bluuebunny/crossref_metadata_2025 huggingface dataset:
Seismic range equation
Authors: Duren Richard E.
Published: October 2002

The seismic range equation is the seismic equivalent to the radar range equation. It unites the relevant factors in a marine data gathering system (source, subsurface, target, and receiving system) into a single formulation and provides a systematic approach to seismic data analysis, which we have used to improve seismic data processing for marine basins around the world. While most of the concepts contained in the seismic range equation are well known, this is the first time all have been put together, described in such detail, and used effectively (by way of modeling) to improve processing. A wavelet’s amplitude spectrum can be calculated using the seismic range equation, and its phase spectrum can be calculated by considering the phase contributions from source to receiver. An amplitude‐versus‐offset (AVO) example supports our approach. Source array geometry and the outgoing waveforms from the array elements are required. The receiving system’s load impedance and the hydrophone array’s geometry, sensitivity, and impedance are also required. Subsurface factors and target strength can be determined by assuming a horizontally layered subsurface and ray theory. The required layer thicknesses, P‐wave velocities, and densities can be generated by hand, statistically, or from well data. Well data are not required at the location of interest. The Zoeppritz equations furnish all P-wave reflection and transmission coefficients along a raypath. Seismic data at the location of interest can be used to estimate an attenuation constant (effective Q).
Thermal regime and hydrodynamics in Tunisia and Algeria
Authors: Dhia Hamed Ben
Published: October 2002

The thermal regime of Algeria and Tunisia and its relation to hydrodynamics is studied by means of available geological and geothermal, and petroleum data. Heat flow densities in the area range from [Formula: see text] to [Formula: see text]. Several Paleozoic to Tertiary aquifers have been identified, together with potential recharge and discharge areas. The area is a transition zone between the African and European plates. The more tectonically active northern Alpine domain does not exhibit an obvious geothermal trend, and high heat flow anomalies that occur there may be related to structure rather than hydrodynamics. The more stable southern Saharan tectonic domain, with background heat flow of approximately [Formula: see text], exhibits anomalous zones correlated to the hydrodynamic regime with low values in recharge areas (Algerian Tinrhert and High Plateaux) and values in discharge areas (Tunisian Jeffara and Algerian Tademait). The hydrodynamic perturbation to the normal heat flow is estimated to be as great as [Formula: see text] in recharge and discharge zones.
Cross‐borehole simulation of wave propagation
Authors: Jean Philippe , Bouchon Michel
Published: October 2002

Synthetic seismograms are used to study elastic wave propagation in multi‐layered media for cross‐borehole geometries. The calculations are done using the discrete wavenumber method. We compute the wavefield for a series of receiver arrays located at various offsets to follow the evolution of the wavefronts and the distribution of the seismic energy in space. The results show the complexity of the wavefield at large offsets. Trapped waves and conical waves perturb the identification of direct and primary reflected phases. The display of polarization diagrams of the guided waves shows elliptical prograde motions. The source position plays an important role in the energy distribution within the medium. In order to study this dependency, we compare the cases of sources located in relatively low and high‐velocity layers. In the former case, most of the energy is trapped within the source layer and in the neighboring region and propagates horizontally. The S‐converted waves generated at the interfaces bounding the source layer have larger amplitude than the direct P‐wave. When the source is placed in a relatively high‐velocity layer the energy of the P‐wavefront spreads rapidly throughout the medium as the offset increases.
Contribution of magnetic modeling to the discovery of a hidden massive sulfide body at Hajar, Morocco
Authors: Bellott A. , Corpel J. , Millon R.
Published: October 2002

The Hajar prospect is located in the Guemassa Paleozoic massif, about 30 km southwest of Marrakesh, Morocco. Visean volcano‐sedimentary formations are present in this massif and in the Jebilets massif north of Marrakesh. In these formations, syngenetic massive sulfides occur, and one of these bodies, Kettara in the Jebilets, has been partially mined. Using the Kettara magnetic anomaly to establish the magnetization parameters, we performed a preliminary interpretation of the Hajar anomaly. Our 2.5-D model determined the depth of the structure to be about 150 to 200 m below the surface. This relatively shallow depth was a decisive factor in siting a reconnaissance drillhole, which encountered massive sulfides between 158 and 276 m. After completing a systematic gravity and magnetic survey, 3-D magnetic modeling was attempted, constrained by the results of four drillholes. Now that more than 20 holes have been drilled, this magnetic model still conforms to the newly revealed geology. Unfortunately, it was not possible to extract useful information concerning the orebody from modeling and interpreting the gravity data. The gravity response is masked by disturbances such as faults and variations in depth and nature of the Visean basement. The discovery of the Hajar deposit shows that magnetic investigations, improved by pertinent modeling techniques, can be used at various stages of exploration to help recognize and define massive sulfide bodies.
A Walsh sequency filtration method for integrating the resistivity log and sounding data
Authors: Pal Poorna C.
Published: October 2002

The integration of resistivity logs and soundings data, essential for resolving the problems of ambiguity and nonuniqueness ubiquitous in the interpretation of electrical resistivity soundings, is generally difficult because the former contain far more details than can be retrieved from the latter. As logarithmic scaling linearizes the behavior of apparent resistivity values and resistivity transform functions, and as the Walsh functions realistically mimic the resistivity logs, the strategy proposed here is to use the resistivity‐stratigraphy schematized from Walsh‐filtration of logarithmically scaled logs‐profile as input model for sounding interpretation. The efficiency of this strategy is demonstrated here with a practical example from groundwater exploration. The synthetic sounding curve based on 29 layers manually schematized from the observed linearly scaled logs‐profile could be modeled by 8 layers, whereas that computed from 14 layers schematized from sequency‐filteration of the logarithmically scaled logs‐profile closely matched the observed sounding curve from a nearby location.
Defining archaeological features with electromagnetic surveys at the Cahokia Mounds State Historic Site
Authors: Dalan Rinita A.
Published: October 2002

Electromagnetic (EM) surveys have been used at the Cahokia Mounds State Historic Site in southwestern Illinois to locate and define a number of buried archaeological features. Two instruments, Geonics EM31-D and EM38 conductivity meters, were employed to locate portions of a wooden stockade known as the Central Palisade; delineate a number of leveled earthen mounds; and explore a broad, flat area in the central portion of the site known as the Grand Plaza. EM surveys, together with limited excavation, provide a cost effective and nondestructive means of exploring a site as large and complex as Cahokia. Archaeological excavations confirmed that EM surveys were able to locate the Central Palisade, and more importantly, that they provided information on anthropogenically modified terrain within the Grand Plaza. The EM survey documented buried ridge and swale topography and borrow pits within this area. This evidence of landscape modification challenges previous conceptions about the extent of earthmoving at this important Mississippian center and suggests a promising area of application for EM surveys in archaeology.
The search for graves
Authors: Bevan Bruce W.
Published: October 2002

Over the decades, grave markers in old cemeteries have been lost. Geophysical exploration can sometimes locate the unmarked burials. The two techniques which may be best for this search are a ground‐penetrating radar survey and a soil conductivity survey. A ground‐penetrating radar survey, with its capability for estimating the depth and shape of buried objects, is particularly suitable. With an electromagnetic induction survey, the disturbed soil in the grave shaft can sometimes be detected as a change in electrical conductivity. Both of these surveys also can locate large metal objects. These surveys have limitations. At some sites, the radar cannot profile deeply enough; at others, the soil strata are so complex that graves cannot be distinguished. A conductivity survey can be degraded by metallic trash and other small objects in the topsoil; it can give the best results where the earth is distinctly stratified. Results from nine surveys are illustrated here. The sites are all in the U.S.A. and the graves are not older than the 17th century. Magnetic and resistivity surveys may be suitable for some sites, but they have not been very successful for the sites discussed here. The success of these surveys has ranged widely, from excellent to poor. While little archaeological excavation has followed these surveys, geophysical tests at marked graves show the capability of the instruments.
Vector wavefields for weakly attenuating anisotropic media by the ray method
Authors: Gajewski Dirk , Pšenčík Ivan
Published: October 2002

The ray method is used to compute high‐frequency seismic vector wavefields in weakly attenuating layered anisotropic structures. The attenuating effects are introduced by substituting the real elastic parameters for perfectly elastic media by complex frequency dependent elastic parameters with small imaginary parts. The imaginary parts are formally considered to be of the order of [Formula: see text] for [Formula: see text]. Under this assumption, it is possible to work with real rays, only the eikonal is complex. The approximate computations based on this algorithm are only a few percent slower than those for perfectly elastic anisotropic media. The range of applicability of the weak attenuation concept is investigated by comparison of ray computations with results of the reflectivity method for an isotropic, constant gradient model. The study indicates that the region of applicability of the weak attenuation concept may be broader than expected. The combined effects of anisotropy and attenuation on the propagation of seismic waves in a three‐dimensional model of the uppermost crust with an anisotropic attenuating layer are then studied. The anisotropy as well as the attenuation are supposed to be caused by aligned partially liquid‐filled cracks. Hudson’s formulas to compute complex effective elastic parameters are used. Frequency responses and VSP synthetic seismograms for different degrees of viscosity of the liquid, and, thus, different degree of attenuation, show the effects of attenuation on the propagating waves. Nine‐component VSP vector wavefields are computed for two different source‐borehole directions along the strike of the cracks and 45 degrees off the strike of the cracks. The seismograms for the attenuating model are compared with seismograms for the corresponding perfectly elastic model.
Effect of temporal and spatial variations of the primary signal on VLF total‐field surveys
Authors: Vallée Marc A. , Chouteau Michel , Palacky G. J.
Published: October 2002

Most of the airborne and ground VLF instruments presently used measure the total‐field response in addition to field ratios. Results of surveys using these instruments are adversely affected by spatial and temporal variations in the VLF primary field. Until now, the nature of such variations has not been studied from the point of view of geophysical surveying practice. Spatial variations are analyzed using radio propagation models. The most important result is the identification of primary field minima where surveys would be unreliable. Their dependence on the transmitter location is rather complex, and modeling should be carried out before specifying VLF stations for a survey area. Spatial and temporal variations have been studied using field monitoring of the transmitted signal. The results of field experiments indicate that the nature of the received VLF fields changes significantly even over moderate distances (20–30 km) and that data cannot be reliably corrected over larger distances. This observation has a significant implication for VLF total‐field surveys, particularly airborne, in which base stations have been routinely used to monitor the primary field strength and to correct the survey data. The results of primary signal monitoring are also used to demonstrate the effect of solar flares on VLF surveys. Because of the large intensity and complex electromagnetic character of solar flares, survey data recorded during such events cannot be used for map compilation and interpretation.
Radiation pattern and seismic waves generated by a working roller‐cone drill bit
Authors: Rector James W. , Hardage Bob A.
Published: October 2002

The seismic body wave radiation pattern of a working roller‐cone drill bit can be characterized by theoretical modeling and field data examples. Our model of drill‐bit signal generation is a pseudo‐random series of bit‐tooth impacts that create both axial forces and tangential torques about the borehole axis. Each drill tooth impact creates an extensional wave that travels up the drill string and body waves that radiate into the earth. The model predicts that P‐waves radiate primarily along the axis of the borehole, and shear waves radiate primarily perpendicular to the borehole axis. In a vertical hole, the largest P‐waves will be recorded directly above and below the drill bit; whereas, the largest shear waves will be recorded in a horizontal plane containing the drill bit. In a deviated borehole, the radiation patterns should be rotated by the inclination angle of the drill bit. This proposed seismic body wave radiation pattern is investigated with field data examples. The presence of the drill string in the borehole creates other wave modes that are not typically observed when conventional vertical seismic profiles (VSPs) are conducted in fluid‐filled wells. For example, the extensional wave traveling up the drill string creates a head wave traveling away from the drill string, provided the formation velocities adjacent to the borehole are less than the drill‐string velocity. Likewise, when the extensional wave traveling up the drill string reaches the drill rig, some of the energy continues through the drill rig structure, re‐enters the earth, and travels away from the rig as ground roll or shallow refractions. Secondary events are radiated at the drill bit after they travel up the drill string, reflect off drill‐string discontinuities, and travel back down the drill string to the bit. Each of these drill‐bit arrivals has a characteristic moveout as a function of wellhead offset and drill‐bit depth. A knowledge of the radiation patterns and the wave modes generated by the drill bit is essential to interpreting drill‐bit wavefields.
Finite‐difference solution of the eikonal equation along expanding wavefronts
Authors: Qin Fuhao , Luo Yi , Olsen Kim B. , Cai Wenying , Schuster Gerard T.
Published: October 2002

We show that a scheme to solve the 2-D eikonal equation by a finite‐difference method can violate causality for moderate to large velocity contrasts [Formula: see text]. As an alternative, we present a finite‐difference scheme in which the solution region progresses outward from an “expanding wavefront” rather than an “expanding square,” and therefore honors causality. Our method appears to be stable and reasonably accurate for a variety of velocity models with moderate to large velocity contrasts. The penalty is a large increase in computational cost and programming effort.
Circularly polarized shear waves used for VSP measurements
Authors: Edelmann Hans A. K.
Published: October 2002

If shear waves are to be recorded, all other types of waves (including P waves) have to be regarded as noise. All data processing applied later is limited in its success, not so much by the character of the signal, but by the character of the noise superimposed on the signal. Therefore an optimum method for simultaneous P‐ and S‐wave recording does not exist per se. All efforts made in the field that help to enhance the relatively weak S‐wave signal enhance the possibility of a more detailed interpretation such as polarization analysis. In the course of shear‐wave investigations over a period of more than ten years, simultaneous P‐ and SV‐wave recording has yielded fairly good results for velocity ratio determination, but has never produced satisfying results for polarization analysis because of the interfering P‐wave events. When generating pure SH‐waves, however, P‐wave arrival amplitudes in a shot record can, under favorable conditions, be kept well below the SH‐wave amplitude (−40 dB). Through additional processing, a ratio of P‐ to SH‐signal amplitude of −60 dB can be reached. The improvement achieved by making separate shear‐wave recordings, obviously, must be weighed against the additional costs caused by these recordings.
On: “Field measurements of azimuthal anistropy: First 60 meters, San Francisco Bay area, CA, and estimation of the horizontal stresses' ratio from Vs1/Vs2” by Heloise Bloxsom Lynn (June 1991 GEOPHYSICS, p. 822–832)
Authors: Winterstein D. F.
Published: October 2002

What I would like to discuss has little to do with the content of Heloise Lynn’s paper, which beautifully illustrates S‐wave birefringence in near‐surface materials. My concern is with the terminology. Inappropriate use of the term azimuthal anisotropy has become so prevalent in both oral and written presentations that someone needs to point out clearly and in detail why such usage is ill‐advised. My comments, thus, while triggered by the usage of this paper, are for an audience that includes many besides the paper’s author.
Direct determination of the natural remanent magnetization effect in a hole drilled in layered ground from magnetic field and susceptibility logs
Authors: Desvignes Guy , Barthes Véronique , Tabbagh Alain
Published: October 2002

A new method as presented, allows the joint interpretation of both electromagnetic (EM) and magnetic logs in layered ground, based on the fact that the susceptibility responses for these two measurements are linear. Thus we can make use of the classical properties of the Fourier transform to extract from these two signals the magnetic field due to remanent magnetization. Theoretical models show that for a sufficient sample step this remanent magnetization can be recovered, even if the Koenigsberger ratio is of the order of 0.2 and if the thickness of the magnetized layer is of the order of 1 m. The results for two case examples in a sedimentary context are also shown. Despite the difficulties due to experimental procedures, we show that the amplitude of the extracted information is significant in these two cases, even if its variations are somewhat structureless and cannot be easily explained by the geology.
3-D physical modeling and pseudospectral simulation of seismic common‐source data volumes
Authors: Chen How‐Wei , McMechan George A.
Published: October 2002

Numerical simulation of common‐source seismic responses of arbitrarily complicated three‐dimensional (3-D) variable‐velocity structures is implemented by pseudospectral solution of the scalar wave equation. Potential applicability of such simulation to data analysis and interpretation is demonstrated by comparing synthetic 3-D (x, y, t) common‐source gathers with those recorded on an areal grid of receivers over a physical scale model of a salt tongue. The iterative model adjustment process in fitting the physical model data is analogous to that which would be required for field data. Comparing differences between 2-D and 3-D synthetic responses allows interpretation of out‐of‐plane propagation. It is necessary to include the effects on the source directivity, because of a shield placed over the source during data acquisition, to numerically approximate the main features in the recorded scale model data.
Comparison of high‐resolution wax‐embedded and pneumatically coupled borehole seismic detectors
Authors: Owen Thomas E. , Parra Jorge O.
Published: October 2002

High‐quality seismic measurements at frequencies up to about 2000 Hz are needed if projected resolution limits on the order of 1 m in spatial dimension are to be realized in reservoir structure delineation, cross‐well sonic logging, and shallow reverse VSP applications. While sources and detectors are critical to this goal, we have investigated detector requirements in an objective way to demonstrate a successful design philosophy capable of achieving unprecedented wide‐band frequency response and data quality in three‐component shallow‐borehole sensors. Two prototype detectors were developed: a nearly ideal responding wax‐embedded “reference” detector and a pneumatically coupled detector exhibiting closely comparable performance. Our approach uses a three‐axis accelerometer sensor assembly installed in a borehole drilled through the weathered surface to a depth at which the ground is competent enough to support practical kilo‐hertz wave propagation. The wax‐coupled detector is planted using a meltable wax embedment to achieve a rigid, stress‐free, conformal coupling at the bottom of the hole. Experimental test results show this wax‐embedded detector to have excellent broadband three‐component response at frequencies up to 2500 Hz; a range heretofore unexplored for seismic applications. The pneumatically coupled detector, although limited by modal resonance distortion effects in the highest range of frequencies, demonstrated useful three‐component response at frequencies up to 1500 Hz. Tests of the two coupling techniques under identical conditions illustrate their high‐quality responses and their differences. Field tests of the prototype pneumatically coupled detector in shallow reverse vertical seismic profiling (VSP) measurements demonstrate the practical effectiveness of the basic high‐resolution probe design concepts.
Migration moveout analysis and depth focusing
Authors: Lafond Claude F. , Levander Alan R.
Published: October 2002

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.
Waveform inversion of seismic velocities and attenuation from low‐frequency waves in cylindrical bars
Authors: Tang Xiao Ming
Published: October 2002

A new technique for laboratory measurement of seismic wave velocities and attenuation in the frequency range of 10–150 kHz consists of measuring extensional waveforms using two cylindrical bars of the same material but unequal length. Based on the dispersion equation of the bar and rough estimates of compressional and shear velocities of the bar material, the waveform measured within the shorter bar is theoretically continued to the length of the longer bar to match with the waveform measured there. An inversion is then performed to minimize the phase difference between the two waveforms. The velocities are obtained when the phase difference reaches a minimum, at which the two waveforms attain the optimum phase match. After the phase match, a further inversion is performed to minimize the amplitude difference between the two waveforms to derive the extensional wave attenuation within the bar. By this inversion procedure, wave velocities and attenuation can be jointly determined at frequencies much lower than those of the ultrasonic measurements. By using the technique, compressional and shear velocities and extensional attenuation values in a lucite material and in dry Sierra White granite were measured. The results from the present technique are consistent with the results from other techniques (resonant bar and ultrasonic), if the effect of intrinsic attenuation is accounted for.
Cavitation‐induced seismic events caused by small explosions in boreholes
Authors: Fisher R. , Mason I. M. , Mosher C. C.
Published: October 2002

An electrolytically recharged sleeve exploder was fired at depths between 15.2 m and 51.8 m in a 200-mm diameter, steel‐cased, water‐filled shallow borehole in Hopkins County, Texas. Oxy‐hydrogen explosive gas charges were varied between 30 and 170 kJ. Seismic traces revealed three distinct, delayed, anomalous arrivals. Two of these moved out nonlinearly with increasing charge. The fact that the anomalies were not peculiar to gaseous sleeve explosions was confirmed by repeating part of the experiment using small high explosive charges. The anomalies appear to stem from the collapse of cavities that are created by shock waves. A model is advanced, in which up‐ and downgoing shock fronts sweep away from the explosion at the tube wave velocity. They reflect from the free and plugged ends of the borehole. Reflection at the free end transforms an upgoing overpressure into a downgoing rarefaction. Momentum transfer surges the fluid. Surges accumulate. Two rarefaction shocks eventually collide at the shot point. The fluid there cavitates if the net pressure drops to zero. Fluid moving above the shot rises. The column splits into two parts. Column separation of itself creates rarefaction shocks that enter, surge, and then break fluid slugs from the ends of the (rising) upper and (stationary) lower columns. The borehole fluid breaks into four parts. Three fly up and descend as weight drops to create a train of seismic events. Model predictions correlate with seismic observations. The model provides a means for explosive source calibration. An oxy‐hydrogen charge of 100 kJ in a minisleeve exploder appears to develop an overpressure of ≈8.8 atm. A 25-gm solid explosive charge yields similar results. A simple extension of the model suggests that the potentially destructive effects of implosion can be avoided by plugging the borehole mouth before shooting in an uncased borehole.
Smoothing operators for waveform tomographic imaging
Authors: Cardimona Steve , Garmany Jan
Published: October 2002

The analytic kernel in the space‐time domain for the Frechet derivative of acoustic waveform data with respect to changes in the slowness model is given by the Born approximation solution to the integral equation of waveform scattering. Preconditioning operators in the solution of this forward problem, which may incorporate a priori information and approximate solutions, are smoothing operators in the imaging problem, the first iteration of a nonlinear inversion for the slowness model. Some preconditioning operators are determined for solutions to the parabolic wave equation, and then used to create new sensitivity functions that retain appropriate characteristics of the true Frechet kernel in forward calculations. The new sensitivity functions define near‐source, near‐receiver and far‐field kernels, as well as kernels that exhibit an amplitude decay off the ray yielding ray‐perpendicular sensitivity that scales with the Fresnel zone size. A sample calculation from a synthetic cross‐well imaging experiment shows the usefulness of introducing physically appropriate model smoothing directly into the sensitivity function of the forward problem, helping to obtain a geologically reasonable image of the velocity model when ray coverage is insufficient.
A transmission‐line model for electrical logging through casing
Authors: Kaufman Alexander A. , Wightman W. Edward
Published: October 2002

Electrical logging in cased holes is a subject of strong current interest. In this paper we develop the conventional theory of physical responses of electrical logging through casing where the formation resistivity changes vertically and where the conductance of the casing varies. The theory is developed for a four‐electrode sonde with one current electrode, and three receiver electrodes that measure current leakage into the formation. All the theoretical developments in the paper are derived using approximate transmission‐line theory. An expression for the array coefficient is first derived and then used to obtain an expression for the apparent conductivity of the formation. Then a relation is established between the array coefficient, geometrical factor and conductance of the casing. This step led to a method of measuring casing conductance. Knowing casing conductance, the response of the array to vertical changes in formation conductivity is measurable. It was established, that when the array length is less than the thickness of the formation layer, the measured apparent conductivity is equivalent to the true conductivity of the formation, unlike the case of normal and induction logs. It was also established that measurement of apparent conductivity can be made accurately inside a casing of finite length when it essentially exceeds the length of the electrode array. The results contained in this paper show that electrical logging through casing is possible in wells with conventional casing strings that penetrate layered sedimentary formations.
Geometrical‐spreading correction by a dual diffraction stack
Authors: Schleicher J. , Hubral P. , Tygel M.
Published: October 2002

Prestack diffraction‐stack migration methods (also often called Kirchhoff‐type migration) play a fundamental role in seismic imaging. In two dimensions, they are widely applied in practice. In three dimensions, however, they still remain the topic of active research. The interested reader can find the relevant literature on the subject in the few references cited in the text.
Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media
Authors: Sena Arcangelo G. , Toksöz M. Nafi
Published: October 2002

We develop asymptotic expressions and outline a procedure to perform Kirchhoff migration in anisotropic media. This technique is based on a new Green’s tensor representation for azimuthally isotropic media obtained by using analytical forms for the ray amplitudes and traveltimes. Since in real applications the usage of general anisotropy in a migration scheme will be limited by the availability and reliability of the velocity model considered, we also develop a new anisotropic velocity analysis scheme to generate realistic anisotropic models for migration in azimuthally isotropic media for nonconverted and converted qP-qSV waves. This velocity analysis technique is based on nonhyperbolic traveltime‐offset formulas explicitly given in terms of the five elastic constants of azimuthal isotropy. The imaging technique is applied to nonconverted‐as well as converted‐wave surface seismic data. In both cases the method provides accurate images of the subsurface. Even with a weak to moderate percentage of anisotropy, we show that an isotropic migration algorithm cannot properly image the subsurface. This paper provides new nonconventional techniques for the velocity analysis and migration in anisotropic media and shows the feasibility of exploiting converted and nonconverted waves.
On: “Why don’t we measure seismic signatures?” by A. Ziolkowski (February 1991 GEOPHYSICS, p. 190–201)
Authors: Mendel J. M.
Published: October 2002

Professor Ziolkowski makes many statements all of which are aimed at denouncing statistical‐based deconvolution methods in favor of his own deterministic‐based method. It is incredible that after almost 40 years confusion still abounds about statistical‐based deconvolution methods. I hope to clarify this confusion in a forthcoming publication (Robinson and Mendel, 1992). Here my purposes are to expose some technical errors in Prof. Ziolkowski’s article that cast doubt on the entire paper.
Ambiguity in analysis of velocity and depth
Authors: Lines Larry
Published: October 2002

Velocity analysis methods generally involve an analysis of the traveltime moveout of seismic events. To investigate ambiguities for such methods, we can start with a simple single layer model and investigate the uncertainty in the estimation of velocity and reflector depths. This analysis will show that the velocity‐depth ambiguity is dependent on the offset‐depth ratio and on the accuracy of traveltime picks.
On: “Removal of static shift in two dimensions by regularized inversion” by Catherine deGroot‐Hedlin (December 1991 GEOPHYSICS, p. 2102–2106).
Authors: Sternberg Ben K.
Published: October 2002

Dr. deGroot‐Hedlin criticizes the use of TEM surveys for static shift correction with the following statement: Sternberg et al. (1988) recommend the use of a central transient electromagnetic (TEM) sounding at each site to determine an absolute measure of the static shift. However, collection of more data at each site may make the method prohibitively costly.
Fast approximate solutions of transient EM response to a target buried beneath a conductive overburden
Authors: Liu Guimin , Asten Michael W.
Published: October 2002

We derive fast transient electromagnetic (TEM) solutions for a thin‐plate conductive target buried in a resistive host rock overlain by thin conductive overburden. For this model, the total TEM field is composed of the overburden response, which is known analytically, and the target response that is approximated by a wire loop. Thus the transient response of the target in free space is approximated with a single exponential function. The interaction between the target and the overburden is approximated by convolving the overburden‐delayed driving field with the exponential function. The target response is then computed from the wire loop by the Biot‐Savart law in free space, thus neglecting the second overburden‐delay effect. Including the second overburden‐delay effect does not yield significantly improved results. The approximate solutions agree reasonably well with scale model and numerical results, but their computation is more than 100 times faster than conventional methods and can be easily done on a small personal computer.
A modified form of diffraction tomography to image boundary structures
Authors: Rekdal Thorbjørn , Doornbos Durk J.
Published: October 2002

Wavefield extrapolation downward from the surface, as applied in migration and associated inversion methods, is a common procedure to image subsurface reflectors. These methods require adequate (i.e., extensive and unaliased) sampling of the surface wavefield. Seismic tomography on the other hand, relates parameters of the upward propagated wavefield to the diffracting image, and sampling requirements are less severe; it is usually the only option to image deep structures from sparse data. The ordinary form of ray tomography, however, imposes a severe smoothness constraint on the boundary; in particular the “tops” and “valleys” of a relatively rough structure are not well‐resolved. We have implemented a generalized form of tomography, which uses both the ray term and the diffraction term linearized in the boundary perturbation. We introduce a generalized reflection coefficient that can be linearized in terms of the (unknown) boundary gradient, and we demonstrate the adequacy of this approximation with the help of synthetic seismograms. We compare the performance of the new inversion method with migration and ray tomography in a number of model experiments where a source and receiver array are used to image (1) a rough sea bottom and (2) a rough sedimentary layer boundary. In these experiments the new method is superior, especially in the outer part of the inversion region where migration and seismic tomography suffer seriously because of the lack of adequate surface information. Even for well‐controlled surveys there is the potential to successfully image a much larger area of the reflector than is possible with migration. Our experiments involved a single reflector in a known velocity‐density structure. The method’s applicability or modifications required when relaxing these assumptions, remains to be investigated.
On: “Decomposition into minimum and maximum phase components” by E. Eisner and G. Hampson (GEOPHYSICS, 55, 897–901, July 1990).
Authors: Saha J. G. , Mehta C. H. , Benjamin S.
Published: October 2002

How to locate the zero time in a recorded, noisy waveform? How to quantify the extent of minimum‐phaseness of a waveform? And how to render a waveform or a seismic trace minimum phase? These are some of the questions with which we approached this paper which describes a new method for locating the time origin in a given waveform and, thereafter, factoring the waveform as a convolution of a causal minimum‐phase component and an anticausal maximum phase component.
Acoustic‐wave propagation in thin‐layered media with steep reflectors
Authors: Deng H. Lydia
Published: October 2002

Seismic waves reflected from steep interfaces beneath layered sediments spend a significant portion of time traveling almost horizontally. Therefore, accurate imaging of steep geologic structure requires knowledge of the behavior of these horizontally propagating waves; in particular, the role of evanescence and tunneling of seismic waves propagating in thin‐layered media. For thin‐layered media, modeling of zero‐offset reflections shows frequency‐dependent amplitude and phase behavior that varies with reflector dip. Waves propagating vertically in a sequence of thin layers lose high frequencies by stratigraphic filtering. However, waves reflected from steep reflectors in a thin‐layered medium are also attenuated and dispersed by the less well‐known evanescent filtering. These two low‐pass filtering actions depend on reflector dip and bed thickness in different ways: evanescent filtering is more severe for steeper reflectors and thicker beds, while stratigraphic filtering is more severe for flat reflectors and thinner beds. Waves traveling in layered media may suffer high‐frequency loss from both these effects.
Fourier finite‐difference migration
Authors: Ristow Dietrich , Rühl Thomas
Published: October 2002

Many existing migration schemes cannot simultaneously handle the two most important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For example, phase‐shift (ω, k) migration is accurate for nearly all dips but it is limited to very simple velocity functions. On the other hand, finite‐difference schemes based on one‐way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events. We propose a new hybrid migration method, named “Fourier finite‐difference migration,” wherein the downward‐continuation operator is split into two downward‐continuation operators: one operator is a phase‐shift operator for a chosen constant background velocity, and the other operator is an optimized finite‐difference operator for the varying component of the velocity function. If there is no variation of velocity, then only a phase‐shift operator will be applied automatically. On the other hand, if there is a strong variation of velocity, then the phase‐shift component is suppressed and the optimized finite‐difference operator will be fully applied. The cascaded application of phase‐shift and finite‐difference operators shows a better maximum dip‐angle behavior than the split‐step Fourier migration operator. Depending on the macro velocity model, the Fourier finite‐difference migration even shows an improved performance compared to conventional finite‐difference migration with one downward‐continuation step. Finite‐difference migration with two downward‐continuation steps is required to reach the same migration performance, but this is achieved with about 20 percent higher computation costs. The new cascaded operator of the Fourier finite‐difference migration can be applied to arbitrary velocity functions and allows an accurate migration of steeply dipping reflectors in a complex macro velocity model. The dip limitation of the cascaded operator depends on the variation of the velocity field and, hence, is velocity‐adaptive.
The three‐parameter equation: An efficient tool to enhance the stack
Authors: Thore Pierre D. , de Bazelaire Eric , Rays Marisha P.
Published: October 2002

We compare the three‐term equation to the normal moveout (NMO) equation for several synthetic data sets to analyze whether or not it is worth making the additional computational effort in the stacking process within various exploration contexts. In our evaluation we have selected two criteria: 1)The quality of the stacked image. 2) The reliability of the stacking parameters and their usefulness for further computation such as interval velocity estimation. We have simulated the stacking process very precisely, despite using only the traveltimes and not the full waveform data. The procedure searches for maximum coherency along the traveltime curve rather than a least‐square regression to it. This technique, which we call the Gaussian‐weighted least square, avoids most of the shortcomings of the least‐square method. The following are our conclusions: 1) The three term equation gives a better stack than the regular NMO. The increase in stacking energy can be more than 30 percent. 2)The calculation of interval velocities using a DIX formula rewritten for the three‐parameter equation is much more stable and accurate than the standard DIX formula. 3) The search for the three parameters is feasible in an efficient way since the shifted hyperbola requires only static corrections rather than dy namic ones. 4) Noise alters the parameters of the maximum energy stack in a way that depends on the noise type. The estimates obtained remain accurate enough for interval velocity estimation (where only two parameters are needed), but the use of the three parameters in direct inversion may be hazardous because of noise corruption. These conclusions should, however, be verified on real data examples.
Reflection point behavior in transversely isotropic solids
Authors: Levin Franklyn K.
Published: October 2002

One way of representing a subsurface that displays azimuthal anisotropy is to assume transverse isotropy with a horizontal symmetry axis. For solids that can be described in this manner, rays for reflection from a horizontal plane lie in a plane of incidence for P-P, SV-SV, and SH-SH reflection but the plane wave direction generally differs from the ray direction. For P-SV reflections, the reflection points are in the plane of incidence only for profiles parallel to or perpendicular to the symmetry direction. Except for profiles perpendicular to the symmetry direction, P-P and SV-SV moveout velocities have no obvious relation to the travel velocities of the rays.
Fast model building using demigration and single‐step ray migration
Authors: Whitcombe David N.
Published: October 2002

This work provides explorationists with simple procedures to perform depth conversion more accurately than can be achieved with simple vertical layer cake depth conversion. The use of image rays, which are inadequate in structurally complex areas, is avoided. Migrated time interpretations are still used and are "demigrated" using the Kirchhoff time migration equations. This backs out the effect of the time migration prior to a ray depth migration and enables the lateral shifts between the time migrated image and a depth migrated image to be quantified. These shifts can be separated into a mismigration component and a refraction component. The relative size of the components define whether time or depth migration is required and may be used to justify a remigration of the seismic image. Furthermore, the tedious layer by layer approach to ray depth migration may be avoided by using the velocity depth model from the vertical layer cake depth conversion of the time‐migrated data for ray depth migration of the unmigrated data for all horizons in a single step. A satisfactory result is usually achieved without the need to iterate. These methods are illustrated with both a synthetic example and a real 3-D data set from the Norwegian North Sea.
Migration of P‐wave reflection data in transversely isotropic media
Authors: Phadke Suhas , Kapotas S. , Dai N. , Kanasewich Ernest R.
Published: October 2002

Wave propagation in transversely isotropic media is governed by the horizontal and vertical wave velocities. The quasi‐P(qP) wavefront is not an ellipse; therefore, the propagation cannot be described by the wave equation appropriate for elliptically anisotropic media. However, for a limited range of angles from the vertical, the dispersion relation for qP‐waves can be approximated by an ellipse. The horizontal velocity necessary for this approximation is different from the true horizontal velocity and depends upon the physical properties of the media. In the method described here, seismic data is migrated using a 45-degree wave equation for elliptically anisotropic media with the horizontal velocity determined by comparing the 45-degree elliptical dispersion relation and the quasi‐P‐dispersion relation. The method is demonstrated for some synthetic data sets.
Finite‐difference solution of the eikonal equation using an efficient, first‐arrival, wavefront tracking scheme
Authors: Cao Shunhua , Greenhalgh Stewart
Published: October 2002

First‐break traveltimes can be accurately computed by the finite‐difference solution of the eikonal equation using a new corner‐node discretization scheme. It offers accuracy advantages over the traditional cell‐centered node scheme. A substantial efficiency improvement is achieved by the incorporation of a wavefront tracking algorithm based on the construction of a minimum traveltime tree. For the traditional discretization scheme, an accurate average value for the local squared slowness is found to be crucial in stabilizing the numerical scheme for models with large slowness contrasts. An improved method based on the traditional discretization scheme can be used to calculate traveltimes in arbitrarily varying velocity models, but the method based on the corner‐node discretization scheme provides a much better solution.