bluuebunny/crossref_metadata_2025 huggingface dataset:
AIRBORNE RESISTIVITY MAPPING USING A MULTIFREQUENCY ELECTROMAGNETIC SYSTEM*
Authors: SINHA AJIT K.
Published: April 2006

Abstract

Airborne electromagnetic methods are most commonly used in mineral exploration. However, new developments, such as multifrequency capability and digital on‐board field recording, as well as improvements in instrumentation resulting in high signal‐to‐noise ratios in recorded data, have made their application in geological mapping possible.

A three‐frequency airborne EM survey carried out over an area northwest of Timmins, Ontario, was interpreted in terms of thickness and resistivity of the layers of a two‐layer earth section. Since both in‐phase and quadrature components are measured, this provides six independent parameters at each point in space. Based on prior geological information and a preliminary interpretation of the field records, two two‐layer models of the subsurface seemed to be appropriate for most of the survey area. An automatic computerized interpretation procedure was devised to interpret the field data at each point in terms of thickness and resistivity parameters of those two models. When the geology is more complex, the data do not fit the models and no interpretations are made. Two maps illustrating the variation of the resistivity and the thicknesses of the layers were constructed from the interpreted data. These maps agree with the known geological information about the distribution of glacial clay in the area. Areas where the layered models do not fit are known to be areas where the geology is complex with a large number of dykes and other lateral inhomogeneities. The study shows that multifrequency airborne EM surveys can be very useful in geological mapping over inaccessible terrain and can significantly help the mapping geologist where outcrops are scarce.
AUTOMATIC PICKING OF FIRST ARRIVALS AND PARAMETERIZATION OF TRAVELTIME CURVES*
Authors: GELCHINSKY B. , SHTIVELMAN V.
Published: April 2006

Abstract

One of the methods for studying the near‐surface low‐velocity zone and for subsequent determination of static corrections is the technique of employing first arrivals. During the past few years several computer algorithms, based on some simplifying assumptions, have been suggested for automatic determination of first arrivals.

This paper suggests a new method for automatic picking of first arrivals, which works under quite general assumptions concerning the character of the data. The method is based on the use of correlation properties of signals and the application of a statistical criterion for the estimation of first arrivals time. A number of dimensionless parameters is used in the algorithm making it possible to regulate the level of reliability and the resolution of the picking procedure.

The second stage of the algorithm is the parameterization of the traveltime curve, that is a division of the previously obtained t—x curve into separate rectilinear segments. The suggested algorithm of parameterization is based on an heuristic use of some properties of maximum likelihood estimates. This permits location of the breakpoints of the t—x curve and the estimation of the parameters of each rectilinear segment.

A computer program has been written based on the picking and parameterization algorithm. This program has been tested on a large amount of field data and the results show that it works at least as well as the hand procedure.
TWO STRUCTURAL MODELS FOR THE WESTERN FLANK OF THE BRABANT MASSIF*
Authors: DE MEYER F.
Published: April 2006

Abstract

This paper is concerned with an interpretation of the Bouguer anomaly on the Western flank of the Brabant Massif (Belgium). The position, shape, and density contrast of elementary bodies in the upper part of the earth's crust are determined in a purely numerical manner. A batholith‐like body and a basin‐type structure both adequately account for the observed surface field, at least from a one‐sided geophysical and mathematical point of view. Since seismological control is lacking the two models are representative of the ambiguity and indeterminacy of the definitions of the geologic cause of the anomalous features, if the data are restricted to gravity information alone.
ANISOTROPY DUE TO BEDDING—A COMPUTER STUDY*
Authors: LEVIN F. K.
Published: April 2006

Abstract

Bedding on a scale small in comparison to the wavelength results in transverse isotropy. On the other hand, anisotropy has been observed in the field, particularly with horizontally polarized shear waves. In this article velocity data from 23 wells are used to estimate the resulting transverse isotropy and to compare these data with anisotropy observations reported in the literature. Since the well data were compressional velocity (or rather transit time) only, the corresponding shear velocity data were estimated on the basis of a reasonable—though arbitrary—assumption of Poisson's ratio. Actual densities were used wherever they were available; for the remainder of the data, density was assumed to be constant throughout the averaging interval.

The anisotropy data estimated on this basis were generally considerably smaller than the observational data that have been reported in the literature. Although both the above assumptions—functional dependence of Poisson's ratio on transit time and constant density—tend to underestimate anisotropy, and although 23 wells is but a small subset of all available data, it appears unlikely that bedding alone could cause anisotropy of the magnitude reported.
STATISTICAL EVALUATION OF MT AND AMT METHODS APPLIED TO A BASALT‐COVERED AREA IN SOUTHEASTERN ANATOLIA, TURKEY*
Authors: ILKISIK O. M. , JONES A. G.
Published: April 2006

Abstract

The efficacy of the magnetotelluric and audiomagnetotelluric (MT/AMT) methods for detailing the structure of a hypothetical geological section is investigated by using the singular value decomposition (SVD) technique. The section is representative of southeastern Turkey, which is mostly covered by basalt and is a prime area for oil exploration. One of the geological units, the Germav shale at a depth of 600 m, is a problem layer for electromagnetic surveys because of its very low resistivity (on average 3 Ωm) and highly variable thickness across the area (200–900 m). In the MT frequency range (0.0004–40 Hz) its total conductance—or, since its resistivity is known from resistivity log information, its thickness—is the best resolved model parameter. The total depth to the Germav shale and the resistivity of the Cambrian/Precambrian basement are the marginally resolved parameters. In the AMT frequency range (4–10000 Hz) the resistivity of the surface basalt layer strongly affects the resolution of the other, less important, model parameters which are the total depth to the Germav shale and the total conductance of the Germav shale. The errors in the measurements determine the number of model parameters resolvable, and are also important for interpretation of the geological model parameters to within a desired accuracy.

It is shown that statistical evaluation of the MT and/or AMT interpretations by using an SVD factorization of the sensitivity matrix can be helpful to define the importance of some particular stage of the interpretation, and also provides a priori knowledge to plan a proposed survey. Arrangements of MT and AMT observations, together with some Schlumberger resistivity soundings, on a large grid will certainly provide three‐dimensional detailed information of the deep geoelectric structure of the area.
SIDESWIPE REFLECTIONS AND OTHER EXTERNAL AND INTERNAL REFLECTIONS FROM SALT PLUGS IN THE NORWEGIAN‐DANISH BASIN*
Authors: HOSPERS J.
Published: April 2006

Sideswipe, foreswipe and backswipe reflections are described from salt plugs situated in the Norwegian‐Danish Basin (southern part of the Norwegian sector of the North Sea). These external reflections can be mapped and are shown to define the shoulders of a salt plug.

Physical three‐dimensional models are described which aid in visualizing the various aspects of the external reflection process. Refracted waves which have been internally reflected in a salt plug have also been identified.
ON THE CALIBRATION OF THE WATER GUN PRESSURE SIGNATURE*
Authors: SAFAR M. H.
Published: April 2006

A simple field method was proposed by the author in 1976 for measuring the absolute amplitude of the pressure pulse radiated by marine seismic sources which radiate a bubble pulse. The proposed method involves the recording of the near‐field pressure signature radiated by the water gun using a wide‐band hydrophone. The key feature of the proposed method is that a knowledge of the hydrophone sensitivity and its distance from the water gun are not required.

It is shown that the absolute amplitudes of the pressure pulses radiated by the S80 and P400 water guns obtained using the proposed method are in agreement with those obtained using a Ref‐Tek hydrophone.
EFFECT OF INCLINED ANISOTROPIC SUBSTRATUM ON MAGNETOTELLURIC RESPONSE*
Authors: SINGH RAMESH P.
Published: April 2006

In tectonically active regions electrical conductivity anisotropies are the dominating features. The importance of conductivity anisotropy in the interpretation of magnetotelluric data is well known. In the present study numerical results presented which show the effect of a substratum with inclined anisotropy on the magnetotelluric response. The pronounced change on the magnetotelluric response is found for the models in which the substratum underlies (i) conductive and (ii) resistive overburden.
DC GEOELECTRIC SOUNDING TO DETERMINE WATER CONTENT IN THE SALT MINE ASSE (FRG)*
Authors: KESSELS W. , FLENTGE I. , KOLDITZ H.
Published: April 2006

In the course of investigations concerning disposal of radioactive waste, DC‐geoelectric soundings were performed in the salt mine Asse in 1982. The survey resulted in the determination of resistivities of various salt formations. A comparison of various resistivities obtained in salt formations in the mine shows that it is possible to estimate the content of free water in salt using Archie's equation.

The significant result of this survey is that salt formations in the mine can be divided into two categories according to their resistivities:

1. Salt with resistivity between 107and 108Ωm (particularly Na2Sp and Na3β). The particularly pure halitic formations are to be found within this resistivity range.

2. Salt with resistivity between 103and 105Ωm (Na2Tl, K2, transition salt). The salt formations with thin layers of anhydrite and a high content of hygroscopic salts are classified in the paper.
THE COMPLEX RESISTIVITY SPECTRA OF MODELS CONSISTING OF TWO POLARIZABLE MEDIA OF DIFFERENT INTRINSIC PROPERTIES*
Authors: SONG LIU , VOZOFF K.
Published: April 2006

Abstract

Theoretical model study shows that when an earth model is composed of two (Cole‐Cole) polarizable media, its normalized complex resistivity spectrum is approximately a multiplicative combination of the contributions of the two media. This also applies on inversion, but the two dispersions thus obtained are apparent rather than intrinsic dispersions.

In models consisting of two media, either a multiplicative or an additive combination of Cole‐Cole functions fits the complex apparent resistivity spectrum. On inversion each combination gives similar parameters except for the apparent chargeability of the component with the shorter time constant. However, this can be compensated simply. In this sense the two representations are almost equivalent.

We show that the apparent spectrum due to a finite polarizable body is actually a true Cole‐Cole dispersion, as is usually assumed in practice.

The behavior of a complex apparent resistivity spectrum and its corresponding apparent Cole‐Cole dispersion parameters is influenced by the variation of the dilution factor with frequency. Hence when estimating intrinsic parameters from the nomogram, based on constant (frequency‐independent) dilution factors, particular care is required to correctly relate apparent parameters to intrinsic parameters.
WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS. PART I: METHODS USING THE ONE‐WAY WAVE EQUATIONS*
Authors: WAPENAAR C. P. A. , BERKHOUT A. J.
Published: April 2006

Abstract

Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one‐way wave equations. In cases of limited propagation angles and weak inhomogeneities these one‐way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90°) an alternative choice of sub‐division into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.
COMPUTER REPRESENTATION OF COMPLEX 3‐D GEOLOGICAL STRUCTURES USING A NEW “SOLID MODELING” TECHNIQUE*
Authors: GJØYSTDAL H. , REINHARDSEN J. E. , ÅSTEBØL K.
Published: April 2006

Abstract

During our recent work with 3‐D dynamic ray‐tracing and velocity inversion problems, a new 3‐D model generation system has been developed using a so‐called “solid modeling” technique. The term “solid modeling” refers to the fact that the logical system governing the internal geometrical properties of the model describes the model as a combination of “solids” or “volumes” in 3‐D space. In each of these volumes the physical parameters (such as seismic velocity, density) vary continuously. Discontinuous changes occur only across the model interfaces separating the volumes.

The model is constructed by firstly forming a number of “simple volumes” from the given interfaces and then combining these simple volumes into more complex volumes which represent the physical volumes of the model. It is easy to make changes to the model, by adding volumes or subtracting volumes and perform more composite operations, all by simple use of Boolean expressions. Every time a model has been specified (or changed), the internal logic automatically carries out a check of physical consistency of the 3‐D model space (no overlapping volumes, no holes).

By including various types of coordinate transformations, different kinds of complex structures can be handled, such as salt domes and vertical and near vertical faulting.
WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS.
Authors: WAPENAAR C. P. A. , BERKHOUT A. J.
Published: April 2006

In one‐way wave field extrapolation downgoing and upgoing waves are treated independently, which is allowed if propagation at small angles against the vertical in (weakly) inhomogeneous media is considered. In practical implementation the slow convergence of the square‐root operator causes numerical deficiencies. On the other hand, in two‐way wave field extrapolation no assumptions need to be made on the separability of downgoing and upgoing waves. Furthermore, in practical implementation the use of the square‐root operator is avoided. To put the two‐way techniques into perspective, it is shown that two‐way wave field extrapolation could be described in terms of one‐way processes, namely: (1) decomposition of the total wave field into downgoing and upgoing waves; (2) one‐way wave field extrapolation; (3) composition of the total wave field from its downgoing and upgoing constituents. This alternative description of two‐way wave field extrapolation is valid for media which are homogeneous along the z‐coordinate as well as for small dip angles in arbitrarily inhomogeneous media. In addition, it is shown that this description is also valid for large dip angles in 1‐D (vertically) inhomogeneous media, including critical‐angle events, when the WKBJ one‐way wave functions discussed in part I of this paper are considered.

For large dip angles in arbitrarily inhomogeneous media the two‐way wave equation is solved by means of Taylor series expansion. For practical implementation a truncated operator is designed, assuming gentle horizontal variations of the medium properties. This operator is stable and converges already in the first order approximation, also for critical‐angle events.
NATURAL POLARIZATION STUDIES AT BALCOVA GEOTHERMAL FIELD*
Authors: ERCAN A. , DRAHOR M. , ATASOY E.
Published: April 2006

Abstract

Contrasting resistivity, temperature, pressure, porosity and fluid migrations are the main causes of ion accumulations along the discontinuities which create coupling‐induced natural current flow which is observed as the Natural Polarization Potential (NPP) on the surface. Natural Polarization Electric Field (NPE) variations were recorded along 13 profiles about 2.5 km each in a north‐south direction. Interpretation of the coincident anomalies of the NPP and the NPE field resulted in determination of the polarization angle, polarization focal depth and the azimuths of the polarized interfaces. Considerable agreement between faults delineated by previous geological and geophysical investigations and polarization discontinuities was observed. The polarization plane was observed to be horizontal in high temperature areas but steepened gradually in relatively colder regions in the northern coastal area. From the polarization depth distribution two depression zones were observed, separated by an uplifted section elongated in a north‐south direction. The basin at the eastern side had an estimated polarization depth of 1.1 km and was limited by the Agamemnon‐2 and ‐1 faults, while the western basin had an estimated depth of 1.3 km and extended in the east‐west direction not previously reported. The eastern basin extends on the north side around the town of Inciralti, the western basin appeared to be elongated towards the town of Cesme.
SLANT STACKING AND ITS SIGNIFICANCE FOR ANISOTROPY*
Authors: HAKE H.
Published: April 2006

Slant stacking transforms seismic data, recorded as a function of source‐receiver offset and traveltime, into the domain of intercept time τ and ray parameter p. The shape of the τ‐p‐curves thus obtained is closely related to the slowness surfaces of the layers. A layer‐stripping operation in the τ‐p‐domain removes all effects of the layers above the target layer. The resulting curve is equal to the slowness surface of the layer except for a scaling factor containing the thickness and dip of the layer. The slowness surface is a characteristic surface for anisotropic media. This makes the τ‐p‐domain very suitable for detecting and describing anisotropic layers. The relationship between the shape of τ‐p‐curves, the slowness surfaces, and the geometry of the layers is derived. Synthetic τ‐p‐curves calculated with the reflectivity method show some difficulties that can arise in determining the shape of the curves and in applying the stripping operation. It is shown that the effects of vertical inhomogeneity on the interpretation of τ‐p‐curves in terms of anisotropy are small.
THE NATURE OF THE NON‐GAUSSIANITY OF PRIMARY REFLECTION COEFFICIENTS AND ITS SIGNIFICANCE FOR DECONVOLUTION*
Authors: WALDEN A. T. , HOSKEN J. W. J.
Published: April 2006

One of the important properties of a series of primary reflection coefficients is its amplitude distribution. This paper examines the amplitude distribution of primary reflection coefficients generated from a number of block‐averaged well logs with block thicknesses corresponding to 1 ms (two‐way time). The distribution is always essentially symmetric, but has a sharper central peak and larger tails than a Gaussian distribution. Thus any attempt to estimate phase using the bi‐spectrum (third‐order spectrum) is unlikely to be successful, since the third‐order moment is almost identically zero. Complicated tri‐spectrum (fourth‐order spectrum) calculations are thus required. Minimum Entropy Deconvolution (MED) schemes should be able to exploit this form of non‐Gaussianity. However, both these methods assume a white reflectivity sequence; they would therefore mix up the contributions to the trace's spectral shape that are due to the wavelet and those that are due to non‐white reflectivity unless corrections are introduced.

A mixture of two Laplace distributions provides a good fit to the empirical amplitude distributions. Such a mixture distribution fits nicely with sedimentological observations, namely that clear distinctions can be made betweensedimentary bedsandlithological unitsthat comprise one or more such beds with the same basic lithology, and that lithological units can be expected to display larger reflection coefficients at their boundaries than sedimentary beds. The geological processes that engender major lithological changes are not the same as those for truncation of bedding. Analyses of sub‐sequences of the reflection series are seen to support this idea. The variation of the mixing proportion parameter allows for scale and shape changes in different segments of the series, and hence provides a more flexible description of the series than the generalized Gaussian distribution which is shown to also provide a good fit to the series.

Both the mixture of two Laplace distributions and the generalized Gaussian distribution can be expressed as scale mixtures of the ordinary Gaussian distribution. This result provides a link with the ordinary Gaussian distribution which might have been expected to be the distribution of a natural series such as reflection coefficients. It is also important in the consideration of the solution of MED‐type methods. It is shown that real (coloured) primary reflection series do not seem to be obtainable as the deconvolution result from MED‐type deconvolution schemes.
A VERSATILE ELECTROMAGNETIC MODELING PROGRAM FOR 2‐D STRUCTURES*
Authors: NISSEN J.
Published: April 2006

A new integral‐equation program for calculation of the E‐polarization response allows modeling of VLF for plane wave or line source input, e.g., magnetotellurics and Turam responses. The anomalous conducting body is modeled by a number of square cells, each of individual size and resistivity, and with arbitrary position in the host medium. This provides a high degree of flexibility and allows for simulation of rather complex conductivity structures. The computation time has been drastically reduced by using techniques such as digital filtering and fast Fourier transformation.

The interpretation of a measured Turam profile and the influence of galvanically channelled currents in the conducting body is discussed.
ORIGIN OF THE ANOMALIES OF GRAVITY AND ITS VERTICAL GRADIENT OVER CAVITIES IN BRITTLE ROCK*
Authors: FAJKLEWICZ Z.
Published: April 2006

Investigations show that the depth range of the gravity method for detecting cavities is considerably greater than expected on the basis of theoretical calculations that consider only the depth and shape of the cavity.

The cavity generates its own gravity field that is the sum of the activity of the cavity itself and the density changes caused in the surrounding rocks by the process of their destruction as a result of the cavity's expansion. The latter factor is decisive for the cavity's detection by the gravity method in several cases.

The extent of the zones of change density in the surrounding rocks and their actual shape depend on many parameters. Thus, the determination of the depth of the cavity cannot be made by comparing measured and theoretical curves of gravity anomalies. The location of the center of gravity of the area disturbed by the cavity or upper boundary of its development towards the ground surface can be determined by denoting the singular point of gravity as a result of the downward analytical continuation of Ag.

The Strakhov‐Grigorieva‐Lapina (1977) method fulfils the necessary conditions in the field.
TUTORIAL INTERPRETATION OF MAGNETOTELLURIC MEASUREMENTS OVER AN ELECTRICALLY DISPERSIVE ONE‐DIMENSIONAL EARTH*
Authors: PATELLA D.
Published: April 2006

Frequency dispersion of electromagnetic parameters of earth materials has been widely documented in recent years. It is claimed that magnetotellurics (MT) may be significantly affected by dispersion. The paper studies the MT plane‐wave interpretative problem for a one‐dimensional earth characterized by the presence of dispersive layers. The theoretical properties of the MT field under the dispersion hypothesis, andthe main features of the dispersion phenomenon are synthetically reviewed. The examination of previously published MT curve responses over some models of dispersive earth section shows that ambiguity can arise when interpreting MT data with no other source of information. Thus it may be almost impossible to distinguish between the response of a dispersive section and an equally probable dispersion‐free section. The dispersion magnetotelluric (DMT) method is proposed as a means to resolve the ambiguity. The DMT method is based on the execution, at the same site, of an MT sounding and of an always dispersion‐free dc geoelectric deep sounding. The latter technique can be used to compute a synthetic dispersion‐free MT wave impedance, to be compared with the measured MT wave impedance. The apparent dispersion function is introduced as a measure of divergence between the two wave impedances.
COMPUTATION OF SIGNATURES OF LINEAR AIRGUN ARRAYS*
Authors: VAAGE S. , URSIN B.
Published: April 2006

Far‐field signatures from an airgun array are usually obtained by carrying out extensive field measurements. In order to decrease the need for such measurements, we have developed a method for computing signatures from linear airgun arrays where the distances between the airguns are such that the non‐linear interaction among the airguns is negligible.

The signature from a single airgun of a given type is computed from the following airgun parameters: airgun chamber volume, chamber pressure, airgun depth and position of the waveshape plate within the chamber. For calibration purposes, a recorded signature for one set of airgun parameters has to be provided for each type of airgun. The signatures are computed by using empirical relations between signature properties and the airgun parameters, and by treating the primary and bubble pulses separately.

The far‐field signature from a linear airgun array can now be computed by summation of the delayed signatures from the airguns in the array. Practical results are shown for an array with different PAR (Bolt) 1500 C airguns.
AN ACCURATE SCHEME FOR SEISMIC FORWARD MODELLING*
Authors: TAL‐EZER H. , KOSLOFF D. , KOREN Z.
Published: April 2006

A new time integration technique for use in forward modelling programmes is introduced. The technique presents an alternative to second‐order temporal differencing. It is based on a Chebyshev expansion of the formal evolution operator to the spatially discretized wave equation. The computational effort in forward modelling based on the new technique is about the same as in methods based on temporal differencing. However, machine accuracy can be obtained. The implementation of the technique to solve the acoustic wave equation in two spatial dimensions is described. Finally, an example of using the technique to solve a problem of wave propagation in a single layer is presented.
FREQUENCY WAVENUMBER APPROACH OF THE τ‐p TRANSFORM: SOME APPLICATIONS IN SEISMIC DATA PROCESSING*
Authors: BENOLIEL S.D. , SCHNEIDER W.A. , SHURTLEFF R.N.
Published: April 2006

Abstract

The τ‐p transform is an invertible transformation of seismic shot records expressed as a function of time and offset into the τ (intercept time) and p (ray parameter) domain. The τ‐p transform is derived from the solution of the wave equation for a point source in a three‐dimensional, vertically non‐homogeneous medium and therefore is a true amplitude process for the assumed model. The main advantage of this transformation is to present a point source shot record as a series of plane wave experiments.

The asymptotic expansion of this transformation is found to be useful in reflection seismic data processing. The τ‐p and frequency‐wavenumber (or f‐k) processes are closely related. Indeed, the τ‐p process embodies the frequency‐wavenumber transformation, so the use of this technique suffers the same limitations as the f‐k technique. In particular, the wavefield must be sampled with sufficient spatial density to avoid wavenumber aliasing.

The computation of this transform and its inverse transform consists of a two‐dimensional Fast Fourier Transform followed by an interpolation, then by an inverse‐time Fast Fourier Transform. This technique is extended from a vertically inhomogeneous three‐dimensional medium to a vertically and laterally inhomogeneous three‐dimensional medium.

The τ‐p transform may create artifacts (truncation and aliasing effects) which can be reduced by a finer spatial density of geophone groups by a balancing of the seismic data and by a tapering of the extremities of the seismic data.

The τ‐p domain is used as a temporary domain where the attack of coherent noise is well addressed; this technique can be viewed as ‘time‐variant f‐k filtering’. In addition, the process of deconvolution and multiple suppression in the τ‐p domain is at least as well addressed as in the time‐offset domain.
PROCESSING SHEAR‐WAVE VSP DATA*
Authors: KNECHT M. , EDELMANN H.A.K.
Published: April 2006

Shear‐wave arrivals in vertical seismic profiling recordings made with Vibroseis can be more accurately determined by wavelet processing and spectrum whitening. This method aids discrimination of shear‐wave arrivals against P‐wave disturbances. The data, thus improved, can be used to determine the main axis of shear‐wave polarization for each sounding depth in order to maximize shear‐wave amplitude by properly adding the two horizontal component signals vectorially.
LEVINSON INVERSION OF EARTHQUAKE GEOMETRY SH‐TRANSMISSION SEISMOGRAMS IN THE PRESENCE OF NOISE*
Authors: SCHERBAUM F.
Published: April 2006

Abstract

The Kunetz‐Claerbout equation for the acoustic transmission problem in a layered medium in its original form establishes the relation between the transmission and the reflec tion response for P‐waves in an horizontally layered medium and with vertical incidence. It states that the reflection seismogram due to an impulsive source at the surface, is one side of the autocorrelation of the seismogram due to an impulsive source at depth and a surface receiver.

By adapting Claerbout's formulation to the transmission of SH‐waves, the Kunetz‐Claerbout equation also holds for reflection and transmission coefficients dependent on the incident angle. Thus, earthquake geometry SH‐transmission seismograms can be used to caculate corresponding pseudoreflection seismograms which, in turn, can be inverted for the impedance structure using the Levinson algorithm. If the average incidence angle is known, a geometrical correction on the resulting impedance model can improve the resolution of layer thicknesses.

In contrast to the inversion of reflection seismograms, the Levinson algorithm is shown to yield stable results for the inversion of transmission seismograms even in the presence of additive noise. This noise stabilization is inherent to the Kunetz‐Claerbout equation.

Results of inverted SH‐wave microearthquake seismograms from the Swabian Jura, SW Germany, seismic zone obtained at recording site Hausen im Tal have been compared with sonic‐log data from nearby exploration drilling at Trochtelfingen. The agreement of the main structural elements is fair to a depth of several hundred metres.
VERTICAL SEISMIC PROFILING—SEPARATION OF P‐ AND S‐WAVES*
Authors: DANKBAAR J.W.M.
Published: April 2006

Abstract

In vertical seismic profile's (VSP's) shot with a large source offset, rays from shot to receiver can have large angles of incidence. Shear waves generated by the source and by conversions at interfaces are likely to be recorded by both the vertical and the horizontal geophones. Varying angles of incidence may give strong variations in the recorded amplitudes. Separation of P‐ and SV‐waves and recovery of their full amplitudes are important for proper processing and interpretation of the data. A P‐S separation filter for three‐component offset VSP data is presented which performs this operation. The separation filter is applied in the k‐f domain and needs an estimate of the P‐ and S‐velocities along the borehole as input. Implementation and stability aspects of the filter are considered. The filter was tested on an 1800 m offset VSP and appeared to be robust. Large velocity variations along the borehole could be handled and results were superior to those obtained by velocity filtering.
BOREHOLE COUPLING OF SEISMIC WAVES IN A PERMEABLE SOLID1
Authors: WHITE J. E. , WELSH E.
Published: April 2006

Expressions are derived for the acoustic pressure in a fluid‐filled borehole due to the passage of plane compressional or shear waves propagating in a porous and permeable medium. The derivation is based on a quasistatic description, yielding results applicable at low frequencies. Computations for a plausible sandstone (with porosity of 0.21 and permeability of 300 millidarcies) show accoustic pressure to be a surprisingly distortion‐free version of the stress waveform in a plane compressional wave. For a plane shear wave, the pressure waveform is visibly distorted.
NUMERICAL RAY GENERATION IN THE COMPUTATION OF SYNTHETIC VERTICAL SEISMIC PROFILES1
Authors: ARNTSEN B.
Published: April 2006

Ray theories are a class of methods often chosen to compute synthetic seismograms due to their efficiency and ability to deal with complex, three‐dimensional inhomogeneous media. To deal with the large number of rays needed to compute synthetic seismograms, a ray generation algorithm is given which is capable of generating a numerical code describing each ray. The code describes a subset of all possible rays by considering only pre‐critical reflections. In a horizontally plane‐layered medium the generation of rays and computation of amplitudes and traveltimes can be efficiently accomplished by grouping the rays into reflection order and dynamic analogue groups. Expressions summing all unconverted rays and rays with a single mode conversion are given for source and receiver located at arbitrary positions within the medium. Examples of zero‐offset synthetic VSPs obtained by this method are given.
IMPROVEMENT OF SIGNAL‐TO‐NOISE RATIO IN RESISTIVITY PROFILES1
Authors: BERNABINI M. , BRIZZOLARI E. , PIRO S.
Published: April 2006

The cross‐correlation technique for increasing the anomaly‐to‐noise ratio is applied to the interpretation of resistivity profiles.

To verify the method theoretically, resistivity profiles above a body having the shape of a parallelepiped were simulated with correlated and uncorrelated noise. Seven different electrode geometries are discussed. As a practical test, we considered profiles of a geoelectrical survey to locate tombs at a site of archaeological interest.

When the shape and dimensions of the anomaly can be foreseen, the cross‐correlation method can be applied and it gives a substantial improvement in the signal‐to‐noise ratio.
THE EFFECT OF THE ASPECT RATIO ON CRACK‐INDUCED ANISOTROPY1
Authors: DOUMA J.
Published: April 2006

Media containing aligned cracks show anisotropy with respect to elastic wave propagation. There are several models describing the wave propagation in cracked media, most of them only valid for cracks with small aspect ratios. One of these models (Crampin's model) is compared with a model valid for all aspect ratios (Nishizawa's model). The elastic constants and the group velocities are compared for both dry and liquid‐filled inclusions with aspect ratios ranging from 0.0001 (flat cracks) up to 1 (spheres). The difference between both models is small for small aspect ratios but becomes larger for increasing aspect ratios. At a crack density of 0.05 both models give‐within an error of 5%–the same results for aspect ratios up to 0.3. Therefore Crampin's model can be applied to a large range of cracked media even if the aspect ratio of the inclusions is not small. The variation of the anisotropy as a function of the aspect ratio can be studied using Thomsen's dimensionless parameters δ, E and y. They show how inclusions with large aspect ratios result in elliptical anisotropy.
ULTRASONIC SPECTROSCOPY IN ROCKS: AN EXPERIMENTAL STUDY OF HIGHLY POROUS SYNTHETIC SANDSTONES1
Authors: ALMOSSAWI H. I. H.
Published: April 2006

Broad‐band ultrasonic impulses and the attenuation spectral ratio technique have been used to investigate the characteristics of synthetic rocks for different saturants, by obtaining the attenuation coefficients in the frequency range of 0.1‐1.0 MHz.

The general trend of the data indicates that the experimental attenuation coefficient increases with an increase in the grain/pore size. Results show that large grains/pores can increase the attenuation coefficient in all mechanisms, and water‐saturated synthetic sandstone rocks result in a higher attenuation coefficient than similar oil‐saturated rocks.
NUMERICAL SOLUTION OF THE ACOUSTIC AND ELASTIC WAVE EQUATIONS BY A NEW RAPID EXPANSION METHOD1
Authors: KOSLOFF DAN , FILHO ANIBAL QUEIROZ , TESSMER EKKEHART , BEHLE ALFRED
Published: April 2006

Abstract

We present a new rapid expansion method (REM) for the time integration of the acoustic wave equation and the equations of dynamic elasticity in two spatial dimensions. The method is applicable to spatial grid methods such as finite differences, finite elements or the Fourier method. It is based on a Chebyshev expansion of the formal solution to the appropriate wave equation written in operator form. The method yields machine accuracy yet it is faster than methods based on temporal differencing. Its disadvantages are that it does not apply to all types of material rheology, and it can also require much storage when many snapshots and time sections are desired. Comparisons between numerical and analytical solutions for simple acoustic and elastic problems demonstrate the high accuracy of the REM.
SENSITIVITY ANALYSIS OF MAGNETOTELLURIC MEASUREMENTS IN RELATION TO STATIC EFFECTS1
Authors: SASAKI YUTAKA
Published: April 2006

Abstract

The relation between the horizontal profiles of the subsurface resistivity and surface magnetotelluric data can be described by the input and output of a moving‐average filter. The impulse response of this spatial filter, which characterizes the averaging process of the magnetotelluric measurements, is given by the sensitivity profile. Thus, the sensitivity analysis can provide insight into the characteristics of the measurements and hence the mechanism of the static effects. The sensitivity analysis presented here consists of constructing the vertical section of the sensitivity distribution using the finite‐element method and then Fourier transforming the selected horizontal profiles. When the dipole is assumed for measuring the electric field, the static effects can be explained by the high‐pass filter characteristics for the near‐surface. When the electrode separation is taken into account, the sensitivity can be obtained by averaging the sensitivities for the dipoles over the horizontal distance equal to the electrode separation. Therefore, the higher‐frequency components at each depth decrease with increasing electrode separation. Thus, although the static effects can be reduced simply by increasing the electrode separation, information on the resistivity variation at depth is also lost. However, such an adverse effect can be reduced by making the EMAP‐type measurements followed by the spatial filtering of the profile data using the tapered weighting function.
APPLICATION OF ELASTIC MODELLING IN PROCESSING AND INTERPRETATION OF VSP DATA: A CASE HISTORY1
Authors: AMINZADEH F.
Published: April 2006

Data from offshore Norway is used to study applications of elastic VSP modelling in detecting shear waves and observing the effects of successive mode conversion in field‐recorded VSP data. The shear‐wave velocities and densities from log data are used in conjunction with compressional wave velocities determined from surface seismic and log data in the VSP modelling.

The time domain non‐normal incidence elastic VSP modelling technique of Aminzadeh and Mendel is used as the modelling algorithm. Two surface seismograms are computed first. One is the vertical component and the other is the horizontal component for plane waves that have specified incident angles. A downward continuation method is then applied to generate seismograms at different depth points. The collection of these seismograms constitutes non‐normal incidence VSPs. Both vertical and horizontal components of VSP data can be obtained by this procedure.

In this paper non‐normal incidence VSPs are generated for a 12.5° incident plane wave. The modelling results of layered earth systems of thin layers and thick layers are both compared with field data, and the effect of mode conversions in thin layers is observed. Several events in the field data can be explained by this elastic VSP modelling.

Comparison of the model data and field data enabled a probable tube wave or out‐of‐plane event to be identified, the removal of which significantly improved the final VSP section. This study also shows how the VSP data helped the interpretation of the surface 3D data.
ELASTIC EXTRAPOLATION OF PRIMARY SEISMIC P‐ AND S‐WAVES1
Authors: WAPENAAR C. P. A. , HAIMÉ G. C.
Published: April 2006

Abstract

The elastic Kirchhoff‐Helmholtz integral expresses the components of the monochromatic displacement vector at any point A in terms of the displacement field and the stress field at any closed surface surrounding A. By introducing Green's functions for P‐ and S‐waves, the elastic Kirchhoff‐Helmholtz integral is modified such that it expresses either the P‐wave or the S‐wave at A in terms of the elastic wavefield at the closed surface. This modified elastic Kirchhoff‐Helmholtz integral is transformed into one‐way elastic Rayleigh‐type integrals for forward extrapolation of downgoing and upgoing P‐ and S‐waves. We also derive one‐way elastic Rayleigh‐type integrals for inverse extrapolation of downgoing and upgoing P‐ and S‐waves. The one‐way elastic extrapolation operators derived in this paper are the basis for a new prestack migration scheme for elastic data.
EFFICIENT COMPUTATION OF TRANSIENT SOUNDING CURVES FOR WIRE SEGMENTS OF FINITE LENGTH USING AN EQUIVALENT DIPOLE APPROXIMATION1
Authors: STOYER C. H.
Published: April 2006

Abstract

Calculations of emf induced in a vertical axis coil by a current step in a straight wire segment of finite length were carried out using an equivalent dipole placed along the source wire. An approximation is valid for homogeneous and layered earth models. The location of the equivalent dipole is calculated by forcing the early‐ and late‐time asymptotes of the transient sounding curve of the equivalent dipole to match those of the finite wire. This approximation works because the early‐time asymptote of the emf depends on the component of the receiver position which is parallel to the wire while the late‐time asymptote does not. Analytical integration of the early‐time asymptote yields an expression for the equivalent dipole location in closed form.

The coil can be placed anywhere in the vicinity of the finite wire. Square or rectangular loop sources can be simulated by one or more finite wire segments depending on the source‐receiver geometry. The equivalent radius calculated for central loop soundings agrees well with the value derived using a circular loop with the same area as the square loop.

Results show that acceptable sounding curves can be generated by the equivalent dipole for coils placed as close as 0.5 source lengths from the finite wire segment. Higher accuracy can be obtained by splitting the finite wire into two or more subsegments. Results for layered models are slightly better than homogeneous earth models when the resistivity increases with depth and slightly worse for models with resistivity decreasing with depth. Approximate calculations are about 10 times less expensive than exact calculations depending on the method used for the numerical integration.
OPTIMIZED FAST HANKEL TRANSFORM FILTERS1
Authors: CHRISTENSEN NIELS BØIE
Published: April 2006

Abstract

In the linear digital filter theory for calculation of Hankel transforms it is possible to find explicit series expansions for the filter coefficients. A method is presented for optimizing the Hankel filters calculated in this way. For a certain desired accuracy of computation, the sampling density and filter length are minimized by choosing the parameters determining the filter characteristics according to the analytical properties of the input function. A new approach to the calculation of the filter coefficients has been developed for these optimized filters. The length of the filters may be further reduced by introducing a shift in the sampling scheme.
A COMPARISON BETWEEN KIRCHHOFF AND GRT MIGRATION ON VSP DATA1
Authors: DILLON P. B.
Published: April 2006

Abstract

A modern approach to migration is to perform wavefield extrapolation, subject to an imaging condition. Correct wavefield extrapolation requires that the boundary conditions at the array of geophones satisfy the wave equation. A sufficient condition is to perform the survey with a single stationary source. Contrary to this condition, many VSPs are conducted in deviated wells, where the source is maintained vertically above the down‐hole geophone at each well station. Such a survey fails to provide the boundary conditions theoretically necessary for wave‐equation migration.

A recently published inversion scheme, referred to as acoustic generalized Radon transform migration (GRT migration), was developed to handle any configuration of sources and geophones, including moving‐source deviated‐well VSP surveys. GRT migration may be viewed as a weighted version of the generalized Kirchhoff migration, derived in this paper from the exploding‐reflector model.

When a VSP‐survey geometry has been specified, GRT migration can be expressed in terms of array parameters, and compared with the equivalent expression for Kirchhoff (wave‐equation) migration. The differences between the two integrals are significant and their effect is demonstrated on VSP data.
FIELD RESULTS WITH DOWNWARD CONTINUATION TECHNIQUE IN INDUCED POLARIZATION PROFILING USING POINT ELECTRODES1
Authors: APPARAO A. , RAO T. GANGADHARA , SARMA V. SUBRAHMANYA
Published: April 2006

Abstract

The method of downward continuation is well known to those working in gravity, magnetic, SP and low‐frequency electromagnetic exploration. It is demonstrated that the method of continuation can also be usefully employed in the interpretation of induced polarization gradient profiling using point electrodes to determine target depth. The apparent resistance Ra and chargeability Ma measurements obtained with point electrode excitation of the ground have been used to compute the values of (Ra)l and (Ma)l that would be obtained with a linear array.

Continuation of the apparent polarizability profile thus obtained with the linear array gives a value for the depth of the target which agrees closely with that obtained by the continuation of the SP profile. On the other hand, continuation of the profile of the secondary transient signal (VS)L alone, yields a depth of the target which is in agreement with the borehole information. However, it is seen that the secondary transient voltage profiling response splits into two anomalies which fall on either side of the SP and/or (Ma)l anomaly centre, and does not coincide with that of the latter.