bluuebunny/crossref_metadata_2025 huggingface dataset:
Imaging discontinuities on seismic sections
Authors: Kanasewich Ernest R. , Phadke Suhas M.
Published: October 2002

In routine seismic processing, normal moveout (NMO) corrections are performed to enhance the reflected signals on common‐depth‐point or common‐midpoint stacked sections. However, when faults are present, reflection interference from the two blocks and the diffractions from their edges hinder fault location determination. Destruction of diffraction patterns by poststack migration further inhibits proper imaging of diffracting centers. This paper presents a new technique which helps in the interpretation of diffracting edges by concentrating the signal amplitudes from discontinuous diffracting points on seismic sections. It involves application to the data of moveout and amplitude corrections appropriate to an assumed diffractor location. The maximum diffraction amplitude occurs at the location of the receiver for which the diffracting discontinuity is beneath the source‐receiver midpoint. Since the amplitudes of these diffracted signals drop very rapidly on either side of the midpoint, an appropriate amplitude correction must be applied. Also, because the diffracted signals are present on all traces, one can use all of them to obtain a stacked trace for one possible diffractor location. Repetition of this procedure for diffractors assumed to be located beneath each surface point results in the common‐fault‐ point (CFP) stacked section, which shows diffractor locations by high amplitudes. The method was tested for synthetic data with and without noise. It proves to be quite effective, but is sensitive to the velocity model used for moveout corrections. Therefore, the velocity model obtained from NMO stacking is generally used for enhancing diffractor locations by stacking. Finally, the technique was applied to a field reflection data set from an area south of Princess well in Alberta.
Reflection and refraction seismic studies in the Great Salt Lake Desert, Utah
Authors: René R. M. , Fitter J. L. , Murray D. J. , Walters J. K.
Published: October 2002

Seismic refraction and CDP reflection profiles were acquired across mud flats of the Great Salt Lake Desert, Utah, during the summer of 1983. a combination of weight drops, horizontal hammers, buried explosives, and explosives detonated in air (Poulter method) was used. A 6.4 km refraction and single‐fold reflection profile indicates the presence of a shallow depression (Donner Reed basin) eastb of Donner Reed pass in the Silver Island Mountains. A basin floor ramp of Paleozoic rocks dipping approximately 30 degrees east into the Crater Island graben is interpreted beneath a 4.6 km 12-fold CDP reflection profile obtained by the Poulter method. This ramp extends beneath at least 0.8 km of condolidated Neogene sediments and 0.8 km of younger (largely unconsolidated) sediments. Weight‐drop and horizontal‐hammer profiles for the critical refraction along the Silurian Laketown dolomite yield P-wave and S-wave velocity estimates of 5270 ± 100 and [Formula: see text], respectively. The mud flats, with their laterally uniform finegrained sediments and shallow water table, provided excellent coupling of seismic energy. Air shots of 4.1 to 5.4 kg explosives without a source array gave good penetration to a depth of about 1.6 km. Partial migration before stack facilitated estimation of moveout velocities in the case of layers onlapping against a basin floor ramp, even though the maximum dips were only about 30 degrees. Gravity modeling and seismic ray tracing through intervals of constant velocity bounded by polynomial interfaces aided synergetic interpretation of the reflection, refraction, and gravity data.
Acoustic modeling and migration of stacked cross‐hole data
Authors: Zhu Xianhuai , McMechan George A.
Published: October 2002

Prestack computations for cross‐hole data are relatively expensive, as they are for prestack surface survey data. It is therefore of interest to develop methodologies for modeling and processing stacked cross‐hole data. In this context, stacking is over sources, not midpoints. Modeling with a line source produces data that are equivalent (by Huygen’s principle) to those obtained by stacking over a line of point sources. Reverse‐time finite‐difference migration may be applied to the resulting stacked section by generalizing the excitation‐ time imaging condition for a point source to a line source. Illustrations include successful applications to both synthetic data and scale‐model data.
Special Report of the SEG Technical Standards Committee
Authors:   SEG standards for specifying marine seismic energy sources, Johnston R. C. , Reed D. H. , Desler J. F.
Published: October 2002

The purpose of these standards is to specify, in an easily understood standard form, measurable characteristics of marine seismic energy sources to assist engineers, scientists, and operations managers in choosing, comparing, and/or specifying particular systems for their exploration programs.
Formation temperature estimation by inversion of borehole measurements
Authors: Cao Song , Lerche Ian , Hermanrud Christian
Published: October 2002

We describe a new numerical method that uses inverse methods to model thermal stabilization of a borehole after drilling mud circulation has stopped. The following five geophysical parameters can be estimated from the method: (1) true formation temperature [Formula: see text] (2) mud temperature [Formula: see text] at the time the mud circulation stops; (3) thermal invasion distance (R) into the formation before the formation is at the true formation temperature[Formula: see text]; (4) formation thermal conductivity (K) perpendicular to the borehole; and (5) efficiency factor (F) for heating mud in the borehole after mud circulation has stopped. Crucial input data for the model are the temperature measurements with shut‐in time taken at a fixed depth, more than two measurements being required, and the mud temperature at the surface at the time circulation stops. Other input data include the radius of the borehole, and the densities and specific heats of the drilling mud and of the formation on which the temperature measurements are made. Applications of the new inverse procedure to both synthetic data and field data show that the true formation temperature in many cases can be estimated precisely (to within about 0.4 percent); that the mud temperature can be estimated with acceptable accuracy (5 percent or so); while the thermal conductivity (K), the thermal invasion distance (R), and the efficiency factor (F) can be roughly estimated, provided high‐quality data are available.
Three‐dimensional acoustic modeling by the Fourier method
Authors: Reshef Moshe , Kosloff Dan , Edwards Mickey , Hsiung Chris
Published: October 2002

A three‐dimensional forward modeling algorithm, allowing arbitrary density and arbitrary wave propagation velocity in lateral and vertical directions, directly solves the acoustic wave equation through spatial and temporal discretization. Spatial partial differentiation is performed in the Fourier domain. Time stepping is performed with a second‐order differencing operator. Modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. Three‐dimensional forward modeling represents a challenge for computer technology. Computation of meaningfully sized models requires extensive calculations and large three‐dimensional data sets which must be retrieved and restored during the computation of each time step. The computational feasibility of the Fourier method is demonstrated by implementation on the multiprocessor CRAY X‐MP computer system using the large secondary memory of the solid‐state storage device (SSD). Calculations use vectorization and parallel processing architecture. The similarity of numerical and analytical results indicates sufficient accuracy for many applications.
Robust and least‐squares estimation of acoustic attenuation from well‐log data
Authors: Patton Steven W.
Published: October 2002

Several least‐squares attenuation (Q) estimation algorithms are tested on various types of models. These algorithms include the spectral ratio method and methods based upon eigenvector decomposition and Wiener filtering. The eigenvector decomposition and Wiener filter methods prove to be unsatisfactory even on model data, while the spectral ratio method yields fairly poor results. Tests indicate that the underlying Q error distribution is non‐Gaussian; hence more robust methods are needed. The errors in Q estimation have an asymptotically Cauchy distribution, with a reasonable noise model and Gaussian input noise. On noise models with Gaussian errors slightly contaminated by Cauchy or Laplacian noise, a maximum‐likelihood (ML) estimator based on Gaussian noise performed best. On heavily contaminated models, the ML estimator based on Laplacian noise performed best; but simple, robust estimators such as the median also did well. On more realistic models with noise, the median and alpha‐trimmed mean (ATM) appear to be the best.
Transformation of nonlinear problems into linear ones applied to the magnetic field of a two‐dimensional prism
Authors: Silva João B. C.
Published: October 2002

I present a magnetic interpretation method which transforms into a linear problem the nonlinear problem of obtaining the geometric and position parameters of a two‐dimensional vertical, infinite prism. The magnetization, the only linear parameter, becomes nonlinear after the transformation. By assuming a few discrete values over a prescribed interval for the magnetization, I obtain several solutions for the geometric and position parameters. By storing only the extreme solutions, bounds for each parameter are produced. The method was applied to synthetic anomalies due to isolated and interfering sources for which robust alternatives performed better than the least‐squares method. The correlation between the magnetization and the prism width is the most important factor controlling ambiguity of parameters. The horizontal position is the least affected parameter, followed by the depth to the top of the prism. Application to a real anomaly confirmed the results from synthetic data, except for a greater uncertainty in the estimation of the horizontal position. The uncertainty results from the requirement in the present method that the observations be reduced to the pole; an imprecise knowledge of the magnetization direction distorts the position, which is highly correlated with the magnetization inclination. Because the estimation of the position, depth, and width is transformed into a linear problem, the method is simple, fast, and independent of the initial guess. The method might, therefore, be useful in automatic interpretation of basement relief. By producing bounds for each parameter estimate, an analysis of parameter precision and ambiguity is also possible.
Detectability levels for central induction transient soundings
Authors: Fitterman David V.
Published: October 2002

A question usually asked during the planning of a transient sounding survey is, “Can information useful to solving the geologic problem at hand be obtained from the measurements?” This question is usually answered by constructing a geologic model for the survey area based upon the best available information to determine which model parameters can be resolved. Specifically, this determination can be accomplished by computing a forward model, varying a parameter of interest, and observing whether the responses of the original and perturbed models are different. Alternatively, inversion‐based methods can be used to estimate parameter resolution (Inman, 1975; Glenn and Ward, 1976).
Aquifer boundaries explored by geoelectrical measurements in the coastal plain of Yemen: A case of equivalence
Authors: van Overmeeren R. A.
Published: October 2002

Until 216 vertical electrical Schlumberger soundings were made, little was known about the subsurface geology at the Wadi Surdud area in the coastal plain of the Yemen Arab Republic. These soundings provide information on the distribution of aquifers, aquitards, and impermeable rocks, and the salinity of the groundwater. A first, qualitative interpretation of the geoelectrical sounding curves gives a general impression of the hydrogeologic setting and the aquifer boundaries. However, a more detailed, quantitative interpretation shows that no single resistivity model completely satisfies all the hydrogeologic and geologic facts and theories. Basically, two different models are possible: in one the thickness of the aquifer is fixed; in the other, its resistivity is fixed. Several geologic and hydrogeologic hypotheses may be put forward to support each model, varying from relying upon tectonic events and sedimentary depositional environments to influences of agriculture and water abstraction. Both models are supported by the data. However, geophysical well logging in two exploratory boreholes provided conclusive evidence for the model in which the thickness of the aquifer was fixed.
Permeability and borehole Stoneley waves: Comparison between experiment and theory
Authors: Winkler Kenneth W. , Liu Hsui‐Lin , Johnson David Linton
Published: October 2002

We performed laboratory experiments to evaluate theoretical models of borehole. Stoneley wave propagation in permeable materials. A Berea sandstone and synthetic samples made of cemented glass beads were saturated with silicone oils. We measured both velocity and attenuation over a frequency band from 10 kHz to 90 kHz. Our theoretical modeling incorporated Biot theory and Deresiewicz‐Skalak boundary conditions into a cylindrical geometry and included frequency‐dependent permeability. By varying the viscosity of the saturating pore fluid, we were able to study both low‐frequency and high‐frequency regions of Biot theory, as well as the intermediate transition zone. In both low‐frequency and high‐frequency regions of the theory, we obtained excellent agreement between experimental observations and theoretical predictions. Velocity and attenuation (1/Q) are frequency‐dependent, especially at low frequencies. Also at low frequencies, velocity decreases and attenuation increases with increasing fluid mobility (permeability/viscosity). More complicated behavior is observed at high frequencies. These results support recent observations from the oil field suggesting that Stoneley wave velocity and attenuation may be indicative of formation permeability.
Fracture evaluation using reflected Stoneley‐wave arrivals
Authors: Hornby B. E. , Johnson D. L. , Winkler K. W. , Plumb R. A.
Published: October 2002

We use the low‐frequency reflected Stoneley‐wave mode to locate permeable fractures intersecting a borehole and to estimate their effective apertures. Assuming a model in which the average aperture of the fracture is roughly constant, theoretical work relates the magnitude of the Stoneley‐wave reflectivity to an effective fracture width, We treat both the case of a horizontal fracture and the case of a fracture crossing the borehole at an angle. Laboratory experiments verify the analytic solution for the case of a horizontal fracture. Full‐waveform array sonic data were also acquired in a wellbore with a long recording time (25.5 ms) in order to capture the late Stoneley‐wave arrivals. The data processing involves computation of the Stoneley‐wave reflectivity response using the measured direct and reflected Stoneley‐wave arrivals. A least‐squares fit to the arrival time of the reflected‐wave arrivals is used to estimate the locations of permeable fractures, and the effective width of the fractures is estimated by comparing the computed Stoneley‐wave reflectivity to the theoretical response from a parallel‐plate model. Test‐well results are consistent with a borehole televiewer analysis.
Dielectric properties of selected minerals at 1 to 22 GHz
Authors: Nelson S. O. , Lindroth D. P. , Blake R. L.
Published: October 2002

Metallurgical mineral separation makes use of the large differences in dielectric properties of individual minerals (Thirumalai, 1970; Jordan et. al, 1980). Microwave heating for thermal rock fragmentation uses differences in the complex electrical properties of rock due to inhomogeneities in composition, structure, and texture. Knowledge of the relative complex permittivity is required to determine the differential absorption of microwave energy in an aggregate of minerals (rock).
Frequency dispersion in finite‐difference migration
Authors: Brzostowski M. A. , Black J. L.
Published: October 2002

We introduce a practical measure that predicts the frequency dispersion in implicit time‐domain finite‐difference migration. This measure of dispersion can be readily computed as a function of velocity, dip, and the sampling parameters (depth interval, time interval, trace interval). One result of this analysis is that smaller sampling intervals can often lead to poorer results by an unbalancing of canceling errors. Another result is that, even if the errors are kept in balance for one event, it is not possible to minimize simultaneously the dispersion for all events, since many different dips and velocities occur on a typical seismic section. We also extend the computation of the dispersion measure to include cascaded finite‐difference migration. Cascading does not reduce the magnitude of wavelet dispersion, but it does make the control of dispersion easier because it avoids the problem of choosing parameters in the presence of multivalued velocity. We calibrate and confirm our theoretical dispersion measure by means of migration tests on model data and field data.
On: “Shear‐wave splitting in cross‐hole surveys: Modeling” by Enru Liu, Stuart Crampin, and David C. Booth (GEOPHYSICS, 54, 57–65, January, 1989)
Authors: Winterstein Don
Published: October 2002

Liu et al. extended consideration of shear‐wave (S‐wave) polarization patterns in anisotropic media from the usual vertical to a predominantly horizontal direction of wave travel. Modeling was for transversely isotropic (TI) media with horizontal symmetry axes. The exposition was accurate in major concepts, but the authors could have been more precise in presenting a couple of incidental properties of TI media. These properties have to do with S‐wave polarizations and certain a priori predictions one can make about them from symmetry considerations. I state and prove two predictions here in a tutorial mode, partly to demonstrate the simplicity and power of symmetry concepts as tools for understanding wave behavior in anisotropic media.
Locating faults in underground coal mines using high‐resolution seismic reflection techniques
Authors: Gochioco Lawrence M. , Cotten Steven A.
Published: October 2002

A high‐resolution seismic reflection technique was used to locate faults in coal seams that were not visible on the surface and could only be observed in underground coal mines. An 8‐gauge buffalo gun, built by the research and development department of Consolidation Coal Company, was used as the seismic source. The coal seam at a depth of 700 ft produces a reflection with a predominant frequency of about 125 Hz. The high‐resolution seismic data permitted faults with vertical displacements of the same magnitude as the seam thickness to be detected at depths of several hundred feet beneath the surface. Several faults were detected and interpreted from the seismic sections, and the magnitudes of their displacement were estimated by matching the recorded seismic data to synthetic seismic data. Subsequent underground mine development in the study area confirmed two interpreted faults and their estimated displacements. Mining engineers were able to use the information provided by the seismic survey to plan an entry system through the fault zone so that less rock needed to be mined, resulting in a safer and more productive mine.
Seismic signature of a Swan Hills (Frasnian) reef reservoir, Snipe Lake, Alberta
Authors: Anderson N. L. , Brown R. J. , Hinds R. C. , Hills L. V.
Published: October 2002

Swan Hills formation (Frasnian stage) carbonate buildups of the Beaverhill Lake group are generally of low relief and considerable areal extent and are overlain by and encased within the relatively high‐velocity shale of the Waterways formation, which thins but does not drape across the reefs. Consistent with this picture, prereef seismic events are not significantly pulled up beneath the reefs nor are postreef events draped across them. Indeed, the seismic images of these reefs are effectively masked by the high‐amplitude reflections from the overlying top of the Beaverhill Lake group and underlying Gilwood member and cannot be distinguished from those of the basin fill. However, it is possible to identify the reefs indirectly on conventionally processed seismic sections because the image of the encompassing Beaverhill Lake/Gilwood interval varies significantly from onreef to offreef positions. One such Swan Hills formation field at Snipe Lake has an areal extent of about [Formula: see text] and typical reef relief of some 50 m above the platform facies. This reef is shown to be recognizable on three example seismic lines from interference phenomena that vary laterally in association with the lateral variations in thickness of the Swan Hills formation. These phenomena include an offreef peak that is one half‐cycle below the Beaverhill Lake reflection trough and that dies out laterally going onreef, a tendency for the amplitude of the Gilwood event to decrease beneath the reef, and thinning of the order of 5 ms of the onreef section relative to the offreef section. Through seismic modeling, these seismic‐image characteristics are seen to be predictable geophysical manifestations of the inherent geologic variations.
Mapping and monitoring electrical resistivity with surface and subsurface electrode arrays
Authors: Asch Ted , Morrison H. Frank
Published: October 2002

Electrical resistivity measurements using combinations of subsurface and surface electrodes are more sensitive to subsurface inhomogeneities than arrays confined to the surface. A further advantage of the subsurface configuration is that the strong influence of near‐surface inhomogeneities can be reduced by differencing the measured apparent resistivities with a reference set of values obtained with the subsurface electrode(s) at a particular depth. This process accentuates the response of features near the downhole electrode while canceling the response of the near‐surface features. An idealized two‐dimensional model of a nuclear waste repository has been used to demonstrate the effectiveness of this differencing scheme. It is shown that resistivity measurements using borehole electrodes well away from the repository and on the surface are sensitive to changes in the repository that could not be practically observed from surface measurements. This sensitivity is preserved in the presence of a conducting and inhomogeneous surface layer and, most importantly, it is preserved even if the resistivities of the near‐surface features also change.
Practical implementation of three‐dimensional poststack depth migration
Authors: Reshef Moshe , Kessler David
Published: October 2002

This work deals with the practical aspects of three‐dimensional (3-D) poststack depth migration. A method, based on depth extrapolation in the frequency domain, is used for the migration. This method is suitable for structures with arbitrary velocity variation, and the number of computations required can be directly related to the complexity of the given velocity function. We demonstrate the superior computational efficiency of this method for 3-D depth migration relative to the reverse‐time migration method. The computational algorithm used for the migration is designed for a multi‐processor machine (Cray-XMP/48) and takes advantage of advanced disk technologies to overcome the input/output (I/O) problem. The method is demonstrated with both synthetic and field data. The migration of a typical 3-D data volume can be accomplished in only a few hours.
Geometrical ray theory: Rays and traveltimes in seismic systems (second‐order approximations of the traveltimes)
Authors: Bortfeld R.
Published: October 2002

In this paper, I establish general laws that represent global properties for the reflected and transmitted rays in seismic systems. The method used for establishing these laws is based on Hamilton’s original ideas; the laws do not depend on the specific seismic system being used. The reflected and transmitted rays, as well as their traveltimes, are described by the same four 2 × 2 matrices. These matrices are interrelated by three equations that provide the basis for the general laws and also provide relations between reflected and transmitted rays that eventually will be exploitable for downward continuation and migration. The traveltimes of reflected and transmitted rays are summed up in single functions, giving the traveltime for any pair of source and receiver positions in a seismic system and corresponding to Hamilton’s point characteristics in optics. The traveltimes of the gathers commonly used in seismic exploration are special cases of the general point characteristics. The consequences from the derived laws are directly available as a priori knowledge before any actual ray tracing and computation of traveltimes are done in any particular seismic system. The laws are also available as a general foundation for future treatments of (1) downward continuation, (2) amplitudes of reflected and transmitted events, (3) true amplitude migration, (4) examples of nonuniqueness of seismic interpretations, (5) focus phenomena, and (6) higher order approximations.
Chirp subbottom profiler for quantitative sediment analysis
Authors: Schock Steven G. , LeBlanc Lester R. , Mayer Larry A.
Published: October 2002

A wide‐band, frequency‐modulated, subbottom profiling system (the chirp sonar) can remotely determine the acoustic attenuation of ocean sediments and produce artifact‐free sediment profiles in real time. The chirp sonar is controlled by a minicomputer which performs analog‐to‐digital and digital‐to‐analog conversion, correlation processing, and attenuation estimation in real time. The minicomputer generates an FM pulse that is phase‐ and amplitude‐compensated to correct for the sonar system response. Such precise waveform control helps suppress correlation noise and source ringing. The chirp sonar, which has an effective bandwidth of 5 kHz, can generate chirp (Klauder) wavelets with a tuning thickness (Rayleigh’s criterion for resolution) of approximately 0.1 ms. After each return is correlated, a computationally fast algorithm estimates the attenuation of subbottom reflections by waveform matching with a theoretically attenuated waveform. This algorithm obtains an attenuation estimate by minimizing the mean‐square error between the autocorrelation function of the theoretically attenuated wavelet and the autocorrelation function of the subbottom reflection. The chirp sonar was tested in Narragansett Bay, R.I. along a line that had been previously cored. Experimental results show that correlation noise from the seafloor reflection was below −60 dB, the quantization noise level, thereby allowing detection of small subbottom impedance contrasts and accurate estimation of attenuation. Attenuation coefficient estimates from this sandy region agree with in‐situ measurements made by other investigators.
Regularized two‐dimensional Fourier gravity inversion method with application to the Silent Canyon caldera, Nevada
Authors: Reamer Sharon K. , Ferguson John F.
Published: October 2002

A modification of the 2‐D Fourier gravity inversion method includes regularization and a linear density variation with depth. Explicit downward continuation in the Fourier inversion of gravity observations from mass distributions at depth produces instability in the presence of noise and shallow mass distributions. A data‐adaptive regularization filter tapers growth of the exponential continuation function. An empirical relationship between the regularization filter parameter and a parametric model of potential field spectra results in automatic selection of the filter parameter for a given continuation depth. Inversion of synthetic data from a random noise‐contaminated basin type model produces a depth model that agrees with the synthetic structure with an rms error commensurate with the data noise. A model of the Silent Canyon caldera, buried beneath Pahute Mesa at the Nevada Test Site, results in a gravity field that agrees with the observations to within a 4 percent rms error. The caldera gravity model supports the hypothesis of a high‐density half‐space (precaldera lithology) beneath a lower density caldera infill (postcaldera volcanic activity).
Three‐dimensional seismic exploration—A cost‐effective approach
Authors: Peterson F. M. , Reynish W. C.
Published: October 2002

Three‐dimensional (3-D) seismic prospecting is generally perceived as a very expensive tool that is not suitable for use by other than major oil companies or for the solution of conventional exploration geophysics problems. We illustrate how 3-D techniques were used to provide a very cost‐effective solution to a specific exploration project. A basic geologic and historical seismic outline establishes the economic and environmental framework for the survey. Drilling results and comparisons with conventional data illustrate the effectiveness of the 3-D approach. This survey was carried out during February of 1982 in the Black Creek basin of northwestern Alberta. Prolific and abundant Devonian Keg River pinnacle reefs with reserves in the 0.2 to 100 million barrel recoverable categories provide the exploration target. A prospective area of approximately [Formula: see text] was covered with a 165 ft subsurface grid of 1200 percent CDP data. Field data were acquired with a conventional 96-trace dynamite crew using a rolling, crossed‐array technique. Data processing was carried out with a flexible, conventional seismic processing package, including wavelet deconvolution, surface‐consistent statics, 3-D migration, and geologic slice displays. Total cost of the survey was $50,000 Canadian per sq mi. This paper demonstrates the interpretive power of 3-D surveys.
A comparison between the Born and Rytov approximations for the inverse backscattering problem
Authors: Rajan Subramaniam D. , Frisk George V.
Published: October 2002

We compare the Born and Rytov approximations in solving the inverse acoustic backscattering problem, i.e., determining medium properties from reflections. For the one‐dimensional problem, we show that the Rytov approximation is generally better than the Born approximation in predicting sound speed changes, while both methods have the same error in determining the positions of reflectors. This is shown analytically for simple models and numerically for more general models. The performance of the Rytov approximation is degraded when low‐velocity regions are present in the medium being probed. The accuracy of the inversion depends on the manner in which the sound speed perturbation is linearized. The location of the receiver affects the accuracy of the inversion, and, in the case of the Rytov approximation, best results are obtained when the receiver is at the interface between the known and unknown regions. Furthermore, the Rytov method is less sensitive to the choice of reference sound speed used in the inversion than is the Born approximation.
Resolution and variance operators of gravity and gravity gradiometry
Authors: Vasco D. W.
Published: October 2002

Gravity gradiometry represents a new potential field data set which may better constrain the density structure of the earth. Using singular value (spectral) decomposition of the gravity and gravity gradient kernels, the model parameter resolution and model parameter variance of the two data types are compared using data from the Defense Mapping Agency and a recently acquired collection of airborne gradient measurements from Bell Aerospace Textron’s Gravity Gradient Survey System (GGSS). The GGSS was flown over a portion of southwestern Oklahoma, where the gravitational anomaly from the buried Wichita basement rocks is over 60 mGal. The corresponding maximum vertical gravity gradient was found to be 46.2 Eötvös. The determination of the subsurface density structure is cast as a linear inverse problem and, for comparison, a nonlinear inverse problem. For both the linear and nonlinear inversions, the gravity gradients improve the resolution and result in smaller variances than the vertical component of gravity. The density resolution and variance were computed for a subset of tracks from an airborne gravity gradient survey made in the summer of 1987. For the linear inversion, the resolution of the density is not adequate below the second layer (20 km). Furthermore, the estimated error of the actual gradient observations for a resolution of 0.9 km is 10E, for which the maximum error of the density values is [Formula: see text]. The linearized resolution of the boundary perturbations is better, with most parameters being well resolved. The standard errors for the layer perturbations are less than 1 km for the shallower layer (5.0 km) when using the gradiometer data. For the deeper layer (25.0 km), the maximum error is larger, 4.3 km.
Aeromagnetic gradiometer program of the Geological Survey of Canada
Authors: Hood Peter J. , Teskey Dennis J.
Published: October 2002

During the past two decades, the Geological Survey of Canada Aeromagnetic Survey Group, consisting of geophysicists, electronic engineers, technicians, and computer scientists, developed the aeromagnetic gradiometer technique for mineral exploration. The same group ran the aeromagnetic survey program in Canada, perhaps the largest such continuing aeromagnetic survey program in the world. In 1973, fabrication commenced on an inboard vertical gradiometer system on the GSC Queenair aeromagnetic survey aircraft. During the period 1978–1981, a number of experimental gradiometer surveys were carried out by the Geological Survey of Canada to demonstrate the efficacy of the aeromagnetic gradiometry technique as a geologic mapping tool in mineral exploration programs. Because of a need for aeromagnetic gradiometer surveys in the topographically rugged Gaspé Peninsula of Quebec, the GSC began in 1983 to foster the development of helicopter‐borne gradiometer systems through R and D contracts. Four companies responded and built towed‐boom helicopter gradiometer systems which have now been used in surveys in four eastern provinces. It is clear that the aeromagnetic gradiometer technique combined with VLF EM is an excellent geophysical tool to improve the accuracy of detailed geologic mapping for mineral exploration programs. VLF EM is an inexpensive add‐on that materially improves the geologic mapping capability of the airborne system. The product in color pixel form is in essence a pseudogeologic map and it is presently being employed as such.
The point of P-S mode‐converted reflection: An exact determination
Authors: Taylor Gary G.
Published: October 2002

The accurate placement of a P-S mode‐converted reflection point on a horizontal reflector is important in stacking surface seismic data for enhancement (Dohr and Janle, 1980; Garotta et al., 1985) and in interpreting results from Zoeppritz’s or Knott’s equations (Tooley et al., 1965; Young and Braile, 1976). This note describes an adaptation of Snell’s law to determine exactly the reflection point of a P-S mode‐converted reflection.
Porosity identification using amplitude variations with offset: Examples from South Sumatra
Authors: Chacko S.
Published: October 2002

Widespread deposition of platform and reefal carbonates of the Baturaja limestone formation occurred during the Miocene epoch in the South Sumatra basin. Although significant oil and gas deposits have been discovered in the porous facies, porosity within the Baturaja limestone has been observed to vary widely between tight platform facies and highly porous reefal facies, making predrill prediction of porosity an important exploration objective. I use amplitude‐versus‐offset seismic modeling to distinguish between porous and tight Baturaja limestone facies. Amplitude variations with offset for reflections from two Baturaja reefs in the South Sumatra basin were studied: one, a proven gas reservoir, the other, an interpreted reef that had not yet been drilled at the time of study. The seismic data were processed judiciously to preserve and enhance amplitude effects, which were then modeled using the Bortfeld approximation for reflection coefficients. A key assumption was that the [Formula: see text] ratio of limestone depends primarily on minerology rather than on porosity or pore‐fluid content. The modeling showed that porous and tight limestone facies have unique and different reflection-coefficient variation patterns with angle of incidence. Good agreement was found between observed data and the modeling results, indicating that the modeling of amplitude variations with offset can be used as a lithology discriminant. In the second case, a predrill prediction of porosity was confirmed by subsequent drilling.
Reference velocity model estimation from prestack waveforms: Coherency optimization by simulated annealing
Authors: Landa Evgeny , Beydoun Wafik , Tarantola Albert
Published: October 2002

Coherency inversion, which consists of maximizing a semblance function calculated from unstacked seismic waveforms, has the potential of estimating reliable velocity information without requiring traveltime picking on unstacked data. In this work, coherency inversion is based on the assumption that reflectors’ zero‐offset times are known and that the velocity in each layer may vary laterally. The method uses a type of Monte Carlo technique termed the generalized simulated annealing method for updating the velocity field. At each Monte Carlo step, time‐to‐depth conversion is performed. Although this procedure is slow at convergence to the global minimum, it is robust and does not depend on the initial model or topography of the objective function. Applications to both synthetic and field data demonstrate the efficiency of coherency inversion for estimating both lateral velocity variations and interface depth positions.
Three‐dimensional time‐slice migration
Authors: Karrenbach Martin
Published: October 2002

Three‐dimensional migration of zero‐offset data using a velocity varying with depth can be performed in one pass using Fourier transforms of time slices. The migration process is carried out entirely in the two‐dimensional spatial Fourier domain. The algorithm consecutively filters and adds time slices of the 3-D data volume in a way that is equivalent to summing energy over the diffraction surface of a point scatterer. The partial energy being distributed along a circle in a time slice is properly added in each summation step. Time‐slice migration is based on an integral solution of the acoustic wave equation known as the “Kirchhoff integral.” The wavelet shape in a 3-D data volume is preserved throughout the entire migration process. The frequency characteristics are maintained by summing weighted differences between time slices instead of summing the time slices themselves. Automatic weighting is achieved by time slicing at equal increments of diffraction radius. Tapering the summation operator reduces effects introduced by limiting the summation window. Time‐slice migration preserves the frequency content of a 3-D data volume during summation in a natural way. Since the migration scheme assumes a constant velocity within the entire time slice, it is a local process in time which migrates a 3-D data volume with a constant velocity or with a velocity which varies with depth. The migration algorithm is applied to numerical and physical model data. This method is especially suitable for a migration of a targeted subset of the 3-D data volume.
Inversion of P and SV waves from multicomponent offset vertical seismic profiles
Authors: Esmersoy Cengiz
Published: October 2002

Downgoing waves in multicomponent VSP experiments are used to obtain seismic P- and S-wave velocities as a function of depth and angle of incidence. If P and SV waveforms do not overlap in time at the depth of interest, local velocities of the medium are obtained by separate analysis of these events. The apparent velocity of the event (P or SV) is computed from the moveout across several neighboring depth locations. The angle of incidence of the same event is computed from the particle‐motion hodogram within an appropriately chosen time window. Then, the local medium velocity (P wave or S wave depending on the chosen event) is given by the apparent velocity multiplied by the cosine of the angle of incidence. Layer interfaces with reasonably sharp velocity contrasts are efficient P-wave to SV-wave converters, even at moderate angles of incidence. In offset VSP experiments, converted SV waves are generated with varying strengths at practically all depths. Consequently, the converted SV waveforms partially overlap with the direct P waveforms, making the separate event analysis difficult and inaccurate. These overlapping waveforms can be handled properly by modeling the data in a given time window as a superposition of several events. In particular, the downgoing data at each depth level are modeled as a superposition of a P wave and an SV wave, with local P and S velocities, angles of incidence, and waveforms as model parameters. These parameters are then estimated by minimizing the squared error between the observed data and the model‐generated data. The unknown waveforms are eliminated from the minimization problem, leaving only four nonlinear parameters (velocities and angles) for estimation. Once these four parameters are found, least‐squares estimates of waveforms are obtained by evaluating a simple expression.
A direct comparison between vibrational resonance and pulse transmission data for assessment of seismic attenuation in rock
Authors: Blair Dane P.
Published: October 2002

For the same volume of rock, I compare the attenuation obtained by seismic pulse transmission over the frequency range 1–150 kHz with that obtained by vibrational resonance techniques over the frequency range 1–50 kHz. The initial studies were performed on a rectangular block of medium‐grained granite which was large enough to permit the installation of a seismic pulse transmission array over a 1.8 m path length, yet small enough to permit whole‐body resonance. A Q of 82, for the P wave, was derived from the vibrational resonance results, whereas a Q of 15 was derived from the pulse transmission results. In light of models proposed for the viscoelastic, geometric, and elastic scattering attenuation mechanisms, the experimental results suggest that this large discrepancy in Q values is due to elastic scattering by grain clusters (rather than individual grains) within the granite. Scattering is significant in the high‐frequency pulse transmission tests, but is considered insignificant in the lower frequency resonance tests. Furthermore, this scattering is represented approximately by a constant-Q loss mechanism, which makes it difficult to separate unambiguously elastic scattering and viscoelastic losses. Subsequent studies performed on a large block of fine‐grained norite yield a resonance Q of 89 and a pulse Q of approximately 102 and suggest a negligible scattering loss for this material. The experimental results for the norite imply that the constant-Q theory of seismic pulse attenuation provides a reasonable description of wave attenuation in a dry, fine‐grained crystalline rock over the frequency range 1–150 kHz.
Surface‐to‐volume ratio, charge density, nuclear magnetic relaxation, and permeability in clay‐bearing sandstones
Authors: Sen P. N. , Straley C. , Kenyon W. E. , Whittingham M. S.
Published: October 2002

Based on measurements on some 100 sandstone core samples, mainly from oil fields from various parts of the world, we found the following regressions between volume‐to‐surface ratio [Formula: see text], permeability to fluid flow k, exchange cation molarity [Formula: see text], and proton NMR decay constant [Formula: see text] in water‐saturated rocks (see Figure 1): [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. Here R is the regression coefficient, ϕ is the porosity and m the conductivity exponent; [Formula: see text] in normality (meq/ml), k in millidarcies, and [Formula: see text] in milliseconds, [Formula: see text] in μm. Including the tortuosity factor [Formula: see text] in conjunction with a pore‐size parameter as represented by [Formula: see text], [Formula: see text], or [Formula: see text] improves the correlation with permeability and reduces the residual error. The best predictor for log k is log [Formula: see text]. The exponents in the above correlations agree reasonably with those expected from simple models. These correlations provide a numerical basis for assessing how well some of these quantities can be estimated from others in log interpretation. They also provide a basis for assessing the importance of the factors that interfere with and thereby weaken the correlations.
Simultaneous reconstruction of permittivity and conductivity for crosshole geometries
Authors: Sena Arcangelo G. , Toksöz M. Nafi
Published: October 2002

We develop the theory and algorithm for the simultaneous inversion of permittivity and conductivity maps in the region between two boreholes in the earth. The three‐dimensional region is modeled as an inhomogeneous annulus of known thickness and height with radial and vertical variations of the electrical properties. The medium of interest is probed by a vertical magnetic dipole located on the axis of the cylindrical geometry and the receivers can be placed anywhere outside the inhomogeneous annulus. The inversion procedure is formulated in terms of a source‐type integral equation using monochromatic data. The integral equation is solved using an iterative approach where a Born approximation is applied at each iteration step. The nonuniqueness of the problem is overcome by imposing additional constraints on the solution using the method of regularization of Tikhonov. The distribution of electrical properties is obtained directly by this method. Numerical simulations, including multisource inversions, show that good results can be obtained for smoothly varying electrical properties, even for large contrast cases. In the case of rapid local variations of such properties, convergence can still be reached but at a slower rate and the reconstructions are smoothed versions of the original properties. In the presence of noise, the permittivity reconstruction is more robust than the conductivity reconstruction for the model considered here.
Sea‐ice thickness measurement using a small airborne electromagnetic sounding system
Authors: Kovacs A. , Holladay J. S.
Published: October 2002

The evaluation of a small electromagnetic induction sounding system for use in airborne measurement of sea‐ice thickness is discussed, as are the results from arctic field testing. Also outlined are the system noise and drift problems encountered during arctic field evaluation, problems which adversely affected the quality of the sounding data. The sea‐ice sounding results indicate that for ice floes with moderate relief it should be possible to determine thickness to within 5 percent, but that because of sounding footprint size and current model algorithm constraints, steep‐sided pressure ridge keels cannot be well defined. The findings also indicate that with further system improvement the day of routine sea‐ice thickness profiling from an airborne platform is close at hand.