bluuebunny/crossref_metadata_2025 huggingface dataset:
A method for computing the geoid height contribution of three‐dimensional bodies within a spherical earth
Authors: Hellinger S. J.
Published: October 2002

A method is presented for calculating the geoid height associated with three‐dimensional bodies of arbitrary shape and anomalous density within a spherical earth. Each three‐dimensional body is specified by giving its shape and anomalous density at a number of successive depths. The method calculates the anomalous gravitational potential due to such bodies and then obtains the geoid height using Bruns’ formula. The calculation utilizes the portion of the density model that lies in a hemisphere centered at the observation point. The method is partly analytical and partly numerical, and it is designed for digital computation. Use of the method to compute the anomalous potential in the vicinity of an anomalous body of simple shape shows that the method can give very accurate results.
Automated identification of rock boundaries: An application of the Walsh transform to geophysical well‐log analysis
Authors: Lanning Eric N. , Johnson Douglas M.
Published: October 2002

A system of orthogonal functions, known as Walsh functions, which assume only the values +1 and −1, are presented as a tool appropriate for the analysis of well‐log data. Many of the characteristics of these rectangular waveforms, such as discrete transitions in signal level, make them ideal for processing borehole data. Using the generalized Fourier transform, the basic equations for the Walsh transform and Walsh power spectrum are developed showing how the energy in a given signal is distributed among these rectangular wave components. As a first application of the Walsh transform to logging data, a method of computeraided rock boundary identification is developed and demonstrated on a set of well logs from a continental basalt sequence. This technique provides a fast, simple yet accurate means of dividing well‐log data into groups of measurements corresponding to different rock units.
Computer processing of vertical seismic profile data
Authors: Lee Myung W. , Balch Alfred H.
Published: October 2002

Vertical seismic profiles (VSP) are a powerful tool in a variety of seismic exploration situations. Only after extensive computer processing of the raw field data, however, can the full value of this tool be realized. With the help of processing, relations between important rock parameters and acoustic properties can sometimes be established and highly reliable ties from well logs to surface seismic profiles can usually be obtained. The basic theory of the processing techniques is well known. However, the techniques used in processing standard surface seismic profiles usually must be modified to adapt them to the unique conditions associated with VSPs. Processing procedures, and their relevance to the interpretation of VSP and surface seismic profile data, are described.
On: “A sum autoregressive formula for the reflection response” by P. Hubral, S. Treitel, and P. R. Gutowski (GEOPHYSICS, November 1980, p. 1697–1705).
Authors: Szaraniec Edward
Published: October 2002

The paper deals with the decomposition of the impulsive reflection seismogram into progressively delayed generalized primary wavelets. This decomposition serves to examine the patterns of primary and multiple reflections arising from the addition of a deeper interface to the layered system. Each of the generalized primary wavelets originates from a layered system augmented by a single deeper layer.
Reversed time migration in spatial frequency domain
Authors: Loewenthal Dan , Mufti Irshad R.
Published: October 2002

During the past decade, finite‐difference methods have become important tools for direct modeling of seismic data as well as for certain interpretation processes. One of the earliest applications of these methods to seismics is the pioneering contribution of Alterman who, in a series of papers (Alterman and Karal, 1968; Alterman and Aboudi, 1968; Alterman and Rotenberg, 1969; Alterman and Loewenthal, 1972) demonstrated the usefulness of such numerical computations for the propagation of seismic waves in elastic media. A clear exposition of these techniques, as well as a comparison of results obtained from them with the corresponding analytical solutions, can be found in Alterman and Karal (1968). This subject was further developed and extended to more complicated models by Boore (1970), Ottaviani (1971), and Kelly et al (1976). Claerbout introduced a somewhat different finite‐difference approach (Claerbout, 1970; Claerbout and Johnson, 1971) for modeling the acoustic waves which often dominate the reflection seismogram. In his approach, the original wave equation, which governs the propagation of the acoustic waves, is modified in such a way so as to allow the propagation of either only upcoming or only downgoing waves. By moving the coordinate frame with the downgoing waves, Claerbout showed that one could greatly reduce computation time. Using the same concepts, he showed (Claerbout and Doherty, 1972) how to use a similar scheme for migrating a seismic section by downward continuation of the upcoming waves. This migration method is an interesting extension of the ideas of Hagedoorn (1954) and was found to be extremely useful with real data (Larner and Hatton, 1976; Loewenthal et al, 1976).
Vertical scale and vertical exaggeration in three‐dimensional contour maps of physical data
Authors: Gay S. Parker
Published: October 2002

Gay (1971) described the application of three‐dimensional (3-D) viewing to geophysical data, principally contoured magnetic and gravity data. Subsequently, the method has been extensively applied to actual physical data, such as structural contour maps, isopach maps, and topography, both subaerial and submarine (e.g., Gay, 1981). These types of data have the same dimensions in the vertical and horizontal directions, i.e., physical distance. The question has therefore arisen many times over the years as to the mathematical relationship between the vertical and horizontal scales in the stereo model—what is the actual vertical exaggeration of a stereo view and how does one go about measuring it, or controlling it in case one is constructing a stereo pair? This question was not addressed in the 1971 paper, because there is no “true” vertical scale for gravity or magnetic maps, and hence no “exaggeration” (different dimensions in vertical and horizontal directions).
Coherent noise in marine seismic data
Authors: Larner Ken , Chambers Ron , Yang Mai , Lynn Walt , Wai Willon
Published: October 2002

Despite significant advances in marine streamer design, seismic data are often plagued by coherent noise having approximately linear moveout across stacked sections. With an understanding of the characteristics that distinguish such noise from signal, we can decide which noise‐suppression techniques to use and at what stages to apply them in acquisition and processing. Three general mechanisms that might produce such noise patterns on stacked sections are examined: direct and trapped waves that propagate outward from the seismic source, cable motion caused by the tugging action of the boat and tail buoy, and scattered energy from irregularities in the water bottom and sub‐bottom. Depending upon the mechanism, entirely different noise patterns can be observed on shot profiles and common‐midpoint (CMP) gathers; these patterns can be diagnostic of the dominant mechanism in a given set of data. Field data from Canada and Alaska suggest that the dominant noise is from waves scattered within the shallow sub‐buttom. This type of noise, while not obvious on the shot records, is actually enhanced by CMP stacking. Moreover, this noise is not confined to marine data; it can be as strong as surface wave noise on stacked land seismic data as well. Of the many processing tools available, moveout filtering is best for suppressing the noise while preserving signal. Since the scattered noise does not exhibit a linear moveout pattern on CMP‐sorted gathers, moveout filtering must be applied either to traces within shot records and common‐receiver gathers or to stacked traces. Our data example demonstrates that although it is more costly, moveout filtering of the unstacked data is particularly effective because it conditions the data for the critical data‐dependent processing steps of predictive deconvolution and velocity analysis.
Three‐dimensional model of the Koyna area of Maharashtra State (India) based on the spectral analysis of aeromagnetic data
Authors: Negi J. G. , Agrawal P. K. , Rao K. N. N.
Published: October 2002

The estimation of thickness of trap rocks in the earthquake‐affected Koyna area is an important parameter for revealing the topography that existed before the Deccan volcanism. In the present work, a case history is presented delineating a three‐dimensional block model for the Koyna area by the spectral analysis of aeromagnetic data. The thickness in the area was found to vary from 700 to 2200 m, which correlates well with the results of other geophysical investigations.
The effects of streamer feathering on stacking
Authors: Levin Franklyn K.
Published: October 2002

When the streamer carrying the hydrophones of a seismic ship is carried off the profile line by currents, i.e. is feathered, the equation relating reflection time and source‐to‐detector separation differs from the equation when there is no streamer feathering. For no feathering, even when the reflector is a dipping plane, for a simple one‐bed system the CMP time‐distance equation is a hyperbola with its apex at a separation corresponding to coincident source and detector. When there is streamer feathering, the reflector is a dipping plane, and the usual CMP traces are gathered, the equation remains that for a hyperbola but in general for a hyperbola whose apex does not occur at zero source‐to‐detector separation. Depending upon the feather angle and the direction of the profile relative to the dip direction, the apex may not occur at any realizable separation or may appear at some nonzero separation. If traces are selected so that the CMP midpoints lie on a line perpendicular to the profile direction, for a dip line there is no displacement of the apex from the zero separation point.
A geophone subarray beam‐steering process
Authors: Biswell Dale E. , Konty Larry F. , Liaw Alfred L.
Published: October 2002

The outputs of geophone array elements are conventionally summed into a single output trace. This summation attenuates incoherent noise, horizontally propagating surface waves, and obliquely incident events. The geophone subarray beam‐steering process is a plane‐wave stacking technique which removes the differential moveout and improves the resolution of seismic data by directing the subarray peak gain to the incident angle of the seismic wavefront. The plane‐wave stacking process transforms the data from the offset domain to the ray parameter (p) domain, and restricts the range of p as a function of time. Studies of synthetic and marine field data show that the beam‐steering process improves the signal‐to‐noise ratio of obliquely incident events as compared to conventional subarray summing operations. The beam‐steering process, compressing high‐density data while preserving the high‐frequency content of the seismic signal, is a cost‐effective technique to process large quantities of closely spaced seismic data for stratigraphic exploration.
Spectral induced polarization parameters as determined through time‐domain measurements
Authors: Johnson Ian M.
Published: October 2002

A method for the extraction of Cole-Cole spectral parameters from time‐domain induced polarization data is demonstrated. The instrumentation required to effect the measurement and analysis is described. The Cole-Cole impedance model is shown to work equally well in the time domain as in the frequency domain. Field trials show the time‐domain method to generate spectral parameters consistent with those generated by frequency‐domain surveys. This is shown to be possible without significant alteration to field procedures. Cole-Cole time constants of up to 100 s are shown to be resolvable given a transmitted current of a 2 s pulse‐time. The process proves to have added usefulness as the Cole-Cole forward solution proves an excellent basis for quantifying noise in the measured decay.
An examination of the exponential decay method of mixed‐phase wavelet estimation
Authors: Lazear Gregory D.
Published: October 2002

Signal processing theory states that an isolated wavelet which is causal and mixed phase may be converted to minimum phase by applying an exponential decay of amplitude with time. The exponential decay might therefore be a useful preprocessing step for seismic wavelet estimation since many estimation methods require that the wavelet in the data be minimum phase. This is the basis of a method proposed by Taner and Coburn (1980). The wavelets in a seismic trace, however, are generally not isolated, but instead are convolved with a densely populated reflection coefficient series causing severe wavelet overlap. Wavelet estimation is generally done using a window of data from the seismic trace which excludes refractions, surface waves, and data with poor signal‐to‐noise ratios. Due to the wavelet overlap, the window generally truncates wavelets at the window edges. When exponential decay is applied to the window, these truncated wavelets dominate the wavelet estimation methods. When no wavelet truncation occurs, the exponential decay converts each wavelet to minimum phase, and complete wavelets dominate the data window. If the reflection series is uncorrelated, then the autocorrelations of these data windows, when averaged over many traces, give an average autocorrelation which equals that of the decayed wavelet. This autocorrelation gives the correct minimum‐phase estimated wavelet. When truncation of wavelets does occur, the autocorrelation of the decayed data window does not equal that of the decayed wavelet, and an erroneous wavelet is estimated. Therefore, the exponential decay method is only useful for seismic wavelet estimation when data windows may be chosen such that no wavelets are truncated at the window onset.
On a modified algorithm for the autoregressive recovery of the acoustic impedance
Authors: Ulrych Tad. J. , Walker Colin
Published: October 2002

In a recent paper, Walker and Ulrych (1983) presented an algorithm for the recovery of the acoustic impedance from band‐limited seismic reflection records. The approach used is based on the autoregressive (AR) modeling of the band‐limited frequency transform of the data. This modeling procedure allows prediction of both the high and low missing frequencies. The low frequencies, which are particularly important in the inversion for the acoustic impedance, are determined by considering the low‐frequency band as a gap of missing data which is centered at zero frequency. The gap is filled by minimizing the sum of the squared forward and backward prediction errors which result when the known spectral data are modeled as an AR process.
Thermoelectrical self‐potential anomalies and their relationship to the solid angle subtended by the source region
Authors: Fitterman David V.
Published: October 2002

The calculation of self‐potential (SP) anomalies produced by thermoelectric sources is shown to be equivalent to calculating the weighted solid angle subtended at the observation point by the source region and its images where the weighting function is the source intensity. This interpretation provides an easy way of visualizing the effect of different source geometries, and describes the nonuniqueness associated with SP sources. For example, changes in a model which keep the product of source intensity and area constant do not appreciably change the produced anomaly. Similarly, deepening a source requires an increase of source intensity or size to produce the same anomaly. When conductivity contrasts become small or nonexistent, the number of image sources becomes finite or zero, respectively, further simplifying the calculation. As an example, the SP anomaly of a dipping rectangular source of constant intensity is computed using the method. This model is applied to SP data from the East Mesa geothermal field.
On: “Microwave properties of saturated reservoirs” by J. N. Lange (GEOPHYSICS, March, 1983, p. 367–375)
Authors: Korringa J. , Brown R. J. S.
Published: October 2002

From measurements at 250 MHz on glass bead packs saturated with water or methanol and similar systems, Lange concludes that “…an interaction between water and the solid matrix has an important effect on the composite dielectric constant.” We are of the opinion that this constitutes an incorrect interpretation of his data, brought about by the use of an unphysical “model.” Lange’s conclusions require a modification of properties of the fluid near the solid surface over distances which extend several orders of magnitude farther into the fluid than shown by most accepted evidence. Our analysis shows none of this.
Automatic fitting of gravity anomalies using two‐dimensional models
Authors: Montalvo Antonio
Published: October 2002

During the last two decades several methods have been reported in the literature (Corbató, 1965; Gerard and Debeglia, 1975; Bhattacharyya, 1978) for the automatic construction of models that fit observed magnetic and gravity measurements by using either space or frequency domains. Whichever approach is employed, the methods proceed as follows. An initial model is proposed and a sequence of corrections is generated in order to improve the fit between the observed and calculated anomalies. These corrections are successively applied to the initial model until a certain convergence criterion is satisfied. The above corresponds to the well‐known trial‐and‐error procedure; the relative advantages of one method over another arise from the way in which the corrections are generated.
On: “Airborne gravity is here!” by S. Hammer (GEOPHYSICS, v. 48, p. 213–223, February, 1983)
Authors: Pearson W. C.
Published: October 2002

In the subject paper, Dr. Sigmund Hammer has overstated the precision of airborne gravity and its impact on the effectiveness of exploration. The overstatement apparently results in part from an error in computations and in part from a misapplication of statistical analysis. Potential users of the method are, therefore, led to believe that airborne gravity can solve some geologic problems which in fact it cannot. This Discussion is an attempt to document these assertions.
Seismic vibrator control and the downgoing P-wave
Authors: Sallas J. J.
Published: October 2002

While the need for phase compensation is well established, the best method to measure the seismic vibrator output is not. Phase control of the force exerted by a seismic vibrator upon the earth’s surface (ground force) is shown to be useful in producing consistent downhole P-wave signatures. Experimental results are presented which compare the downhole correlation wavelets produced by phase‐locking to ground force; reaction mass acceleration and baseplate acceleration as changes in vibrator type, sweep bandwidth, drive level, and coupling medium are made. The empirical results support earlier theoretical work which predicts with suitable assumptions that ground force and far‐field particle displacement are in phase except for a time delay.
A method of determining a preferred P‐wave velocity profile in a borehole using surface explosions
Authors: Wright C. , Huang C.
Published: October 2002

The interpretation of seismic velocity variations in crystalline rocks in terms of fracture parameters requires velocity measurements with errors no greater than 1–2 percent. To achieve optimum resolution, we have devised a method of calculating P velocity‐depth profiles from crystal‐cable well surveys that makes maximum use of the data redundancy. Relative time corrections are computed iteratively for the entire set of shots using the overlapping portions of the hydrophone array between consecutive shots. From the resulting travel time versus distance curve, a family of possible velocity solutions is obtained for data windows of various lengths using Bolt’s modification of the method of summary values devised by Jeffreys. Trade‐off curves between the number of data points in the window and the variance of the velocity estimates are then drawn for different regions of the velocity profile. This enables a preferred solution to be constructed for each section of the velocity profile. The preferred velocity‐depth curve for a region of a gneiss‐monzonite rock body at depths between 25 and 254 m shows minima that correlate with the positions of major fractures or high concentrations of fractures inferred from optical examination of core samples, laboratory measurement of velocities, and tube wave studies.
A single digital linear filter for computations in electrical methods—A unifying approach
Authors: Das U. C.
Published: October 2002

A major contribution to the interpretation of electrical measurements was made with the application of digital linear filtering introduced by Ghosh (1970, 1971a, b). This rendered the computations easy and fast. In a recent publication, I showed (Das, 1982) that the filters for computing responses for any electrode or coil configurations employed in electrical methods could be derived easily from stored basic spectra of the two filter functions, namely, [Formula: see text] and [Formula: see text]. One has to multiply the stored spectra by simple factors to arrive at the required spectra. I show here that a simple mathematical manipulation transforms a [Formula: see text] domain integral into its corresponding [Formula: see text] domain integral, thereby leading to the use of a single [Formula: see text] filter for a variety of computations in electrical methods.
GEOTHERMAL METHODS OF ESTIMATING THE AGE OF THE EARTH.
Authors: Van Orstrand C. E.
Published: October 2002

Tables are given by means of which the temperatures in a homogeneous radioactive and non‐radioactive earth, subject to a constant temperature at the surface, can be calculated rigorously with a minimum amount of labor. The rigorous calculations lead to some unexpected results. Among them is the fact that a temperature of 76000°C. at the center of the earth is consistent with observed temperature gradients and that melting of the rocks at a depth of 500 kilometers is a possible result of radioactive heat.
A PERSPECTIVE OF EXPLORATION FOR PETROLEUM
Authors: Rosaire E. E.
Published: October 2002

The first petroleum prospecting technique, based on the recognition of visible seeps of oil and gas, was rational and direct. The exhaustive application of megascopic geochemical prospecting led to diminishing returns, and a period of rule‐o’‐thumb prospecting ensued. Geological prospecting appeared on the scene, and, as a result, the anticlinal theory was evolved, to become a bone of contention for years within that profession. Eventually, however, the anticlinal theory was accepted by petroleum geologists, and so structural prospecting developed. The exhaustive application of structural prospecting by geological methods led to the discovery of many oil fields, but, eventually, diminishing returns ensued. A period of pessimism as to the nation’s reserve followed, as rule‐o’‐thumb prospecting became the only possible prospecting procedure. Geophysical prospecting appeared on the scene in 1923, and was successful in the solution of a highly specialized problem without reliance upon depth estimations. With the passage of time, geophysical prospecting took on a structural complexion, and with the development of the reflection seismograph, a renaissance in structural prospecting took place. The geophysical phase of structural prospecting opened the vast basins for prospecting, and so revolutionized exploration for petroleum. However, geological prospecting did not experience a similar renaissance. Structural prospecting, in both its geological and geophysical phases, has been a rational but indirect prospecting method. Outstandingly successful, its exhaustive application is leading to diminishing returns. However, it has imposed a specialization upon both geological and geophysical prospecting which has stifled the natural development of geochemical prospecting from geological prospecting, has directed geophysical prospecting into an unduly narrow path, and, in permitting prospecting to greater depths, has resulted in an impasse wherein its success involves capital investments with prohibitive payouts. Though tacitly neglected in the past, there exists a geochemistry of a petroleum deposit, depending primarily upon the effects of the slow effusion of hydrocarbons through the sedimentary environment of the petroleum deposit throughout geologic time. Geochemical prospecting depends upon the chemical and physical measurement of one or more of the geochemical manifestations of a petroleum deposit, and the interpretation of the resulting data in terms of the local geology. Since structure is a necessary but not a sufficient condition for the accumulation of petroleum, geochemical prospecting is a rational and direct approach to exploration for petroleum, and in its turn will revolutionize prospecting to at least the extents that geological and geophysical prospecting did in the phases of structural prospecting which they initiated.
Residual migration: Applications and limitations
Authors: Rothman Daniel H. , Levin Stewart A. , Rocca Fabio
Published: October 2002

The correct migration of seismic data depends on the accuracy of the chosen velocity model. Rocca and Salvador (1982) showed that small errors in the velocity model may be efficiently corrected by applying a residual migration to previously migrated data, rather than remigrating the original data with a corrected velocity field. The effective velocity used in this residual processing is usually small compared to the original migration velocity. This decreases computational cost relative to a full migration, and allows the initial migration to be done with a less accurate but faster algorithm than would otherwise be required. The possible advantages are many. The overall cost of migration may be reduced, a consideration especially important when migrating 3-D data sets. Migration quality may be improved, because the location of mispositioned reflectors can be corrected and because of the freedom to choose initial migration with a high dip, low dispersion method such as Stolt migration. Interactive residual sharpening of the migrated image also becomes feasible. We discuss the theoretical and practical limitations of residual migration and quantify the related reductions of effective dip, velocity, and frequency after initial migration. We determine how accurate the initial migration velocity must be to justify use of this approach and analyze aliasing and numerical artifacts. Field data examples using Kirchhoff summation and finite‐difference migration illustrate the features and drawbacks of the method.
On: “Predictive deconvolution and the zero‐phase source” by B. Gibson and K. Larner (GEOPHYSICS, 49, 379–397, April 1984).
Authors: Mayne W. Harry
Published: October 2002

The authors are to be complimented on a most courageous attempt to solve a difficult (and perhaps intractable) problem. As an active advocate of using nonlinear sweeps to combat earth attenuation, I was very interested in the results reported when inverse Q-filters were applied. Use of an appropriately selected logarithmic time function sweep (dB/Hz response in the frequency domain) can provide the necessary amplitude (but not the phase) correction of any chosen inverse Q-filter.
Anisotropy and fracture zones about a geothermal well from P‐wave velocity profiles
Authors: Leary P. C. , Henyey T. L.
Published: October 2002

The feasibility of locating fracture zones and estimating their crack parameters was examined using an “areal well shoot” method centered on Utah State Geothermal Well 9‐1, Beaver County, Utah. High‐resolution traveltime measurements were made between a borehole sensor and an array of shotpoints distributed radially and azimuthally about the well. The directional dependence of velocity in the vicinity of the well was investigated by comparing traveltimes from different azimuths. Velocity anisotropy was detected; this condition is consistent with, but not required by, the existence of fractures in the basement rock having orientations subparallel to the latest episode of local faulting. The interpretation is complicated by a variable thickness of overburden around the well. Traveltime delays also suggest the presence of a low‐angle fracture zone intersecting the well at a depth of ∼1 500 ft.
A geophysical study on the Abu Gharadig basin, Egypt
Authors: Awad Ghareeb M.
Published: October 2002

The area of study comprises one of the most hydrocarbon‐potential basins of the Egyptian Western Desert, the Abu Gharadig basin. Major marine transgression and regression cycles dominated the territory during different geologic times. Those depositional cycles, together with at least three tectonic cycles—the end of the Paleozoic Hercynean, the close of the Jurassic until the Late Cretaceous and, the close of the Cretaceous until Mid‐Teritary—resulted in a highly deformed, thick sedimentary cover. A study of the geophysical anomalies of the basin, including those indicated by aeromagnetic, gravity, and seismic data as well as the study of about 60 deep wells drilled within and around the Abu Gharadig basin, has revealed that the major tectonic disturbances of the area were caused by basement complex block faulting. These major tectonic disturbances have produced great variations in the thickness and distribution of the various geologic units throughout the region. Aeromagnetic anomalies and the wells which reached the basement indicate great variations in the depths and type of the basement complex and the presence of major intrusions in the region. The major fracturing is indicated to be mainly along an east‐west, west‐northwest and east‐northeast directions. The Bouguer gravity anomalies indicate major basement fracturing as well as variations in sedimentary patterns, erosions, and subsequent tectonic disturbances. The most obvious anomalous trends on the gravity map, based on frequency and amplitude, are the north‐east to east‐northeast, the east‐west and the west‐northwest. The main Abu Gharadig depositional center does not show sharp variations because of the homogeneity of the near‐surface rocks and the great basement depth (20 000-40 000 ft). Seismic interpretation has confirmed the presence of all these fracturing trends. It also identified some major structural trends. These are closely related to the depositional centers, and represent potential drilling locations, especially those associated with Late Cretaceous‐Tertiary active contemporaneous faulting.
Solving cylindrical geothermal problems using the Gaver‐Stehfest inverse Laplace transform
Authors: Villinger Heinrich
Published: October 2002

The inhomogeneous one‐dimensional heat‐diffusion equation is solved semianalytically in a cylindrically layered whole space. An analytic solution of the problem can be derived in the Laplace domain in a straightforward way assuming continuity of temperature and heat flow at the layer boundaries. The time‐dependent heat sources can be distributed spatially over the layered whole space. Due to the complexity of the solution in the Laplace domain, the inverse Laplace transform is calculated using a numerical procedure (Gaver‐Stehfest algorithm). It is shown that the algorithm is fast, stable, easy to use, and simple to adjust to various models and boundary conditions. The results obtained are accurate to about 0.01 percent. Therefore, it is an excellent tool for geothermal model calculations with cylindrical symmetry and could be useful for the correction of BHT-values or marine heat flow measurements.
Finite‐difference synthetic acoustic logs
Authors: Stephen R. A. , Cardo‐Casas F. , Cheng C. H.
Published: October 2002

The finite‐difference method is a powerful technique for studying the propagation of elastic waves in boreholes. Even for the simple case of an open borehole with vertical homogeneity, the snapshot format of the method displays clearly the interaction between the borehole and the rock, and the origin and evolution of phases. We present an outline of the finite‐difference method applied to the acoustic logging problem, including a boundary condition formulation for liquid‐solid cylindrical interfaces which is correct to second order in the space increments. Absorbing boundaries based on the formulations of Reynolds (1978) and Clayton and Engquist (1977) were used to reduce reflections from the grid boundaries. Results for a vertically homogeneous sharp interface model are compared with the discrete‐wavenumber method and excellent agreement is obtained. The technique is also demonstrated by considering sharp and continuous transitions (damaged zones) at the borehole wall and by considering the effects of washouts and horizontal fissures on acoustic logs. The latter two cases are examples of wave propagation in media with properties which vary in two dimensions. For the models considered, amplitudes of head waves and head wave multiples (leaky PL modes) are frequently enhanced by washouts. The compressional body waves are less affected by the washouts and horizontal fissures than the guided Stoneley waves which are reflected and only partially transmitted at changes in borehole radius. Amplitude changes of up to 6 dB are observed in the compressional wave due to the borehole deformation. For the Stoneley wave, borehole deformations can cause changes in amplitude of 20 dB and dramatic changes in waveform.
Velocity inversion using a stratified reference
Authors: Cohen Jack K. , Hagin Frank G.
Published: October 2002

We present an inversion algorithm for backscattered (“stacked”) seismic data which will reconstruct the velocity profile in realistic earth conditions. The basic approach follows that of the original (constant reference speed) Cohen and Bleistein paper (1979a) in that hig‐hfrequency asymptotics and perturbation methods are used. However, we use a reference speed which may vary with depth, and this greatly enhances the validity of the perturbation assumption and hence the inversion results. The new algorithm enjoys the same economies and stability properties of the original algorithm, making it very competitive with current migration schemes. Four major assumptions are made: (1) the acoustic wave equation is an adequate model; (2) stacked data have amplitude information worth preserving fairly accurately; (3) the actual reflectivity coefficients can be adequately modeled as perturbations from a continuous reference velocity which depends only on the depth variable; and (4) the subsurface can be adequately modeled as a series of layers with jump discontinuities in the velocity (or impedance) at the interfaces. While the algorithm is particularly suited for data generated by a number of reflecting surfaces, its validity for a single reflector is demonstrated by applying the algorithm to Kirchhoff data for a quite general surface. A key feature of the approach used is the repeated application of high‐frequency asymptotic methods. A noteworthy point is that the underlying integral equation is in the form of a generalized Fourier integral equation; the method for its (approximate) inversion may prove to be applicable to a wide range of such problems.
Geophysical investigations of the Cove Fort‐Sulphurdale geothermal system, Utah
Authors: Ross Howard P. , Moore Joseph N.
Published: October 2002

The Cove Fort‐Sulphurdale KGRA is part of one of the largest thermal anomalies in the western United States. Since 1975 an extensive data base has been developed which includes the results of detailed and regional geologic, gravity, magnetic, seismic, and resistivity investigations. Geologic studies have delineated the major tectonic elements of the thermal system and have led to the recognition of large‐scale gravitational glide blocks that act as a leaky cap to portions of the geothermal system. Gravity and magnetic data have delineated major throughgoing structures beneath alluvium and basalt cover, and have indicated the importance of the Cove Fort‐Beaver graben in localizing the geothermal reservoir. The presence of these structures and a high level of microearthquake activity suggest other target areas within the larger thermal anomaly. Electrical resistivity surveys and thermal gradient holes both contribute to the delineation of the known reservoir. Four deep exploration wells which test the geothermal system were drilled between 1975 and 1979. One well, CFSU 42–7, recorded temperatures of 178°C. The high cost of drilling, high corrosion rates, low reservoir pressures, and the apparent limited extent of the high‐temperature reservoir led to a premature conclusion in 1980 that the field was not economic for large‐scale electric power production. More recent drilling in the vicinity of CFSU 42–7 resulted in the discovery of high‐temperature (200°C?) geothermal fluids at a depth of approximately 350 m. A well‐head generator was installed and power production is expected in 1985. Additional development of the geothermal reservoir is anticipated in the 1985 to 1987 time frame.
Surface‐consistent suppression of multiples
Authors: Nedlin G.
Published: October 2002

A primary reflection from any layer located somewhere below a water bottom (Figure 1a) is accompanied on a seismic record by series of multiples whose raypaths include one or more extra reflections from a water bottom (Figure 1b) either at a shot and/or at a geophone location. These multiples often have comparable or larger amplitudes than some primary reflections from deeper layers, making interpretation confusingly complicated. Therefore, extensive efforts have been devoted and different methods have been elaborated for suppression of such multiples. An interesting method formulated by Morley and Claerbout (1983) is generally applicable in the case of variable water depth (i.e., when the seafloor on Figures 1a and 1b is not exactly horizontal). The method presented here is similar to the Morley and Claerbout method.
Migration and inversion of seismic data
Authors: Stolt R. H. , Weglein A. B.
Published: October 2002

Seismic migration and inversion describe a class of closely related processes sharing common objectives and underlying physical principles. These processes range in complexity from the simple NMO‐stack to the complex, iterative, multidimensional, prestack, nonlinear inversion used in the elastic seismic case. By making use of amplitudes versus offset, it is, in principle, possible to determine the three elastic parameters from compressional data. NMO‐stack can be modified to solve for these parameters, as can prestack migration. Linearized, wave‐equation inversion does not inordinately increase the complexity of data processing. The principal part of a migration‐inversion algorithm is the migration. Practical difficulties are considerable, including both correctable and intrinsic limitations in data quality, limitations in current algorithms (which we hope are correctable), and correctable (or perhaps intrinsic) limitations in computer power.
Stratigraphic filtering, Part II: Model spectra
Authors: Banik N. C. , Lerche I. , Resnick J. R. , Shuey R. T.
Published: October 2002

We describe filtering by short‐period multiples in one dimension using a combination of the O’Doherty‐Anstey (1971) formula with a stochastic model in which the autocorrelation of acoustic impedance decreases exponentially with lag [Formula: see text] while the spectrum of reflection coefficients rises with frequency up to a corner, then is approximately constant, [Formula: see text] An impedance log with these statistics is a generalization of the classic random telegraph wave. The parameter [Formula: see text], the mean‐square fractional fluctuation of impedance, is typically less than 1 percent, although we show an example where it is as high as 13 percent. The corner frequency [Formula: see text] is inversely related to average bed thickness. Typical values are 50–100 Hz, at the upper end of the normal seismic band. The cyclic stratification discussed by O’Doherty and Anstey (1971) and others corresponds to [Formula: see text] above the seismic band. Some logs have more reflection power at low frequencies than predicted from high frequencies by this model. We describe in both frequency and time domains the filtering of a seismic wavelet by multiples in such a stratigraphic sequence. The impulse response has a direct arrival, followed by a long tail of multiply scattered energy. The greater the impedance fluctuations or the longer the traveltime, the more amplitude is transferred from the primary to the multiples. We discuss in less detail several other models, including periodic and nearly periodic bedding. We also include two numerical applications of the O’Doherty‐Anstey formula; we show on a specific logged interval the formula’s remarkable accuracy for both attenuation and time delay; and we describe the reduction in computed time delay due to coarser sampling of the log.
Nonlinear inversion, statistical mechanics, and residual statics estimation
Authors: Rothman Daniel H.
Published: October 2002

Nonlinear inverse problems are usually solved with linearized techniques that depend strongly on the accuracy of initial estimates of the model parameters. With linearization, objective functions can be minimized efficiently, but the risk of local rather than global optimization can be severe. I address the problem confronted in nonlinear inversion when no good initial guess of the model parameters can be made. The fully nonlinear approach presented is rooted in statistical mechanics. Although a large nonlinear problem might appear computationally intractable without linearization, reformulation of the same problem into smaller, interdependent parts can lead to tractable computation while preserving nonlinearities. I formulate inversion as a problem of Bayesian estimation, in which the prior probability distribution is the Gibbs distribution of statistical mechanics. Solutions are then obtained by maximizing the posterior probability of the model parameters. Optimization is performed with a Monte Carlo technique that was originally introduced to simulate the statistical mechanics of systems in equilibrium. The technique is applied to residual statics estimation when statics are unusually large and data are contaminated by noise. Poorly picked correlations (“cycle skips” or “leg jumps”) appear as local minima of the objective function, but global optimization is successfully performed. Further applications to deconvolution and velocity estimation are proposed.
On: “Causes of compressional wave anisotropy in carbonate bearing deep sea sediment” by R. L. Carlson, C. H. Schaftenaar, and R. P. Moore (GEOPHYSICS, 49, 525– 532, May, 1984).
Authors: Collins H. N.
Published: October 2002

In the course of presenting data on the application of linear regression, the authors included in Figure 1 an equation representing the regression of wet‐bulk density on porosity in the form [Formula: see text], where [Formula: see text] and [Formula: see text] are wet‐bulk and grain densities, respectively, in [Formula: see text]. Based on the data of the selected samples shown in Figure 1, they have inferred a grain density of [Formula: see text], and a fluid density of [Formula: see text], not unreasonable values for a brine‐saturated calcareous sediment. However, it is incorrect to draw such inferences from this regression equation without the qualification that the independent variable, in this case porosity, is error free. Based on the porosity values shown in Table 1 (see my Table 1) those data are indeed subject to error.
Algorithms of phase and group correlation
Authors: Gelchinsky B. , Landa E. , Shtivelman V.
Published: October 2002

In this paper we consider algorithms of phase and group correlation which are based on different assumptions regarding the character of wave field. In order to construct the correlation algorithm, the wave field is presented as a product of an envelope and a normalized seismogram. Phase correlation is performed on the normalized seismogram, while group correlation is performed on the perigram, a low cut version of the envelope function. The central point of the correlation algorithm is the construction of a functional which characterizes the main correlation properties of the wave field. This functional is computed for different values of parameters which appear in the expressions approximating phase and group traveltime curves. Several types of correlation functionals are considered. The next step of the correlation algorithm is analysis of the previously obtained functionals; this is performed using a system of inequalities based on a number of assumptions regarding the properties of wave fields. The results of this analysis permit us to make a decision regarding the presence of a signal and to estimate the parameters of detected waves. Examples illustrating application of the proposed algorithm to synthetic and field data are presented.
Single‐borehole and cross‐borehole resistivity anomalies of thin ellipsoids and spheroids
Authors: Yang F. W. , Ward S. H.
Published: October 2002

Hole‐to‐hole resistivity measurement is a useful method of detecting deeply buried fractures and ore deposits in the subsurface. With drilling costs continually rising, there is a growing need for developing methods of borehole geophysics such as this. In this study, we present theoretical results relating to detection of thin oblate spheroids and ellipsoids with arbitrary attitude. If we assume that individual fractures within a fracture zone are connected to each other and are of finite lateral and vertical extent, then we can model the fracture zone as a thin conductive oblate ellipsoid or spheroid with arbitrary orientation of the major axis. Detection of such deeply buried fracture zones is the object of this study. Here the effects of the surface of the Earth are neglected and the body is assumed to be enclosed within an infinite homogeneous mass. The surface of the body is divided into a series of subsurfaces, and a numerical solution of the Fredholm integral equation is applied. Once a solution for the surface charge distribution is determined, the potential can be specified anywhere by means of Coulomb’s law. The theoretical model results indicate that cross‐borehole resistivity measurements are a more effective technique than single‐borehole measurements for delineating resistivity anomalies in the vicinity of a borehole. In some cases, the depth to the center of the body and the dip and strike of the major axes of the body can be estimated.