bluuebunny/crossref_metadata_2025 huggingface dataset:
DOWNHOLE SYNTHETIC SEISMIC PROFILES IN ELASTIC MEDIA1
Authors: XU XIAOHONG
Published: April 2006

Abstract

A multichannel lattice filter structure is utilized to represent seismic waves propagating in adjacent layers in an elastic medium. Using this model, an explicit time‐domain solution for arbitrary source and receiver locations is obtained as an ARMA (AutoRegressive and Moving‐Average) process. The lattice and ARMA structures have given rise to an effective algorithm for the calculation of offset/downhole synthetic seismograms.

A large range of recently developed offset/downhole seismic survey geometries, such as the ‘Yo‐Yo’ arrangement, can thus be simulated. In addition, the explicit solutions for upgoing and downgoing waves provide new insight into the properties of general downhole seismic signals, including wave‐mode conversion effects and multiple reflections. Furthermore, offset/downhole seismograms generated by a line source (i.e. 2D point source) can also be constructed by superposition of plane waves with different incidence angles.

Synthetic seismograms generated using a different source‐receiver arrangement indicate that the properties especially associated with offset/downhole seismic signals can be predicted by this modelling method. These properties include arrival times, amplitude attenuation and wave‐mode conversion effects. Finally, utilizing this numerical modelling method to a real downhole survey with Yo‐Yo geometry may lead to a proper data acquisition and processing procedure, and improves the interpretation confidence of the field section.
INVERSION OF FIRST‐BREAK TRAVELTIME DATA OF DEEP SEISMIC REFLECTION PROFILES1
Authors: RÜHL THOMAS , LÜSCHEN EWALD
Published: April 2006

Abstract

First breaks of 2D deep reflection data were used to construct velocity‐depth models for improved static corrections to a deeper datum level and for geological interpretations. The highly redundant traveltime data were automatically picked and transformed directly into a velocity‐depth model by maximum depth methods such as the Giese‐ and the Slichter‐method. Comparisons with the results of synthetic calculations and a tomographic approach using iterative inversion methods (ART, SIRT) showed that maximum depth methods provide reliable velocity models as a basis for the computation of static corrections. These methods can economically be applied during data acquisition in the field. They provide particularly long‐period static anomalies, which are of the order of 20–40 ms (0.5‐1 wavelength) within CMP gathers of an example of a deep reflection profile in SW‐Germany sited on crystalline basement. Reprocessing of this profile, which was aimed at the comparison between the effects of the originally used and the new statics, did not result in dramatically improved stacking quality but showed a subtle influence on the detailed appearance of deep crustal events.
MINIMUM RELATIVE ENTROPY INVERSION OF 1D DATA WITH APPLICATIONS1
Authors: ULRYCH T. , BASSREI A. , LANE M.
Published: April 2006

Abstract

The pioneering work of E. T. Jaynes in the field of Bayesian/Maximum Entropy methods has been successfully explored in a number of disciplines. The principle of maximum entropy (PME) is remarkably powerful and versatile and leads to results which are devoid of spurious structure. Minimum relative entropy (MRE) is a method which has all the important attributes of the maximum‐entropy (ME) approach with the advantage that prior information may be easily included. These ‘soft’ prior constraints play a fundamental role in the solution of underdetermined problems. The MRE approach, like ME, has achieved considerable success in the field of spectral analysis where the spectrum is estimated from incomplete autocorrelations. In this paper we apply the MRE philosophy to 1D inverse problems where the model is not necessarily positive, and thus we show that MRE is a general method of tackling linear, underdetermined, inverse problems. We illustrate our discussion with examples which deal with the famous die problem introduced by Jaynes, the question of aliasing, determination of interval velocities from stacking velocities and, finally, the universal problem of band‐limited extrapolation. It is found that the MRE solution for the interval velocities, when a uniform prior velocity is assumed, is exactly the Dix formulation which is generally used in the seismic industry.
STRUCTURE OF THE SOUTHWESTERN FRASER RIVER DELTA AS DETERMINED FROM GEOELECTRIC SOUNDING1
Authors: NOBES D.C. , HAMILTON T. S. , CARTWRIGHT P.
Published: April 2006

Abstract

Geoelectrical sounding profiles were collected on the southern part of the Fraser River delta, to provide a geophysical estimate of the subsurface structure and geotechnical properties. The differences between emergent and intertidal areas were assessed, and the geoelectric technique was found to be a viable one in an intermittently exposed tidal‐flat environment. The subsurface geoelectric structure provides a link between reflection seismic data sets for Georgia Strait and the lower mainland. The survey was intentionally designed to complement the conventional exploration information for this basin and the shallow high‐resolution seismic and drilling which focused on the unconsolidated Quaternary section. The electrical models consist of three layers: (I) electrically‐conductive, porous, saturated and under‐saturated marine silts, sands and gravels, overlying (II) less conductive and more consolidated marine clays, and variably reworked glaciomarine deposits together with weathered clastic sedimentary bedrock, which in turn overlies (III) less porous, more resistive, relatively unweathered bedrock. Estimates of thickness and geotechnical properties are obtained for shallow layers which are not available from either the short boreholes or shallow high‐resolution seismic lines. This information is particularly useful in appraising the liquefaction potential of the unconsolidated layers due to earthquake risk.
3D ACOUSTIC PRESTACK REVERSE‐TIME MIGRATION1
Authors: CHANG WEN‐FONG , McMECHAN GEORGE A.
Published: April 2006

Abstract

A prestack reverse‐time migration algorithm which operates on common‐source gathers, recorded at the Earth's surface, from 3D structures, is conceived, implemented and tested. Reverse‐time extrapolation of the recorded wavefield (a boundary‐value problem), and computation of the excitation‐time imaging condition for each point in a 3D volume (an initial‐value problem), are both performed using a second‐order finite‐difference solution of the full 3D scalar wave equation. The algorithm is illustrated by processing synthetic data for a point diffractor, an oblique wedge, and the French double dome and fault model.
TRACE INTERPOLATION BY SLANT‐STACK MIGRATION1
Authors: NOVOTNÝ M.
Published: April 2006

Abstract

The slant‐stack migration formula based on the Radon transform is studied with respect to the depth step Δz of wavefield extrapolation. It can be viewed as a generalized trace‐interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz= 0 the formula yields the familiar plane‐wave decomposition, while for Δz > 0 it provides a robust tool for migration transformation of spatially undersampled wavefields. Using the stationary phase method, it is shown that the slant‐stack migration formula degenerates into the Rayleigh‐Sommerfeld integral in the far‐field approximation. Consequently, even a narrow slant‐stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the Radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period.
TRANSFORMATION OF LINE‐SOURCE RESISTIVITY DATA TO POINT‐SOURCE DATA AND VICE VERSA USING THE MATRIX METHOD1
Authors: NIWAS SRI
Published: April 2006

Abstract

Investigations have shown the existence of a linear relationship between point‐source resistivity data and line‐source resistivity data through a matrix operator, which paves the way for the efficient transformation of line‐source data to the corresponding point‐source data and vice versa. The power of these equations has been established by computational examples. The relationship will be useful in the modelling and inversion of resistivity data from 2D structures.
GEOMETRIC CORRECTIONS IN ATTENUATION MEASUREMENTS1
Authors: KLIMENTOS THEODOROS
Published: April 2006

Abstract

Seismic wave attenuation in porous rocks consists of intrinsic or anelastic attenuation (the lost energy is converted into heat due to interaction between the waves and the rocks) and the extrinsic or geometric attenuation (the energy is lost due to beam spreading, transmission loss and scattering). The first is of great importance because it can give additional information on the petrophysical properties of rocks (permeability, degree of saturation, type of saturant, etc.). The most difficult problem in attenuation measurements is estimating or eliminating extrinsic attenuation, so that the intrinsic attenuation can be obtained. To date, in laboratory attenuation measurements using wave propagation, several methods have been used. The difficulties vary with the method. The coupling effect and the geometric divergence or beam spreading are the major problems.

Papadakis’ diffraction corrections have been used extensively by Winkler and Plona in their modified pulse‐echo high‐pressure attenuation measurements. These corrections are computed for homogeneous liquid media and their failure to fit data for solid material implies that these corrections must be used with caution, especially for high Q values.

Three new methods for laboratory ultrasonic attenuation measurements are presented. The first is the ‘ultrasonic lens’ method for attenuation measurements at atmospheric pressure, in which an ultrasonic lens placed between transmitter and sample transforms the initially oblique incident beam into normal incidence so that the geometric divergence is eliminated. The second method is the ‘panoramic receiver’, in which the beam spreading can be eliminated by integrating the ultrasonic energy over a large area. The third method is called 'self‐spectral ratio’ and is applicable for all pressure conditions. Attenuation is estimated by comparing two signals recorded on the same rock but with two slightly different thicknesses under the same pressure conditions. Hence the extrinsic attenuation for both thicknesses is approximately the same. A comparison between the self‐spectral ratio method and that of Winkler and Plona demonstrates a very good agreement for a broad band of frequencies. Hence the Winkler‐Plona technique and Papadakis’ diffraction corrections can be accepted as reliable in any future work.
LAYERED PERMEABLE SYSTEMS1
Authors: SCHOENBERG MICHAEL
Published: April 2006

Abstract

Permeability is a second rank tensor relating flow rate to pressure gradient in a porous medium. If the permeability is a constant times the identity tensor the permeable medium is isotropic; otherwise it is anisotropic. A formalism is presented for the simple calculation of the permeability tensor of a heterogeneous layered system composed of interleaved thin layers of several permeable constituent porous media in the static limit. Corresponding to any cumulative thickness H of a constituent is an element consisting of scalar H and a matrix which is H times a hybrid matrix function of permeability. The calculation of the properties of a medium equivalent to the combination of permeable constituents may then be accomplished by simple addition of the corresponding scalar/matrix elements. Subtraction of an element removes a permeable constituent, providing the means to decompose a permeable medium into many possible sets of permeable constituents, all of which have the same flow properties. A set of layers of a constituent medium in the heterogeneous layered system with permeability of the order of 1/h as h→ 0, where h is that constituent's concentration, acts as a set of infinitely thin channels and is a model for a set of parallel cracks or fractures. Conversely, a set of layers of a given constituent with permeability of the order of h as h→ 0 acts as a set of parallel flow barriers and models a set of parallel, relatively impermeable, interfaces, such as shale stringers or some faults. Both sets of channels and sets of barriers are defined explicitly by scalar/matrix elements for which the scalar and three of the four sub‐matrices vanish. Further, non‐parallel sets of channels or barriers can be ‘added’ and 'subtracted’ from a background homogeneous anisotropic medium commutatively and associatively, but not non‐parallel sets of channels and barriers reflecting the physical reality that fractures that penetrate barriers will give a different flow behaviour from barriers that block channels. This analysis of layered media, and the representations of the phenomena that can occur as the thickness of a constituent is allowed to approach zero, are applicable directly to layered heat conductors, layered electrostatic conductors and layered dielectrics.
ADAPTIVE PICKING OF REFRACTED FIRST ARRIVALS1
Authors: SPAGNOLINI UMBERTO
Published: April 2006

Abstract

Static correction computations require knowledge of the refracted traveltimes. Zero‐phase wavelet sources cannot be picked reliably when incoherent picking techniques are used.

Assuming a complex convolutional model for Vibroseis, a coherent picking technique based on the matched filter is described. In order to match the filter to the first arrival wavelet an adaptive algorithm is used. This allows the filter to change both with shot and offset so that all the properties of matched filtering such as improvement of S/N and resolution can be exploited. Incoherent picking is used before coherent picking to improve the convergence of adaptive picking.
A FIRST‐ORDER CORRECTION TO THE THEORY FOR THE ELECTROMAGNETIC RESPONSE OF A THIN CONDUCTING SHEET1
Authors: HURLEY D. G. , SIEW P. F.
Published: April 2006

Abstract

The eddy currents induced in a thin conducting sheet by a sinusoidally varying primary magnetic field are investigated in the low‐frequency limit when the depth of penetration of the primary field is much greater than the thickness of the sheet. A perturbation scheme in terms of the small parameter, δ, which is the ratio of the thickness of the sheet to the length scale of the primary field is initiated. The zero‐order terms in δ give the familiar results that were first obtained by Maxwell. The first‐order terms in δ depend on the tangential as well as the normal component of the primary field and give eddy‐current distributions that vary quadratically across the sheet. The boundary conditions that determine the accompanying secondary magnetic field are derived. Detailed results are given when the primary field is that due to a dipole.
A SIMULATED ANNEALING APPROACH TO SEISMIC MODEL OPTIMIZATION WITH SPARSE PRIOR INFORMATION1
Authors: MOSEGAARD KLAUS , VESTERGAARD PETER D.
Published: April 2006

Abstract

It is well known that seismic inversion based on local model optimization methods, such as iterative use of linear optimization, may fail when prior information is sparse. Where the seismic events corresponding to reflectors of interest remain to be identified, a global optimization technique is required.

We investigate the use of a global, stochastic optimization method, that of simulated annealing, to solve the seismic trace inversion problem, in which the two‐way traveltimes and reflection coefficients are to be determined. The simulated annealing method is based on an analogy between the model‐algorithm system and a statistical mechanical system. We exploit this analogy to produce improved annealing schedules. It is shown that even in cases of virtually no prior information about two‐way traveltimes and reflection coefficients, the method is capable of producing reliable results.
DETECTION OF AN AIR‐FILLED DRAINAGE GALLERY BY THE VLF RESISTIVITY METHOD1
Authors: OGILVY R. D. , CUADRA A. , JACKSON P. D. , MONTE J. L.
Published: April 2006

Abstract

VLF wave impedance measurements have been successfully used to detect air‐filled drainage galleries near the town of Alcala, Spain. The galleries are detectable by H‐polarization electric field measurements due to the electric field anomalies associated with the galleries and overlying gravel deposits. The forced deviation of the primary current flowlines around the 2D void results in a higher‐than‐normal apparent resistivity and a relative phase low above the gallery.

The findings support earlier theoretical predictions that at very low frequencies (VLFs), galvanic current effects may dominate over vortex currents in moderately conductive terrains. Theoretical modelling confirmed that for a resistive target no detectable E‐polarization response can be expected from either magnetic or electric field measurements since current line deviations and vortex effects are negligible under such circumstances.

The results demonstrate the importance of using at least two orthogonal VLF transmitters in order that anomalies arising from both galvanic and inductive effects may be identified, irrespective of orientation.
THE INSENSITIVITY OF REFLECTED SH WAVES TO ANISOTROPY IN AN UNDERLYING LAYERED MEDIUM1
Authors: SCHOENBERG MICHAEL , COSTA JESSE
Published: April 2006

Abstract

Propagation in the plane of mirror symmetry of a monoclinic medium, with displacement normal to the plane, is the most general circumstance in anisotropic media for which pure shear‐wave propagation can occur at all angles. Because the pure shear mode is uncoupled from the other two modes, its slowness surface in the plane is an ellipse. When the mirror symmetry plane is vertical the pure shear waves in this plane are SH waves and the elliptical SH sheet of the slowness surface is, in general, tilted with respect to the vertical axis. Consider a half‐space of such a monoclinic medium, called medium M, overlain by a half‐space of isotropic medium I with plane SH waves incident on medium M propagating in the vertical symmetry plane of M. Contrary to the appearance of a lack of symmetry about the vertical axis due to the tilt of the SH‐wave slowness ellipse, the reflection and transmission coefficients are symmetrical functions of the angle of incidence, and further, there exists an isotropic medium E with uniquely determined density and shear speed which gives exactly the same reflection and transmission coefficients underlying medium J as does monoclinic medium M. This means that the underlying monoclinic medium M can be replaced by isotropic medium E without changing the reflection and transmission coefficients for all values of the angle of incidence. Thus no set of SH seismic experiments performed in the isotropic medium in the symmetry plane of the underlying half‐space can reveal anything about the monoclinic anisotropy of that underlying half‐space. Moreover, even when the underlying monoclinic half‐space is stratified, there exists a stratified isotropic half‐space that gives the identical reflection coefficient as the stratified monoclinic half‐space for all angles of incidence and all frequencies.
MULTICOMPONENT COMMON‐RECEIVER GATHER MIGRATION OF SINGLE‐LEVEL WALK‐AWAY SEISMIC PROFILES1
Authors: JACKSON G. M. , MASON I. M. , LEE DELMAN
Published: April 2006

Abstract

Seismic data are usually separated into P‐waves and S‐waves before being put through a scalar (acoustic) migration. The relationship between polarization and moveout is exploited to design filters that extract the desired wavetype. While these filters can always be applied to shot records, they can only be applied to a triaxial common‐receiver gather in special cases since the moveout of scattered energy on the receiver gather relates to path differences between the surface shots and the scatterer while the polarization is determined by the path from scatterer to downhole geophone. Without the ability to separate wavefields before migration, a ‘vector scalar’ or an elastic migration becomes a necessity.

Here the propagation of the elastic wavefield for a given mode (e.g. P‐S) is approximated by two scalar (acoustic) propagation steps in a ‘vector scalar’ migration. ‘Vector’ in that multicomponent data is migrated and 'scalar’ in that each propagation step is based on a scalar wave equation for the appropriate mode. It is assumed that interaction between the wavefields occurs only once in the far‐field of both the source and receiver. Extraction of the P, SV and SH wavefields can be achieved within the depth migration (if one assumes isotropy in the neighbourhood of the downhole receiver) by a projection onto the polarization for the desired mode. Since the polarization of scattered energy is only a function of scatterer position and receiver position (and not source position), the projection may be taken outside the migration integral in the special case of the depth migration of a common‐receiver gather. The extraction of the desired mode is then performed for each depth migration bin after the separate scalar migration of each receiver gather component.

This multicomponent migration of triaxial receiver gathers is conveniently implemented with a hybrid split‐step Fourier‐excitation‐time imaging condition depth migration. The raytracing to get the excitation‐time imaging condition also provides the expected polarization for the post‐migration projection. The same downward extrapolated wavefield can be used for both the P‐P and P‐S migrations, providing a flexible and efficient route to the migration of multicomponent data.

The technique is illustrated on a synthetic example and a single‐level Walk‐away Seismic Profile (WSP) from the southern North Sea. The field data produced images showing a P‐P reflector below the geophone and localized P‐P and P‐S scatterers at the level of the geo‐phone. These scatterers, which lie outside the zone of specular illumination, are interpreted as faults in the base Zechstein/top Rotliegendes interface.
PARAMETRIZATION OF GRT INVERSION FOR ACOUSTIC AND P–P SCATTERING1
Authors: IKELLE L. T. , KITCHENSIDE P. W. , SCHULTZ P. S.
Published: April 2006

Abstract

The generalized Radon transform (GRT) inversion contains an explicit relationship between seismic amplitude variations, the reflection angle and the physical parameters which can be used to describe the earth efficiently for inversion purposes. Using this relationship, we have derived parametrizations for acoustic and P–P scattering so that the variations in seismic amplitude with reflection angle for each parameter are sufficiently independent. These parametrizations show that small offset and large offset amplitudes are related to different physical parameters. In the case of acoustic scattering, the small‐offset amplitudes are related to impedance variations while large‐offset amplitudes are related to velocity variations. A similar result has been established for P–P scattering.

The Born approximation (which is used to derive the GRT inversion) does not correctly predict the amplitude due to velocity variations at large offsets, and thus the inversion of velocity is not as satisfactory as the inversion of impedance.
A THEORETICAL TREATMENT OF THE EFFECT OF MICROSCOPIC FLUID DISTRIBUTION ON THE DIELECTRIC PROPERTIES OF PARTIALLY SATURATED ROCKS1
Authors: ENDRES ANTHONY L. , KNIGHT ROSEMARY
Published: April 2006

Abstract

Microscopic fluid distribution can have a significant effect on the dielectric properties of partially saturated rocks. Evidence of this effect is found in the laboratory data presented by Knight and Nur in which different methods for controlling saturation produced very different results for the dependence of the dielectric response on water saturation. In this study, previously derived models for the dielectric response of a heterogeneous medium are generalized and the case of a pore space occupied by multiple pore fluids is considered. By using various geometrical distributions of water and gas, it is observed that both the pore geometry in which saturation conditions are changing and the gas–water geometry within a given pore space are critical factors in determining the effective dielectric response of a partially saturated rock.

As an example, data for a tight gas sandstone undergoing a cycle of imbibition and drying are analysed. Previous research has demonstrated that significantly different microscopic fluid distributions result from the application of these two techniques to control the level of water saturation. By approximating these microscopic fluid distributions using simple geometrical models, good agreement is found between experimental data and calculated dielectric properties.
BURGER'S EQUATION AS A MODEL FOR THE IP PHENOMENON1
Authors: WYLLER J. , WELLANDER N. , LARSSON F. , PARASNIS D. S.
Published: April 2006

Abstract

The dynamic response characterizing the induced‐polarization (IP) phenomenon is modelled by a non‐linear diffusion equation (Burger's equation) supplemented by relevant initial and boundary values. The analysis of the model yields a voltage step response and an impedance curve in the frequency domain which agree qualitatively with experimental measurements. Curve fits based on the model have been made in the case of electrochemical cell measurements. The diffusion coefficients estimated by means of these curves are of the same order of magnitude as those calculated using experimental measurements. The normalized transient with these diffusion coefficients agrees with observations, but probably has a shorter discharge time. We have also carried out a comparison with predictions obtained from a linear, finite diffusion layer model, thus showing that for most practical situations the nonlinear term modelling the migration effect can be neglected.
WHEN LEAST‐SQUARES SQUARES LEAST1
Authors: AL‐CHALABI M.
Published: April 2006

Abstract

There is a general lack of awareness among ‘lay’ professionals (geophysicists included) regarding the limitations in the use of least‐squares. Using a simple numerical model under simulated conditions of observational errors, the performance of least‐squares and other goodness‐of‐fit criteria under various error conditions are investigated. The results are presented in a simplified manner that can be readily understood by the lay earth scientist. It is shown that the use of least‐squares is, strictly, only valid either when the errors pertain to a normal probability distribution or under certain fortuitous conditions. The correct power to use (e.g. square, cube, square root, etc.) depends on the form of error distribution. In many fairly typical practical situations, least‐squares is one of the worst criteria to use. In such cases, data treatment, ‘robust statistics’ or similar processes provide an alternative approach.
ELASTIC REDATUMING OF MULTICOMPONENT SEISMIC DATA1
Authors: WAPENAAR C. P. A. , COX H. L. H. , BERKHOUT A. J.
Published: April 2006

Abstract

Elastic redatuming can be carried out before or after decomposition of the multicomponent data into independent PP, PS, SP, and SS responses. We argue that from a practical point of view, elastic redatuming is preferably applied after decomposition. We review forward and inverse extrapolation of decomposed P‐ and S‐wavefields. We use the forward extrapolation operators to derive a model of discrete multicomponent seismic data. This forward model is fully described in terms of matrix manipulations.

By applying these matrix manipulations in reverse order we arrive at an elastic processing scheme for multicomponent data in which elastic redatuming plays an essential role. Finally, we illustrate elastic redatuming with a controlled 2D example, consisting of simulated multicomponent seismic data.
AN INTEGRAL EQUATION FOR THE GEOELECTRIC RESPONSE OF THIN RESISTIVE BODIES1
Authors: FURNESS PETER
Published: April 2006

Abstract

Thin sheet‐like forms are common target bodies in geoelectric prospecting. Depending on their mineralogy and other factors these bodies may be relatively conductive or relatively resistive with respect to their surroundings. For suitably remote field points (relative to the thickness) these features manifest themselves geoelectrically in terms of their conductivity‐thickness product for relatively conductive bodies or in terms of their resistivity‐thickness product for resistive forms.

While the case of a conductive sheet has received some attention in the geophysical literature, resistive sheets have been largely ignored. Accordingly an efficient technique to model the geoelectric responses of a resistive lamina is presented here. The technique involves representing the lamina in terms of a distribution of normally directed current dipole moment whose density is shown to satisfy an inhomogeneous Fredholm integral equation of the second kind.

The technique is rigorously tested in a 2D environment and is shown to produce reliable and suitably accurate results. An application of the method is presented in which the apparent resistivity and chargeability responses measured with a gradient array over a dipping resistive ribbon are computed. These are compared with the responses observed over a relatively conductive ribbon in the same orientation.
OPTIMAL ESTIMATION OF CRACK‐STRIKE1
Authors: MacBETH COLIN , YARDLEY GARETH S.
Published: April 2006

Abstract

The accuracy of estimating crack‐strike from the algebraic equivalent of a popular technique, the dual source cumulative technique (DCT), for analysing shear‐wave splitting in seismic experiments is evaluated for earth models permeated by different alignments of micro‐cracks. A complementary analysis is performed using another analysis procedure, the dual‐independent source‐geophone technique (DIT), to investigate any benefits of the alternative formulation. The investigation considers synthetic vertical seismic profile (VSP) and reflection data for an earth model with two layers over a half‐space, and three different classes of crack‐strike variation with depth: uniform crack‐strike, an abrupt change of crack‐strike between the upper and lower layer, and a continuous increase over both layers. The synthetic data for zero‐offset and near‐offset VSPs and a reflection profile are computed using a full‐wave modelling package in which equivalent anisotropic media simulate distributions of aligned vertical, parallel, water‐filled microcracks. Estimates from the two techniques agree for the constant crack‐strike model, but differ for the VSP data with crack‐strike changes. The asymptotic behaviour of the two angular parameters θG and θS from DIT suggest that it may be used to determine crack‐strike under appropriate circumstances in these VSPs, when the time‐delay between the split shear‐waves for the layer of interest exceeds the peak period of the wavelet. In this limit, θG tends to follow the crack‐strike change with θS tending to a constant value, whereas DCT will give a misleading value between the upper and lower crack‐strike. Although the behaviour of DIT is not understood in all cases, θG and θS values from the VSP data always appear to diverge near the point where an abrupt crack‐strike change takes place. This could be used as a qualitative indicator for layer stripping. Both techniques agree for the reflection data as the recorded data matrix is necessarily symmetric, but still give misleading results for deeper layers in the presence of crack‐strike changes. This study suggests that more care should be taken when designing and analysing experimental configurations for detecting crack properties in reservoir rocks, to consider the response and resolution limits of the analysis techniques. A note of caution is offered to those who directly interpret polarization estimates as crack‐strike.
INDUCED GRAVITY ANOMALIES AND ROCK‐BURST RISK IN COAL MINES: A CASE HISTORY1
Authors: CASTEN U. , FAJKLEWICZ Z.
Published: April 2006

Abstract

The use of the gravity method to predict rock bursts in mines is based on the relationship between the development of a dilatancy process in the exploited rock mass and the time‐dependent gravity anomalies induced by this phenomenon. The differences between successive observations of anomalies and the time behaviour of their trend amplitudes as precursors of preceding changes of rock stability are interpreted. The centres of zones of induced rock density variation are determined by computing the position of singular points of the differences between anomalies.

Two gravity surveys have been carried out in the Radbod coal mine (Germany). The first survey took place at the level of the Dickebank seam (depth 1030 m), the second in the Sonnenschein seam (depth 1090 m). The observations were made with Worden and LaCoste‐Romberg (D‐type) gravimeters. The differences between successive anomalies were less than 100 μGal.

In the case of the Dickebank seam, the position of singular points demonstrates the effect of two approaching longwalls on a previously mined‐out seam and on the gallery in which the gravity observations were made. In the case of the Sonnenschein seam, the trend amplitudes show distinct variations in the formation of the approaching longwall below the edges of all previously mined‐out seams. In particular, the effect of a remnant pillar has caused the largest gravity gradients. This result corresponds to the existence of a zone of rock‐burst hazard known from test drilling. The computed singular points are grouped together under the remnant pillar indicating two local hazard zones.

Both results, the observed development of rock instability with time and the information about the position of the disturbed rock mass relative to the mine workings, are of importance, subsurface gravity surveying can therefore be a valuable tool for predicting rock‐bursts.
DEGHOSTING USING A TWIN STREAMER CONFIGURATION1
Authors: POSTHUMUS B. J.
Published: April 2006

Abstract

A processing method is presented to attenuate the surface ghost using marine twin streamer data. It is an extension to the dephase and sum method which corrects for the phase of the ghost in both streamer outputs and then adds them in an attempt to fill the notches in the amplitude spectrum. The method presented corrects both the phase and the amplitude effect of the surface ghost by combining both signals as a weighted sum.

This method is applicable to all types of twin streamer data, ranging from deep exploration data to very shallow high‐resolution surveys. Both the synthetic and real data examples shown are of the high‐resolution type, using frequencies above 2 kHz and short streamers (active sections of the order of one metre).

Both the dephase and sum method and the weighted sum method are applied to synthetic high‐resolution data and the results are compared. This has been done for noise‐free data, data with a high noise level and data with strong geometrical spreading on the ghost reflections. From these test results it can be concluded that in general the weighted sum method gives better results. The improvement in the signal‐to‐noise ratio appears to be the same, due to the additive character of both methods. In the case of high‐resolution twin streamer data recorded in shallow water, the delay time of the ghost reflection can be of the same order of magnitude as the traveltime of the primary. For this situation, geometrical spreading can have a considerable effect on the amplitude of the ghost reflection. If no correction can be made for the spreading function, it might be better to use the dephase and sum method.

Both methods are also applied to a real data set recorded in a high‐resolution survey. Because the ghost delay is of the same order of magnitude as the arrival time of the primary, the ghost reflection is strongly affected by geometrical spreading. Since the spreading function of the source is unknown, it cannot be corrected for. This causes the result of the weighted sum method to be less reliable compared to the case where no spreading is involved.
SECONDARY SHEAR WAVES FROM SOURCE BOREHOLES1
Authors: MEREDITH J. A. , TOKSÖZ M. N. , CHENG C. H.
Published: April 2006

Abstract

Previous studies of radiation from point sources in fluid‐filled boreholes have most often been based on far‐field, stationary phase analysis. In these papers, the explicit contribution of the borehole itself acting as a waveguide has not been properly considered, with a few exceptions. In general, these studies accurately describe S‐wave radiation in high‐velocity rocks such as granites and limestones and P‐wave radiation in most rocks, and experiments have confirmed this. However, tube waves directly influence the external wavefield and in fact create a shear‐wave ‘wake’ outside the borehole due to constructive interference of tube‐wave emission if a velocity condition is met. This constructive interference or wake is generated when the tube‐wave velocity is greater than the shear‐wave velocity. When this happens, a tube‐wave complex pole invalidates the mathematical assumptions for stationary phase analysis and the stationary phase predictions do not agree with experimentally derived radiation patterns. Shales at shallow depths and other soft sediments characteristically have tube‐wave velocities greater than shear‐wave velocities. Because the tube‐wave is of relatively high amplitude compared to body waves generated directly by the source, these secondary shear waves can be the highest amplitude arrivals on receiver arrays.

The shape and properties of these secondary shear waves are calculated and shown to have identical properties to Mach waves of aerodynamics and seismology. For instance, these waves are geometrically conical and the aperture of the cone and the moveout velocity can be calculated. This paper also demonstrates the important effect that casing has on the Mach waves and provides predictions about when these waves are likely to be observed. Finally, evidence of Mach waves in data sets is examined and it is shown how these waves have been confused with receiver borehole tube waves.

It is possible, though rare, that the tube‐wave velocity of the borehole is greater than the compressional‐wave velocity of the surrounding medium. In this case secondary compressional or compressional Mach waves would be generated although this problem is not addressed here.
BOREHOLE STONELEY WAVE PROPAGATION ACROSS PERMEABLE STRUCTURES1
Authors: TANG X. M. , CHENG C. H.
Published: April 2006

Abstract

This study investigates the propagation of borehole Stoneley waves across permeable structures. By modelling the structure as a zone intersecting the borehole, a simple 1D theory is formulated to treat the interaction of the Stoneley wave with the structure. This is possible because the Stoneley wave is a guided wave, with no geometric spreading as it propagates along the borehole. The interaction occurs because the zone and the surrounding formation possess different Stoneley wavenumbers. Given appropriate representations of the wavenum‐ber, the theory can be applied to treat a variety of structures, including a fluid‐filled fracture. Of special interest are the cases of permeable porous zones and fracture zones. The results show that, while Stoneley wave reflections are generated, strong Stoneley wave attenuation is produced across a very permeable zone. This result is particularly important in explaining the observed strong Stoneley wave attenuation at major fractures where it has been difficult to explain the attenuation in terms of the single planar fracture theory. In addition, by using a simple and sufficiently accurate theory to model the effects of the permeable zone, a fast and efficient method is developed to characterize the fluid transport properties of a permeable fracture zone.
WAVE‐EQUATION MULTIPLE SUPPRESSION USING CONSTRAINED GROSS‐EQUALIZATION1
Authors: MONK DAVID J.
Published: April 2006

Abstract

A method for improving the attenuation of water‐layer multiple energy is suggested. The improvement is achieved using wave‐equation extrapolation to generate an initial model of the multiple energy, and then constraining the way in which this model is modified to fit the observed multiple energy. Reconciling the initial multiple model with the input data is a critical part of this process and several techniques have been suggested previously by other authors. The approach used here is to fit the time, amplitude and phase of the wavelets by adapting the initial model trace using a weighted sum of four traces which can each be derived from the initial multiple model trace.

Results on real data suggest that attenuation of primary energy is minimized using this technique, without diminishing the level of multiple attenuation.
FREQUENCY‐DEPENDENT COMPLEX RESISTIVITY OF ROCK‐SALT SAMPLES AND RELATED PETROPHYSICAL PARAMETERS1
Authors: KULENKAMPFF J. M. , YARAMANCI U.
Published: April 2006

Abstract

The presence of water is one of the main concerns of nuclear waste disposal in rock‐salt. It can be investigated using electrical properties of the rock. Laboratory measurements of frequency‐dependent resistivity and other petrophysical parameters, such as porosity, water content, and specific internal surface area, have been carried out on rock‐salt from the Asse mine in Germany, in order to obtain characteristic resistivity responses for the evaluation of geoelectric field methods and to develop new methods for the estimation of the water content and saturation. The laboratory method, on a.c. half‐bridge for very high impedances, allows measurements of the resistivity spectrum of rock‐salt in the frequency range from 15 Hz to 10 kHz. The saturation of the samples was varied artificially and was approximately 5%, 10%, 20% and 100%.

The porosity varies between 0.1% and 0.5%, the water content is approximately 0.05% or less, and the initial saturation is less than 50%. The resistivity ranges from 10 MΩm at the initial saturation down to 1 kΩm for fully saturated samples. In the low‐frequency range up to 100 Hz, an Archie‐type relationship may be used to estimate the water content of the rock‐salt from resistivity measurements. The Archie exponent m is found to be approximately 2.

The resistivity is observed to be strongly dependent on frequency. The resistivity decreases with increasing frequency, with a greater decrease for small saturations and vanishing frequency dependence at complete saturation. The relative dielectric constant was found to be 6 ± 1. Saturation dependence was not observed within this error range.

The measurements imply that, by measuring resistivity in rock‐salt, estimations of water content and saturation, and thus the porosity, can be made in situ. This is particularly important for the safety of nuclear waste disposal in rock‐salt.
2D finite‐difference elastic wave modelling including surface topography1
Authors: Hestholm Stig , Ruud Bent
Published: April 2006

A 2D numerical finite‐difference algorithm accounting for surface topography is presented. Higher‐order, dispersion‐bounded, cost‐optimized finite‐difference operators are used in the interior of the numerical grid, while non‐reflecting absorbing boundary conditions are used along the edges. Transformation from a curved to a rectangular grid achieves the modelling of the surface topography. We use free‐surface boundary conditions along the surface. In order to obtain complete modelling of the effects of wave propagation, it is important to account for the surface topography, otherwise near‐surface effects, such as scattering, are not modelled adequately. Even if other properties of the medium, for instance randomization, can improve numerical simulations, inclusion of the surface topography makes them more realistic.
Normal moveout in focus1
Authors: de Bazelaire Eric , Viallix Jean Rene
Published: April 2006

Improving the accuracy of NMO corrections and of the corresponding interval velocities entails implementing a better approximation than the formula used since the beginning of seismic processing. The exact equations are not practical as they include many unknowns. The approximate expression has only two unknowns, the reflection time and the rms velocity, but becomes inaccurate for large apertures of the recording system and heterogeneous vertical velocities. Several methods of improving the accuracy have been considered, but the gains do not compensate for the dramatic increase in computing time. Two alternative equations are proposed: the first containing two parameters, the reflection time and the focusing time, is not valid for apertures much greater than is the standard formula, but has a much faster computing time and does not stretch the far traces; the other, containing three parameters, the reflection time, like focusing time and the tuning velocity, retains high frequencies for apertures about twice those allowed by the standard equation. Its computing time can be kept within the same limits. NMO equations, old and new, are designed strictly for horizontal layering, but remain reliable as long as the rays travel through the same layers in both the down and up directions.

An equation, similar to Dix's formula, is given to compute the interval velocities. The entire scheme can be automated to produce interval‐velocity sections without manual picking.
On small‐scale near‐surface distortion in controlled source tensor electromagnetics1
Authors: Qian W.
Published: April 2006

Based on a Born approximation of a thin sheet integral equation, it is shown that small‐scale surficial heterogeneity significantly distorts the electromagnetic field excited by electric dipoles only when either the source or the receiver are located on the heterogeneities. When a surface heterogeneity is beneath the source, the associated distortion of the electromagnetic field is manifest as a change in the effective electric dipole moment. Hence the magnetotelluric transfer functions and impedance relations remain undistorted in this case. When a surface heterogeneity is beneath the receiver, the electric field is severely distorted, but the magnetic field is only slightly distorted. The impedance tensor is therefore strongly distorted, but the tipper vector is almost unaltered. Since the controlled source tipper is a function of 1D earth conductivity, it is proposed that tipper data should be used in the first stage of 1D interpretation. For a 1D earth, the tipper vector must always point towards the source and, in the near‐field limit, should have unit length. These two necessary conditions must be met by the measured tipper before it is interpreted one dimensionally.
Sign‐change correction for prestack migration of P‐S converted wave reflections1
Authors: Balch A.H. , Erdemir Cemal
Published: April 2006

The polarization direction or 'sign’ of reflected converted P–S waves depends upon the angle of incidence of the incident P‐wave. Sign reversal due to reversal of the angle of incidence is often encountered and is an impediment to P–S wave processing and imaging, because when P–S events or P‐S migrated images with mixed signs are stacked, destructive interference occurs. We have created and demonstrated a means of correcting for this reversal. To do this, a P‐wave angle of incidence is calculated for every point in the image space. This is done by calculating a P–S reflected waveform for every point, by extrapolating the reflected S‐wavefield backwards from the receiver line, and then cross‐correlating this waveform with the S‐wave reflections observed at the receiver line. A multiplier, (sgn α) is assigned to each point in the image space, where α is the angle of incidence of the P‐wave.

The multiplier was applied to a set of prestack reverse time migration images derived from a cross‐borehole physical elastic model data set. The improvement in the stacked image when the sign correction is applied is spectacular. The P‐S image quality is comparable to, or better than, stacked migrated P‐P images.

The method appears to be applicable to all reflection modes and to all recording geometries.