bluuebunny/crossref_metadata_2025 huggingface dataset:
Improving plane‐wave decomposition and migration
Authors: Tieman Hans J.
Published: October 2002

Plane‐wave data can be produced by slant stacking common geophone gathers over source locations. Practical difficulties arise with slant stacks over common receiver gathers that do not arise with slant stacks over common‐midpoint gathers. New techniques such as hyperbolic velocity filtering allow the production of high‐quality slant stacks of common‐midpoint data that are relatively free of artifacts. These techniques can not be used on common geophone data because of the less predictive nature of data in this domain. However, unlike plane‐wave data, slant stacks over midpoint gathers cannot be migrated accurately using depth migration. A new transformation that links common‐midpoint slant stacks to common geophone slant stacks allows the use together of optimized methods of slant stacking and accurate depth migration in data processing. Accurate depth migration algorithms are needed to migrate plane‐wave data because of the potentially high angles of propagation exhibited by the data and because of any lateral velocity variations in the subsurface. Splitting the one‐way wave continuation operator into two components (one that is a function of a laterally independent velocity, and a residual term that handles lateral variations in subsurface velocities) results in a good approximation. The first component is applied in the wavenumber domain, the other is applied in the space domain. The approximation is accurate for any angle of propagation in the absence of lateral velocity variations, although with severe lateral velocity variations the accuracy is reduced to 50°. High‐quality plane‐wave data migrated using accurate wave continuation operators results in a high‐quality image of the subsurface. Because of the signal‐to‐noise content of this data the number of sections that need to be migrated can be reduced considerably. This not only saves computer time, more importantly it makes computer‐intensive tasks such as migration velocity analysis based on maximizing stack power more feasible.
High‐resolution velocity notch filter without Gibbs effect
Authors: Lichman Eugene , Northwood E. John
Published: October 2002

A new technique has been developed to reject or pass constant velocity coherent energy. Compared to the widely used frequency‐wavenumber (ο‐k) filtering method, this technique does not show either spatial aliasing or Gibbs effect. The filter operator is designed analytically as an infinite continuous function in the ο‐k domain. This function has the property that, when transformed by the integral inverse Fourier transform into the time‐space (t‐x) domain, it becomes a short discrete function with the same properties as the continuous infinite function in the ο‐k domain. No sampling or truncation of the filter operator is needed, hence no Gibbs oscillations are introduced into the operator impulse response or into the filtered data. Because of the extremely high‐velocity resolution and dynamic range of the designed coherent energy filter, it is particularly useful for the up‐ and downgoing energy separation on the vertical seismic profile data and for the peg‐leg multiples attenuation.
Turning wave migration by horizontal extrapolation
Authors: Zhang Jie , McMechan George A.
Published: October 2002

Conventional migration based on depth stepping extrapolation fails to migrate turning wave energy because of its inability to propagate energy with dips beyond 90°. A viable strategy for imaging turning waves is to use horizontal, rather than depth, extrapolation. This can be implemented by a 90° rotation of the extrapolator so that the data are extrapolated horizontally rather than vertically. In this geometry, the energy associated with turned rays consistently moves in the same direction as the extrapolation, and so only one pass is necessary to image turned reflections. The viability of this strategy is demonstrated with both synthetic and field poststack data that include turned reflections from salt flanks. Depth extrapolation images the near‐horizontal structure and horizontal extrapolation images the near‐vertical structure, and combining them gives a full image containing all dips.
Belated comments on electromagnetic cylinder scattering and the ubiquitous galvanic current contribution
Authors: Wait James R.
Published: October 2002

Many years ago (prior to the birth of many SEG members), I published a paper on the electromagnetic fields of a line current in the presence of a homogeneous cylinder (Wait, 1952). Although the general solution presented there was correct, an omission occurred in the reduction to the quasi‐static form. Indeed, Ward and Hohmann (1988) indicated the corresponding expression for [Formula: see text] in my 1952 paper was “wrong” after they had replicated my general derivation. Also, they correctly pointed out that I should not have omitted then n = 0 term in the series expansion for [Formula: see text] in the quasi‐static limit.
On: “Interpretation of two dimensional magnetic bodies using Hilbert transforms,” by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri Rao (March 1982 GEOPHYSICS, 52, p. 376–387)
Authors: Agarwal B. N. P.
Published: October 2002

While going through some of the publications (Mohan and Babu, 1995), I became interested in the work of Mohan et al. (1982) which proposed a technique for interpretation of magnetic field anomalies over different geometrical sources using the Hilbert transform (HT). Before I put forward my observations, it would be appropriate to look into some important properties of HT (Whalen, 1971, pages 63 and 69.)
Straightforward inversion of vertical electrical sounding data
Authors: Gupta Pravin K. , Niwas Sri , Gaur Vinod K.
Published: October 2002

A straightforward inversion scheme (SIS) has been developed to interpret vertical electrical sounding data. This scheme does not require quasi‐linearization of the inverse resistivity problem and thereby dispenses with the iterative process and the necessity of guessing the number of layers and their resistivities and thicknesses. The entire solution domain is divided into uniform thickness layers, whose scale must be judiciously selected for the desired resolution. The apparent resistivity formula can now be posed as an underdetermined matrix equation whose minimum norm solution is downward continued to obtain the reflection coefficients which, in turn, yield the vertical resistivity distribution. A recurrence relation has been developed especially for this purpose. In general, when data are expected to be noisy, a regressed minimum norm solution is used. Exhaustive tests of the algorithm have established its numerical efficiency. Results of six typical synthetic models, representing diverse geological conditions, as well as results of two field examples are included to demonstrate this claim.
Seismic attenuation tomography using the frequency shift method
Authors: Quan Youli , Harris Jerry M.
Published: October 2002

We present a method for estimating seismic attenuation based on frequency shift data. In most natural materials, seismic attenuation increases with frequency. The high‐frequency components of the seismic signal are attenuated more rapidly than the low‐frequency components as waves propagate. As a result, the centroid of the signal's spectrum experiences a downshift during propagation. Under the assumption of a frequency‐independent Q model, this downshift is proportional to a path integral through the attenuation distribution and can be used as observed data to reconstruct the attenuation distribution tomographically. The frequency shift method is applicable in any seismic survey geometry where the signal bandwidth is broad enough and the attenuation is high enough to cause noticeable losses of high frequencies during propagation. In comparison to some other methods of estimating attenuation, our frequency shift method is relatively insensitive to geometric spreading, reflection and transmission effects, source and receiver coupling and radiation patterns, and instrument responses. Tests of crosswell attenuation tomography on 1-D and 2-D geological structures are presented.
A quasi‐Monte Carlo approach to 3-D migration: Theory
Authors: Sun Yonghe , Schuster Gerard T. , Sikorski K.
Published: October 2002

A mathematical breakthrough was recently achieved in understanding the tractability of multidimensional integration using nearly optimal quasi‐Monte Carlo methods. Inspired by the new mathematical insights, we have studied the feasibility of applying quasi‐Monte Carlo methods to seismic imaging by 3-D prestack Kirchhoff migration. This earth imaging technique involves computing a large [Formula: see text] number of 3-D or 4-D integrals. Our numerical studies show that nearly optimal quasi‐Monte Carlo migration can produce the same or better quality earth images using only a small fraction (one fourth or less) of the data required by a conventional Kirchhoff migration. The explanation is that an image migrated from a coarse quasi‐random array of seismic data is less likely, on average, to be aliased than an image migrated from a regular array of data. In migrating these data, the geophones act as an incoherent arrangement of loud‐speakers that broadcast the reflected wavefield back into the earth; the broadcast will produce reinforcement or cancellation of seismic energy at the diffractor or grating lobe locations, respectively. Thus quasi‐Monte Carlo migration contains an inherent anti‐aliasing feature that tends to suppress migration artifacts without losing bandwidth. The penalty, however, is a decrease in the dynamic range of the migrated image compared to an image from a regular array of geophones. Our limited numerical results suggest that this loss in dynamic range is acceptable, and so justifies the anti‐aliasing benefits of migrating a random array of data.
Anatomy of the southern Cordilleran hingeline, Utah and Nevada, from deep electrical resistivity profiling
Authors: Wannamaker Philip E. , Johnston Jeffery M. , Stodt John A. , Booker John R.
Published: October 2002

To address outstanding questions in Mesozoic‐Cenozoic structure and present‐day deep physicochemical state in the region of the southern Cordilleran hingeline, a detailed, east‐west profile of magnetotelluric (MT) soundings 155 km in length was acquired. From these soundings, a resistivity interpretation was produced using an inversion algorithm based on a structural parameterization. In the upper ten kilometers of the transect, the interpretation shows two segments of low resistivity lying beneath allochthonous rocks of the Late Mesozoic, Sevier thrust sheet. Subsequent industry drilling motivated in part by our surveying confirms the existence and position of the eastern subthrust conductor and, more spectacularly, identifies the presence of yet deeper, autochthonous Mesozoic rocks. The conductors cannot be specified uniquely with present public data, because their electrical characteristics appear consistent with Paleozoic, pyrolized graphitic strata of either Late Devonian‐Mississippian or Middle Ordovician age. However, the drilling results show that Late Paleozoic and younger rocks lie underthrust much farther west than recognized previously, and perhaps as far west as the Utah‐Nevada border. A simple structural interpretation is offered where one underthrust segment of low‐resistivity sediments was created originally, but this segment was broken later into two major ones during higher‐angle Tertiary extension. For the middle and lower crust, the MT data imply a nearly 1-D resistivity structure of remarkable uniformity across the entire transect. In particular, there occurs a deep low‐resistivity layer most pronounced (about 8 ohm-m) in the nominal depth interval of 17.5 to 40 km. The MT data indicate that the layer cannot be confined to a single thin layer in the lower crust but instead represents vertically distributed low resistivity. With temperatures estimated from surface heat flow to range from 550°C to 1050°C with depth in the layer, and with a metaigneous mineralogy of high metamorphic grade assumed, mechanisms to produce the low resistivity can be constrained. The deep layer is thus consistent with [Formula: see text] brines at its upper levels, fluids of lower [Formula: see text] activity toward middle levels, and [Formula: see text] melting below about 30 km. The marked uniformity of the deep conductive layer across the transect suggests a similar uniformity of deep physicochemical state. However, this is not at odds with recent analyses of heat flow, Curie depth, Quaternary extension, and basaltic volcanism. Pre‐existing structural fabrics have had no measureable influence on localizing regions of high temperature, fluids and melting in the lower crust, at least averaged over the scale of tens of kilometers. Given its uniformity over a distance of 155 km or more, the depth to the regional deep conductor does not appear related to the distribution of high‐temperature geothermal resources.
3-D electromagnetic modeling for near‐surface targets using integral equations
Authors: Xiong Zonghou , Tripp Alan C.
Published: October 2002

Three‐dimensional electromagnetic (EM) modeling in the frequency range from 100 kHz to about 200 MHz using integral equations is examined. The modeling algorithm is formulated in the frequency domain. Time‐domain responses for ground‐penetrating radar (GPR) and very early time time‐decaying transients are computed via Fourier transforms. Of vital importance to the modeling problem is the computation of the Hankel transforms in the Green's functions. The kernels of those Hankel transforms vary rapidly at high frequencies where displacement currents become important and are even singular for sources in the air, with poles approaching the real axis or branch cuts lying on the real axis. We use high density Hankel filters and a singularity extraction technique to circumvent these problems. Our modeling for GPR applications shows that dielectric targets are very obvious in radargrams, with waves reflected by target boundaries arriving at distinctive times, depending on the path they travel. While GPR signals are absorbed in conductive media, very early time‐transient responses can detect conducting targets in conductive media. Our modeling shows that 1-D shallow conductors can have large transient anomalies in the time window from 50 ns to 100 ms. Thus 1-D near‐surface conductors may be detected by conventional systems operating at μs ranges. However, shallow 3-D conductors of practical interest can have much earlier anomaly time windows around 100 ns. These targets can only be detected by very early time‐transient equipment. Moreover, very early time transients contain little information on dielectric permittivities, being primarily determined by the conductivities of the media. Thus GPR and very early time transients are excellent complements to each other.
Ground‐penetrating radar responses of dispersive models
Authors: Xiong Zonghou , Tripp Alan C.
Published: October 2002

Ground‐penetrating radar (GPR) has been a very efficient tool for mapping shallow targets for applications such as those in geological engineering and environmental management (Fisher et al. 1992). Since the application of GPR depends on the complex electrical properties of the ground, it is important to study this dependence in all its manifestations. The depth of investigation for GPR applications depends strongly on the conductivity of the ground. If the ground is very conductive, GPR waves will be absorbed before they reach the target region. Earth materials can be dispersive, i.e., the conductivity and permittivity of rocks are frequency dependent (Levitskaya and Sternberg, 1994). This is especially true at high frequencies. GPR waves will also be absorbed in dispersive media. Hence modeling the GPR response in dispersive materials can reveal behaviors of importance in understanding field responses.
3-D migration of cross‐spread data: Resolution and amplitude aspects
Authors: Wapenaar C. P. A.
Published: October 2002

Ideally, full prestack migration involves a 4-D integration along the source and receiver coordinates. Obviously, for cross‐spread data (typical for land acquisition) this 4-D integration cannot be effectuated. An analysis is presented of the resolution and amplitude behavior of full prestack migration, applied to cross‐spread data. Moreover, a proposal is made to modify operators that partly compensate for the diminishing effects of the cross‐spread aquisition geometry on amplitudes and resolution.
True‐amplitude common‐shot migration revisited
Authors: Sun Jianguo , Gajewski Dirk
Published: October 2002

In Kirchhoff‐type migration, two dynamic ray‐tracing computations are usually needed for computing the complex weighting (Green's) functions necessary for recovering the source pulse with true amplitude. One computation is from the source point to the image point, the other is from the receiver point to the image point. Since it is a time‐consuming procedure, dynamic ray tracing is a main factor slowing down the performance speed of weighted diffraction stack migration. Here, the known weighting function for a common‐shot configuration is revisited and a new, alternative formula is developed. Because only the takeoff angles of rays are involved in this alternative formula, the module of the complex weighting function can be computed solely by kinematic ray tracing. Further, it is shown that the phase (caustic) correction is not essential for the stack process. As a consequence, the weighted diffraction stack migration can be implemented without using dynamic ray tracing at all. In other words, the subsurface structure can be imaged without using any Green's function. Therefore, using the new formula may accelerate the performance of the Kirchhoff‐type migration, especially in 3-D cases. In addition, the new formula may affect the model smoothing process necessary for using some traveltime computing methods based on ray tracing. As is known, kinematic quantities associated with a given ray are less sensitive to the velocity distribution than the dynamic ones. Thus, the new formula allows one to use a model less smoothed than that demanded for using dynamic ray tracing. As a result, less smoothing operation is needed by building a velocity model without interfaces. The latter points are vital for the accuracy and efficiency of the ray tracers for computing the traveltime of point‐diffracted rays.
3-D coherency filtering
Authors: Li Qing , Vasudevan Kris , Cook Frederick A.
Published: October 2002

Coherency filtering is a tool used commonly in 2-D seismic processing to isolate desired events from noisy data. It assumes that phase‐coherent signal can be separated from background incoherent noise on the basis of coherency estimates, and coherent noise from coherent signal on the basis of different dips. It is achieved by searching for the maximum coherence direction for each data point of a seismic event and enhancing the event along this direction through stacking; it suppresses the incoherent events along other directions. Foundations for a 2-D coherency filtering algorithm were laid out by several researchers (Neidell and Taner, 1971; McMechan, 1983; Leven and Roy‐Chowdhury, 1984; Kong et al., 1985; Milkereit and Spencer, 1989). Milkereit and Spencer (1989) have applied 2-D coherency filtering successfully to 2-D deep crustal seismic data for the improvement of visualization and interpretation. Work on random noise attenuation using frequency‐space or time‐space prediction filters both in two or three dimensions to increase the signal‐to‐noise ratio of the data can be found in geophysical literature (Canales, 1984; Hornbostel, 1991; Abma and Claerbout, 1995).
Application of instantaneous rotations to S‐wave vertical seismic profiling
Authors: Boulfoul M. , Watts Doyle R.
Published: October 2002

The petroleum exploration industry uses S‐wave vertical seismic profiling (VSP) to determine S‐wave velocities from downgoing direct arrivals, and S‐wave reflectivities from upgoing waves. Seismic models for quantitative calibration of amplitude variation with offset (AVO) data require S‐wave velocity profiles (Castagna et al., 1993). Vertical summations (Hardage, 1983) of the upgoing waves produce S‐wave composite traces and enable interpretation of S‐wave seismic profile sections. In the simplest application of amplitude anomalies, the coincidence of high amplitude P‐wave reflectivity and low amplitude S‐wave reflectivity is potentially a direct indicator of the presence of natural gas.
Design, calibration, and application of an airborne gamma spectrometer system in Switzerland
Authors: Schwarz Georg F. , Rybach Ladislaus , Klingelé Emile E.
Published: October 2002

Airborne radiometric surveys are finding increasingly wider applications in environmental mapping and monitoring. They are the most efficient tool to delimit surface contamination and to locate lost radioactive sources. To secure radiometric capability in survey and emergency situations, a new sensitive airborne system has been built that includes an airborne spectrometer with 256 channels and a sodium iodide detector with a total volume of 16.8 liters.

A rack mounted PC with memory cards is used for data acquisition, with a GPS satellite navigation system for positioning. The system was calibrated with point sources using a mathematical correction to take into account the effects of gamma‐ray scattering in the ground and in the atmosphere. The calibration was complemented by high precision ground gamma spectrometry and laboratory measurements on rock samples.

In Switzerland, two major research programs make use of the capabilities of airborne radiometric measurements. The first one concerns nuclear power plant monitoring. The five Swiss nuclear installations (four power plants and one research facility) and the surrounding regions of each site are surveyed annually. The project goal is to monitor the dose‐rate distribution and to provide a documented baseline database. The measurements show that all sites (with the exception of the Gösgen power plant) can be identified clearly on the maps. No artificial radioactivity that could not be explained by the Chernobyl release or earlier nuclear weapons tests was detected outside of the fenced sites of the nuclear installations.

The second program aims at a better evaluation of the natural radiation level in Switzerland. The survey focused on the crystalline rocks of the Central Massifs of the Swiss Alps because of their relatively high natural radioactivity and lithological variability.
Radon emanation and soil moisture effects on airborne gamma‐ray measurements
Authors: Grasty Robert L.
Published: October 2002

A theoretical model is developed to explain variations in airborne gamma‐ray measurements over a calibration range near Ottawa, Ontario. The gamma‐ray flux from potassium and the thorium decay series showed an expected decrease with increasing soil moisture. However, the gamma‐ray flux from the uranium decay series was highest in the spring when the ground was water‐saturated and even covered with snow. These results are explained through the build‐up of radon and its associated gamma‐ray—emitting decay products in the clay soil of the calibration range with increasing soil moisture. Similar results were found from airborne measurements over other clay soils. However, measurements over sandy soils showed that the count rates from all three radio elements increased with decreasing soil moisture. This difference between soil types was attributed to the lower radon emanation of the more coarse‐grained sandy soils compared to finer‐grained clay soils. The theoretical and experimental results demonstrate that any estimate of the natural gamma‐ray field caused by radium in the ground must take into consideration the radon emanation coefficient of the soil. The radon diffusion coefficient of the soil must also be considered since it depends strongly on soil moisture. This has significant implications for the assessment of outdoor radiation doses using laboratory analyses of soil samples and the use of ground and airborne gamma‐ray measurements for radon potential mapping.
Modeling velocity changes associated with a miscible flood in the Prudhoe Bay Field
Authors: Withers Robert J. , Batzle Michael L.
Published: October 2002

The Prudhoe Bay Field, Alaska, is produced by a number of recovery processes. A miscible gas (MI) injection pilot was studied to see if repeated seismic surveys could detect the progress of the MI gas. Gassmann's equation was used on the injection, producing and monitor wells where a detailed reservoir simulation was available. Time‐varying saturations of the three fluid phases and the pressure were used to calculate the expected velocity of the reservoir at different stages of the injection. The differences between the modeled velocities at two extremes of gas saturation after the water‐after‐gas (WAG) range up to 500 ft/s (150 m/s). It was concluded that it have been possible to detect the fluid saturation had a baseline survey been collected early in the field's development. Unfortunately, initial production introduced 2% gas into the fluid, muting later attempts to map changes in saturation that varied from between 30% and 60%. Additionally, the use of a WAG process further complicated the gas mapping by both increasing and decreasing the reservoir fluid velocities. Collecting new seismic data over this pilot was not recommended. The modeling exercise highlighted a number of issues that are important in monitoring other reservoirs. Amongst these are the timing of data collection and the weakness of the petrophysical models caused by the numerous assumptions that are required in the absence of field observations. It was demostrated that modeling exercises can both save unnecessary field expenses and provide considerable insight in reservoir behavior.
Electrical detection of leaks in lined waste disposal ponds
Authors: Frangos William
Published: October 2002

A method for detecting and locating leaks in the plastic liner of a waste disposal pond has been implemented and tested at a site near Budmerice in Slovakia. The method is based on detecting electric current flowing through holes in the insulating lining membrane. Unlike similar methods employed elsewhere, this implementation allows monitoring for leaks that may develop during and after filling the pond with electrically inhomogeneous solid waste. To accomplish this goal, sensing electrodes were placed below the membrane during construction. In operation, current was passed between an electrode inside the pond and another outside; the voltage caused by this current was observed on the buried sensing electrodes. The data were then processed to detect and locate any leaks in the membrane. An important practical concern is achieving acceptable detectability and location accuracy while using a sufficiently sparse grid of sensing electrodes. This problem was overcome by two processing steps: (1) calculating electrical potentials from the observed voltages and (2) performing a nonlinear inversion on subsets of the data. With this technique, observations made with a 10- × 8-m grid of electrodes, a relatively low‐power current source, and a simple receiver can provide accurate location information, even for small leaks. In a blind test, the system accurately predicted the locations of six leaks that were subsequently verified visually. Five of the leaks were cuts in the plastic typically measuring less than 2 × 0.1 cm, whereas the sixth leak was a group of many small holes. For the five, the typical location accuracy was about 30 cm, comparable to the basic survey location accuracy of the sensing electrodes.
Ground‐penetrating radar velocity tomography in heterogeneous and anisotropic media
Authors: Vasco Don W. , Peterson John E. , Lee Ki Ha
Published: October 2002

A ray series solution for Maxwell's equations provides an efficient numerical technique for calculating wavefronts and raypaths associated with electromagnetic waves in anisotropic media. Using this methodology and assuming weak anisotropy, we show that a perturbation of the anisotropic structure may be related linearly to a variation in the traveltime of an electromagnetic wave. Thus, it is possible to infer lateral variations in the dielectric permittivity and magnetic permeability matrices. The perturbation approach is used to analyze a series of crosswell ground‐penetrating radar surveys conducted at the Idaho National Engineering Laboratory. Several important geological features are imaged, including a rubble zone at the interface between two basalt flows. Linear low‐velocity anomalies are imaged clearly and are continuous across well pairs.
Comparison of weights in prestack amplitude‐preserving Kirchhoff depth migration
Authors: Hanitzsch Christian
Published: October 2002

Three different theoretical approaches to amplitude‐preserving Kirchhoff depth migration are compared. Each of them suggests applying weights in the diffraction stack migration to correct for amplitude loss resulting from geometric spreading. The weight functions are given in different notations, but as is shown, all of these expressions are similar. A notation that is well suited for implementation is suggested: entirely in terms of Green's function quantities (amplitudes or point‐source propagators). For the most common prestack configurations (common‐shot and common‐offset) and 3-D, 2.5-D, and 2-D migrations, expressions of the weights are given in this notation. The quantities needed for calculation of the weights can be computed easily, e.g., by dynamic ray tracing.
Analytic study of the effective parameters for determination of the NMO velocity function in transversely isotropic media
Authors: Cohen Jack K.
Published: October 2002

In their studies of transversely isotropic media with a vertical symmetry axis (VTI media), Alkhalifah and Tsvankin observed that, to a high numerical accuracy, the normal moveout (NMO) velocity for dipping reflectors as a function of ray parameter p depends mainly on just two parameters, each of which can be determined from surface P‐wave observations. They substantiated this result by using the weak‐anisotropy approximation and exploited it to develop a time‐domain processing sequence that takes into account vertical transverse isotropy. In this study, the two‐parameter Alkhalifah‐Tsvankin result was further examined analytically. It was found that although there is (as these authors already observed) some dependence on the remaining parameters of the problem, this dependence is weak, especially in the practically important regimes of weak to moderately strong transverse isotropy and small ray parameter. In each of these regimes, an analytic solution is derived for the anisotropy parameter η required for time‐domain P‐wave imaging in VTI media. In the case of elliptical anisotropy (η = 0), NMO velocity expressed through p is fully controlled just by the zero‐dip NMO velocity—one of the Alkhalifah‐ Tsvankin parameters. The two‐parameter representation of NMO velocity also was shown to be exact in another limit—that of the zero shear‐wave vertical velociy. The analytic results derived here are based on new representations for both the P‐wave phase velocity and normal moveout velocity in terms of the ray parameter, with explicit expressions given for the cases of vanishing onaxis shear speed, weak to moderate transverse isotropy, and small to moderate ray parameter. Using these formulas, I have rederived and, in some cases, extended in a uniform manner various results of Tsvankin, Alkhalifah, and others. Examples include second‐order expansions in the anisotropy parameters for both the P‐wave phase‐velocity function and NMO‐velocity function, as well as expansions in powers of the ray parameter for both of these functions. I have checked these expansions against the corresponding exact functions for several choices of the anisotropy parameters.
Analysis of reflection traveltimes in 3-D transversely isotropic heterogeneous media
Authors: Grechka Vladimir Y. , McMechan George A.
Published: October 2002

A two‐point ray‐tracing technique for rays reflected from irregular, but smooth, interfaces in 3-D transversely isotropic heterogeneous media is developed. The method is based on Chebyshev parameterization of curved segments of the reflected rays, of the reflectors, and of the velocity and anisotropy distributions in the model. Chebyshev approximation also can describe the reflection traveltime surfaces to compress traveltime data by replacing them with coefficients of the corresponding Chebyshev series. The advantage of the proposed parameterization is that it gives traveltime as an explicit function of the model parameters. This explicitly provides the Frechét derivatives of the traveltime with respect to the model parameters. The Frechét derivatives are used in two ways. First, a two‐term Taylor series is constructed to relate variations in the model parameters to the corresponding perturbations in the traveltimes. This makes it possible, based on the results of a single ray tracing in a relatively simple model, to predict traveltimes for a range of more complicated models, without any additional ray tracing. Second, singular‐value decomposition of the Frechét matrix determines the influence of various model parameters on common‐source and common‐midpoint traveltimes. The singular‐value analysis shows that common‐source traveltimes depend mainly on the reflector position and shape. The common‐midpoint traveltimes also contain additional information about lateral velocity heterogeneity and anisotropy. However, both of these parameters affect the traveltimes in similar ways and so usually cannot be determined separately.
Source signature estimation based on the removal of first‐order multiples
Authors: Ikelle Luc T. , Roberts Graham , Weglein Arthur B.
Published: October 2002

The estimation of the source signature is often one of the necessary first steps in the processing of seismic reflection data, especially if the processing chain includes prestack multiple removal. However, most methods for source estimation are based on poststack data or assume that the earth is 1-D. In this work, a new source estimation method for prestack data is presented. It consists of finding the source signature that permits the removal of events attributable to the first‐order free‐surface reflections (i.e., first‐order multiples). The method exploits the formulation of the relationship between the free‐surface reflections and the source signature as a scattering Born series. In this formulation, the order of the scattering series coincides with that of the free‐surface reflections, and the series is constructed exclusively with seismic data and the source signature without any knowledge of the subsurface other than the velocity of sea water. By restricting the problem to first‐order free‐surface reflections, we have rendered the relationship between free‐surface reflections and the source signature linear, which also corresponds to a truncation of the scattering Born series to its first two terms. Thus, the source signature estimation can be formulated as a linear inverse problem. Assuming that the removal of first‐order free‐surface events produces a significant reduction in the energy of the data, we posed the inverse problem as finding the source signature that minimizes this energy. The optimization leads to an iterative solution. The iterations are needed to correct for the truncation effects. Synthetic and real data examples show the applicability and stability of the source estimation method as well as its use for attenuating free‐surface multiples.
Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth
Authors: Schoenberg Michael , Helbig Klaus
Published: October 2002

Vertical fractures and horizontal fine layering combine to form a long, wavelength equivalent orthorhombic medium. Such media constitute a subset of the set of all orthorhombic media. Orthorhombic elastic symmetry is the lowest symmetry for which the slowness surface (the solution of the Christoffel equation) is bicubic rather sextic. Various properties of orthorhombic media, such as the number and location of conical points and longitudinal directions, may be derived from the slowness surface or, because of its bicubic character, the squared slowness surface, which is a cubic surface. From the occurrence and angular orientation of some of these distinctive features, conclusions can be drawn with respect to the properties of the medium and to the parameters of the assumed underlying causes of the anisotropy. The estimation of these more subtle properties gains greater importance with the proliferation of multiazimuthal seismic surveys and the ability to drill along ever more complicated 3‐D well trajectories.
New objective functions for waveform inversion
Authors: Frazer L. Neil , Sun Xinhua
Published: October 2002

Inversion is an organized search for parameter values that maximize or minimize an objective function, referred to here as a processor. This note derives three new seismic processors that require neither prior deconvolution nor knowledge of the source‐receiver wavelet. The most powerful of these is the fourwise processor, as it is applicable to data sets from multiple shots and receivers even when each shot has a different unknown signature and each receiver has a different unknown impulse response. Somewhat less powerful than the fourwise processor is the pairwise processor, which is applicable to a data set consisting of two or more traces with the same unknown wavelet but possibly different gains. When only one seismogram exists the partition processor can be used. The partition processor is also applicable when there is only one shot (receiver) and each receiver (shot) has a different signature. In fourwise and pairwise inversions the unknown wavelets may be arbitrarily long in time and need not be minimum phase. In partition inversion the wavelet is assumed to be shorter in time than the data trace itself but is not otherwise restricted. None of the methods requires assumptions about the Green’s function.
Parallel 3-D pseudospectral simulation of seismic wave propagation
Authors: Furumura Takashi , Kennett B. L. N. , Takenaka Hiroshi
Published: October 2002

Three‐dimensional pseudospectral modeling for a realistic scale problem is still computationally very intensive, even when using current powerful computers. To overcome this, we have developed a parallel pseudospectral code for calculating the 3-D wavefield by concurrent use of a number of processors. The parallel algorithm is based on a partition of the computational domain, where the field quantities are distributed over a number of processors and the calculation is concurrently done in each subdomain with interprocessor communications. Experimental performance tests using three different styles of parallel computers achieved a fairly good speed up compared with conventional computation on a single processor: maximum speed‐up rate of 26 using 32 processors of a Thinking Machine CM-5 parallel computer, 1.6 using a Digital Equipment DEC‐Alpha two‐CPU workstation, and 4.6 using a cluster of eight Sun Microsystems SPARC-Station 10 (SPARC-10) workstations connected by an Ethernet. The result of this test agrees well with the performance theoretically predicted for each system. To demonstrate the feasibility of our parallel algorithm, we show three examples: 3-D acoustic and elastic modeling of fault‐zone trapped waves and the calculation of elastic wave propagation in a 3-D syncline model.
A frequency‐space 2-D scalar wave extrapolator using extended 25-point finite‐difference operator
Authors: Shin Changsoo , Sohn Heejeung
Published: October 2002

Finite‐difference frequency‐domain modeling for the generation of synthetic seismograms and crosshole tomography has been an active field of research since the 1980s. The generation of synthetic seismograms with the time‐domain finite‐difference technique has achieved considerable success for waveform crosshole tomography and for wider applications in seismic reverse‐time migration. This became possible with the rapid development of high performance computers. However, the space‐frequency (x,ω) finite‐difference modeling technique is still beyond the capability of the modern supercomputer in terms of both cost and computer memory. Therefore, finite‐difference time‐domain modeling is much more popular among exploration geophysicists. A limitation of the space‐frequency domain is that the recently developed nine‐point scheme still requires that G, the number of grid points per wavelength, be 5. This value is greater than for most other numerical modeling techniques (for example, the pseudospectral scheme). To overcome this disadvantage inherent in space‐frequency domain modeling, we propose a new weighted average finite‐difference operator by approximating the spatial derivative and the mass acceleration term of the wave equation. We use 25 grid points around the collocation. In this way, we can reduce the number of grid points so that G is now 2.5. This approaches the Nyquist sampling limit in terms of the normalized phase velocity.
A physical model for porosity reduction in sandstones
Authors: Gal Doron , Dvorkin Jack , Nur Amos
Published: October 2002

The experimental elastic moduli‐porosity trends for clean sandstones can be described by the modified upper Hashin‐Shtrikman (MUHS) bound. One geometrical (but not necessarily geological) realization is: as porosity decreases, the number of the pores stays the same and each pore shrinks while maintaining its shape. This concept of uniform porosity reduction implies that permeability is proportional to the effective porosity squared, and that formation factor is proportional to the inverse of the effective porosity. The effective porosity here refers to the part of the pore‐space that dominates fluid flow. The proposed relations for permeability and formation factor agree well with the experimentally observed values. These laws are different from the often used forms of the Kozeny‐Carman equation and Archie’s law, where permeability is proportional to the total porosity cubed and formation factor is proportional to the inverse of the total porosity squared, respectively. We suggest that the uniform porosity reduction concept be used in consolidated rocks with porosities below 0.3. The transition from high‐porosity unconsolidated sands to consolidated sandstones can be described by the cementation theory: the MUHS moduli‐porosity curves connect with those predicted by the cementation theory at the porosity of about 0.3. This scheme is not appropriate for modeling other porosity reduction mechanisms such as glass bead sintering because, during sintering, the pores do not maintain their shapes, rather they gradually evolve to rounder, stiffer pores.
Detection of lateral velocity contrasts by crosswell traveltime tomography
Authors: Goudswaard Jeroen C. M. , ten Kroode Fons P. E. , Snieder Roel K. , Verdel Arie R.
Published: October 2002

Crosswell traveltime tomography is a common technique in the oil industry for determining the velocity function in the plane between two boreholes. However, the method suffers from the well‐known problem that the lateral resolution is far less than the vertical resolution because of the unfavorable illumination conditions for survey geometries comprising vertical wells. Consequently, it is very difficult to image sudden lateral changes in the velocity function accurately using this technique. We propose a method for determining such changes, which severely constrains the solution space by inverting for the position of a lateral velocity contrast only. The velocity model on each side of the contrast is derived from the well logs. The potential of the method is first demonstrated in two synthetic examples in which its properties are compared with those of an unconstrained 2-D tomographic inversion. As expected, the constrained method has much better convergence properties than the unconstrained one in these examples. We also compare the two methods in a real setting, in which a sudden lateral velocity change, associated with a geological transition, is expected. It turns out that a lateral contrast can be imaged with both methods in this real data example. However, the image obtained with the new method better explains the observed facts.
Azimuth moveout for 3-D prestack imaging
Authors: Biondi Biondo , Fomel Sergey , Chemingui Nizar
Published: October 2002

We introduce a new partial prestack‐migration operator called “azimuth moveout” (AMO) that rotates the azimuth and modifies the offset of 3-D prestack data. Followed by partial stacking, AMO can reduce the computational cost of 3-D prestack imaging. We have successfully applied AMO to the partial stacking of a 3-D marine data set over a range of offsets and azimuths. When AMO is included in the partial‐stacking procedure, high‐frequency steeply dipping energy is better preserved than when conventional partial‐stacking methodologies are used. Because the test data set requires 3-D prestack depth migration to handle strong lateral variations in velocity, the results of our tests support the applicability of AMO to prestack depth‐imaging problems. AMO is a partial prestack‐migration operator defined by chaining a 3-D prestack imaging operator with a 3-D prestack modeling operator. The analytical expression for the AMO impulse response is derived by chaining constant‐velocity DMO with its inverse. Equivalently, it can be derived by chaining constant‐velocity prestack migration and modeling. Because 3-D prestack data are typically irregularly sampled in the surface coordinates, AMO is naturally applied as an integral operator in the time‐space domain. The AMO impulse response is a skewed saddle surface in the time‐midpoint space. Its shape depends on the amount of azimuth rotation and offset continuation to be applied to the data. The shape of the AMO saddle is velocity independent, whereas its spatial aperture is dependent on the minimum velocity. When the azimuth rotation is small (⩽20°), the AMO impulse response is compact, and its application as an integral operator is inexpensive. Implementing AMO as an integral operator is not straightforward because the AMO saddle may have a strong curvature when it is expressed in the midpoint coordinates. An appropriate transformation of the midpoint axes to regularize the AMO saddle leads to an effective implementation.