bluuebunny/crossref_metadata_2025 huggingface dataset:
Migration error in transversely isotropic media with linear velocity variation in depth
Authors: Larner Ken L. , Cohen Jack K.
Published: October 2002

Given the sensitivity of imaging accuracy to the velocity used in migration, migration founded (as in practice) on the erroneous assumption that a medium is isotropic can be expected to be inaccurate for steep reflectors. Here, we estimate errors in interpreted reflection time and lateral position as a function of reflector dip for transversely isotropic models in which the axis of symmetry is vertical and the medium velocity varies linearly with depth. We limit consideration to media in which ratios of the various elastic moduli are independent of depth. Tests with reflector dips up to 120 degrees on a variety of anisotropic media show errors that are tens of wavelengths for dips beyond 90 degrees when the medium (unrealistically) is homogeneous. For a given anisotropy, the errors are smaller for inhomogeneous media; the larger the velocity gradient, the smaller the errors. For gradients that are representative of the subsurface, lateral‐position errors tend to be minor for dips less than about 60 degrees, growing to two to five wavelengths as dip passes beyond 90 degrees. These errors depend on reflector depth and average velocity to the reflector only through their ratio, i.e., migrated reflection time. Migration error, which is found to be unrelated to the ratio of horizontal to vertical velocity, is such that reflections with later migrated reflection times tend to be more severely overmigrated than are those with earlier times. Over a large range of dips, migration errors that arise when anisotropy is ignored but inhomogeneity is honored tend to be considerably smaller than those encountered when inhomogeneity is ignored in migrating data from isotropic, inhomogeneous media.
Thin layers and shear‐wave splitting
Authors: Slack Richard D. , Ebrom Daniel A. , McDonald John A. , Tatham Robert H.
Published: October 2002

The near‐surface weathering layer is considered by many to be strongly anisotropic. Any shear‐wave signal passing through this low‐velocity layer will inherit, to some degree, the anisotropic response of this layer. For thin weathering layers, information about previous anisotropic events may be distorted; when the thickness of this layer approaches some physically defined limit, however, a previous layer’s anisotropic signature is completely overwritten. Hodograms and Alford rotations are typically used to analyze shear‐wave splitting in the presence of azimuthal anisotropy. When the time‐delay generated by an azimuthally anisotropic layer is ⩾τ/8, where τ = one period of the wavelet’s dominant frequency, distortion of a shear‐wave signal is great enough to degrade the accuracy of the interpretation in hodogram analysis. We found that Alford rotations are superior to visual hodogram analysis when the time delay between the fast and slow shear‐waves is less than τ/8. When two azimuthally anisotropic layers with different symmetry axes exist, however, interpretations generated through both hodogram analysis and Alford rotations begin to deteriorate when the time‐delay generated by the second layer is ⩾τ/8. Recent field work has shown that the weathering layer may possess differential shear‐wave birefringence in excess of 25 percent. If we assume a dominant frequency of 40 Hz and shear‐wave velocities of [Formula: see text] and [Formula: see text], then an azimuthally anisotropic weathering layer may be as little as 5.8 m (19 ft) thick when it begins to overwrite a previous layer’s anisotropic response. When the time delay generated by a second anisotropic layer is ⩾τ (46.4 m, 152 ft thick), information about earlier anisotropic events are completely overwritten.
Spatial averaging of the vertical magnetic field in central‐loop configuration
Authors: Qian Wei , Pedersen Laust B.
Published: October 2002

Local resistivity heterogeneities can cause static shifts in the magnetotelluric (MT) impedance tensor that severely complicate data interpretation; the apparent resistivity is shifted on a logarithmic scale across the recorded frequency range while the phase has a band‐limited response. Different techniques such as electromagnetic array profiling (EMAP) (Torres‐Verdín and Bostick, 1992) and tensor decomposition (Zhang et al., 1987; Groom and Bailey, 1989; 1991) have been developed in the MT community to recognize and remove static shifts. Sternberg, et al. (1988) and Pellerin and Hohmann (1990) suggest that central‐loop transient electromagnetic (TEM) soundings can obtain an unbiased estimate of the regional resistivity structure of the earth and thereby correct for magnetotelluric static shifts. The regional resistivity structure of the earth must be one‐dimensional (1-D) for this method to work well.
Description of a scanless method of stacking velocity analysis
Authors: Tieman Hans J.
Published: October 2002

Stacking velocities can be directly estimated from seismic data without recourse to a multivelocity stack and subsequent search techniques that many current procedures use. This is done as follows: (1) apply NMO to the data (over a window, for a particular common midpoint) using initial estimates for zero offset time and velocity; (2) produce two stacks by summing the data over offset after applying different weighting functions; (3) cross correlate the two stacks; and (4) translate the lag into velocity and time updates. The procedure is iterated until convergence has occurred. Referred to as ARAMVEL (U.S. Patent No. 4,813,027), the method is best implemented as an interactive continuous velocity analysis. Although very simple, both empirical studies and theoretical analysis have shown that it determines velocities more accurately than more traditional approaches based on a scan approach. Convergence is fast, with only one or two iterations usually necessary. The method is robust, as only approximate information is necessary initially. Results with real data show that the method can economically give the detailed velocity control necessary for processing data from areas with considerable lateral velocity variation, as well as provide traveltime information that can be used for sophisticated inversion into interval velocity and depth.
Estimation of reflection coefficients from zero‐offset field data
Authors: Arntsen Børge , Ursin Bjørn
Published: October 2002

The classical one‐dimensional (1-D) inverse problem consists of estimating reflection coefficients from surface seismic data using the 1-D wave equation. Several authors have found stable solutions to this problem using least‐squares model‐fitting methods. We show that the application of these plane‐wave solutions to seismic data generated with a point source can lead to errors in estimating reflection coefficients. This difficulty is avoided by using a least‐squares model fitting scheme describing vertically traveling waves originating from a point source. It is shown that this method is roughly equivalent to deterministic deconvolution with built‐in multiple removal and compensation for spherical spreading. A true zero‐offset field data set from a specially designed seismic experiment is then used as input to estimate reflection coefficients. Stacking velocities from a conventional seismic survey were used to estimate spherical spreading. The resulting reflection coefficients are shown to correlate well with an available well log.
Microcrack‐induced versus intrinsic elastic anisotropy in mature HC‐source shales
Authors: Vernik Lev
Published: October 2002

Recent experimental studies of ultrasonic velocity anisotropy in kerogen‐rich shales indicate that these rocks are characterized by a very strong anisotropic response related to a very fine, bedding‐parallel lamination of organic matter and preferred orientation of clay particles in the rock matrix (Vernik and Nur, 1992). This intrinsic anisotropy is further enhanced in thermally mature shales by bedding‐parallel microcracks caused by the processes of hydrocarbon generation (Vernik, paper in preparation). However, the potential of recognizing mature source‐rocks in situ using downhole sonic, crosshole seismic, or VSP data clearly depends on our ability to discriminate between these two major causes of elastic anisotropy, remove the effect of the intrinsic anisotropy, and estimate crack density and crack porosity from velocity measurements.
Anisotropic velocity tomography: A case study in a near‐surface rock mass
Authors: Pratt R. G. , McGaughey W. J. , Chapman C. H.
Published: October 2002

Cross‐borehole data were acquired in the surface crown pillar of a massive sulfide ore mine. The data consist of five, two‐dimensional (2-D), cross‐borehole panels, each with approximately 900 source‐receiver pairs. The panels were located within the crown pillar at either side of and within a major subvertical fault zone that intersects the orebody. An initial analysis of the data indicates that the bedrock containing the orebody is seismically anisotropic. A rigorous analysis of the traveltimes using anisotropic velocity tomography confirms the initial assessment that anisotropy exists within the crown pillar rock mass. Anisotropic velocity tomography is the generalization of tomographic methods to anisotropic media. As in any geophysical problem, the data are insufficient to completely resolve the distributions of the rock properties at all scale lengths; we use external constraints on the roughness of the final solution to ensure an algebraically well‐posed problem. Plots of the data residuals (the “traveltime surfaces”) are an essential tool in determining an optimal level of constraint. Of equal importance are plots of the relationship between the solution roughness and the rms level of the residuals. The final results of anisotropic velocity tomography are a set of images (tomograms) of the velocity and selected anisotropy parameters for the five panels. Our images do not contain the distortions typically exhibited when using isotropic tomography in anisotropic media. The velocity tomograms clearly show the geometry of the overburden contact at the top of the bedrock. The anisotropy tomograms show a decrease in anisotropy with depth on two of the panels. They also show a decrease in anisotropy with proximity to the fault zone. These features of the seismic velocity anisotropy are consistent with observations of fracture orientation and distribution. The results of the crosshole data interpretation contribute to the overall site investigation and provide a reliable interrogation of the bulk properties of the rock mass.
Static image principle for anisotropic conducting half‐space problems: Impedance boundary
Authors: Lindell Ismo V. , Ermutlu Murat E. , Nikoskinen Keijo I. , Eloranta Esko H.
Published: October 2002

The image principle developed for static problems involving an anisotropic half‐space and bounded by either a perfect electric or magnetic conductor is extended to problems with an anisotropic surface impedance boundary. Such a boundary can be applied to approximate a thin layer of anisotropic conducting material above the anisotropic half‐space. The problem is limited by requiring similar anisotropy for the surface impedance and the transverse part of the resistivity dyadic of the half‐space. It is seen that, instead of a point image for a point source, the image consists of a combination of a point image and a line image obeying an exponential law. The effect of the impedance surface on the potential field of a point source is considered in terms of a numerical example.
Experimental study of viscosity effects on air‐gun signatures
Authors: Langhammer Jan , Landrø Martin
Published: October 2002

In computer modeling of air guns the theory is often based on the assumption of an ideal freely oscillating spherical air bubble in an ideal fluid. Theoretical and experimental air‐gun signatures do not match perfectly. Synthetic signatures are under‐damped compared to real signatures. Several physical effects have been proposed as an explanation of this mismatch, among them viscosity effects. The viscosity of the surrounding liquid may contribute to the damping of the bubble oscillation. The numerical value of the viscosity of the surrounding liquid has to be increased considerably beyond the actual value of water to obtain sufficient damping of the synthetic signatures. We therefore performed an experiment to study the effect upon the pressure signature from an air gun when changing the viscosity of the surrounding medium. The motivation for the experiment was to quantify the influence of viscous terms on the output pressure waveform from an air gun. The experiment was carried out in an [Formula: see text] tank. The source was a BOLT 600 B air gun with a firing chamber of [Formula: see text] [Formula: see text]. The gun was placed at 0.5 m depth, and the hydrophone was placed 0.22 m from the gun ports. This configuration was kept constant during the experiment. We observed changes in the output pressure waveform generated by the gun at different liquid viscosities. Sets of five signatures recorded at 12 viscosity values in the range 6–723 centipoise, were analyzed. The effects on the pressure signature when increasing the viscosity of the liquid surrounding the gun are to decrease the primary to bubble ratio and the bubble period; thus, the opposite of what one should expect. We therefore conclude that viscosity is not the main physical effect that explains the damping of an air gun signature.
Three‐dimensional magnetotelluric modeling using difference equations—Theory and comparisons to integral equation solutions
Authors: Mackie Randall L. , Madden Theodore R. , Wannamaker Philip E.
Published: October 2002

We have developed an algorithm for computing the magnetotelluric response of three‐dimensional (3-D) earth models. It is a difference equation algorithm that is based on the integral forms of Maxwell’s equations rather than the differential forms. This formulation does not require approximating derivatives of earth properties or electromagnetic fields, as happens when using the second‐order vector diffusion equation. Rather, one must determine how averages are to be computed. Side boundary values for the H fields are obtained from putting two‐dimensional (2-D) slices of the model into a larger‐scale 2-D model and solving for the fields at the 3-D boundary positions. To solve the 3-D system of equations, we propagate an impedance matrix, which relates all the horizontal E fields in a layer to all the horizontal H fields in that same layer, up through the earth model. Applying a plane‐wave source condition and the side boundary H field values allows us to solve for the unknown fields within the model. The results of our method compare favorably with results from previously published integral equation solutions.
Squeezing dip moveout for depth‐variable velocity
Authors: Hale Dave , Artley Craig
Published: October 2002

In dip‐moveout (DMO) processing, velocity variations with depth can be handled approximately by squeezing a constant‐velocity DMO operator to narrow its impulse response. This squeezed DMO approximation provides a computationally efficient and reasonably accurate method of DMO correction for depth‐variable velocity. DMO is squeezed by two modifications to constant‐velocity DMO. One modification is a squeezing function of time that depends only on simple time averages of velocity that are likely to be known before DMO is applied. This squeeze function ensures that squeezed DMO accurately handles moderately steep reflections and can be incorporated with simple time stretching before and after DMO, without any changes to existing constant‐velocity DMO methods. The second modification is a constant squeezing factor, which may be used to tune squeezed DMO to better handle steep reflections. This factor requires only trivial changes to constant‐velocity DMO methods. Tests with both synthetic and recorded seismic data suggest that squeezed DMO is an effective method for handling velocity variations with depth. These tests also show that the differences between constant‐velocity DMO and squeezed DMO can be significant.
Gravity due to a body with rotational symmetry about a vertical axis
Authors: Kwok Yue‐Kuen , Beyer Larry A.
Published: October 2002

Mass distributions encountered in gravity modeling are sometimes approximately symmetrical about a vertical axis. Examples include salt domes and other types of piercement structures, fluid behavior surrounding an injection or pumping well, formation damage and mudcake surrounding a drillhole, natural impact craters, human induced craters and underground explosions, and some volcanic and intrusive structures. Occasionally, gravity surveys are conducted in boreholes or vertical shafts that may or may not coincide with the axis of symmetry. The formulations presented here are useful for the interpretation of such gravity surveys.
A transient method of measuring the thermal properties of rocks
Authors: Middleton Mike F.
Published: October 2002

The aim of the paper is to describe a new, rapid transient method for the determination of thermal diffusivity and thermal conductivity of rocks. The present transient method is based on the application of a constant heat flux to the top surface of a block of rock that is insulated on all other surfaces. Results of a sensitivity analysis of the method indicate that thermal diffusivity can be measured to a best accuracy of about 3 percent, and thermal conductivity of saturated rocks can be determined to a best accuracy of about 8 percent. The method provides estimates of thermal conductivity that are consistent with estimates made using the steady‐state divided‐bar apparatus. The method is applied to determine the thermal conductivity of a suite of rocks from western Australian sedimentary basins.
Efficient migration through complex water‐bottom topography
Authors: Lynn Walt , MacKay Scott , Beasley Craig J.
Published: October 2002

An efficient means of imaging structures beneath complex water‐bottom topography is obtained using a conventional time‐migration algorithm with a simple modification to the migration‐velocity field. The process consists of two migration steps: one with the migration velocity set to zero below the water bottom and the other with the migration velocity set to zero above the water bottom. Between the two steps the data are vertically time shifted to account for the lateral velocity variations between the water‐sediment interface. The time shifts used are equivalent to the so‐called “thin‐lens” term used in depth‐migration algorithms. Efficiency is obtained by applying the thin‐lens term only once and by using computationally optimized time‐migration algorithms. Results obtained from this technique are nearly identical to more costly wave‐equation, layer‐replacement, and depth‐migration techniques.
Sensitivity of prestack depth migration to the velocity model
Authors: Versteeg Roelof Jan
Published: October 2002

To get a correct earth image from seismic data acquired over complex structures it is essential to use prestack depth migration. A necessary condition for obtaining a correct image is that the prestack depth migration is done with an accurate velocity model. In cases where we need to use prestack depth migration determination of such a model using conventional methods does not give satisfactory results. Thus, new iterative methods for velocity model determination have been developed. The convergence of these methods can be accelerated by defining constraints on the model in such a way that the method only looks for those components of the true earth velocity field that influence the migrated image. In order to determine these components, the sensitivity of the prestack depth migration result to the velocity model is examined using a complex synthetic data set (the Marmousi data set) for which the exact model is known. The images obtained with increasingly smoothed versions of the true model are compared, and it is shown that the minimal spatial wavelength that needs to be in the model to obtain an accurate depth image from the data set is of the order of 200 m. The model space that has to be examined to find an accurate velocity model from complex seismic data can thus be constrained. This will increase the speed and probability of convergence of iterative velocity model determination methods.
3-D time‐variant dip moveout by the f-k method
Authors: Meinardus Hans A. , Schleicher Karl L.
Published: October 2002

The standard seismic imaging sequence consists of normal moveout (NMO), dip moveout (DMO), stack, and zero‐offset migration. Conventional NMO and DMO processes remove much of the effect of offset from prestack data, but the constant velocity assumption in most DMO algorithms can compromise the ultimate results. Time‐variant DMO avoids the constant velocity assumption to create better stacks, especially for steeply dipping events. Time‐variant DMO can be implemented as a 3-D, f-k domain process using the dip decomposition method. Prestack data are moved out with a set of NMO velocities corresponding to discrete values of in‐line and crossline dips. The dip‐dependent NMO velocity is computed to remove the trace offset and azimuth dependence of event times for an arbitrary velocity function of depth. After stacking the moved out CMP gathers, a three‐dimensional (3-D) dip filter is applied to select the particular in‐line and crossline dip. The final zero‐offset image is obtained by summing all the dip‐filtered sections. This process generates a saddle‐shaped 3-D impulse response for a constant velocity gradient. The impulse response is more complicated for a general depth‐variable velocity function, where the response exhibits secondary branches, or triplications, at steeper dips. These complicated impulse responses, including amplitude and phase effects, are implicitly produced by the f-k process. The dip‐decomposition method of 3-D time‐variant DMO is an efficient and accurate process to correct for the effect of offset in the presence of an arbitrary velocity variation with depth. The impulse response of this process implicitly contains complex features like a 3-D saddle shape, triplications, amplitude, and phase. Field data from the Gulf of Mexico shows significant improvement on a steep salt flank event.
Conjugate direction relaxation solutions for 3-D magnetotelluric modeling
Authors: Mackie Randall L. , Madden Theodore R.
Published: October 2002

In recent years, there has been a tremendous amount of progress made in three‐dimensional (3-D) magnetotelluric modeling algorithms. Much of this work has been devoted to the integral equation technique (e.g., Hohmann, 1975; Weidelt, 1975; Wannamaker et al., 1984; Wannamaker, 1991). This method has contributed significantly to our understanding of electromagnetic field behavior in 3-D models. However, some of the very earliest work in 3-D modeling concentrated on differential methods (e.g., Jones and Pascoe, 1972; Reddy et al., 1977). It is generally recognized that differential methods are better suited than integral equation methods to model arbitrarily complex geometries, and consequently this area has recently been receiving a great deal of attention (e.g., Madden and Mackie, 1989; Xinghua et al., 1991; Mackie et al., 1993; Smith, 1992, personnal communication). Differential methods lead to large sparse systems of equations to be solved for the unknown field values. It is possible to use relaxation algorithms to quickly obtain approximate solutions to these systems of equations without resorting to standard matrix inversion routines or sparse matrix solvers.
Shortest path ray tracing with sparse graphs
Authors: Fischer Robert , Lees Jonathan M.
Published: October 2002

A technique for improving the efficiency of shortest path ray tracing (SPR) is presented. We analyze situations where SPR fails and provide quantitative measures to assess the performance of SPR ray tracing with varying numbers of nodes. Our improvements include perturbing the ray at interfaces according to Snell’s Law, and a method to find correct rays efficiently in regions of low velocity contrast. This approach allows the investigator to use fewer nodes in the calculation, thereby increasing the computational efficiency. In two‐dimensional (2-D) cross‐borehole experiments we find that with our improvements, we need only use 2/3 as many nodes, saving up to 60 percent in time. Savings should be even greater in three dimensions. These improvements make SPR more attractive for tomographic applications in three dimensions.
Depth‐focusing analysis using a wavefront‐curvature criterion
Authors: MacKay Scott , Abma Ray
Published: October 2002

Depth‐focusing analysis (DFA), a method of refining velocities for prestack depth migration, relies on amplitude buildups at zero offset to determine the extrapolation depths that best focus the migrated data. Unfortunately, seismic energy from dipping interfaces, diffractions, and noise often produce spurious amplitude indications of focusing. To reduce possible ambiguity in the DFA interpretation process, we introduce a new attribute for determining focusing that is relatively independent of amplitude. Our approach is based on estimates of the radius of wavefront curvature. The estimates are derived from normal moveout analysis of nonzero‐offset data saved during migration. By relating steeper moveout to smaller radius of wavefront curvature, focusing is defined by a wavefront curvature of zero radius. Additionally, we show that applying inverse‐radius weights to the amplitude data attenuates nonfocused events due to their large radius of curvature. Using the Marmousi data set, our weighting scheme resulted in reduced spurious focusing and enhanced velocity resolution in DFA.
Modeling of attenuation and dispersion
Authors: Varela Carlos Lopo , Rosa Andre L. R. , Ulrych Tadeusz J.
Published: October 2002

At the present time, proper solutions for absorption modeling are based on wavefield extrapolation techniques which, in some instances, may be considered expensive. Two alternative, low cost, but incomplete solutions exist in the literature. The first models dispersion in the frequency domain in accordance with the Futterman dispersive relations but does not consider attenuation. The second models both attenuation and dispersion in the time domain but assumes a digital minimum‐phase formulation that results in an inadequate treatment of the dispersion. We show that this second solution can be adapted to perform attenuation and/or dispersion modeling in agreement with the Futterman attenuation‐dispersion relationships thus obviating the shortcoming mentioned above. Synthetic and real data examples are shown to illustrate the performance of the proposed algorithm.
Full‐waveform processing and interpretation of kilohertz cross‐well seismic data
Authors: Khalil Ashraf A. , Stewart Robert R. , Henley David C.
Published: October 2002

High‐frequency, cross‐well seismic data, from the Midale oil field of southeastern Saskatchewan, are analyzed for direct and reflected energy. The goal of the analysis is to produce interpretable sections to assist in enhanced oil recovery activities ([Formula: see text] injection) in this field. Direct arrivals are used for velocity information while reflected arrivals are processed into a reflection image. Raw field data show a complex assortment of wave types that includes direct compressional and shear waves and reflected shear waves. A traveltime inversion technique (layer stripping via ray tracing) is used to obtain P‐ and S‐wave interval velocities from the respective direct arrivals. The velocities from the cross‐well inversion and the sonic log are in reasonable agreement. The subsurface coverage of the cross‐well geometry is investigated; it covers zones extending from the source well to the receiver well and includes regions above and below the source/receiver depths. Upgoing and downgoing primary reflections are processed, in a manner similar to the vertical seismic profiling/common‐depth‐point (VSP/CDP) map, to construct the cross‐well images. A final section is produced by summing the individual reflection images from each receiver‐gather map. This section provides an image with evidence of strata thicknesses down to about 1 m. Synthetic seismograms are used to interpret the final sections. Correlations can be drawn between some of the events on the synthetic seismograms and the cross‐well image.
Acoustic wave propagation in a fluid‐filled borehole surrounded by a formation with stress‐relief‐induced anisotropy
Authors: Renlie Lasse , Raaen Arne M.
Published: October 2002

The stress relief associated with the drilling of a borehole may lead to an anisotropic formation in the vicinity of the borehole, where the properties in the radial direction differ from those in the axial and tangential directions. Thus, axial and radial compressional acoustic velocities are different, and similarly, the velocity of an axial shear‐wave depends on whether the polarization is radial or tangential. A model was developed to describe acoustic wave propagation in a borehole surrounded by a formation with stress‐relief‐induced radial transverse isotropy (RTI). Acoustic full waveforms due to a monopole source are computed using the real‐axis integration method, and dispersion relations are found by tracing poles in the [Formula: see text] plane. An analytic expression for the low‐frequency Stoneley wave is developed. The numerical results confirm the expectations that the compressional refraction is mainly given by the axial compressional velocity, while the shear refraction arrival is due to the shear wave with radial polarization. As a result, acoustic logging in an RTI formation, will indicate a higher [Formula: see text] ratio than that existing in the virgin formation. It also follows that the shear velocity may be a better indicator of a mechanically damaged zone near the borehole than the compressional velocity. The Stoneley‐wave velocity was found to decrease with the increasing degree of RTI.
High‐resolution, cross‐well reflection imaging: Potential and technical difficulties
Authors: Lazaratos Spyros K. , Rector James W. , Harris Jerry M. , Van Schaack Mark
Published: October 2002

The case study presented in this paper demonstrates that reflections can be found in high‐frequency cross‐well data. These reflections can be enhanced by a processing sequence similar to the one applied to VSP data to produce very high‐resolution images. Vertical resolution of the order of 3–5 ft (1–1.5 m) for well distances of a few hundred feet is potentially feasible. Although this study produced a good tie between the cross‐well reflection image and the sonic log, our research also illustrated some of the technical difficulties associated with cross‐well reflection imaging. Specifically, we found that the signal‐to‐noise ratio of the image decreases as the distance between the imaged reflection points and the wells increases, and that aliased tube waves as well as shear and converted waves were the main components of the noise. We also observed that interpretation of wide‐angle reflections might be misleading, since these events are significantly stretched, both horizontally and vertically, during imaging. Improvements are required both in data acquisition (denser data collection, more fold, smaller angles of incidence) and processing/imaging (optimal use of fold) to make cross‐well reflection imaging useful. Still, the quality of these preliminary results, produced from a single gather of aliased data, indicates the promise of the approach.
Limitations on digital filtering of the DNAG magnetic data set for the conterminous U.S.
Authors: Grauch V. J. S.
Published: October 2002

The magnetic data set compiled for the Decade of North American Geology (DNAG) project presents an important digital data base that can be used to examine the North American crust. The data represent a patchwork from many individual airborne and marine magnetic surveys. However, the portion of data for the conterminous U.S. has problems that limit the resolution and use of the data. Now that the data are available in digital form, it is important to describe the data limitations more specifically than before. The primary problem is caused by datum shifts between individual survey boundaries. In the western U.S., the DNAG data are generally shifted less than 100 nT. In the eastern U.S., the DNAG data may be shifted by as much as 300 nT and contain regionally shifted areas with wavelengths on the order of 800 to 1400 km. The worst case is the artificial low centered over Kentucky and Tennessee produced by a series of datum shifts. A second significant problem is lack of anomaly resolution that arises primarily from using survey data that is too widely spaced compared to the flight heights above magnetic sources. Unfortunately, these are the only data available for much of the U.S. Another problem is produced by the lack of common observation surface between individual pieces of the U.S. DNAG data. The height disparities introduce variations in spatial frequency content that are unrelated to the magnetization of rocks. The spectral effects of datum shifts and the variation of spatial frequency content due to height disparities were estimated for the DNAG data for the conterminous U.S. As a general guideline for digital filtering, the most reliable features in the U.S. DNAG data have wavelengths roughly between 170 and 500 km, or anomaly half‐widths between 85 and 250 km. High‐quality, large‐region magnetic data sets have become increasingly important to meet exploration and scientific objectives. The acquisition of a new national magnetic data set with higher quality at a greater range of wavelengths is clearly in order. The best approach is to refly much of the U.S. with common specifications and reduction procedures. At the very least, magnetic data sets should be remerged digitally using available or newly flown long‐distance flight‐line data to adjust survey levels. In any case, national coordination is required to produce a consistent, high‐quality national magnetic map.
Wavepath eikonal traveltime inversion: Theory
Authors: Schuster Gerard T. , Quintus‐Bosz Aksel
Published: October 2002

We present a general formula for the back projection of traveltime residuals in traveltime tomography. For special choices of an arbitrary weighting factor this formula reduces to the asymptotic back‐projection term in ray‐tracing tomography (RT), the Woodward‐Rocca method, wavepath eikonal traveltime inversion (WET), and wave‐equation traveltime inversion (WT). This unification provides for an understanding of the differences and similarities among these traveltime tomography methods. The special case of the WET formula leads to a computationally efficient inversion scheme in the space‐time domain that is, in principle, almost as effective as WT inversion yet is an order of magnitude faster. It also leads to an analytic formula for the fast computation of wavepaths. Unlike ray‐tracing tomography, WET partially accounts for band‐limited source and shadow effects in the data. Several numerical tests of the WET method are used to illustrate its properties.
Geometrical ray theory: Edge‐diffracted rays and their traveltimes (second‐order approximation of the traveltimes)
Authors: Sun Jianguo
Published: October 2002

The general laws presenting global properties of reflected and transmitted rays are extended to the edge‐diffracted rays by the use of the law of edge diffraction. Similar to reflected and transmitted rays, edge‐diffracted rays and their traveltimes are described by the same four 2 × 2 matrices that are submatrices of the symplectic ray transformation matrix. If the incident rays have no line and point focus in the reflector having edges, one cone of diffracted rays corresponds just to one diffraction point. Otherwise, there may be an infinite number of cones of diffracted rays that are from one and the same diffraction point, and there may be no diffracted ray if the incident rays have a point focus in the reflecting surface with edges. For some cases, edge diffractions are the same as those from point diffractors and all diffracted rays are focused on the point focus of the reflected rays in the earth’s surface.
Precise source location of AE doublets by spectral matrix analysis of triaxial hodogram
Authors: Moriya Hirokazu , Nagano Koji , Niitsuma Hiroaki
Published: October 2002

We have developed a precise relative source location technique using acoustic emission doublets (AE doublets) in the triaxial hodogram method to evaluate the direction and distance of subsurface extension cracks. An AE doublet is a pair of acoustic emissions with similar waveforms and adjacent locations on the same crack but which occur at different times. The relative source location is estimated by an analysis in the frequency domain. The relative distance between two AE sources is determined from the difference of P-S arrival time delays by cross‐spectrum analysis. The relative direction is derived using a spectral matrix from the difference in P‐wave polarization directions. We also propose a method to optimize the estimated relative location by using a group of AE doublets. The accuracy of the estimated source location was confirmed by performing field experiments. The relative locations of artificial wave sources about 150 m from a triaxial detector can be estimated with distance errors of less than 1 m, and direction errors of less than 3.8 degrees in both azimuth and inclination. Results of the application of this analysis on AE doublets in a geothermal field demonstrate its ability to evaluate deeper subsurface fractures.
Comparison of P‐ and S‐wave velocities and Q’S from VSP and sonic log data
Authors: De Gopa S. , Winterstein Donald F. , Meadows Mark A.
Published: October 2002

We compared P‐ and S‐wave velocities and quality factors (Q’S) from vertical seismic profiling (VSP) and sonic log measurements in five wells, three from the southwest San Joaquin Basin of California, one from near Laredo, Texas, and one from northern Alberta. Our purpose was to investigate the bias between sonic log and VSP velocities and to examine to what degree this bias might be a consequence of dispersion. VSPs and sonic logs were recorded in the same well in every case. Subsurface formations were predominantly clastic. The bias found was that VSP transit times were greater than sonic log times, consistent with normal dispersion. For the San Joaquin wells, differences in S‐wave transit times averaged 1–2 percent, while differences in P‐wave transit times averaged 6–7 percent. For the Alberta well, the situation was reversed, with differences in S‐wave transit times being about 6 percent, while those for P‐waves were 2.5 percent. For the Texas well, the differences averaged about 4 percent for both P‐ and S‐waves. Drift‐curve slopes for S‐waves tended to be low where the P‐wave slopes were high and vice versa. S‐wave drift‐curve slopes in the shallow California wells were 5–10 μs/ft (16–33 μs/m) and the P‐wave slopes were 15–30 μs/ft (49–98 μs/m). The S‐wave slope in sandstones in the northern Alberta well was up to 50 μs/ft (164 μs/m), while the P‐wave slope was about 5 μs/ft (16 μs/m). In the northern Alberta well the slopes for both P‐ and S‐waves flattened in the carbonate. In the Texas well, both P‐ and S‐wave drifts were comparable. We calculated (Q’s) from a velocity dispersion formula and from spectral ratios. When the two Q’s agreed, we concluded that velocity dispersion resulted solely from absorption. These Q estimation methods were reliable only for Q values smaller than 20. We found that, even with data of generally outstanding quality, Q values determined by standard methods can have large uncertainties, and negative Q’s may be common.
Porosity, permeability, shear strength: Crosswell tomography below an iron foundry
Authors: Yamamoto Tokua , Nye Tom , Kuru Murat
Published: October 2002

Crosswell tomography of a sedimentary foundation at an iron foundry was affected by very high background noise; nevertheless, high‐resolution velocity images were obtained between wells separated by long distances (120 to 250 m). A piezoelectric source in a water‐filled well used long sequences (4095 cycles) of pseudorandom binary codes at high carrier frequencies (1 to 10 kHz). A 24‐channel hydrophone array in another well received the signal. Beamforming of common‐source data selected the directions and arrival times of multiple raypaths and tube waves and further enhanced the signal‐to‐noise ratio. Inversion of first‐arrival times by damped least squares imaged the compressional wave velocities. Assuming the normal consolidation condition, the porosity and shear strength images are predicted from the compressional wave velocity image. The direct measurements of porosity and shear strength conducted on the cores and boreholes were used to verify the tomographic predictions. The slight differences in the compressional wave velocity images obtained using different carrier frequencies can be used to determine the permeability image of sediments based on the Biot theory.
An automatic technique for presentation of coincident‐loop, impulse‐response, transient, electromagnetic data
Authors: Smith Richard S. , Edwards R. N. , Buselli G.
Published: October 2002

Coincident‐loop TEM sounding data are often presented by plotting the half‐space apparent conductivity as a function of delay time. A new algorithm generates an improved presentation that plots the apparent conductivity as a function of depth. The resulting data may be further processed to sharpen or “spike” the smoothly varying apparent‐conductivity/depth curves in an attempt to better represent the rapid changes in conductivity that often exist in the earth. The algorithm described involves an approximation, but is simple, easy to use, and computationally efficient. A layered conductivity structure is assumed, so the algorithm is best for areas where the geology is approximately horizontal. However, the algorithm can also be used to identify anomalous features that are not infinite horizontal layers. The spiked conductivity models derived from synthetic data are consistent with the original layered‐earth models and show a greater resolution than the apparent‐conductivity/depth curves, and sometimes amplify noise in the data. When data are collected along a profile line, the conductivity/depth information can be converted to a color image. For profile data collected over the Elura orebody, the image of the spiked conductivity section shows an anomalous feature at the orebody, and the color contrast is more marked than it is on the apparent‐conductivity/depth image.
Single‐channel digital filter design for seismic applications
Authors: Linville A. Frank
Published: October 2002

A general least‐squares, time‐domain filter design methodology has been developed that is easy to use for a variety of seismic filtering applications. The 1-D finite‐impulse response frequency filter can efficiently provide the noise attenuation and selectivity needed in modern data processing. Flexibility of design allows a choice of all basic types of single‐channel filters commonly used in processing. These include low‐pass, high‐pass, band‐pass, band‐reject, and notch filters. In addition, multiple bands may be passed or rejected using a single operator design without increasing the length of the filter. The ability to reject multiple noise bands with one filter is convenient and also reduces data processing costs. The filter can be viewed as a minimum‐phase Wiener‐Levinson predictive deconvolution filter designed to reject specified frequency bands. The filter is designed from an exact mathematical description of the specified stop bands that provide an explicit expression for the required autocorrelation lags in the normal equations. The filter’s desired frequency response (transition zone width and rejection level) is simply related to two input parameters—operator length and white noise level.
Modeling seismic waves in transversely isotropic media
Authors: Yan Pin , He Qiaodeng
Published: October 2002

Seismic waves in anisotropic media are more complex than in isotropic media. Here we derive the propagating matrices for seismic waves in 2-D transversely isotropic medium (TIM). With eigen‐decomposition, eigenvalues and eigenvectors are given in analytical forms, therefore, calculation of propagators are simple and accurate. For a 2-D model of layered media, we compute the seismic responses to an impulse in the f-k domain, and then do a 2-D inverse Fourier transformation. Clear qP and qSV waves can be recognized from the resultant sections.
Borehole dc resistivity response for a transitional invaded zone
Authors: Roy K. K. , Dutta D. J.
Published: October 2002

A borehole direct‐current resistivity boundary value problem for normal and lateral elctrode configuratin is soved assuming axial symmetry. The borehole mud, a flushed zone, an invaded zone, and an unciontaminated zone are all assumed to be present. A linear transition in resistivity is assumed for the invaded zone. Frobenius extended power series and the method of separation of variables are used to solved the 1-D problem. Single-run borehole resistivity sounding and solution of the inverse problem are suggested fo estimatingthe resisitivity of the uncontaminated zone and the radius of invasion. Finite‐difference modeling is dione to estimate the effect of shoulder beds ion borehole sounding. Some of the computed 1-D and 2-D model apparent reisivity curves are compared with the existing scale model data. The analysis reveals that the mud cake effect is negligible for normal and lateral electrode array and the invasion zone thickness is feflected in the forward models. Apparent resistivity curves with and without a transitional invaded zone are well separated. Resistivity departure curves are well separated for fixed resistivity and variable resistivity invaded zone models. A normal electrode configuration can feel the presence of the shoulder bed in a 2-D model when the bed thickness is about 12 time the electrode separation. One‐dimensional ridge regression inversion the synthetic forward model data is presented to suggest an alternative approach for determining the resistivey of the uncontaminated zone ([Formula: see text]) and the radius of invasion [Formula: see text]. We conclude that (1) a single run borehole sounding with 10 or 12 data points from a normal or lateral log may be used, rather than 3 points from a dual laterolog [Formula: see text] tool, for better estimation of [Formula: see text], and (2) a borehole forward model should include a transitional invaded zone. Finally, an alternative approach for the estimation of the radius of invasion is proposed.
The wave equation in generalized coordinates
Authors: Carcione José M.
Published: October 2002

This work introduces a spectral collocation scheme for the viscoelastic wave equation transformed from Cartesian to generalized coordinates. Both the spatial derivatives of field variables and the metrics of the transformation are calculated by the Chebychev pseudospectral method. The technique requires a special treatment of the boundary conditions, which is based on 1-D characteristics normal to the boundaries. The numerical solution of Lamb’s problem requires two 1-D stretching transformations for each Cartesian direction. The results show excellent agreement between the elastic numerical and analytical solutions, demonstrating the effectiveness of the differential operator and boundary treatment. Another example, requiring 1-D transformations, tests the propagation of a Rayleigh wave around a corner of the numerical mesh. Two‐dimensional transformations adapt the grid to topographic features: a syncline, and an anticlinal structure formed with fine layers.