bluuebunny/crossref_metadata_2025 huggingface dataset:
A downhole magnetometric resistivity technique for electrical sounding beneath a conductive surface layer
Authors: Edwards R. N.
Published: October 2002

The magnetometric resistivity (MMR) method has not been used systematically for vertical electrical sounding because surficial measurements of the magnetic field caused by static current flow from a point source of current at the surface are independent of the form of the variation of earth resistivity with depth. However, data obtained from an adaptation of the MMR method in which the ratio of the magnetic fields below and above a known conductive surface layer is measured as a function of the horizontal range from the current source can be inverted to obtain the unknown resistivity of deeper material. The practical limitation is that the integrated conductivity of the surface layer must not be much smaller than the integrated conductivity of the unknown zone in order to observe diagnostic ratios significantly different from unity. The expressions derived for the magnetic‐field ratio and for the sensitivity of the ratio to changes in the resistivity of a plane‐layered unknown zone are closed‐form inverse Hankel transforms. The transforms are evaluated analytically for a model of constant, uniform resistivity. One possible geotechnical application of the method is the detection of offshore, resistive permafrost beneath the shallow Beaufort Sea. A theoretical design study in which ratios of the magnetic fields at the bottom and top of the sea are synthesized and the sensitivity of those ratios to changes in sea‐floor resistivity is determined as a function of range and depth, respectively, reveals that the resistivity of a permafrost zone 50 m thick buried 20 m below the sea floor can be identified. The maximum range needed is of the order of 200 m, which appears to be smaller than the maximum spacing required for a Schlumberger sounding to yield similar information.
On: “k-t scattering formulation of the absorptive acoustic wave equation: Wraparound and edge‐effect elimination” by B. Compani‐Tabrizi (GEOPHYSICS, 51, 2185–2192, December 1986)
Authors: Binzhong Zhou
Published: October 2002

Mr. Compani‐Tabrizi attributes data contamination in the snapshots for the nonabsorptive model to wraparound and edge reflections. In fact, there is no edge reflection in the snapshots for the nonabsorptive model. This can be supported by my culations for the nonabsorptive model.
On: “A case for upward continuation as a standard separation filter for potential‐field maps” by Bo Holm Jacobsen (GEOPHYSICS, 52, 1138–1148, August 1987)
Authors: Steenland Nelson C.
Published: October 2002

This paper deals with gradients, not residuals. Computing a field up, then subtracting the “up” field from the original field to find residuals obviously involves shifting datums. Apparently the author got caught up in his equation (17) concerning the simple case of deriving the anomaly of a slab by subtracting the anomaly of one infinite prism from another of the same cross‐section but at a slightly smaller depth. That the anomaly of a slab behaves like the gradient (first vertical derivative) of the prism’s anomaly is apparent from the fact that the field of an infinitely thick slab attenuates by one power less than the field of a slab which approximates an infinitely thin body.
Two‐dimensional terrain correction in magnetotelluric surveys
Authors: Chouteau Michel , Bouchard Karl
Published: October 2002

Field distortions caused by topography hamper the interpretation of magnetotelluric (MT) data. Topographic features that can be simulated by two‐dimensional models seriously affect the H-polarization results. A technique to reduce those effects in MT data uses a finite‐element program to compute correction coefficients. After correction, the resulting data can be interpreted as if they were obtained over a flat surface and depended only on the subsurface structure. The technique is applied to four examples representative of MT survey targets in high‐relief terrain. Results indicate that terrain correction removes the misleading topographic anomalies and improves the quality of subsurface interpretation in regions where the surface relief is two‐dimensional. The correction technique yields some geometrical distortion of the original subsurface structure, but the distortion is usually of small importance. In practice, telluric dipoles of realistic length do not smooth out topographic effects having wavelengths longer than the telluric dipole. A practical procedure derived from the proposed technique allows terrain correction when the relief is approximately two‐dimensional.
Cascaded f-k migration: Removing the restrictions on depth‐varying velocity
Authors: Beasley Craig J. , Lynn Walt , Larner Ken , Nguyen Hung
Published: October 2002

Stolt’s frequency‐wavenumber (f-k) method is computationally efficient and has unlimited dip accuracy for constant‐velocity media. Although the f-k method can handle moderate vertical velocity variations, errors become unacceptable for steep dips when such variations are large. This paper describes an extension to the f-k method that removes its restrictions on vertical velocity variation, yielding accuracy comparable to phase‐shift migration at only a fraction of the computational time. This extension of the f-k method is based on partitioning the velocity field, just as in cascaded finite‐difference migration, and performing a number of stages of f-k migration. In each stage, the migration‐velocity field is closer to a constant—the ideal situation for the f-k migration method—than when the migration is done conventionally (i.e., in just one stage). Empirical results and error analyses show that, at most, four stages of the cascaded f-k algorithm are sufficient to migrate steep events as accurately as by the phase‐shift method for virtually any vertically inhomogeneous velocity field. Given its accuracy and efficiency, cascaded f-k migration can become the method of choice for 2-D, two‐pass 3-D, and single‐pass 3-D time migrations.
Asymptotic elastic Green’s tensor
Authors: Cohen Jack K.
Published: October 2002

The Green’s function for the acoustic wave equation has been an essential ingredient in obtaining frequency inversion formulas in the acoustic limit (Cohen and Bleistein, 1979; Clayton and Stolt, 1981; Beylkin, 1985; Cohen et al., 1986; Bleistein et al., 1987). Similarly, the Green’s tensor is required for inversions based on the elastic wave equations. Indeed, Kuo and Dai (1984) and Dai and Kuo (1986) have already used an approximation to this tensor to derive a migration result for two‐component seismic data in the case of a homogeneous medium.
Free‐boundary conditions of arbitrary polygonal topography in a two‐dimensional explicit elastic finite‐difference scheme
Authors: Jih Rong‐Song , McLaughlin Keith L. , Der Zoltan A.
Published: October 2002

We present a simple method for simulating 2-D elastic waves in a model with free‐surface topography of polygonal shape, i.e., a continuous but irregular surface composed of line segments. Our method requires special treatment for each of the six specific cases involving line segments of various slopes as well as transition points between the sloping segments. For brevity, only nonnegatively sloping segments are specifically included. On an inclined free surface, vanishing stress conditions are implemented using a rotated coordinate system parallel to the inclined boundary. At transition points on the topography between line segments, we use a first‐order approximate boundary condition in a locally rotated coordinate system aligned with the bisector of the corner. As in the classical one‐sided explicit approximation scheme widely used for the flat free‐surface case, these extrapolation formulas are accurate to first order in spatial increment. Numerical tests indicate that the present scheme is stable over a range of Poisson’s ratios of practical interest (v > 0.3) for fairly complicated geometric shapes consisting of ridges and valleys with both steep and gentle slopes. Stability for complicated shapes enables us to study realistic problems for which the topography plays a significant role in shaping the wave field and for which analytical solutions are not generally available.
A Markov‐Gauss algorithm for blocking well logs
Authors: Chouinard Paul N. , Paulson Ken V.
Published: October 2002

A characteristic common among petrophysical sections is “blockiness,” which results from the high probability that a given rock and the rocks above and below it are all of the same type. Furthermore, if a new rock type is encountered, the next rock’s type is dependent upon this new type and not on a previous type. This suggests that a Markov chain would be an appropriate basis for modeling such physical parameters as acoustic impedance, electrical resistivity, etc.
Computational errors in closed‐form expressions with an electromagnetic example: The conducting‐sphere response
Authors: Brown R. James
Published: October 2002

Errors are expected to result from the numerical evaluation of approximate mathematical expressions such as truncated series and finite‐element solutions, from exact expressions based on approximate theory (e.g., perfect gas law), or from analysis based on field data. Many theoretical problems in science—and geophysics is no exception—involve a wholly correct mathematical expression that is beset with computational difficulties arising solely from numerical calculations using the expression. For example, even with modern computers, computation from a slowly convergent series expression can demand an amount of computation time for convergence that is impractically great. Recurrence formulas themselves sometimes propagate errors, often in a nonlinear manner; Acton (1970) provides further insight into this and other aspects of numerical methods generally. Another potential trouble area is the application of slowly convergent iterative matrix methods to least‐squares problems. (Olson, 1987). For such cases, numerical difficulty should be expected.
Physical modeling of the full acoustic waveform in a fractured, fluid‐filled borehole
Authors: Zlatev Petko , Poeter Eileen , Higgins Jerry
Published: October 2002

Three concrete models were constructed, one each with a fracture oriented at 90, 45, and 10 degrees to the axis of the borehole. These were used to simulate physically the propagation of the full acoustic waveform through a fluid‐filled borehole in crystalline rock and to ascertain the effects of fracture aperture and orientation of fluid‐filled fractures on the waveform. The tube‐wave mode of the waveform was most indicative of the magnitude of fracture aperture. Normalized tube‐wave amplitude decreased as a negative exponential function of aperture over the range of fracture apertures studied (closed to 0.66 cm). The 90 degree fracture orientation caused greater tube‐wave amplitude reduction than the 45 degree fracture. We hypothesize that this reduction can be attributed to the borehole wall’s guiding the wave across the 45 degree fracture. However, the 10 degree model gave ambiguous results, which are believed to be related to the low ratio of tube‐wave wavelength to aperture as measured parallel to the borehole axis, i.e., axial aperture.
Time slices from two‐dimensional seismic surveys
Authors: Miller M. Hugh , French William S.
Published: October 2002

Many seismic base maps reveal a network of 2-D seismic lines whose total line mileage approaches that of a modern 3-D survey. Modern 3-D processing systems can now be used to interpolate these multivintage 2-D seismic surveys onto a 3-D data volume that can then be 3-D migrated. After 3-D migration, time slices, as well as arbitrary lines, are available for review just as in a true 3-D survey. This process has been conducted with varying degrees of success in a number of prospect areas. Our first area, which comes from the offshore Gulf of Mexico, serves to illustrate the basic steps in the interpolation method. This example is followed by a decimated 3-D survey example for use in a “controlled experiment” case. The final example of the paper focuses on the Slick Ranch area in Starr County, Texas, where the existing 2-D grid is sparse and somewhat random. In this last example, well results whose locations were based on the interpolated data are discussed. This method provides a valuable new alternative for the interpretation of old 2-D seismic surveys where new 3-D acquisition is not possible or economical. As the gaps between the 2-D lines increase, the resolution of the final product decreases. Interpretation involves simultaneous use of the 2-D lines (reprocessed for maximum 2-D resolution) and the 3-D migrated interpolated data with an emphasis on the derived time slices.
Traveltime inversion of both direct and reflected arrivals in vertical seismic profile data
Authors: Salo Edward L. , Schuster Gerard T.
Published: October 2002

Traveltimes from both direct and reflected arrivals in a VSP data set (Bridenstein no. 1 well in Oklahoma) are inverted in a least‐squares sense for velocity structure. By comparing the structure from inversion to the sonic log, we conclude that the accuracy of the reconstructed velocities is greater than that found when only the direct arrivals are used. Extensive tests on synthetic VSP data confirm this observation. Apparently, the additional reflection traveltime equations aid in averaging out the traveltime errors, as well as reducing the slowness variance in reflecting layers. These results are consistent with theory, which predicts a decrease in a layer’s slowness variance with an increase in the number and length of terminating reflected rays. For the Bridenstein data set, 130 direct traveltimes and 399 primary reflection traveltimes were used in the inversion.
Shear‐wave splitting in cross‐hole surveys: Modeling
Authors: Liu Enru , Crampin Stuart , Booth David C.
Published: October 2002

Shear‐wave splitting, diagnostic of some form of effective seismic anisotropy, is observed along almost all near‐vertical raypaths through the crust. The splitting is caused by propagation through distributions of stress‐aligned vertical parallel fluid‐filled cracks, microcracks, and preferentially oriented pore space that exist in most crustal rocks. Shear waves have severe interactions with the free surface and may be seriously disturbed by the surface and by near‐surface layers. In principle, cross‐hole surveys (CHSs) should be free of much of the near‐surface interference and could be used for investigating shear waves at higher frequencies and greater resolution along shorter raypaths than is possible with reflection surveys and VSPs. Synthetic seismograms are examined to estimate the effects of vertical cracks on the behavior of shear waves in CHS experiments. The azimuth of the CHS section relative to the strike of the cracks is crucial to the amount of information about seismic anisotropy that can be extracted from such surveys. Interpretation of data from only a few boreholes located at azimuths chosen from other considerations is likely to be difficult and inconclusive. Application to interpreting acoustic events generated by hydraulic pumping is likely to be more successful.
Interpretation of a vertical seismic profile conducted in the Columbia Plateau basalts
Authors: Pujol J. , Fuller B. N. , Smithson S. B.
Published: October 2002

Seismic reflection data are often of poor quality when recorded in areas where volcanic rocks are present at or near the surface. In order to investigate this phenomenon, a vertical seismic profiling (VSP) experiment was conducted in the Columbia Plateau basalts so that the behavior of seismic energy in subsurface volcanic rocks could be observed directly, thus giving insight into data acquisition in volcanic terrains. The lithologic section at the VSP site consists of low‐velocity (400 m/s to 900 m/s) alluvium in the uppermost 50 m, beneath which are layers of high‐velocity (about 5800 m/s), high‐density basalts interbedded with clay layers with much lower velocities (about 1700 m/s) and densities. These large velocity and density contrasts dramatically influence wave generation and propagation. In spite of the small source‐borehole offset (61 m), large‐amplitude S waves are generated by the downgoing P waves when they reach a shallow (250 m) clay‐basalt boundary. These S waves, in turn, generate strong reflected P waves when they interact with another clay layer at 500 m. On the other hand, strong primary P‐wave reflections are also present in the data but are affected by various interfering effects which reduce their amplitudes. The VSP data are also characterized by large‐amplitude reverberations caused by seismic energy trapped in the upper 250 m of the lithologic section. Reverberations are also observed in surface data recorded near the VSP site. We conclude from our analysis that volcanic rocks, at least in the Columbia Plateau, do not exhibit unusual energy transmission characteristics and that the observations can be explained in terms of the large contrast in the elastic properties of interbedded clay and basalt.
Monitoring fluid movement with the borehole gravity meter
Authors: Schultz Alton K.
Published: October 2002

Use of the borehole gravity (BHG) meter as a detector of density distribution suggests that a reservoir could be monitored for bulk density changes caused by redistribution of fluids after hydrocarbons have been partially extracted from it. In a simple situation in which liquid hydrocarbons are being extracted from a well, an overlying gas zone might begin to penetrate toward the perforations from above, while an underlying water‐zone formation might begin to penetrate toward the perforations from below. One idealized reservoir and one real reservoir are modeled for BHG meter responses in prepump and postpump reservoir conditions. Results suggest that the BHG meter density differences could be detected if the survey had a high degree of quality control.
Sampling two‐dimensional seismic data and their Radon transforms
Authors: Bardan Virgil
Published: October 2002

2‐D seismic data are usually sampled and processed in a rectangular grid, for which sampling requirements are generally derived from the usual 1‐D viewpoint. For a 2‐D seismic data set, the band region (the region of the Fourier plane in which the amplitude spectrum exceeds some very small number) can be approximated by a domain bounded by two triangles. Considering the particular shape of this band region, I use 2‐D sampling theory to obtain results applicable to seismic data processing. The 2‐D viewpoint leads naturally to weaker sampling requirements than does the 1‐D viewpoint; i.e., fewer sample points are needed to represent data with the same degree of accuracy. The sampling of 2‐D seismic data and of their Radon transform in a parallelogram and then in a triangular grid is introduced. The triangular sampling grid is optimal in these cases, since it requires the minimum number of sample points—equal to half the number required by a parallelogram or rectangular grid. The sampling of 2‐D seismic data in a triangular grid is illustrated by examples of synthetic and field seismic sections. The properties of parallelogram grid sampling impose an additional sampling requirement on the 2‐D seismic data in order to evaluate their Radon transform numerically; i.e., the maximum value of the spatial sampling interval must be half of that required by the sampling theorem.
On plane‐wave decomposition: Alias removal
Authors: Singh S. C. , West G. F. , Chapman C. H.
Published: October 2002

The delay‐time (τ‐p) parameterization, which is also known as the plane‐wave decomposition (PWD) of seismic data, has several advantages over the more traditional time‐distance (t‐x) representation (Schultz and Claerbout, 1978). Plane‐wave seismograms in the (τ, p) domain can be used for obtaining subsurface elastic properties (P‐wave and S‐wave velocities and density as functions of depth) from inversion of the observed oblique‐incidence seismic data (e.g., Yagle and Levy, 1985; Carazzone, 1986; Carrion, 1986; Singh et al., 1989). Treitel et al. (1982) performed time migration of plane‐wave seismograms. Diebold and Stoffa (1981) used plane‐wave seismograms to derive a velocity‐depth function. Decomposing seismic data also allows more rapid modeling, since it is faster to compute synthetic seismograms in the (τ, p) than in the (t, x) domain. Unfortunately, the transformation of seismic data from the (t, x) to the (τ, p) domain may produce artifacts, such as those caused by discrete sampling, of the data in space.
On: “Structural interpretation of the Rukwa Rift, Tanzania” by J. W. Peirce and L. Lipkov (GEOPHYSICS, 53, 824–836, June 1988).
Authors: Anfiloff Vadim
Published: October 2002

While I commend the gravity survey which overcame serious operational difficulties to delineate the apparently pristine Rukwa Rift, I believe there are aspects of the rift analysis which require discussion. It would have been useful to analyze the main bounding faults in combination with the steep flanking escarpments using the comprehensive 2‐D method demonstrated by Anfiloff and Flavelle (1982), which allows for automatic terrain corrections and upward‐continuation effects but requires a detailed gravity traverse set out so that major inflections in topography are not avoided, as is the usual practice.
Suppression of high‐energy noise using an alternative stacking procedure
Authors: Haldorsen Jakob B. U. , Farmer Paul A.
Published: October 2002

Occasionally, seismic data contain transient noise that can range from being a nuisance to becoming intolerable when several seismic vessels try simultaneously to collect data in an area. The traditional approach to solving this problem has been to allocate time slots to the different acquisition crews; the procedure, although effective, is very expensive. In this paper a statistical method called “trimmed mean stack” is evaluated as a tool for reducing the detrimental effects of noise from interfering seismic crews. Synthetic data, as well as field data, are used to illustrate the efficacy of the technique. Although a conventional stack gives a marginally better signal‐to‐noise ratio (S/N) for data without interference noise, typical usage of the trimmed mean stack gives a reduced S/N equivalent to a fold reduction of about 1 or 2 percent. On the other hand, for a data set containing high‐energy transient noise, trimming produces stacked sections without visible high‐amplitude contaminating energy. Equivalent sections produced with conventional processing techniques would be totally unacceptable. The application of a trimming procedure could mean a significant reduction in the costs of data acquisition by allowing several seismic crews to work simultaneously.
Crosshole seismic tomography
Authors: Bregman N. D. , Bailey R. C. , Chapman C. H.
Published: October 2002

Many tomographic interpretations of crosshole seismic traveltimes have approximated the raypaths with straight lines connecting the source and receiver. This approximation is valid where the velocity does not vary greatly, but in many regions of interest velocity variations of 10–20 percent or more are observed, causing significant ray curvature. Other work has taken this nonlinear effect into account, but there do not appear to be many cases of demonstrated success in its application to the crosshole seismic problem. We present here an iterative inversion scheme based on two‐dimensional ray tracing and its successful application to field data. The interpretation method iteratively ray traces and then updates the velocity model. Within each iteration, the differences between the data and the current model traveltimes obtained by ray tracing are related to the unknown velocity perturbations through a system of linear equations. A damped least‐squares method solves for the velocity perturbations which update the model. The iterations continue until the synthetic traveltimes fit the data to within the data error or until no improvement in the fit of the traveltimes is observed. The method is demonstrated on a small synthetic data set, where convergence to the correct solution is achieved in a few iterations. The method is then applied to field data from a crosshole experiment in crystalline rock. The frequency range of the seismograms is 1 to 6.6 kHz, allowing resolution of velocity structure on a scale of several meters. The resulting velocity image shows good agreement with other geologic and geophysical data. Synthetic Maslov seismograms calculated for the derived velocity model agree well with the waveform data, providing an independent test of the validity of the inversion method.
On: “Imaging discontinuities on seismic sections by E. R. Kanasewich and S. M. Phadke (GEOPHYSICS, 53, 334–345, March 1988)
Authors: Bhattacharjee S. K.
Published: October 2002

As a regular reader of Geophysics, I often find articles directly applicable to practicing petroleum geophysicists, and the above article is one of them. I would like to make the following comments. Attributing geologic meaning to a recorded seismic diffraction pattern has always been a great challenge to geophysicists. The above paper is certainly an appreciable and serious effort to find a useful meaning. Any new idea needs two ladders to climb—technical acceptability and economic sense.
Recursive wavenumber‐frequency migration
Authors: Kim Y. C. , Gonzalez R. , Berryhill J. R.
Published: October 2002

There are many approaches for migrating seismic data using velocities varying only with depth. These methods are capable of accommodating quasi‐continuous vertical velocity variation at the expense of a considerably larger amount of computation than with the Stolt method, which assumes a constant velocity for the subsurface of the earth. However, the errors involved in estimating migration velocities from seismic data are often too large to justify such a large amount of computational effort. Furthermore, because there is a resolution limit in velocity estimation, a time‐depth curve based on the velocity estimates may be represented by a series of line segments that typically are much larger than the migration step size. For a time‐depth curve segmented in this way, we may successively apply the fast Stolt method interleaved with phase shift for downward continuation. This approach, recursive wavenumber‐frequency (k-f ) migration, retains the speed of the Stolt method and produces from seismic data a subsurface image as good as that from the phase‐shift method. The recursive k-f method is a powerful tool, particularly for the migration of 3-D data.
Stoneley‐wave attenuation and dispersion in permeable formations
Authors: Norris Andrew N.
Published: October 2002

The tube wave, or low‐frequency manifestation of the Stoneley wave, has been modeled previously using the quasi‐static approximation; I extend this method to include the effect of the formation matrix compressibility, which tends to marginally increase the tube‐wave attenuation. Using the Biot theory of poroelasticity, I develop a fully dynamic description of the Stoneley wave. The dispersion relation derived from Biot’s equations reduces in the low‐frequency limit to the quasi‐static dispersion relation. Comparisons of the quasi‐static and dynamic theories for typical sandstones indicate the former to be a good approximation to at least 1 kHz for oil and water infiltration. At higher frequencies, usually between 5 and 20 kHz for the formations considered, a maximum in the Stoneley Q is predicted by the dynamic theory. This phenomenon cannot be explained by the quasi‐static approximation, which predicts a constantly increasing Q with frequency. Instead, the peak in Q may be understood as a transition from dispersion dominated by bore curvature to a higher frequency regime in which the Stoneley wave behaves like a wave on a flat fluid‐porous interface. This hypothesis is supported by analytical and numerical results.
Two‐dimensional circularly symmetric filter design via coefficient mapping
Authors: Özdemir Huseyin
Published: October 2002

Two‐dimensional (2-D) filters are used in geophysics for processing seismic, potential field, and remotely sensed data, and in other applied sciences for purposes such as image processing. These filters can be designed using optimum one‐dimensional (1-D) algorithms via mapping techniques: the 2-D desired response is mapped into the 1-D response either in the time domain or the frequency domain and mapped back after an approximation is obtained. A coefficient mapping algorithm is presented here for designing 2-D circularly symmetric filters. The 2-D frequency‐domain coefficients are mapped to the 1-D frequency axis after being sorted according to their distances from the origin. This kind of sorting brings together the coefficients of a particular passband, reject band, or transition band of the circularly symmetric filter before the coefficients are mapped into the 1-D frequency axis. As a result, there are as many prescribed bands in the 1-D domain as in the corresponding 2-D domain, which leads to optimal approximations in the 1-D domain and, consequently, in the 2-D domain. The mapping is performed between the Nyquist regions. A Chebychev or “min‐max” algorithm has been used for 1-D approximations. Due to a complete mapping between the 2-D and the 1-D domains, the 2-D filters designed via mapping show equiripple behavior similar to that of the 1-D filters. The new mapping algorithm is suitable for designing low‐pass, high‐pass, band‐pass, and band reject filters with multiple bands. The circular symmetries of the approximated responses improve with an increased number of filter coefficients. For a 2-D filter with [Formula: see text] coefficients, [Formula: see text] and [Formula: see text] must be odd; but they need not be equal. Applications of low‐pass and high‐pass circularly symmetric filters to data from a regional gravity field survey demonstrate that these filters can effectively separate anomalies of different wavelengths when there is no spectral overlap.
Application of microgravimetric survey in Samawa salt deposit, Iraq
Authors: Al‐Rawi F. R. , Al‐Badri A. S. , Rezkalla J. S.
Published: October 2002

The applicability of microgravimetric surveys for determining the thickness and shape of a salt deposit has been explored by carrying out field measurements. The survey includes five profiles crossing a Samawa salt deposit that attains a maximum thickness of about 8.5 m. The results indicate that the method can be applied successfully if a few boreholes are available as control points to define the local regional field. A simple sheet formula with a fixed density value was used in determining the bed thickness and the general shape of the deposit. The thicknesses calculated in this way agree well with the available borehole information.
Application of mode‐converted shear waves to rock‐property estimation from vertical seismic profiling data
Authors: Ahmed Hassan
Published: October 2002

Three‐component vertical seismic profiling (3-CVSP) data were acquired and processed to yield separate estimates of the compressional (P)-wave and shear (S)-wave fields. Interval velocities, [Formula: see text] and [Formula: see text] (of the P and S waves), are computed from the identified onset times at many seismometer positions along the borehole. The ratio [Formula: see text] is calculated and used to compute the Poisson’s ratio and the ratio of incompressibility to rigidity. In a North Sea well, the variation in these elastic parameters was highly correlated with the variation in stratigraphy. Of particular interest was the ability to indicate pore fluids such as gas or water within a reservoir. Abrupt changes of the calculated parameters can be an indicator of the gas‐water to water transition zone.
Generalized two‐pass three‐dimensional migration for imaging steep dips in vertically inhomogeneous media
Authors: Pan Naide , French William S.
Published: October 2002

Conventional two‐pass 3-D time migration is exactly equivalent to full 3-D time migration in a homogeneous medium. For vertically inhomogeneous media representing typical earth velocities, however, conventional two‐pass 3-D migration fails to correctly image dips beyond about 45 degrees. This failure is the result of an inherent velocity error incurred during the first pass of a two‐pass 3-D migration. For a vertically inhomogeneous medium, the theory of residual migration can be combined with the results for homogeneous media to derive a series of successive two‐pass migration stages which are equivalent to a full 3-D migration. Each stage of this generalized two‐pass 3-D migration is implemented using an appropriate constant migration velocity. In practice, the required number of two‐pass stages can be reduced to a computationally manageable few; and the I/O can be reduced by one‐third to one‐half of that required using a straightforward application of repeated two‐pass migrations. This procedure allows existing 2-D migration programs to be upgraded to steep‐dip 3-D migration programs by use of a simple I/O structure. Any of the basic 2-D migration algorithms can be used, but we have employed a 50-degree finite‐difference algorithm. In addition, generalized two‐pass 3-D migration overcomes the dip limitations of the underlying 2-D finite‐difference migration algorithm for the same reasons that cascaded 2-D migration extends the dip range of 2-D migration algorithms. Synthetic data examples clearly show the success of this method in imaging steep dips in vertically inhomogeneous media.
Shear‐wave logging with quadrupole sources
Authors: Chen S. T.
Published: October 2002

This paper provides laboratory verification of a novel technique for direct, on‐line, shear (S)-wave velocity logging in hard and soft formations using a quadrupole source as recently suggested by theory. Conventional monopole logging tools are not capable of directly measuring the shear‐wave velocity in soft formations. Previous theoretical and laboratory experimental work has already shown that a dipole source can be used for direct shear‐wave velocity logging in hard and soft formations. I demonstrate in this paper that quadrupole sources can also achieve this objective. Furthermore, the quadrupole source can produce higher resolution of S-wave velocity, since it can be operated at higher frequencies. A power comparison of monopole, dipole, and quadrupole indicates that a field quadrupole logging tool may be expected to produce strong enough signals for practical operation. The present studies were conducted on laboratory scale models representative of sonic logging conditions in the field. I used a limestone model to represent hard formations and a plastic model to simulate a soft formation such as Gulf Coast soft shale or near‐surface materials.
Relations between horizontal and vertical gradients of potential fields
Authors: Pedersen Laust B.
Published: October 2002

Nabighian (1984) and Nelson (1986) have both derived relations between horizontal and vertical gradients of magnetic fields (or any other potential field), whereby a knowledge of one enables one to calculate the other. As pointed out by Nelson, Nabighian’s derivation is quite lengthy. In the following, I offer an alternative derivation in the wavenumber domain, which is even shorter than that given by Nelson.
Source signature estimation using fictitious source and reflector
Authors: Loewenthal Dan , Shtivelman Vladimir
Published: October 2002

Source wavelet estimation is an important step in processing and interpreting seismic data. In the context of this work, the term (source wavelet) includes the pure source signature (the source response measured in a homogeneous medium) along with certain model‐related events (such as the ghost and interbed reflections). An estimate of the source wavelet can be used to increase the resolution of seismic data by signature deconvolution, deghosting, and dereverberation. However, pure source signature determination is of particular importance as a first step in direct inversion schemes, as demonstrated by Bube and Burridge (1983) and by Foster and Carrion (1985).
Estimating phase velocity and attenuation of guided waves in acoustic logging data
Authors: Ellefsen K. J. , Cheng C. H. , Tubman K. M.
Published: October 2002

In acoustic logging, the guided waves which propagate along the borehole are affected by the properties of the formation. For acoustic logging tools with many receivers, array processing methods can be used to calculate the phase velocity and attenuation of these waves. This information is crucial in estimating formation properties like permeability, transverse isotropy, and S-wave velocity.
Borehole seismic surveys for fault delineation in the Dutch North Sea
Authors: van der Poel N. J. , Cassell B. R.
Published: October 2002

A significant share of gas production in the Dutch sector of the southern North Sea Basin comes from Permian Rotliegend fault blocks. Precise knowledge of the positions of these faults is necessary for efficient exploitation of the reservoir structures and for future field development strategies. Two areas are presented where the lateral resolution of the surface seismic data was not sufficient to determine positions of major fault block boundaries accurately. Walkaway borehole seismic profiles were shot over each of these areas with the objective of illuminating the fault boundaries to obtain an image with a higher resolution. The images were generated using borehole seismic reflection‐point mapping and migration techniques. Large‐aperture migrations tend to produce unacceptable migration smiles, while reflection‐point mapping is a model‐dependent process. A hybrid approach to these processes was necessary to avoid problems associated with the limited angular illumination permitted by the field acquisition geometries. Reliable images of the fault boundaries were obtained using migration apertures of less than ±5° relative to the structural dips in the background model and by matching that model with the surface seismic and borehole seismic data. The stability of the process and, therefore, the accuracy of the lateral positioning were verified by testing the migration process using a range of apertures.
Absorbing boundary condition for the elastic wave equation: Velocity‐stress formulation
Authors: Randall C. J.
Published: October 2002

This paper describes an absorbing boundary condition for finite‐difference modeling of elastic wave propagation in two and three dimensions. The boundary condition is particularly effective for obliquely incident waves, typically quite troublesome for absorbing boundaries. Analytical predictions of the boundary reflection coefficients of a few percent or less for angles of incidence up to 89° are verified in example finite‐difference applications. The algorithm is appropriate for use in a velocity‐stress finite‐difference (vs‐fd) formulation. It is computationally simpler than a similar absorbing boundary given previously for the standard displacement formulation. A second algorithm is presented which may be advantageous when the boundary of interest is exposed to strong evanescent waves. Both algorithms require that the adjacent elastic medium be locally homogeneous.
Absence of magnetic anomalies due to seepage‐induced “magnetoelectric effects” and implications for sulfide self‐potentials
Authors: Baag Czango , Lee Deok Kyo
Published: October 2002

The magnetic field due to an azimuthally symmetric distribution of subsurface electric current, which may be associated with vertical hydrocarbon seepage, vanishes above the ground surface. However, geologic conditions in general do not provide perfect isotropic conditions, and, in theory, some magnetic fields can be generated by the magnetoelectric effect. Sedimentary rock sections are relatively isotropic, particularly in the stratigraphic plane. Thus, hydrocarbon seepage‐induced magnetic fields above the ground surface may never be significant, even if strong electric currents are associated with the seepage. All current‐generated magnetic fields, of whatever origin, must obey Ampère’s law; no line integral operation can distinguish a magnetic field having one origin from that of any other origin. Therefore, seepage‐induced magnetic anomalies, if they exist at all, are probably useless for hydrocarbon exploration because it is virtually impossible to distinguish them from other anomalies of unknown origin. Thus, even if hydrocarbon seepage is capable of producing oxidized and reduced zones, the significance of any generated electric currents is very doubtful. Since the seepage‐induced electrochemical model lacks a conducting mass in the columnar reducing zone and/or an electric barrier around the reducing zone, electric potential due to excess electric charges developed between the two zones would tend to dissipate.
On: “Gravity and magnetic fields of polygonal prisms and application to magnetic terrain corrections,” by Donald Plouff [GEOPHYSICS, 41, 727–741, August 1976 and (Erratum) GEOPHYSICS, 41, 1488–1491, December 1976].
Authors: Ivan M.
Published: October 2002

Testing the position of the field point relative to the mass center of the prism (resulting from the computation of [Formula: see text]) can be avoided in Plouff’s equation (3) by assuming [Formula: see text]where [Formula: see text] and [Formula: see text] are the vertical coordinates (not their absolute values) of the top and bottom, respectively, of the prism. An absolute value is necessary for the computation of the angle; i.e., [Formula: see text].
The validity of Q estimates from borehole data using spectral ratios
Authors: Sams Mark , Goldberg David
Published: October 2002

The measurement from borehole sonic data of Q, the acoustic attenuation coefficient of an earth section, can be achieved in three ways: forward modeling (Chuen and Toksöz, 1981), spectral ratios (Gladwin and Stacey, 1974), and inversion (Cheng et al., 1986). The spectral‐ratio technique has been applied to real data (Goldberg et al., 1985) but is unstable and not very reliable. Experiments have shown that the spectral‐ratio technique applied to waveforms gives Q estimates which are lower than those measured from cores in the laboratory (Goldberg and Zinszner, 1989). We investigate this phenomenon using synthetic and real data.
Inversion for magnetic anomalies of arbitrary three‐dimensional bodies
Authors: Wang X. , Hansen R. O.
Published: October 2002

Two‐dimensional (profile) inversion techniques for magnetic anomalies are widely used in exploration geophysics: but, until now, the three‐dimensional (3-D) methods available have been restricted in their geologic applicability, dependent upon good initial values or limited by the capabilities of existing computers. We have developed a fully 3-D inversion algorithm intended for routine application to large data sets. The algorithm based on a Fourier transform expression for the magnetic field of homogeneous polyhedral bodies (Hansen and Wang, 1998), is a 3-D generalization of CompuDepth (O’Brien, 1972). Like CompuDepth, the new inversion algorithm employs thespatial equivalent of frequency‐domain autoregression to determine a series of coefficients from which the depths and locations of polyhedral vertices are calculated by solving complex polynomials. These vertices are used to build a 3-D geologic model. Application to the Medicine Lake Volcano aeromagnetic anomaly resulted in a geologically reasonable model of the source.
Gaussian beam migration
Authors: Hill N. Ross
Published: October 2002

Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflections from structure in the velocity model. Unlike other raypath methods, Gaussian beam migration has guaranteed regular behavior at caustics and shadows. In addition, the method determines the beam spacing that ensures efficient, accurate calculations. The images produced by Gaussian beam migration are usually stable with respect to changes in beam parameters.
Geostatistical simulation for geophysical applications—Part I: Simulation
Authors: Easley D. H. , Borgman L. E. , Shive P. N.
Published: October 2002

Geostatistical simulation is used to create a synthetic three‐dimensional geologic environment such that randomly generated values of a physical property have a required covariance and mean. We create a spatially stationary, multivariate Gaussian simulation with a Gaussian covariance. This type of simulation permits modeling of natural variations which may be an important source of noise in geologic investigations, whereas interpolation techniques such as kriging tend to smooth out those variations. Computationally efficient frequency‐domain methods allow the rapid creation of multiple scenarios, each having the required statistical distribution. For the particular problem considered, a given porosity distribution is simulated and then functionally related to physical properties needed for input into geophysical models. Additionally, megascopic cavities having random size, shape, and orientation similar to those observed in karst settings are emplaced in the physical model. Geostatistical simulation plays a particularly important role in exploring the degree to which natural variations in physical parameters lower the resolution of target anomalies that have similar signatures. In the accompanying paper, we discuss the geophysical methods tested and the results of the tests.
Apparent layering in common‐midpoint stacked images of two‐dimensionally heterogeneous targets
Authors: Gibson Bruce S. , Levander Alan R.
Published: October 2002

Model studies with finite‐difference synthetic data demonstrate a fundamental spatial bias in the appearance of common‐midpoint (CMP) stacked images. The CMP stack of data recorded over a target having 2-D random variations in velocity shows numerous short reflection segments; similar reflection patterns in field data are often interpreted in terms of 1-D fine‐scale layering. The stacked image appears layered because of enhanced lateral continuity attributable to the well‐known dip filter of the stacking process. The stack filter can be characterized using the formulation of Bolondi et al. (1982). Lateral correlation in the target and its seismic image is quantified with a measure based on the spectral coefficient of coherence. Broadband primary reflectivity (defined as the vertical‐incidence, primaries‐only reflection coefficients of the 2-D target) is often taken as an ideal seismic image. The primary reflectivity section of a 2-D random target, however, shows greater apparent lateral correlation than is present in the random structure. This apparent increase in lateral continuity is attributable to the fact that reflectivity measured from the surface depends on the vertical derivative of velocity but depends on horizontal changes in velocity directly. The dip‐filtering effects of stacking cannot be reversed by poststack migration; the synthetic data demonstrate the necessity of migration before stack or equivalent processing (such as dip moveout correction). A field data example illustrates the effects of CMP stack filtering using lateral coherence functions measured on stacked and unstacked sections.