bluuebunny/crossref_metadata_2025 huggingface dataset:
TUTORIAL DISTRIBUTION OF ALTERNATING ELECTRICAL CHARGES IN A CONDUCTING MEDIUM*
Authors: KAUFMAN A. A.
Published: April 2006

The main features of the distribution of volume and surface charges in a conducting medium can be described separately for direct and alternating electromagnetic fields. The density of charges depends on the conductivity of a medium and on the electrical field. The relation is particularly simple for the quasi‐stationary field, i.e., when the influence of displacement currents is negligible. Conditions are formulated under which electrical charges arise in a conducting medium: electrical charges are shown to exist for direct and quasi‐stationary fields when there is a component of electric field parallel to the gradient of conductivity. The density of these charges is proportional to the applied electric field.
A NONITERATIVE PROCEDURE FOR INVERTING PLANE‐WAVE REFLECTION DATA AT SEVERAL ANGLES OF INCIDENCE USING THE RICCATI EQUATION*
Authors: BREGMAN N. D. , CHAPMAN C. H. , BAILEY R. C.
Published: April 2006

Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane‐wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately.

Rather than invert each plane‐wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane‐wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time‐domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.
STABILIZATION OF NORMAL‐INCIDENCE SEISMOGRAM INVERSION REMOVING THE NOISE‐INDUCED BIAS*
Authors: FERBER R.‐G.
Published: April 2006

A main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well‐known inversion schemes for normal‐incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half‐spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two‐stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson‐recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large).

In the non‐linear terms of dynamic deconvolution and Levinson‐recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson‐recursion, which are set to zero if they are not significantly different from noise.

The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum.
FORWARD MODELING IN THE FREQUENCY‐SPACE DOMAIN*
Authors: KELAMIS P. G. , KJARTANSSON E.
Published: April 2006

Forward modeling of zero‐offset data is performed in the frequency‐space domain using a one‐way extrapolation equation. The use of the frequency domain offers several advantages over conventional time domain methods. The greatest advantage of the frequency domain is that all time derivatives are evaluated exactly by a simple multiplication. Synthetic zero‐offset sections are computed with a high degree of accuracy for arbitrary velocity and reflectivity structures. Examples are shown for realistic complicated models and compared with results from physical modeling.
INVERSION FROM FINITE OFFSET DATA AND THE SIMULTANEOUS RECONSTRUCTION OF THE VELOCITY AND DENSITY PROFILES*
Authors: EIGES R. , RAZ S.
Published: April 2006

Recursive inversion algorithms are described which facilitate (a) a direct inversion of a one‐dimensional velocity distribution from finite offset data and (b) the related simultaneous reconstruction of a two‐parameter, say velocity‐density, medium. The suggested procedures are based on an extended format of the WKBJ‐Bremmer scattering model. The attained accuracy levels and the limitations are highlighted by computer simulations against synthetic data.
ON THE IMPROVEMENT IN PENETRATIO ACHIEVED BY USING EXTENDED MARINE SOURCE ARRAYS*
Authors: SAFAR M. H.
Published: April 2006

In dealing with the problem of large amplitude multiple reflections arising from a hard water‐bottom, it has been found that the use of extended source array techniques resulted in a considerably better penetration than that obtained using either computer simulated long arrays or the conventional air‐gun array systems. The purpose of this paper is to use the concept of the array directivity factor in discussing the reason for the improvement in penetration achieved by using extended marine source arrays.

Examples are given showing that the low frequency power radiated within the so called “penetration window” can be increased by a factor of two by choosing the correct spacing of the point sources forming the extended array. It is concluded that to ensure that most of the low frequency energy is concentrated within the penetration window to achieve deep penetration, a source array with spacing comparable with the wavelength is required.
A METHOD TO DETERMINE THE VELOCITIES OF THE SEAFLOOR AND NEAR‐SURFACE SEDIMENTS*
Authors: BERGE A. M. , BESKOW B.
Published: April 2006

Shotpoint gathers from conventional reflection seismic surveys contain both reflected and refracted waves. In this study shot records were processed and analyzed, and the data were modeled with reflected, refracted, and reflected‐refracted waves to fit the recorded data. The result is a detailed velocity model. The inverse problem for refracted waves was solved by using the Wiechert‐Herglotz inversion.

A 500‐km‐long 26‐fold reflection seismic line from the Barents Sea, north of Norway, has been investigated. The data show high velocities, multiple reflections, and various types of noise. To test the method a total of 34 shot gathers were analyzed along this line. The aim of the interpretation was to determine the velocity in the seafloor and the near‐surface sediments. It is possible to map the vertical as well as the lateral velocity distribution in detail. Depending on the length of the streamer and the velocity gradient in the sediments, the calculated depth varies between 300 and 500 m below the seafloor. These velocities were also compared to the stacking velocities obtained from the reflection seismic data to see how the velocities determined by different methods were related.

The velocity distribution in the sediments is one of the key factors in seismic interpretation. The technique discussed in this paper can contribute to velocity information both in the processing and interpretation of seismic data.
VERTICAL SEISMIC PROFILING IN COAL*
Authors: GREENHALGH S. A. , SUPRAJITNO M.
Published: April 2006

Abstract

The intellection of seismic wave propagation in coal measures demands direct observation of the wavefield progression. Two vertical seismic profiles with high spatial and temporal sampling, were recently recorded in the Sydney Basin coalfields as part of an experimental coal seismic program.

Static corrections and interval velocities were obtained by an automated system to determine first kicks and pulse rise times. Upgoing and downgoing waves were separated in the f—k‐plane using a novel technique of contour slice filtering. The isolated upgoing waves clearly display reflections from the major coal seams within the stratigraphic sequence. The downgoing wave spectra were subjected to attenuation analysis. The deduced specific quality factor Q for Permian coal measure rocks lies in the range 20–70. Similar estimates were obtained in the time domain from measurements of pulse broadening.

Synthetic VSP seismograms, computed using an exact recursive formulation, are an indispensable aid to interpretation. They illustrate the filtering effects of coal seams and sequences, and the effects of the contribution of internal and free‐surface multiple reflections in the recorded wavetrains.
ESTIMATION OF MARINE SOURCE SIGNATURES FROM DIRECT ARRIVALS TO HYDROPHONE GROUPS*
Authors: KRAVIS S. P.
Published: April 2006

Abstract

Deterministic deconvolution of seismic data recorded with a non‐minimum phase source, such as a sparker, requires an estimate of the source signature. Present methods of deterministic signature estimation and deconvolution require additional field equipment (near‐ or far‐field hydrophones), or else make a deterministic estimate of the effective source signature (the free‐field source signature convolved with source and receiver ghosts). By analyzing the direct arrival signal to normal hydrophone groups it is shown that extraction of the free‐field source signature from this signal is possible for a spherically symmetric source, and it is demonstrated that the use of this signature for a preliminary deterministic deconvolution gives better results on sparker data than minimum‐phase whitening deconvolution applied on its own. The applicability of the method to non‐spherically symmetric sources, such as arrays, is also discussed.

This paper is published with the permission of the Director, Bureau of Mineral Resources, Geology and Geophysics, Canberra, Australia.
INTERPRETATION AND DEPTH OF INVESTIGATION OF GRADIENT MEASUREMENTS IN DIRECT CURRENT GEOELECTRICS*
Authors: SCHULZ R.
Published: April 2006

Abstract

Gradient measurements in a homogeneous electrical primary field can easily be interpreted for simple models. The simplified solution (conducting or resistant body in a homogeneous space in a homogeneous electrical field) is often sufficiently accurate, as comparisons with the exact solution (body of finite resistivity in a homogeneous half‐space in a quasihomogeneous electrical field) show. The exact geometry of the body cannot be determined by gradient measurements; the same anomaly of apparent resistivity can be caused by different bodies. In particular, the similarity between a sphere and a cube of the same volume is very high.

There is a distinct influence of the resistivity of the overburden: the higher this resistivity is, the stronger is the effect caused by a buried body.

If a deviation of 10% of the apparent resistivity is assumed as the lower boundary at which a buried body can be detected by gradient measurements, the depth of investigation for a three‐dimensional body is approximately equal to its width; in the two‐dimensional case the thickness of the overburden can be twice the width. If the overburden has a resistivity which is higher than the resistivity of the substratum, these depths are greater. The greatest possible depth is approximately three times the width of the body.
SIGNAL‐TO‐NOISE RATIO ENHANCEMENT IN SEISMIC MULTIFOLD DATA USING BAYESIAN STATISTICS*
Authors: WALTHAM D.A. , BOYCE J.F.
Published: April 2006

Bayesian statistics are applied to the problem of signal‐to‐noise ratio enhancement from a common‐midpoint gather. By maximizing the a posteriori probability distribution of the gather with respect to the minimum‐offset trace and suppressing multiples via a semblance criterion, a statistically biased stack is formed with signal‐to‐noise ratio comparable to that of the usual stack while preserving the resolution and registration of the original noisy trace.

Application of the algorithm to real data reveals geologically significant features which are indistinct in the standard stacked section.
EXPERIMENTAL EVIDENCE OF S*‐WAVE*
Authors: KIM J.Y. , BEHRENS J.
Published: April 2006

During development of theoretical methods to compute synthetic seismograms, a new type of wave called S*‐wave was discovered by Hron and Mikhailenko. This wave propagates with the shear‐wave velocity and can be interpreted as a non‐geometrical wave arrival with large amplitudes strongly depending on the depth of a pure P‐point source.

In this first experimental verification of the existence of S*‐waves by means of two‐dimensional model‐seismics it is demonstrated that:

1. the S*‐wave exists and depends on the source distance from the free surface; 2. the S*‐wave is generated as an ordinary shear wave on the free surface at the point located directly above the P‐source, as illustrated in the synthetic seismograms. The measured seismograms agree remarkably well with the computed ones.
RESISTIVITY AND IP MODELING OF THE THREE‐ARRAY DOWN‐HOLE PROSPECTING TECHNIQUE*
Authors: BUSBY J.P. , DABEK Z.K.
Published: April 2006

The resistivity and induced polarization responses due to a number of IP targets for a down‐hole three‐array have been calculated numerically. The IP targets are approximated by triangle‐faceted polyhedra; number and size of the facets are limited by the numerical procedure. Despite this limitation a number of profiles have been obtained for a sphere, lens, prolate spheroid and thin dipping slab. The profiles obtained do not differentiate between the shapes of the IP targets, but depend upon the vertical extent of the target within the search‐radius of the borehole. The type curves produced could be of use for preliminary interpretation and in the field for planning the next stages of a geophysical survey.

The lateral and vertical search radii of the borehole are increased by the use of such an array. For the bodies used it is estimated that the search radii are extended by 2.0 dipole units.
IN‐LOOP PULSE EM RESPONSE OF A STRATIFIED EARTH*
Authors: RAI S. S. , SARMA G. S.
Published: April 2006

The in‐loop pulse electromagnetic response of a stratified earth has been expressed in terms of an apparent resistivity‐ time plot using the PEM response over a homogeneous half‐space which is typically unipolar with monotonic decay. This half‐space response characteristic provides a unique relationship between Crone PEM channel amplitude and the apparent half‐space resistivity. The possibility to resolve a thin intermediate conductive and resistive layer with the in‐loop PEM system has been investigated. The system is well in shallow geoelectric mapping.
INVERSION OF INDUCTION LOGGING MEASUREMENTS*
Authors: RAMM A.G.
Published: April 2006

Model problems of induction logging are considered. Some new inversion algorithms are given.
RESISTIVITY SOUNDING ON A HORIZONTALLY STRATIFIED MULTI‐LAYERED EARTH*
Authors: RAGHUWANSHI S.S. , SINGH BIJENDRA
Published: April 2006

The electrical potential due to a point source of current placed on the ground surface is studied for a multi‐layered earth consisting of homogeneous overburden of constant conductivity over a stack of transition layers where conductivity varies with depth according to power and exponential laws in even and odd layers, respectively. The general recursion relations are derived and are used to obtain expressions for the apparent resistivities for Schlumberger and Wenner electrode arrays. Their asymptotic behavior has been studied. The solutions for some particular cases are given: (i) odd layers with conductivities exponentially varying with depth while all even layers (and the first) have constant conductivities; (ii) even layer conductivities varying as a power law while odd number layers are of constant conductivity; and (iii) any two successive layers as transition layers and all others having constant conductivities. Further it is shown that Patella's theory is a particular case of the present study. It is concluded, therefore, that the present treatment is more general as all earlier models consisting of trasition layers can be derived from this study.
GEOELECTRIC AXIAL DIPOLE SOUNDING CURVES FOR A CLASS OF TWO‐DIMENSIONAL EARTH STRUCTURES*
Authors: PATELLA D. , TRAMACERE A.
Published: April 2006

With the aim of studying the behaviour of geoelectric axial dipole vertical soundings over complex geology, a systematic theoretical approach is presented for a class of earth structures characterized by horizontal and vertical parallel boundary planes. The two‐dimensional cylindrical bodies of infinite length and rectangular cross‐section are constrained to have resistivities satisfying Alfano's condition at every intersection line of the graticule, in order to adopt the image‐point theory. A detailed analysis is performed for models with any number of horizontal boundaries and two vertical discontinuities. The apparent resistivity formulas are obtained and selected apparent resistivity curves are drawn for different parameter combinations and various directions of the sounding expansion axis. The class under consideration contains as a particular case the HVC model elaborated in Alpin's monograph, where only a small collection of master curves is available for the axial array. The reconstruction of those curves by the present formulation shows the existence of large discrepancies. A test based on the transformation to equivalent half‐Schlumberger sounding curves supports the conclusion that an unidentified error must exist in some part of the theoretical approach of the Russian researchers. Finally, some field sounding curves based on geothermal and volcanological surveys are presented and interpreted by complete curve matching, essentially to show the applicability of the theoretical solutions.
THE ABEL‐FOURIER METHOD OF HANKEL TRANSFORMATION: APPLICATIONS TO SEISMIC DATA*
Authors: WILSON C.R.
Published: April 2006

Abstract

The formal equivalency between a Hankel transform and an Abel transform followed by a Fourier transform is used as a basis for the computation of synthetic seismograms and for performing plane‐wave decomposition of both synthetic and field seismograms. The Abel‐Fourier method performs better for near‐offset or small ray‐parameter, although at greater computational effort than calculations based upon the asymptotic Hankel transform.
THEORETICAL TRANSIENT EM RESPONSE CURVES OVER A THIN DIPPING DYKE IN FREE SPACE–SEPARATED INLINE LOOP CONFIGURATION*
Authors: OGILVY R.D.
Published: April 2006

Theoretically exact type curves are presented to show the effect on response shape of changing dip, strike, transmitter‐receiver separation, depth of burial and target conductance. Relatively small dip variations produce a marked asymmetry in response shape. For steeply dipping conductors, strike can be determined from the cross‐over width of the anomaly. The curves illustrate the dynamic character of the transient process, and suggest how the spatial disposition and quality of large sheet conductors might be inferred from the extent of peak‐amplitude displacement with time, and rate of eddy‐current diffusion. A generalized interpretation scheme is proposed based on dimensionless response characteristics which will facilitate the rapid determination of conductor dip, conductance and depth of burial for any time regime.
ON REVERSE‐TIME MIGRATION*
Authors: GAZDAG J. , CARRIZO E.
Published: April 2006

Migration is a process whereby events in ‘image space’ are mapped into their correct positions in ‘object space’. The wave equations associated with this mapping may be defined and solved numerically either in image space or in object space. In the former the CMP section, which represents the initial conditions, is extrapolated toward increasing depths, and the migrated data are recovered at zero time. In the latter, the wave‐field extrapolation takes place in the coordinate frame of the depth section, and the CMP data serve as boundary conditions at the surface. Computations begin at the last sample of the record section and continue ‘reverse time’ until time zero.

This paper describes a reverse‐time migration (RTM) method and compares its performance with that of an image‐space method based on the idea of phase shift plus interpolation (PSPI). Synthetic zero‐offset sections serve as examples for migration experiments with the RTM and PSPI methods. It is shown that the RTM approach to migration is rather expensive, but its robustness and accuracy are difficult to surpass.
ON THE POSSIBILITY OF THE TELLURIC METHOD: SOME RESULTS ON FAULTED STRUCTURES*
Authors: ILICETO V. , SANTARATO G.
Published: April 2006

The telluric method of geophysical investigation is re‐evaluated and several improvements are suggested. Besides the traditional Jacobian, several new parameters that bear information on the structure under investigation are proposed as sounding tools. These parameters are calculated for several two‐dimensional models and plotted as pseudo‐sections.

The model results, calculated over a wide frequency band (10‐4‐10‐2 Hz) suggest that these new parameters can give very detailed information about the subsurface structures.

By way of example, we present experimental results obtained along two profiles across familiar structures. The interpretation of the results leads to two‐dimensional models of the subsurface that are in good agreement with known geophysical and geological features of these two sections.
CONSIDERATIONS IN ESTIMATING THE MINIMUM‐PHASE PROPERTIES OF SAMPLED DATA*
Authors: ELLENDER S.A.
Published: April 2006

Analysis of the phase spectra from the signatures, impulse responses and other wavelets observed in seismic data leads to the construction of equivalent minimum‐phase functions. The accuracy of such computations using digitally sampled data is questioned with special reference to Texas Instruments DFS IV and DFS V recording filters. Results vary with the lengths and sample rates of the time functions, and further errors may be introduced when implementing the Hilbert transform. Such problems are related to poor resolution in the low amplitude areas of the spectrum. Techniques for correction are described. With appropriate shaping a reasonably accurate phase spectrum may be computed for the minimum‐phase function. The generation of minimum‐phase wavelets within the processing sequence is briefly discussed.
COMPLETE INVERSION OF ZERO‐OFFSET SEISMIC DATA*
Authors: URSIN B.
Published: April 2006

The one‐dimensional seismic inverse problem consists of recovering the acoustic impedance (or reflectivity function) as a function of traveltime from the reflection response of a horizontally layered medium excited by a plane‐wave impulsive source. Most seismic sources behave like point sources, and the data must be corrected for geometrical spreading before the inversion procedure is applied. This correction is usually not exact because the geometrical spreading is different for primary and multiple reflections.

An improved algorithm is proposed which takes the geometrical spreading from a point source into account. The zero‐offset reflection response from a stack of homogeneous layers of variable thickness is used to compute the thickness, velocity and density of each layer. This is possible because the geometrical spreading contains additional information about the velocities.
RESISTIVITY AND INDUCED POLARIZATION RESPONSES OF ARBITRARILY SHAPED 3‐D BODIES IN A TWO‐LAYERED EARTH*
Authors: DAS U.C. , PARASNIS D.S.
Published: April 2006

Numerical computations using the integral equation method are presented for resistivity and IP responses due to arbitrarily shaped 3‐dimensional bodies in a layered earth. The unknown surface charge density distribution is expressed as the solution of Fredholm's integral equation of the second kind. Use of moment method (with pulse basis function and point‐collocation) yields the matrix equations for the unknowns. The contributions to Green's function are solved (a) analytically for the primary and (b) by convolution for the secondary contributions resulting in a fast algorithm. The further step of computing potential, apparent resistivity, chargeability etc., for any electrode system, is straightforward. Our results show a good agreement with those from finite difference methods and physical tank experiments. The CPU time is only 138 s on a super‐minicomputer for an apparent resistivity pseudo‐section, even with 96 elementary cells as used for discretization. A large number of models for different geological situations were studied; some are presented here.
FREQUENCY ELECTROMAGNETIC SOUNDING USING A VERTICAL MAGNETIC DIPOLE*
Authors: MUNDRY E. , BLOHM E.‐K.
Published: April 2006

A horizontal transmitter loop (vertical magnetic dipole) is used for frequency electromagnetic (FEM) soundings. The frequency ranges from approximately 6 Hz to about 4000 Hz. The vertical and radial magnetic field components are measured for 20 frequencies per decade several hundred meters from the transmitter loop. A very small bandwidth is selected for amplification using a reference signal. An Apple computer is used for data acquisition.

A computer program for Marquardt inversion optimizes the parameters for the n‐layer case: the resistivities and thicknesses of individual beds and a correction factor for the primary magnetic field. Interpretation of each component individually yields practically the same parameters. Examples from the field are given with interpretation; comparison with dc resistivity measurements is provided.

The ratio of vertical/radial magnetic field components vs. frequency can be transformed simply into apparent resistivity vs. apparent depth. This can be done in the field to obtain an estimation of the depth of the layer boundaries. FEM results are compared with Schlumberger d.c. sounding obtained at the same site.
THE GENERALIZED SPECTRAL FUNCTION OF A PLANE LAYERED MEDIUM*
Authors: FERBER R.‐G.
Published: April 2006

The spectral function of a plane layered medium, which represents the net downgoing energy in the first layer due to a normally incident impulsive plane wave, plays an important role in the solution of the one‐dimensional inverse problem in reflection seismology. Hitherto the extension to non‐normal incidence was known only for a medium with free surface. By giving the extension for arbitrary surface reflection coefficients, this paper fills a gap.
EVANESCENT EFFECTS IN ACOUSTICAL WAVE PROPAGATION*
Authors: KUHN M. J.
Published: April 2006

The propagation of transient acoustic pressure waves in a layer enclosed between two, not necessarily identical, half‐spaces is considered. The source and the receivers are always located in the same half‐space and at the same depth. The source excitation function is a narrow causal spike. Several thicknesses of the layer are examined including the case in which the embedded layer vanishes.

The phenomena of ‘constricted’ head waves and wide‐angle reflections in the layer are examined in detail using a ‘numerical experimentation’ approach. First, a closed‐form solution is numerically evaluated. Then this solution is developed in series and each term is evaluated separately using the same numerical techniques. When the contribution of an individual high‐order term becomes unimportant, all higher order terms are discarded, and the response is constructed by superposition of the previously computed low‐order terms only.

Propagation by wide‐angle reflections from inside the layer is of interest. When the thickness of the layer is reduced to a fraction of the wavelength, these events consist typically of a low amplitude, high frequency, geometrical acoustics arrival, followed by higher amplitude, low frequency, non‐geometrical coda. When all important low‐order terms are added, the non‐geometrical events tend to interfere destructively, leaving a waveform nearly identical to that obtained by integration of the closed‐form solution.

When the thickness of the embedded layer is measured in fractions of the dominant wavelength, none of the individual terms of the series development can be duplicated by asymptotic ray tracing. However, because the codas of the various terms interfere destructively, the total response may be well‐represented by the addition of a few low‐order rays, using asymptotic approximation. This discovery extends the usefulness of Huygens‐Kirchhoff ray tracing to modeling of wave propagation in thin layers.
ANALYSIS AND IMPROVEMENT OF THE PRIMARY FIELD WAVEFORM OF THE GROUND TEM METHOD*
Authors: QIAN BIN
Published: April 2006

Many ground TEM systems use an on‐off type of primary field waveform and measure the secondary field only in the transmitter off‐time, so as to realize the pure secondary field measurement. The width of the trailing edge of the primary pulses and the duration of the transmitter on‐time form a time‐constant (Tc) window. Most effective excitation is achieved if the target conductor has a Tc falling into this window.

To be able to measure in the transmitter on‐time, two primary field waveforms are proposed. The first is a series of unipolar pulses with identical steep ramps at both leading and trailing edges. Measurements made in the on‐time after the leading edges simply reduce the stacking time needed and power consumption by half. Also, long‐ Tc conductors are better excited. The second is a series of bipolar pulses with long ramps as the leading edges and short ramps as the trailing edges. This waveform presents two different Tc‐windows at the same time and helps to improve the detection of long‐Tc conductors in the presence of short‐ Tc ones.
AN APPLICATION OF FAST ALGORITHMS TO NUMERICAL ELECTROMAGNETIC MODELING*
Authors: BEZVODA V. , SEGETH K.
Published: April 2006

Numerical electromagnetic modeling by the finite‐difference or finite‐element methods leads to a large sparse system of linear algebraic equations. Fast direct methods, requiring an order of at most q log q arithmetic operations to solve a system of q equations, cannot easily be applied to such a system. This paper describes the iterative application of a fast method, namely cyclic reduction, to the numerical solution of the Helmholtz equation with a piecewise constant imaginary coefficient of the absolute term in a plane domain. By means of numerical tests the advantages and limitations of the method compared with classical direct methods are discussed. The iterative application of the cyclic reduction method is very efficient if one can exploit a known solution of a similar (e.g., simpler) problem as the initial approximation. This makes cyclic reduction a powerful tool in solving the inverse problem by trial‐and‐error.
LOVE SEAM‐WAVES IN A HORIZONTALLY INHOMOGENEOUS THREE‐LAYERED MEDIUM*
Authors: DOBRÓKA M.
Published: April 2006

Using the WKBJ‐method the absorption‐dispersion relation and the amplitude functions are derived for Love seam‐waves that propagate in a horizontally inhomogeneous three‐layered medium. To describe the anelastic friction the constant Q‐model is applied. The inhomogeneity that appears in either the elastic moduli or quality factors is assumed to remain weak in the coal as well as in the adjacent layers, which are assumed to have different material properties (asymmetric channel). Using numerical solutions of the dispersion relation, it is shown that the weak horizontal inhomogeneities can be optimally detected using channel‐wave constituents of a frequency near to the Airy frequency while inhomogeneities of the adjacent rock can only be detected at frequencies close to, but higher than, the cut‐off frequency.
IDEAL PERFORMANCE CRITERIA FOR DECONVOLUTION OPERATORS*
Authors: DIMRI VIJAY P. , SRIVASTAVA KIRTI
Published: April 2006

A technique to evaluate an ideal performance of a deconvolution operator has been obtained by dividing the input trace into a number of sections. The error energy is seen to decrease with an increase in the number of sections. Numerical examples show that the error energy becomes zero following a relation between the number of sections, the length of input and the length of the filter.
THE PERFECTLY REFLECTING WEDGE USED AS A CONTROL MODEL IN SEISMIC DIFFRACTION MODELLING*
Authors: HUTTON G.D.
Published: April 2006

The numerical modelling of seismic diffraction, e.g., at faults and other discontinuities, generally requires the use of fast approximate methods. The geophysicist responsible for the development of such numerical methods has a real need of exact solutions to certain ideal geometries to check the accuracy of his calculations.

One such exact solution, which is available, is the acoustic wave solution to the perfectly reflecting wedge. The solution is three‐dimensional and the source is an explosive point source. This model is ideal for seismic diffraction; the solution has the advantage of being exact, truly three‐dimensional and of being in the convenient form of the temporal and spatial impulse response. More complicated sources which are extended in either space or time can, therefore, be modelled exactly by numerical integration.

This paper presents some examples of the use of the perfectly reflecting wedge as a control model for an asymptotic high frequency diffraction modelling method. This control model has revealed that certain survey and wedge configurations can yield significant disagreement with, e.g., the Kirchhoff approximation. Such configurations could occur during VSP modelling when the survey lies in the near field or in the shadow zone of a high contrast fault. This control model has also been instructive in demonstrating why the high frequency, asymptotic, approximation is generally very good and has indicated a possible improvement to the Kirchhoff approximation for edge diffraction.
COMPUTING FIELD STATICS WITH THE HELP OF SEISMIC TOMOGRAPHY*
Authors: DE AMORIM W.N. , HUBRAL P. , TYGEL M.
Published: April 2006

Field static corrections in general need be applied to all onshore seismic reflection data to eliminate the disturbing effects a weathering layer or near‐surface low velocity zone has on the continuity of deep seismic reflections. The traveltimes of waves refracted at the bottom of the low velocity zone (or intermediate refracting interfaces) can often be observed as first breaks on shot records and used to develop a laterally inhomogeneous velocity model for this layer, from which the field static corrections can then be obtained. A simple method is described for computing accurate field statics from first breaks. It is based on a linearization principal for traveltimes and leads to the algorithms that are widely and successfully applied within the framework of seismic tomography. We refine an initial model for the low velocity layer (estimated by a standard traveltime inversion technique) by minimizing the errors between the observed first arrivals on field records and those computed by ray theory through an initial model of the low velocity layer. Thus, one can include more lateral velocity variations within the low velocity layers, which are important to obtain good field static corrections. Traditional first break traveltime inversion methods cannot, in general, provide such refined velocity values. The technique is successfully applied to seismic data from the Amazon Basin. It is based on a simple model for the low velocity layer that consists of an undulating earth surface and one planar horizontal refractor overlain by a laterally changing velocity field.
MATHEMATICAL ANALYSIS OF D.C. RESISTIVITY SOUNDING OVER A PARABOLOID*
Authors: DASGUPTA S.P.
Published: April 2006

A complete mathematical analysis is proposed for direct current resistivity prospecting over the surface of a layered paraboloid. The analysis evaluates the Green's function in parabolic coordinates for a current source at the vertex. The general solution is obtained as a Fourier‐Bessel integral involving those curvilinear coordinates that have a kernel function which is similar to that of a half‐plane containing inhomogeneous layers. This similarity permits the computation of a class of sounding curves over such an oval surface providing a way to analyse field data over hilly terrain.
PARAMETER ESTIMATION AND FAULT DETECTION BY THREE‐COMPONENT SEISMIC AND GEOELECTRICAL SURVEYS IN A COAL MINE*
Authors: BREITZKE M. , DRESEN L. , CSOKAS J. , GYULAI A. , ORMOS T.
Published: April 2006

Abstract

Three‐component seismic and geoelectrical in‐mine surveys were carried out in Lyukobanya colliery near Miskolc, Hungary to determine the in situ petrophysical parameter distributions and to detect inhomogeneities in the coal seam. The seismic measurements comprise an underground vertical seismic profile, using body waves, and an in‐seam seismic amplitude‐depth distribution and transmission survey, using channel waves. The geoelectrical measurements are based on the drift‐ and seam‐sounding method.

Interval traveltime‐, amplitude‐, multiple‐filter‐ and polarization analysis methods are applied to the seismic data. They lead to a five‐layer model for the strata including the coal seam. The coal seam and two underlying beds act as a seismic waveguide. The layer sequence supports the propagation of both normal and leaky mode channel waves of the Love‐ and Rayleigh type. A calculation of the total reflected energy for each interface using Knott's energy coefficients shows that the velocity ranges of high reflection energy and of normal and leaky mode wavegroups coincide. The excitation of wavegroups strongly depends on the seismic source. A simultaneous inversion of a geoelectrical drift‐ and seam‐sounding survey prevents misinterpretations of the seismic data by clearly identifying the low‐velocity coal seam as a high‐resistivity bed. Calculations of dispersion and sounding curves improve the resolution of the slowness and resistivity in each layer.

Both diminished amplitudes and distortions in the polarization of transmission seismo‐grams and decreasing resistivities in a geoelectrical pseudosection of the coal seam are related to an inhomogeneity.

A calculation of synthetic seismograms for Love and Rayleigh channel waves with the finite‐difference and the Alekseev‐Mikhailenko method agrees well with the field data for the main features, i.e., particular arrivals in the wave train, wavegroups, velocities and symmetries or asymmetries.

This in‐mine experiment demonstrates that the simultaneous acquisition, processing and interpretation of seismic and geoelectrical data improve the lithological interpretation of petrophysical parameter distributions. Coal seam inhomogeneities can also be detected more reliably by the two independent surveys than by one alone.
CONVOLUTIONAL BACK‐PROJECTION IMAGING OF PHYSICAL MODELS WITH CROSSHOLE SEISMIC DATA1
Authors: EAST R. J. R. , WORTHINGTON M. H. , GOULTY N. R.
Published: April 2006

The development of crosshole seismic tomography as an imaging method for the subsurface has been hampered by the scarcity of real data. For boreholes in excess of a few hundred metres depth, crosshole seismic data acquisition is still a poorly developed and expensive technology. A partial solution to this relative lack of data has been achieved by the use of an ultrasonic seismic modelling system. Such ultrasonic data, obtained in the laboratory from physical models, provide a useful test of crosshole imaging software.

In particular, ultrasonic data have been used to test the efficacy of a convolutional back‐projection algorithm, designed for crosshole imaging. The algorithm is described and shown to be less susceptible to noise contamination than a Simultaneous Iterative Reconstruction Technique (SIRT) algorithm, and much more computationally efficient.
SEISMIC ATTENUATION IN THE VICINITY OF THE GEOTHERMAL ANOMALY AT URACH OBTAINED FROM NEAR‐VERTICAL REFLECTION PROFILES1
Authors: TRAPPE H.
Published: April 2006

The attenuation in the vicinity of the geothermal anomaly at Urach was determined by means of two near‐vertical reflection profiles. The attenuation in the sediments and in the upper crust (3‐4 km depth) was estimated by interpretation of the first (refracted) arrivals. For calculating the attenuation, the amplitude decay with respect to distance was used. Corrections for the spread factor, i.e. the geometric amplitude divergence was deduced from the traveltime curves. Below the anomaly, higher attenuation values (Q−1∼ 0.008) were observed compared with those in the undisturbed crust (Q−1∼ 0.002). This effect is probably due to the cracks and fissures in the upper part of the crystalline basement.

The attenuation in the middle and lower crust was determined using near‐vertical reflections from this depth interval. The use of the spectral ratio method leads to higher values of the effective attenuation Q−1eff below the heat flow anomaly compared to those of the‘ normal’crust. This zone of high Q−1eff coincides with the low velocity body below the heat flow anomaly. Both effects, the higher attenuation and the lower velocities, could be caused by high temperatures, cracks and fissures in the crust.
A NOVEL FIXED‐SOURCE ELECTROMAGNETIC SYSTEM1
Authors: JOHNSON I. , DOBORZYNSKI Z.
Published: April 2006

A novel fixed‐source electromagnetic system has been developed. The transmitter is a large rectangular loop or grounded dipole. The transmitted waveform consists of up to five superimposed pure sinusoids at well‐separated frequencies. The receiver measures the amplitude and phase at two frequencies from a single receiver coil. The amplitude ratio is routinely calculated. Field trials with both surface and downhole configurations show that the method has advantages over the more traditional frequency‐domain Turam type and downhole electromagnetic (DHEM) systems. Among such advantages are the use of a single receiver coil and the removal of noise due to free‐space variations in transmitter‐receiver geometry. The latter is important for DHEM surveys. In terms of field procedures and quantities measured, the system is similar to time‐domain methods.
SOME SOURCES OF DISTORTION IN TOMOGRAPHIC VELOCITY IMAGES1
Authors: DYER B. , WORTHINGTON M. H.
Published: April 2006

Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated.

Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data.

Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi‐ray rather than straight‐ray inversion techniques, despite the occurrence of pronounced ray bending.
METHOD FOR DETERMINATION OF VELOCITY AND DEPTH FROM SEISMIC REFLECTION DATA1
Authors: LANDA E. , KOSLOFF D. , KEYDAR S. , KOREN Z. , RESHEF M.
Published: April 2006

The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity‐depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots.

The process input consists of unstacked seismic data and an initial velocity‐depth model. This model is often based on nearby well information and an interpretation of the stacked section.

Inversion is performed iteratively layer after layer; during each iteration synthetic travel‐time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non‐linear programming.

The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data.
A NON‐GEOMETRICAL SH‐ARRIVAL1
Authors: DALEY P. F. , HRON F.
Published: April 2006

The existence of‘*‐waves’has, in recent years, prompted a renewed interest in these non‐geometrical arrivals, which are generated by point sources located adajcent to plane interfaces. It has led to the re‐evaluation of seismic data aquisition techniques and to the question of how to use this real phenomena in enhancing existing seismic interpretation methods.

This paper considers a non‐geometrical SH‐arrival which is generated by a point torque source unrealistically buried within a half‐space. The method of solution is essentially the same as presented in an earlier paper, with the modification that the limitation placed on the distance of the source from the interface has been removed in the saddle point method used to obtain a high‐frequency approximate solution. In the earlier paper, a preliminary assumption forced the saddle point, which corresponded to the *‐wave arrival, to be real when it is generally complex. However, for offsets removed from the distinct ray, the imaginary part of this complex quantity is negligible.

A problem which arose when comparing exact synthetic traces with those obtained using zero‐order saddle point methods, was the inability to match either the amplitude or phase of the geometrical arrival in the range of offsets when the *‐wave and this corresponding geometrical ray were well separated. For this range of offsets the geometrical arrival was approaching grazing incidence and another term in the saddle point expansion of the integral was necessary to rectify this error. This method is also being used to validate the results for higher order terms obtained using asymptotic ray theory.

Analytical formulae are given for both the *‐wave and the higher order expansion of the geometrical event, together with a comparison of synthetic seismograms using the method developed here and a numerical integration algorithm.
POST‐CRITICAL WAVELET ESTIMATION AND DECONVOLUTION1
Authors: KELAMIS P. G. , CHIBURIS E. F.
Published: April 2006

Using synthetic data, it is demonstrated that the amplitude spectra of post‐critical plane‐wave components are stable and equal to the amplitude spectrum of the input wavelet (critical reflection theorem). Our analysis and physical explanation of the theorem are based only on amplitude versus offset arguments. The stability of the spectra in the post‐critical region is directly related to a high amplitude post‐critical reflection that dominates the trace in the slant‐stack domain. The validity of the theorem for both the acoustic and elastic cases, its assumptions and limitations, are also examined with emphasis on applications for processing seismic reflection data. Based on the theorem, a deterministic procedure is developed (assuming minimum‐phase properties) for wavelet estimation and subsequent deconvolution. We call this method Post‐critical Deconvolution, which emphasizes reliance on post‐critical reflection data. The performance of the method is shown with real data and the results are compared to those obtained with conventional deconvolution techniques.