A NEW TYPE OF EFFICIENT SMALL AIRGUN ARRAY*
Authors: SAFAR M. H.
Published: April 2006

Abstract

Recently the author developed and demonstrated (Safar 1980) an efficient method for operating the airgun. The method involves the generation of a short seismic pulse from the pressure bubble pulses radiated by an airgun when fired several times at the same optimum depth but with different chamber pressures.

The purpose of this paper is to present and discuss the test results obtained when implementing the same method using a two‐dimensional airgun array. The array consists of seven 0.65 liter airguns fired simultaneously at the same depth but with different chamber pressures.

It is shown that the far‐field pressure pulse radiated by the seven 0.65 liter airgun array is similar to that radiated by the Flexichoc seismic source. It is concluded that the proposed airgun array can be used as a subarray to form an extremely powerful super‐long array suitable for deep seismic exploration.

The author would like to thank the Chairman and Board of Directors of the British Petroleum Co. Ltd for permission to publish this paper. Thanks are also due to Mike Symes and Lovell Cox for carrying out the field tests and Seismograph Service (England) Ltd for providing the airguns.
RADIATION AND RECEIVER PATTERN OF SHEAR AND COMPRESSIONAL WAVES AS A FUNCTION OF POISSON'S RATIO*
Authors: KÄHLER S. , MEISSNER R.
Published: April 2006

Abstract

Shear (= S) wave studies in addition to compressional (= P) wave surveys have revealed that S‐wave velocities are much more variable than P‐wave velocities. This strongly affects Poisson's ratio σ, especially in young sediments. It is shown that σ has a great influence on the directivity pattern, i.e., on the radiation and receiving characteristic of horizontal sources and receivers. For their calculation, well‐known surface boundary conditions and White's statement of the reciprocity relation (White 1965) are used. They also form the basis for the combination of source and receiver patterns essential for practical field work. The various combinations of horizontally and vertically arranged sources and receivers are investigated with regard to their directivity pattern, their amplitude ratio and, in general, to their usefulness in seismic prospecting.
THEORETICAL AND EXPERIMENTAL APPROACHES TO THE GEOPHONE SPURIOUS FREQUENCY*
Authors: CHEN SHI JUNG , DALTON CH.
Published: April 2006

Abstract

The geophone spurious frequency is modeled as the resonance of the planar motion of a spider spring carrying a moving mass. An analytic solution is found using the Castigliano method by assuming that the spring arm is a single‐mode vibrating cantilever beam. The spring shape is found from this analysis. When the typical spring has a circumferentially varying cross‐section, the Castigliano method is no longer applicable. A dimensional analysis is used as an approximate method for general design. Based on the theoretical result, a rotational fixture and a translational fixture were designed for experimental purposes. A low‐noise fixture and a phase‐averaging technique provide the amplitude and spurious resonance in the frequency domain. Finally, a test is run by using a rotational fixture to compare with the approximate method of spurious frequency prediction. Very good agreement between prediction and experiment is found.
AUTOMATIC THREE‐LAYER, THREE‐DIMENSIONAL DECONVOLUTION OF THE PAYS DE BRAY ANTICLINE*
Authors: ALESSANDRELLO E. , BICHARA M. , LAKSHMANAN J.
Published: April 2006

Abstract

Gravity data have been transformed into a three‐layer, three‐dimensional model by using an automatic procedure based on linear filtering. The Bouguer anomaly is first transformed by linear filtering into density variations located between two planes 1100 and 2500 m deep. These densities are then transformed into thicknesses with a constant density contrast of 0.4 g/cm3 with two geological constraints for the second and third interface:

—minimum at 2500 m depth;

—maximum below a variable limit given by geology.

This gives the contact between the second and third layer. Differences between measured and computed gravity are then applied by a similar procedure to a layer located between depths of 0 and 500 m, giving the contact between the first and second layer. Interesting secondary anticlines and transverse faults are shown by various structural maps.
A BOREHOLE MAGNETOMETRIC RESISTIVITY EXPERIMENT*
Authors: ACOSTA J. E. , WORTHINGTON M. H.
Published: April 2006

Abstract

A borehole magnetometric resistivity (MMR) experiment is described in which an attempt is made to determine the extent and orientation of zones of fissuring within an otherwise massive sequence of carboniferous limestone. The region under investigation lies beneath a landfill site and the main parameter of interest is the direction of flow of ground water, which will be influenced by the orientation of the faults or fissures within the rock. The MMR method possesses some extremely advantageous features for application to hydro‐geological problems of this kind. The method is sensitive to electrical current channelling within an otherwise relatively resistive medium, and the detection of the magnetic field within the borehole does not depend upon electrical contact of the receiver with the ground. Consequently, the method can be used in dry or plastic‐cased boreholes. A direction of maximum electrical current flow is deduced from the MMR data which coincides with the predominant direction of jointing within the region.

We are most grateful to the Water Research Centre, Medmenham, Berkshire, for supporting this research and particularly to Dr M. Fleet and Mr K. Beesley for their help and advice.
TUTORIAL: RESEARCH, APPLICATIONS, AND PUBLICATIONS IN ELECTRICAL AND ELECTROMAGNETIC METHODS*
Authors: PALACKY G. J.
Published: April 2006

Abstract

How do papers on electrical and electromagnetic methods published in Geophysics and Geophysical Prospecting reflect the actual field application of the various techniques? Our study based on 10 volumes of the journals (1973–1982) suggests a rather good agreement. EM techniques are the most important both in the field and in print. However, an imbalance was detected in the subject matter. Too many published papers deal with theory, and too few with new instrumentation and techniques, case histories, and physical properties of rocks. Papers presented at annual meetings of the EAEG and SEG give a more even‐handed and accurate view of geophysical activities. Unfortunately, many of our colleagues around the world are not able to attend the annual meetings regularly and depend on journals for their information. Practicing and research geophysicists should submit more papers on subjects that at present are not adequately covered.
GEOELECTRICAL MODEL CALCULATIONS FOR TWO‐DIMENSIONAL RESISTIVITY DISTRIBUTIONS*
Authors: MUNDRY E.
Published: April 2006

Abstract

For the calculation of geoelectrical model curves for a two‐dimensional resistivity distribution, the potential equation is transformed by means of a Fourier cosine transform into a two‐dimensional Helmholtz equation containing the separation parameter λ.

The numerical solution of this equation for different values of λ for an irregular grid is obtained using the method of finite differences combined with the method of overrelaxation. The method by which derivatives are replaced by finite differences turned out to be very important, especially for high resistivity contrasts. After testing several methods designed to deal with any type of resistivity distribution, a method of discretization similar to that used by Brewitt—Taylor and Weaver (1976) for magnetotelluric modeling for H polarization was found the best.

Examples are given of model curves for Schlumberger soundings over a vertical fault covered by overburden. The incorrect use of horizontal‐layer models leads to erroneous interpretations that are more complex than the real subsurface situations.
ON THE POSSIBILITY OF SEISMIC EXPLORATION USING SURFACE TORQUE SOURCE AND RELATED TOPICS*
Authors: KUHN M. , DRACH V.
Published: April 2006

Abstract

In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer.

In order to evaluate the closed‐form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray‐tracing techniques.

It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high‐velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields.

In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples.

Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis.

The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company.
L'EGALISATION SPECTRALE: UN MOYEN D'AMELIORER LA QUALITE DES DONNEES SISMIQUES*
Authors: COPPENS F. , MARI J. L.
Published: April 2006

Abstract

In land seismic surveys spectrum equalization can increase the quality of seismic data in a selected frequency band. The power of lower frequencies in the spectrum of input traces is generally greater than that of higher frequencies, particularly in land seismic surveys because of ground roll. In order to improve the quality of seismic data it is necessary to raise the energy of higher frequencies to the same level as that of lower frequencies, without alteration of the phases.

The first step of the method is to compute the amplitude spectrum of each input trace to determine a weighting function which is then applied to the amplitude spectrum in order to balance it. The function is the inverse of the short wavelength variation of the amplitude spectrum. The short wavelength variation can be obtained by interpolation between average values of the modulus of the amplitude spectrum computed in narrow bands within a selected band of frequencies. Another way of obtaining the short wavelength variation is to apply a low‐pass filter to the amplitude spectrum. The calculations are readily performed in the frequency domain by the Fourier transform.

Spectrum equalization is automatically adjusted to each trace and does not modify the average amplitude in the time domain. However, as the frequency band and energy of the ground roll both vary according to the distance from the shot, spectrum equalization tends to make the spectrum of output traces independent of the offset distance.

The use of spectrum equalization before any two‐dimensional filtering improves ground roll elimination. Continuity and resolution of horizons are also increased by spectrum equalization before CDP stack.

Several examples of applications of spectrum equalization to seismic land and marine surveys are shown.
ELECTRICAL POTENTIAL DUE TO A POINT CURRENT SOURCE OVER AN INHOMOGENEOUS ANISOTROPIC EARTH*
Authors: PAL BARUN PROSAD , DASGUPTA S. P.
Published: April 2006

Abstract

A mathematical expression for potential of a direct current point source in an inhomoge‐neous anisotropic earth is derived. The coefficient of anisotropy is given by f= (σr/σz), where σr and σz are the conductivities parallel and perpendicular to the bedding plane. It is assumed that σz varies with depth, whereas σr varies transversely. This potential may be useful in interpretation of geoelectrical data in specified geological situations. Master curves for Wenner and Schlumberger configurations are presented
THE CROSS‐HOLE MAGNETOMETRIC RESISTIVITY (MMR) RESPONSE OF A DISC CONDUCTOR*
Authors: EDWARDS R. N.
Published: April 2006

Abstract

The cross‐hole variant of the magnetometric resistivity (MMR) method requires two bore holes in the vicinity of a conductive target. In the first, two fixed current electrodes are located, one above the other. They are linked to a low frequency current source by cables, the whole system forming a vertical current bipole. In the second, a sensitive coil measures the axial magnetic field as a function of depth. For a uniform earth, if both holes are vertical, the measured component vanishes by symmetry. However, the presence of a local conductor channels the current and causes an anomalous magnetic component which is interpreted to indicate the position, shape and relative conductance of the target.

Mineral deposits are often lamellar in form. The conductive disc is the simplest bounded lamella for which MMR responses may be computed. It is excited by a single current source on its axis. The second source and the surface of the earth are assumed to be far away, a valid assumption for down‐hole measurements.

The numerical method introduces a new integral equation describing the interaction of current dipoles located in the plane of the disc. The equation is solved analytically for a disc of infinite radius, a layer, and the result is compared with a corresponding known boundary value solution.

The computed radial current in the disc and the magnetic field generated by it are described in terms of a current channelling number. The magnitude of the computed field is of the order of one nanoTesla for a typical mining problem.
LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*
Authors: TARANTOLA A.
Published: April 2006

Abstract

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form
image
. The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).
VELOCITY ANALYSIS IN THE p—x‐PLANE FROM A SLANT STACK WAVEFIELD*
Authors: TANG R. , CARSWELL A. , MOON WOOIL
Published: April 2006

Abstract

Classical methods of interpretation of reflection seismic data are such that interpretation and processing usually occur in the “collected” frame of reference. However, in recent times other data planes have gained increasing acceptance in seismology as a viable alternative. Through linear transformations applied to a record section, both the t—p‐ and p—x‐planes can be produced. The r—p‐domain may be obtained from the t—x‐plane by a transformation known as slant stacking. Normal practice has been to do most of the data processing in the t—x‐plane and then transforming to the r—p‐plane. However, many of the procedures used in the t—x‐domain can be modified for use in the t—p‐plane to increase the coherence.

Velocity inversion may be carried out either in the r—p‐domain or further transformed to the p—x‐plane where the modified Herglotz‐Wiechert inversion may be applied. To perform the inversion, the t—p‐wavefield is converted to a p—x‐representation by the use of a new linear transformation technique, the cross‐stack. By a simple sampling process along a particular p—x‐trajectory, the Herglotz‐Wiechert method can be used to reconstruct an acceptable velocity model of the subsurface. A comparison of derived velocity structures is made between that produced by the Herglotz‐Wiechert technique and that of the Dix method.
A NUMERICAL DIRECT INTERPRETATION METHOD OF RESISTIVITY SOUNDINGS USING THE PEKERIS MODEL*
Authors: BASOKUR A. T.
Published: April 2006

Abstract

A numerical method is presented for direct interpretation of resistivity sounding measurements. The early part of the resistivity transform curve derived from field observations by standard methods is approximated by a two‐layer curve. The resistivity of the first layer is determined from the arithmetic mean of the successive computations which are carried on each of three successive discrete values of the resistivity transform curve. Using this mean value of the resistivity, the thickness of the first layer is computed from the sample values in pairs of the resistivity transform curve. After these determinations, the top layer is removed by Pekeris's reduction equation. The parameters of the second layer are obtained from the discrete values of the reduced transform curve (which corresponds to the second part of the resistivity transform curve) by the same procedure as described for the first layer.

The same computational scheme is repeated until the parameters of all intermediate layers are obtained. The resistivity of the substratum is determined from the reduction equation.
ON THE DETERMINATION OF THE DOWNGOING P‐WAVES RADIATED BY THE VERTICAL SEISMIC VIBRATOR*
Authors: SAFAR M. H.
Published: April 2006

Abstract

It is well recognized that in order to realize the full potential of the Vibroseis technique, one needs to ensure accurate phase locking and a meaningful cross‐correlation. To achieve these two important objectives we require an accurate estimate of the compressional stress wave radiated by the vibrator into the ground.

In this paper a simple method (subject of a patent application) is developed for predicting the compressional stress waves radiated by a vertical vibrator. The main feature of the proposed method is that it involves the field measurement of the acceleration of the reaction mass and the baseplate, respectively.

The method is illustrated by computing the compressional stress waves generated by a typical vertical vibrator radiating into ice, chalk, sand, and mud. It is shown that for a seismic vibrator radiating into hard ground the pressure of the downgoing P‐wave is 180° out of phase with the baseplate velocity. It is also shown that when the driving force of the seismic vibrator has a flat amplitude spectrum, the amplitude spectrum of the downgoing P‐wave falls off by 6 dB/octave towards low frequencies.
INFLUENCE OF AMPLITUDE AND PHASE ERRORS ON MIGRATION RESULTS*
Authors: VAN DER WAL L. F. , BERKHOUT A. J.
Published: April 2006

Abstract

Random amplitude and phase errors in seismic input data introduce a coherent distribution of migration half‐circles or “smiles”, the occurrence of which may cause a significant decrease of signal‐to‐noise ratio. In addition, the effect of quantization errors is discussed for different wordlengths, used both during acquisition and during data processing. Results of sign‐bit recordings are shown.
INTERVAL VELOCITY ANALYSIS BY WAVE EXTRAPOLATION*
Authors: GAZDAG J. , SGUAZZERO P.
Published: April 2006

Abstract

A method for interval velocity analysis is formulated on the basis of wavefield extrapolation, i.e., on the basis of wave‐equation migration. When this scheme is applied to multioffset seismic sections or to an ensemble of CMP gathers, it allows for the proper treatment of dipping events. The underlying assumptions are that local velocities should be derived from data associated with events within the interval under consideration. To minimize the effect of the region above the layer of interest, the data are first extrapolated to the top of the analysis interval. Subsequent analysis of these data then pertains to the events within this interval. Velocity estimation consists of repeated wavefield extrapolations through the analysis interval using a set of trial velocities. The optimal velocity is chosen on the basis of coherency measures designed to express the collective phase agreement among a set of offset Fourier modes. The reliability of this approach to interval velocity estimation is demonstrated on synthetic multi‐offset data.
THE EFFECT OF A SUPERPARAMAGNETIC LAYER ON THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A GROUND*
Authors: LEE T.
Published: April 2006

Abstract

A thin superparamagnetic layer on the earth's surface greatly affects the transient electromagnetic response of a conducting ground. The effect of the layer is most evident for singleloop transient electromagnetic data where transient voltages decay as 1/t. Even when a separate transmitter and receiver are used, the effect of the superparamagnetic layer is still pronounced. In this case the effect of the 1/t term in the equation is much less. More dominant now is a 1/t2 term. The effect of the superparamagnetism can readily be seen in the analytical expressions for the apparent resistivities. If the presence of the superparamagnetic layer is not recognized, then the apparent resistivities decrease with time rather than approach the true value of the host rock.
TUTORIAL MINIMUM PHASE FOR CONTINUOUS TIME AND DISCRETE TIME FUNCTIONS*
Authors: EISNER E.
Published: April 2006

Abstract

The concept of minimum phase is clarified for geophysicists by collecting in one place the properties of minimum phase functions. The “earliest energy arrival” property in the time domain, the “minimum phase‐slope property” in the frequency domain, and of the role of causal all‐pass filters are demonstrated. The emphasis is placed on keeping the mathematics within the realm familiar to geophysicists and on making clear the somewhat imperfect match between physical continuous time functions and their associated discrete time representations.
RESISTIVITY AND MAGNETIC SURVEYS IN GROUNDWATER PROSPECTING IN VOLCANIC AREAS—CASE HISTORY MAAR OF BEAUNIT, PUY DE DOME, FRANCE*
Authors: AUBERT M. , CAMUS G. , FOURNIER C.
Published: April 2006

Abstract

Volcanic maar structures sometimes contain important groundwater reserves. The volcanic formations of the Beaunit maar have a much higher magnetization than their granite substrata. The structure of the maar and its volcanoclastic infill can therefore be defined by magnetic surveying and resistivity soundings. Resistivities of the geological formations present in the Beaunit maar are comparable to those recorded in other volcanic systems. The geophysical data, confirmed by drilling tests, contain useful information on the hydrogeological regime of the volcanic system under investigation.
VSP INTERVAL VELOCITIES FROM TRAVELTIME INVERSION*
Authors: STEWART R. R.
Published: April 2006

Abstract

A principal use of the vertical seismic profile (VSP) is to determine the variation of seismic velocity with depth. Presented here is a discussion of the errors involved with the time picks of a VSP survey and several methods currently used to calculate a velocity section from these time picks. Another technique is proposed, based on the least‐squares inversion of the traveltimes, to arrive at a better estimate and statistical description of the velocity section. This technique uses the Levenberg‐Marquardt damped least‐squares formulation and ray tracing through a horizontally‐layered medium to iteratively refine the velocity section. The accuracy and robustness of the procedure are investigated by inverting noisy traveltime curves and comparing these results to the original model velocity section. Agreement is found to be good. One interesting feature of the inverse procedure is that, for certain geometries, it can resolve a few velocity layers, even though there are no measurements made inside those layers. Three actual VSP surveys are analyzed and compared to their corresponding sonic logs. In two of the surveys, it appears that there is some velocity dispersion. Velocity changes associated with gas saturation are evident on one of the surveys.
IN‐SEAM SEISMIC LOVE WAVE SCATTERING MODELED BY THE FINITE ELEMENT METHOD*
Authors: ASTEN M. W. , DRAKE L. A. , EDWARDS S.
Published: April 2006

Abstract

The dynamic finite‐element method allows frequency‐dependent reflection and transmission coefficients to be computed for Love waves scattered by two‐dimensional inhomogeneities in coal seams.

Clean faults of zero hade angle show a throw‐dependent cross‐over frequency in reflection spectra, and throw‐dependent conversion from fundamental to first higher mode energy in transmission spectra. Oblique faults show mode conversion in reflection spectra which is relatable to the fault hade angle by simple Huygens‐theory models. Thin fracture zones or dykes normal to the seam show a reflection maximum when thickness of the zone is of order one quarter of the seam wave wavelength.

Published field data from two known faults and a dyke are compared with the modeling results and support the belief that broad‐band seam‐wave data are capable of characterizing a seam discontinuity (throw, hade angle, dyke thickness) as well as locating it. Development of such procedures will require extensions to existing field practice and processing.

This research was funded in part by the National Energy Research Development and Demonstration Council of Australia. The authors thank The Broken Hill Proprietary Company Limited for permission to quote from company case histories.
PRACTICAL ASPECTS OF THE DETERMINATION OF 3‐D STACKING VELOCITIES*
Authors: LEHMANN H. J. , HOUBA W.
Published: April 2006

Proper stacking of three‐dimensional seismic CDP‐data generally requires the knowledge of normal moveout velocities in all source‐receiver directions contributing to a CDP‐gather. The azimuthal variation of the stacking velocities mainly depends on the dip of the seismic interfaces. For a single dipping plane a simple relation exists between the dip and the azimuthal variation of NMO‐velocity. Varying strike and dip of subsequent reflectors, however, result in a complex dependency of the seismic parameters.

Reliable information on the spatial distribution of the normal moveout (NMO)‐velocity can be derived from a wavefront curvature estimation using a 3‐D ray‐tracing technique. These procedures require additional information, e.g. reflection time gradients or depth maps to show interval velocities between leading interfaces. Moreover, their application to an extended 3‐D data volume is restricted by high costs.

The need for a routine 3‐D procedure resulted in a special data selection to create pseudo 2‐D profiles and to apply existing velocity estimation routines to these profiles. At least three estimates in different directions are necessary to derive the full azimuthal velocity variation, characterized by the large and the small main axis and the orientation of the velocity ellipse.

Errors are estimated by means of computer models. Stacking velocities obtained by mathematical routines (least‐squares fit) and by seismic standard routines (NMO‐correction and correlation) are compared.

Finally, a general 3‐D velocity procedure using cross‐correlation of preliminarily NMO‐corrected traces is proposed.
COMPUTATION OF ZERO‐OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION*
Authors: URSIN B. , ARNTSEN B.
Published: April 2006

Synthetic vertical seismic profiles (VSP) provide a useful tool in the interpretation of VSP data, allowing the interpreter to analyze the propagation of seismic waves in the different layers. A zero‐offset VSP modeling program can also be used as part of an inversion program for estimating the parameters in a layered model of the subsurface.

Proposed methods for computing synthetic VSP are mostly based on plane waves in a horizontally layered elastic or anelastic medium. In order to compare these synthetic VSP with real data a common method is to scale the data with the spherical spreading factor of the primary reflections. This will in most cases lead to artificial enhancement of multiple reflections.

We apply the ray series method to the equations of motion for a linear viscoelastic medium after having done a Fourier transformation with respect to the time variable. This results in a complex eikonal equation which, in general, appears to be difficult to solve. For vertically traveling waves in a horizontally layered viscoelastic medium the solution is easily found to be the integral along the ray of the inverse of the complex propagation velocity. The spherical spreading due to a point source is also complex, and it is equal to the integral along the ray of the complex propagation velocity.

Synthetic data examples illustrate the differences between spherical, cylindrical, and plane waves in elastic and viscoelastic layered media.