bluuebunny/crossref_metadata_2025 huggingface dataset:
THREE‐DIMENSIONAL INTERPRETATION OF MULTIPLE‐SOURCE BIPOLE‐DIPOLE RESISTIVITY DATA USING THE APPARENT RESISTIVITY TENSOR1
Authors: BIBBY H.M. , HOHMANN G.W.
Published: April 2006

Abstract

The bipole‐dipole resistivity technique, which uses a single current source (bipole) to map variations in (apparent) resistivity has been much criticized in the past. A series of 3D models are used to show that the use of two distinct current bipoles in the same location but with different orientations, combined with analysis in the form of a previously defined tensor apparent resistivity, can greatly improve many aspects of bipole‐dipole mapping.

The model study shows that, for measurement stations more than a few bipole lengths from the current source, the apparent resistivity tensor behaves, to a close approximation, as though the current bipoles are idealized dipoles, and hence is independent of the orientation of the individual current sources used. Any pair of current bipoles (in the same location but with different orientations) can therefore be used to determine the tensor resistivity properties.

The invariants of the apparent resistivity tensor have considerable advantages over the normal scalar apparent resistivities. Modelling shows that although the electric field vector corresponding to a single current bipole can be highly perturbed by a local inhomogeneity for some considerable distance beyond the inhomogeneity itself, the tensor invariants are virtually unperturbed beyond the extent of the inhomogeneity. Hence false anomalies, which are a characteristic of apparent resistivity measured using only single current bipole models, are almost completely eliminated by the use of tensor invariants. Of the possible tensor invariants, the invariant given by the square root of the determinant gives the best representation of a buried 3D body. Resistivity anomalies are localized, and occur only over the causative body. Even with complex models involving several buried bodies, the tensor invariants clearly delineate the extent of each body. Outside the bounds of perturbing bodies, the tensor data can be analysed by conventional techniques, for example, to determine layered structure.
APPROXIMATIONS TO SHEAR‐WAVE VELOCITY AND MOVEOUT EQUATIONS IN ANISOTROPIC MEDIA1
Authors: LI XIANG‐YANG , CRAMPIN STUART
Published: April 2006

Abstract

Backus and Crampin derived analytical equations for estimating approximate phase‐velocity variations in symmetry planes in weakly anisotropic media, where the coefficients of the equations are linear combinations of the elastic constants. We examine the application of similar equations to group‐velocity variations in off‐symmetry planes, where the coefficients of the equations are derived numerically. We estimate the accuracy of these equations over a range of anisotropic materials with transverse isotropy with both vertical and horizontal symmetry axes, and with combinations of transverse isotropy yielding orthorhombic symmetry. These modified equations are good approximations for up to 17% shear‐wave anisotropy for propagations in symmetry planes for all waves in all symmetry systems examined, but are valid only for lower shear‐wave anisotropy (up to 11%) in off‐symmetry planes.

We also obtain analytical moveout equations for the reflection of qP‐, qSH‐, and qSV‐ waves from a single interface for off‐symmetry planes in anisotropic symmetry. The moveout equation consists of two terms: a hyperbolic moveout and a residual moveout, where the residual moveout is proportional to the degree of anisotropy and the spread length of the acquisition geometry. Numerical moveout curves are computed for a range of anisotropic materials to verify the analytical moveout equations.
VARIATION OF REFLECTION AND TRANSMISSION COEFFICIENTS WITH CRACK STRIKE AND CRACK DENSITY IN ANISOTROPIC MEDIA1
Authors: LI XIANG‐YANG , CRAMPIN STUART
Published: April 2006

Abstract

Recent observations show that the differential amplitudes between the faster and slower split shear‐waves in reflection surveys contain information about lateral variations of crack density in cracked reservoirs. However, the variation of amplitude with crack geometry when the crack strike changes with depth has not been reported previously. In this paper, we derive expressions for reflection and transmission coefficients of plane split shear‐waves at vertical incidence at an interface separating two cracked (anisotropic) media with different crack strikes. We examine the effects on these coefficients as crack strike and crack density vary. For interfaces with large velocity‐contrasts, the reflection coefficients carry little information about crack geometry, and the effects of crack strike varying with depth are negligible. In such cases, the polarization and time‐delay of the split shear‐waves are the only features which reliably diagnose anisotropy and contain information about the variation of crack strike and density. However, for interfaces with small velocity‐contrasts, the effects of any variation of crack strike with depth cannot be neglected. In such cases, in addition to the polarization and time‐delays of split shear‐waves, both the differential amplitude of faster and slower shear‐waves and the amplitude ratio of the two off‐diagonal elements in the reflected data matrix after separation of split shear‐waves, contain information about the variation of crack strike and crack density. In contrast, effects of crack strike changing with depth on transmitted waves are more sensitive regardless of the velocity‐contrast and the degree of anisotropy.
IMAGING CAPABILITY OF CROSS‐HOLE SEISMIC REFLECTION SURVEYS1
Authors: ROWBOTHAM P. S. , GOULTY N. R.
Published: April 2006

Abstract

In seismic migration, it is important to sample a range of dips around the local structural dip at each image point. Meaningful images are obtained only where this condition holds. For cross‐hole seismic reflection surveys, the distribution of dips sampled at each image point is controlled principally by the survey geometry, including source and receiver array lengths and their element spacings. Using a real data set as an example, we show how survey geometry can limit imaging capability close to the boreholes and even in the middle of the section between the boreholes.

At the processing stage, effective removal of direct waves and accurate estimation of the velocity field are essential for optimizing image quality. For migration, we propose a generalized Berryhill (GB) scheme which is based on the Kirchhoff integral and takes into account both the near‐field and far‐field terms. This should improve the ability to image close to source and receiver arrays, provided that the element spacing in the nearby array is small enough.
THE FRACTAL DIMENSION OF GRAVITY DATA SETS AND ITS IMPLICATION FOR GRIDDING1
Authors: KEATING PIERRE
Published: April 2006

Abstract

Gravity survey station locations are, in general, inhomogeneously distributed. This inevitably results in interpolation errors in the computation of a regular grid from the gravity data. The fractal dimension of the station distribution can be used to determine if an interpolated map is aliased at a specific wave‐length and, moreover, it is often possible to determine an optimum gridding interval. Synthetic distributions of gravity station locations have been used for theoretical studies and it is found that for randomly distributed data there is a range of sizes for which the spatial data distribution has a fractal dimension of 2; that is, Euclidean. The minimum length scale at which the distribution ceases to be Euclidean is the optimum interpolation interval obeying Shannon's sampling theorem. For dimensions less than 2, the optimum interpolation interval is the shortest length at which the scaling regime is constant. In this case the gravity field cannot be interpolated without introducing some aliasing. As the fractal dimension characterizes the data distribution globally over the whole study area, the actual gridding interval, in some cases, will be smaller in order to represent short‐wavelength features properly in the more densely sampled sub‐areas, but this may generate spurious anomalies elsewhere. The proposed technique is applied to the station distribution of the Canadian national gravity data base and a series of sub‐areas. A fractal dimension of 1.87 is maintained over a range of sizes from 15 km to over 1600 km. Although aliasing occurs, since the gravity field certainly contains much shorter wavelength anomalies, aliasing errors may be minimized by selecting the proper interpolation interval from the fractal analysis.
ALGEBRAIC PROCESSING TECHNIQUES FOR ESTIMATING SHEAR‐WAVE SPLITTING IN NEAR‐OFFSET VSP DATA: THEORY1
Authors: ZENG XINWU , MACBETH COLIN
Published: April 2006

Abstract

A vector convolutional model for multicomponent data acquired in an anisotropic earth is used as a basis for developing algebraic solutions to interpret near‐offset VSP data. This interpretation of the cumulative or interval medium response (Green's tensor) for shear waves, determines a polarization azimuth for the leading shear wave and the time‐delay between the fast and slow split waves. The algebraic solutions effectively implement least‐squares eigenanalysis or singular value decomposition. Although the methodology for shear‐wave analysis is strictly relevant to a transmission response, it can be adapted to surface data for a uniform anisotropic overburden. The techniques perform well when calibrated and tested using synthetic seismograms from various anisotropic models. Noise tests demonstrate the sensitivity of the interval measurements to local interferences, particularly if the shear waves are generated by one source. Although the algorithms are faster than numerical search routines, this is not seen as their major advantage. The solutions may have potential in near real‐time interpretation of shear‐wave data in well logging, where they may be coded on a microchip to provide a direct stream of separated shear waves, or polarization and birefringence information. There may also be some benefit for large prestack multicomponent surface data sets, where the solutions provide a direct transformation to the split‐shear‐wave components, reducing the storage space for further processing.
On reducing ambiguity in the interpretation of transient electromagnetic sounding data1
Authors: Goldman M. , Du Plooy A. , Eckard M.
Published: April 2006

An attempt to resolve non‐uniqueness in the interpretation of transient electromagnetic (TEM) sounding data using measured data alone is made. It is shown in the various examples studied that sufficiently early time measurements can be the determining factor in reducing the ambiguity caused by model equivalence. The early delay times thus play a dual role in transient soundings: they are responsible for resolving shallow structures and they may eliminate the ambiguity in the interpretation of geoelectric parameters of deeper targets. This is illustrated by the results of a follow‐up TEM survey at the Dead Sea coast of Israel where the use of supplementary early time measurements allowed non‐uniqueness in the determination of the depth to fresh/saline groundwater interface to be resolved.
Seismic velocities in fractured rocks: an experimental verification of Hudson's theory1
Authors: Peacock S. , McCann C. , Sothcott J. , Astin T.R.
Published: April 2006

Flow of fluids in many hydrocarbon reservoirs and aquifers is enhanced by the presence of cracks and fractures. These cracks could be detected by their effects on propagation of compressional and shear waves through the reservoir: several theories, including Hudson's, claim to predict the seismic effects of cracks. Although Hudson's theory has already been used to calculate crack densities from seismic surveys, the predictions of the theory have not yet been tested experimentally on rocks containing a known crack distribution. This paper describes an experimental verification of the theory. The rock used, Carrara marble, was chosen for its uniformity and low porosity, so that the effect of cracks would not be obscured by other influences. Cracks were induced by loading of laboratory specimens. Velocities of compressional and shear waves were measured by ultrasound at 0.85 MHz in dry and water‐saturated specimens at high and low effective pressures. The cracks were then counted in polished sections of the specimens. In ‘dry’ specimens with both dry and saturated cracks, Hudson's theory overpredicted observed crack densities by a constant amount that is attributed to the observed value being systematically underestimated. The theory made poor predictions for fully saturated specimens. Shear‐wave splitting, caused by anisotropy due to both crystal and crack alignment, was observed. Cracks were seen to follow grain boundaries rather than the direction of maximum compression due to loading. The results demonstrate that Hudson's theory may be used in some cases to determine crack and fracture densities from compressional‐ and shear‐wave velocity data.
Migration to multiple offset and velocity analysis1
Authors: Ferber R.‐G.
Published: April 2006

The stacking velocity best characterizes the normal moveout curves in a common‐mid‐point gather, while the migration velocity characterizes the diffraction curves in a zero‐offset section as well as in a common‐midpoint gather. For horizontally layered media, the two velocity types coincide due to the conformance of the normal and the image ray. In the case of dipping subsurface structures, stacking velocities depend on the dip of the reflector and relate to normal rays, but with a dip‐dependent lateral smear of the reflection point. After dip‐moveout correction, the stacking velocities are reduced while the reflection‐point smear vanishes, focusing the rays on the common reflection points. For homogeneous media the dip‐moveout correction is independent of the actual velocity and can be applied as a dip‐moveout correction to multiple offset before velocity analysis.

Migration to multiple offset is a prestack, time‐migration technique, which presents data sets which mimic high‐fold, bin‐centre adjusted, common‐midpoint gathers. This method is independent of velocity and can migrate any 2D or 3D data set with arbitrary acquisition geometry. The gathers generated can be analysed for normal‐moveout velocities using traditional methods such as the interpretation of multivelocity‐function stacks. These stacks, however, are equivalent to multi‐velocity‐function time migrations and the derived velocities are migration velocities.
The fast Hankel transform1
Authors: Mohsen Adel A. , Hashish E.A.
Published: April 2006

An efficient algorithm is presented to compute the Hankel transform. The algorithm yields simultaneously all the required weights for a given order of the Bessel function using the fast Fourier transform. An additional shift is introduced to the filter abscissa besides Koefoed's shift to give a better filter performance.
Layer‐stripping reverse‐time migration1
Authors: Shih Ruey‐Chyuan , Levander Alan R.
Published: April 2006

We present a layer‐stripping method of migration for irregularly layered media in which first‐order velocity discontinuities separate regions of constant or smoothly varying velocity. We use the reverse‐time method to migrate seismic data layer by layer, from the surface downwards. As part of the migration of a given layer, the bottom boundary of the layer is defined based on power in the migrated signal, and a seismic section is collected along it. This new section serves as the boundary condition for migration in the next layer. This procedure is repeated for each layer, with the final image formed from the individual layer images. Layer‐stripping migration consists of three steps: (1) layer definition, (2) wavefield extrapolation and imaging, and (3) boundary determination. The migration scheme when used with reverse‐time extrapolation is similar to datuming with an imaging condition. The reverse‐time method uses an explicit fourth‐order time, tenth‐order space, finite‐difference approximation to the scalar wave equation.

The advantages of layer‐stripping reverse‐time migration are: (1) it preserves the benefits of the reverse‐time method by handling strong velocity contrasts between layers and steeply dipping structures; (2) it reduces computer memory and saves computation time in high‐velocity layers, and (3) it allows interpretational control of the image.

Post‐stack layer‐stripping reverse‐time migration is illustrated with a synthetic CMP data example. Prestack migration is illustrated with a synthetic data set and with a marine seismic reflection profile across the Santa Maria Basin and the Hosgri Fault in central California.
Two‐level magnetovariational measurements for the determination of underground resistivity distributions1
Authors: Patella D. , Siniscalchi A.
Published: April 2006

We investigate, from a theoretical point of view, the possibility of performing marine two‐level magnetovariational measurements. An apparent resistivity function is denned and calculated after solving the differential equation governing the behaviour of the natural magnetic field variations inside a one‐dimensional earth. In order to generalize the problem, a frequency‐dependent resistivity is assumed to characterize the layers and the distortions caused by the polarization effects are carefully analysed. The computation of three‐layer amplitude and phase diagrams for the apparent resistivity function shows that, in the case of an intermediate polarizable layer, sandwiched between a non‐dispersive overburden and substratum, the H‐type sequence results are the most affected by the dispersion phenomenon as it occurs in magnetotellurics. Finally we consider the problem of the sensitivity of the method, since, in practice, it requires top and bottom sensors separated by a vertical finite distance. It is found that in the higher‐frequency range, due to the strong attenuation of the relative components of the field, the depth of the bottom sensor must be small enough to guarantee detectable signals, well above the full‐scale resolution of the acquisition system. Conversely, in the lower‐frequency range such a depth must be large enough to allow the difference between the top and bottom signals to be above the same recording sensitivity threshold.
AVO signatures of actual and synthetic reflections from different petrophysical targets1
Authors: Mazzotti A. , Melis A.M. , Ravagnan G. , Bernasconi G.
Published: April 2006

We use a marine seismic dataset to examine the reflections from two gas sands, a lignitic sand and a cineritic bed, by means of their amplitude versus offset (AVO) responses. This offset‐dependent signature is related to specific petrophysical and thus elastic situations or to peculiar interference patterns and may help to distinguish the nature of the amplitude anomalies on the stack sections.

The prestack analysis is carried out on seismic data which have undergone an accurate true‐amplitude processing.

It is found that the lignitic‐sand reflections exhibit a decreasing AVO while the two‐gas sands show markedly increasing AVO trends. Also the reflections from the cineritic layer show increasing amplitudes with offset that may be due either to the petrophysical nature of the cinerites or to thin‐layer interference or to both.

In order to verify the reliability of the actual AVO responses we develop a detailed model from well data and compute a synthetic CMP seismogram. In order to account for mode conversions and thin‐layer effects, the synthetic seismograms are computed using the reflectivity method. The wavelets used in the synthetics are retrieved from actual seismic and borehole data by means of wavelet processing. When finely layered structures are present, the estimation of a reliable wavelet is extremely important to get the correct synthetic AVO response. In particular, the AVO responses of the cineritic layer differ substantially if we make use in the computation of the synthetics of a Ricker wavelet or of a wavelet estimated through wavelet processing.

The good match between the observed and modelled data confirms the reliability of the processing sequence and of the final AVO signatures.
Backus averaging, scattering and drift1
Authors: Sams M.S. , Williamson P.R.
Published: April 2006

Differences between traveltimes from sonic to seismic frequencies, commonly known as drift, can be attributed to a combination of multiple scattering and absorption. The portion due to scattering can be estimated directly by calculating synthetic seismograms from sonic logs. A simple alternative approach is suggested by the long‐wave equivalent averaging formulae for the effective elastic properties of a stack of thin layers, which gives the same traveltime delays as the low‐frequency limit of the scattering dispersion. We consider the application of these averaging formulae over a frequency‐dependent window with the hope of extending their use to frequencies higher than those allowed by the original validity conditions. However, comparison of the time delay due to window‐averaging with the scattering dispersion predicted by the O'Doherty‐Anstey formula reveals that it is not possible to specify a form of window that will fit the dispersion across the spectrum for arbitrary log statistics. A window with a width proportional to the wavelength squared matches the behaviour at the low‐frequency end of the dispersive range for most logs, and allows an almost exact match of the drift across the entire spectrum for exponential correlation functions.

We examine a real log, taken from a hole in nearly plane‐layered geology, which displays strong quasi‐cyclical variations on one scale as well as more random, smaller‐scale fluctuations. The details of its drift behaviour are studied using simple models of the gross features. The form of window which gave a good theoretical fit to the dispersion for an exponential log correlation function can only fit the computed drift at high or low frequencies, confirming that there are at least two significant scale‐lengths of fluctuation. A better overall fit is obtained for a window whose width is proportional to the wavelength. The calculated scattering drift is significantly less than that observed from a vertical seismic profile, but the difference cannot be wholly ascribed to absorption. This is because the source frequency of the sonic tool is not appropriate for its resolution (receiver spacing) so that the scattering drift from sonic to seismic frequencies cannot be fully estimated from the layer model derived from the log.
Using fractal crustal magnetization models in magnetic interpretation1
Authors: Pilkington M. , Gregotski M.E. , Todoeschuck J.P.
Published: April 2006

Evidence from borehole susceptibility logs and the spectral analysis of aeromagnetic data suggests that the three‐dimensional distribution of magnetization within the crust can be described as fractal. This property can be exploited in magnetic interpretation methods which explicitly require statistical information on the spatial variation of magnetization. Specifically, we address the problem of magnetic source depth estimation through downward continuation and gridding aeromagnetic survey data using the method of kriging.

When magnetic data are continued downwards the depth at which the power spectrum flattens out (the ‘white’ depth) can be taken to be an estimate of the top of the source distribution. This procedure assumes that individual sources are uncorrelated with each other. Taking into account the correlation of the magnetization using a fractal description leads to a reduction in this depth estimate.

Gridding of randomly distributed magnetic measurements using kriging requires an estimate of the covariance of the data. Compared with the assumption of a white (uncorrelated) magnetization distribution, using fractal covariances for kriging produces gridded estimates which more closely reflect the statistics of the underlying magnetization process and produce maps with a justifiable degree of smoothness.
Resistivity measurements on the sea bottom to map fracture zones in the bedrock underneath sediments1
Authors: Lile O.B. , Backe K.R. , Elvebakk H. , Buan J.E.
Published: April 2006

Refraction seismics with the shotpoints and the hydrophone cable on the sea‐bottom, have become the standard geophysical method for investigating rock quality before constructing offshore tunnels in Norway. In connection with the construction of a sub‐sea tunnel by the Norwegian Public Roads Administration, research work was carried out to compare two low‐velocity zones, indicated by refraction seismics with other methods. A special resistivity cable for pole‐dipole measurements on the sea‐floor, with 10 m between the electrodes, was constructed. A 200 m long profile, crossing the two low‐velocity zones, was measured with all combinations of electrode distances. The two zones were detected as low‐resistivity zones. A special data processing technique to enhance the anomalies is described. Resistivity soundings in a seawater environment to detect fracture zones in the bedrock underneath the bottom sediments, are discussed. It is concluded that severely fractured zones, which may cause difficulties for the tunnel construction, can be detected both with sea‐surface and sea‐floor arrays using long electrode spacings.
Inversion for seismic anisotropy using genetic algorithms1
Authors: Horne Steve , MacBeth Colin
Published: April 2006

A general inversion scheme based on a genetic algorithm is developed to invert seismic observations for anisotropic parameters. The technique is applied to the inversion of shear‐wave observations from two azimuthal VSP data sets from the Conoco test site in Oklahoma. Horizontal polarizations and time‐delays are inverted for hexagonal and orthorhombic symmetries. The model solutions are consistent with previous studies using trial and error matching of full waveform synthetics. The shear‐wave splitting observations suggest the presence of a shear‐wave line singularity and are consistent with a dipping fracture system which is known to exist at the test site. Application of the inversion scheme prior to full waveform modelling demonstrates that a considerable saving in time is possible whilst retaining the same degree of accuracy.
Determination of electrical resistivity, its anisotropy and heterogeneity on drill cores: a new method1
Authors: Rauen A. , Soffel H.C.
Published: April 2006

This paper presents a new method for the measurement on core samples of their electrical resistivity, its anisotropy and heterogeneity. The equipment used has been developed in the field laboratory of the German Continental Deep Drilling program KTB in the north‐east of Bavaria on the western rim of the Bohemian Massif. The apparatus measures the resistivity at a fixed frequency as a function of the drill core azimuth and along the core by moving point electrode configurations.

From these azimuth and depth dependences, mean values of resistivity and additional information about its anisotropy and heterogeneity are determined. Geometrical averaging is used, because the resistivity data follows a log normal distribution. The quantitative parameters ‘azimuth factor’, corresponding to horizontal anisotropy, and ‘heterogeneity factor’ are introduced.

The depth logs of resistivity, azimuth factor and heterogeneity factor, measured on cores obtained from the KTB main drill hole (gneisses and amphibolites) at depths between 4150 m and 8080 m are presented. The geometrically averaged mean values of resistivity of gneisses and amphibolites are in the same range (≅ 103Ωm). The resistivities tend to decrease with depth. The stress release of the drill cores during recovery produces microcracks which may partially account for this effect.

Reduced resistivities (down to 150 Ωm) within an amphibolite core correlate with an alteration zone. One sample of this core displays alteration from fresh to completely altered. This sample is also electrically heterogeneous (heterogeneity factor ≅ 2). Other samples with uniform low alteration are more homogeneous heterogeneity factor ≅ 1.4).

In general, higher anisotropies are observed in gneisses (mean azimuth factor 2.8), lower anisotropies in amphibolites (mean azimuth factor 1.3). Examples of isotropic and homogeneous samples, as well as anisotropic and heterogeneous samples are also presented.
Median filter behaviour with seismic data1
Authors: Duncan G. , Beresford G.
Published: April 2006

Abctract

Median filters may be used with seismic data to attenuate coherent wavefields. An example is the attenuation of the downgoing wavefield in VSP data processing. The filter is applied across the traces in the ‘direction’ of the wavefield. The final result is given by subtracting the filtered version of the record from the original record. This method of median filtering may be called ‘median filtering operated in subtraction’. The method may be extended by automatically estimating the slowness of coherent wavefields on a record. The filter is then applied in a time‐ and‐space varying manner across the record on the basis of the slowness values at each point on the record.

Median filters are non‐linear and hence their behaviour is more difficult to determine than linear filters. However, there are a number of methods that may be used to analyse median filter behaviour: (1) pseudo‐transfer functions to specific time series; (2) the response of median filters to simple seismic models; and (3) the response of median filters to steps that simulate terminating wavefields, such as faults on stacked data. These simple methods provide an intuitive insight into the behaviour of these filters, as well as providing a semiquantitative measurement of performance. The performance degradation of median filters in the presence of trace‐to‐trace variations in amplitude is shown to be similar to that of linear filters. The performance of median filters (in terms of signal distortion) applied obliquely across a record may be improved by low‐pass filtering (in the t‐dimension). The response of median filters to steps is shown to be affected by background noise levels. The distortion of steps introduced by median filters approaches the distortion of steps introduced by the corresponding linear filter for high levels of noise.
Using the pseudospectral method on curved grids for 2D elastic forward modelling1
Authors: Nielsen Per , If Flemming , Berg Per , Skovgaard Ove
Published: April 2006

When applying the conventional Fourier pseudospectral method (FSM) on a Cartesian grid that has a sufficient size to propagate a pulse, spurious diffractions from the staircase representation of the curved interfaces appear in the wavefield. It is demonstrated that these non‐physical diffractions can be eliminated by using curved grids that conform to all the interfaces of the subsurface. Methods for solving the 2D acoustic wave equation using such curved grids have been published previously by the authors. Here the extensions to the full 2D elastic wave equations are presented.

The curved grids are generated by using the so‐called multiblock strategy which is a well‐known concept in computational fluid dynamics. In principle the sub‐surface is divided into a number of contiguous subdomains. A separate grid is generated for each subdomain patching the grid lines across domain boundaries to obtain a globally continuous grid. Using this approach, even configurations with pinch outs can be handled.

The curved grid is taken to constitute a generalized curvilinear coordinate system. Thus, the elastic equations have to be written in a curvilinear frame before applying the numerical scheme. The method implies that twice the number of spatial derivatives have to be evaluated compared to the conventional FSM on a Cartesian grid. However, it is demonstrated that the extra terms are more than compensated for by the fewer grid points needed in the curved approach.
The stochastic inversion of magnetics and resistivity data using the simulated annealing algorithm1
Authors: Dittmer J.K. , Szymanski J.E.
Published: April 2006

Simulated annealing is a stochastic combinatorial optimization technique, based on ideas from statistical mechanics, thermodynamics and multivariable probability theory. This paper presents the use of simulated annealing as a means of inversion for both linear magnetics and non‐linear resistivity problems. The subsurface is viewed as being constructed of smaller elemental blocks which possess either uniform internal magnetization or conductivity, enabling larger structures to be modelled. Simulated annealing is employed to calculate the distribution of the particular physical property which causes a measured anomalous field curve.

A general description of simulated annealing and its application is given, followed by specific descriptions of its application to the magnetics and resistivity cases.

For the magnetics case the subsurface consists of 2D prismatic elements as the basis for the forward model. Synthetic model data is used to test the algorithm and an example of actual field data; a survey across an igneous dike is used to demonstrate the use of the method with real data. In the resistivity case, the finite‐element method is used to generate the forward models. Synthetic vertical profiling data is used to test the application of the simulated annealing method to the resistivity case. Actual data from an archaeological survey is used to show again the use of the method with real data.

Simulated annealing is shown to be capable of inverting both the linear and non‐linear methods of magnetic surveying and resistivity surveying respectively.
Long period multiple suppression by predictive deconvolution in the x–t domainl1
Authors: Taner M. Turhan , O'Doherty Ronan F. , Koehler Fulton
Published: April 2006

Abctract

There are two forms of systematic error in conventional deconvolution as applied to the problem of suppressing multiples with periodicities longer than a hundred milliseconds. One of these is the windowing effect due to the assumption that a true autocorrelation function can be computed from a finite portion of data. The second form of error concerns the assumption of periodicity, which is strictly true only at zero offset for a 1D medium. The seriousness of these errors increased with the lengthening of the multiple period.

This paper describes and illustrates a rigorous 2D solution to the predictive deconvolution equations that overcomes both of the systematic errors of conventional 1D approaches. This method is applicable to both the simple or trapped system and to the complex or peg‐leg system of multiples. It does not require that the design window be six to ten times larger compared to the operator dimensions and it is accurate over a wide range of propagation angles. The formulation is kept strictly in the sense of the classical theory of prediction. The solution of normal equations are obtained by a modified conjugate gradient method of solution developed by Koehler. In this algorithm, the normal equations are not modified by the autocorrelation approximation.

As with all linear methods, approximate stationary attitude in the multiple generating process is assumed. This method has not been tested in areas where large changes in the characteristic of the multiple‐generating mechanism occur within a seismic spread length.
Reflections from a randomly grooved interface: ultrasonic modelling and finite‐diff erence calculation1
Authors: Schultz Craig A. , Tokcöz M. Nafi
Published: April 2006

This study utilizes ultrasonic water tank modelling to examine the complexities which can result when seismic energy is diffracted by even a simple 3D interface structure. Ultrasonic laboratory modelling is carried out in our in‐house water tank, using an aluminum block to simulate very simple ocean‐bottom topography. The topography consists of parallel depressions which simulate valleys running parallel to a mid‐ocean spreading ridge. This study shows that the phase and amplitude of primary ocean‐bottom reflections can vary strongly with the azimuth of propagation. The trailing energy coda also varies dramatically as a function of propagation direction, showing the importance of developing a seismic model which includes the full 3D azimuthal distribution of interface structure.
Surface NMR applied to an electroconductive medium1
Authors: Trushkin D.V. , Shushakov O.A. , Legchenko A.V.
Published: April 2006

An integrated electromagnetic and nuclear magnetic resonance (NMR) method is proposed for investigating highly conductive soil areas. Using a simple model of a homogeneous half‐space and the same antenna for both methods, a significant improvement in the NMR data interpretation is obtained. A case study has shown fair agreement between the results from computer modelling, field tests, and data from a nearby observation well. The electromagnetic method and the half‐space model were selected for easy integration into an existing instrument used for the NMR method. A more accurate knowledge of the conductivity distribution with depth will further improve the final result.
Monitoring soil contaminations using a contactless conductivity probe1
Authors: Huang Ming , Liu Ce , Shen Liang C. , Shattuck David
Published: April 2006

In order to investigate the possibility of using low‐frequency electromagnetic waves to detect and monitor oil contamination of soils, a series of laboratory measurements were performed. A new measurement system to monitor the resistivities of soil and sand samples while samples are being contaminated by diesel oil is presented. The frequency used in measurements is 100 kHz. Since the measurement system is composed of coil‐type transmitters and receivers, there is no need for electrodes to be in contact with samples. The contamination process is simulated using diesel oil dripping on top of soil and sand samples. The conductivity distributions in samples along the sample length are recorded as a function of time. Water‐wet sand and soil samples were measured during diesel oil contamination. The measured data show that the conductivities of soil and sand samples change during the contamination process. The change in resistivity for measured samples before and after diesel oil contamination is in the range of 20% to 50%, giving a reflection coefficient change in the low‐frequency limit of 4.7% to 7%. This amount of change in the reflection coefficient makes it very challenging to detect and monitor oil contamination based on EM reflection from the contaminants. The results suggest that EM methods based on propagation and induction, such as tomography and borehole induction, could be used for this purpose.
Point‐to‐curve ray tracing in complicated geological models1
Authors: Hanyga Andrzej , Pajchel Jan
Published: April 2006

Boundary‐value problems (BVPs) for seismic rays generally have multiple solutions. In practical applications the number of solutions can be large. The algorithm presented below solves a one‐parameter family of BVPs and makes it easy to obtain all the solutions of a BVP.
The stable‐beam seismic modelling method1
Authors: Wang Xiutian , Waltham Dave
Published: April 2006

The stable‐beam method for forward modelling of seismic data is introduced. The method is applicable to geometries which may be approximated by a series of single‐valued (in depth) interfaces separating constant‐velocity layers. For models of this restricted type, the results are of similar accuracy to those from waveequation‐based methods whilst the run times are similar to, or better than, those for simple ray‐tracing approaches. The basis of the method is to approximate interfaces by a series of straight‐line segments. This allows very rapid and stable ray tracing through the model. Pseudodiffractions are then added from all of the interface discontinuities formed between adjacent segments. These pseudodiffractions have the effect of correcting for the phase, amplitude and wavefront continuity errors introduced by the interface approximation. Comparison of the stable‐beam results to analytical, Kirchhoff, finite‐difference and physical model results confirm the accuracy ofthe technique.
Non‐linear inversion of resistivity profiling data for some regular geometrical bodies1
Authors: Chunduru Raghu K. , Sen Mrinal K. , Stoffa Paul L. , Nagendra R.
Published: April 2006

The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve‐matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting.

We apply three different non‐linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non‐linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). We compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.
Smoothing seismically derived velocities1
Authors: Grubb H.J. , Walden A.T.
Published: April 2006

It is often very useful to be able to smooth velocity fields estimated from exploration seismic data. For example seismic migration is most successful when accurate but also smooth migration velocity fields are used. Smoothing in one, two and three dimensions is examined using North Sea velocity data.

A number of ways for carrying out this smoothing are examined, and the technique of locally weighted regression (LOESS) emerges as most satisfactory. In this method each smoothed value is formed using a local regression on a neighbourhood of points downweighted according to their distance from the point of interest. In addition the method incorporates ‘blending’ which saves computations by using function and derivative information, and ‘weighting and robustness’ which allows the smooth to be biased towards reliable points, or away from unreliable ones.

A number of other important factors are also considered: namely, the effect of changing the scales of axes, or of thinning the velocity field, prior to smoothing, as well as the problem of smoothing on to irregular subsurfaces.
Plane‐layered models for the analysis of wave propagation in reservoir environments1
Authors: Carcione José M.
Published: April 2006

The long‐wavelength propagation and attenuation characteristics of three geological structures that frequently occur in reservoir environments are investigated using a theoretical model that consists of a stack of fine and viscoelastic plane layers, with the layers being either solid or fluid. Backus theory properly describes fine layering and a set of fluid‐filled microfractures, under the assumption that interfaces between different materials are bonded. The effects of saturation on wave attenuation are modelled by the relative values of the bulk and shear quality factors.

The anisotropic quality factor in a fine‐layered system shows a variety of behaviours depending on the saturation and velocities of the single constituents. The wave is less attenuated along the layering direction when the quality factors are proportional to velocity, and vice versa when inversely proportional to velocity. Fractured rocks have very anisotropic wavefronts and quality factors, in particular for the shear modes which are strongly dependent on the characteristics of the fluid filling the microfractures.

When the size of the boundary layer is much smaller than the thickness of the fluid layer, the stack of solid‐fluid layers becomes a layered porous media of the Biot type. This behaviour is caused by the slip‐wall condition at the interface between the solid and the fluid. As in Biot theory, there are two compressional waves, but here the medium is anisotropic and the slow wave does not propagate perpendicular to the layers. Moreover, this wave shows pronounced cusps along the layering direction, like shear waves in a very anisotropic single‐phase medium.
Estimation of effective source signatures from marine VSP data1
Authors: Hokstad K. , Landrø M. , Mittet R.
Published: April 2006

We present a simple method for estimating an effective source wavelet from the first arrival in marine vertical seismic profiling (VSP) data. The method, which utilizes the free‐space Green's function of the Helmholz equation, is simple and very computer efficient. We show examples from synthetic and real offset and walkaway VSP data.

In the synthetic examples, we show that data modelled with the estimated wavelet give small residuals when subtracted from the reference data. In the real data examples, we show that when modelling with the wavelet estimated from the real data, in a smooth macromodel, we obtain a good fit between the first arrivals in the real and modelled data.
Optimum expression for computation of the magnetic field of a homogeneous polyhedral body12
Authors: Ivan M.
Published: April 2006

An expression which is optimum with respect to the simplicity of the numerical computations is obtained for the magnetic field of a polyhedron with constant magnetization. The high accuracy of the results is illustrated using a realistic numerical model.

The existence of the magnetic field at points inside the source and on its boundary is discussed and related to real magnetic data modelling.
An iterative method for finding small magnetic objects in the subsurface by linear and non‐linear inversion1
Authors: Mirzaei M. , Bredewout J.W.
Published: April 2006

A method to determine the position and magnetization vector of buried objects producing a magnetic anomaly is described. The data used were collected in boreholes. Since the anomaly is due to a number of objects, a ‘stripping’ procedure is employed for finding them, and therefore the process of inversion for finding all objects causing the anomaly consists of a few inversion steps.

In each inversion step, two dipoles are considered as a model which approximates an object. The position and magnetic moments of the dipoles are the unknown parameters. The initial parameters are optimized by minimization of an objective function. The optimization procedure consists of a combination of linear and non‐linear inversion. The solution of the linear inversion is obtained by singular value decomposition and that of the non‐linear inversion by a six‐dimensional simplex method (polytope algorithm). After finding one object, its effect is subtracted (‘stripped’) from the data and a new inversion step is started with new initial models and with a reduced data set. The inversion steps for finding different objects are continued until the absolute norm of the data becomes less than some adjustable value.

The data will also be inverted assuming a three‐dipole model in order to find the effect of using a more complex model in the inversion.

The efficiency of the method is demonstrated using synthetic and real borehole data.