bluuebunny/crossref_metadata_2025 huggingface dataset:
Reduction of a two‐gravimeter base network by linear regression
Authors: Ervin C. Patrick
Published: October 2002

In the exploration environment, a primary application of gravity surveying is regional reconnaissance. The first step in such a survey is to establish a base‐station network. Since an error in the network will propagate to many stations in the subsequent survey, careful field work and accurate reduction of these data are particularly critical. Optimally, successive base stations are tied by minimum‐time loops using at least two meters read simultaneously. Using two meters has the obvious advantage of doubling the number of ties with minimal increase in time and cost. Erroneous readings are also much easier to detect and correct with two meters. Furthermore, the simultaneous operation of the meters allows calibrations of the two to be compared by computing a linear regression of the readings of one meter against the corresponding readings of the other. If the meter calibrations are identical, the regression line should have a slope of 1. A significant deviation from 1 indicates a systematic variation in calibration.
The determination of spectral parameters with pulse‐train induced polarization
Authors: Lewis R. J. G.
Published: October 2002

It was suggested in Soininen (1984) on the basis of noise‐free data that pulse‐train induced‐polarization (IP) measurements are of little value in determining the spectral characteristics of complex resistivity. Here it is shown that, in at least some cases, use of appropriate techniques can readily obtain the Cole‐Cole parameters from pulse‐train measurements with both noise‐free data and data contaminated with low levels of random noise. Consider the current waveform shown in Figure 1 as used in Soininen (1984) and Tombs (1981) and in practice in some commercial IP equipment. Practical equipment measures a limited number of samples averaged over a time gate as shown in the voltage waveform of Figure 1. The result of Tombs [1981, equation (5)] is easily generalized to calculate the average voltage V over the time gate from [Formula: see text] to [Formula: see text].
Geophysical case history of the Two Hills Colony gas field of Alberta
Authors: Focht G. W. , Baker F. E.
Published: October 2002

Seismic waveform changes, which in their most obvious form are known as “bright spots,” have been known for some years to give direct indications of hydrocarbons. An example of successful application of waveform analysis and direct detection of gas in a shallow Lower Cretaceous formation of east‐central Alberta, Canada, is detailed. At a depth of approximately 1 800 ft, the Colony formation typically consists of only thin (10 ft) blanket sands interbedded with shale. However, in 1976, Hudson’s Bay Oil and Gas Company Ltd., encountered a 100 ft thick occurrence of channel sand (with substantial gas pay) in this formation. After some hit and miss attempts at extending the channel trend through geologic interpretation, seismic methods were applied. A seismic line over the channel well revealed a classic bright spot. Several other lines also showed bright spots in the Colony zone. The conclusions from seismic modeling are as follows. Gas within the Colony sand is seismically detectable. The relatively low velocity of the gas sand, combined with the lateral consistency of the sediments above the Colony formation, permits detection. However, the inconsistency and complexity of sediments underlying the Colony resulted in interference patterns that prevented exact quantitative analysis of gas pays. Furthermore, other geologic phenomena provided waveform changes similar to that of gas sand. Through detailed examination of the geology and evaluation of the alternative explanations of the waveform changes, successful interpretation was accomplished. Estimations of net gas pay were generally accurate within 20 percent. In some areas, very subtle anomalies in wave character representing gas pays as thin as 5 ft can now be interpreted with confidence. Several examples are given of successful detection and prediction of gas. To date (October, 1979) seismic waveform analysis has led to the drilling of 86 wells; 67 of these are commercial gas wells in the Colony formation, representing a success ratio of 78 percent. Total reserves discovered geophysically (by Hudson’s Bay Oil and Gas Co. Ltd.) to date in the Colony formation are estimated at 110 Bcf.
Seismic waves generated by an impulsive point source in a solid/fluid configuration with a plane boundary
Authors: de Hoop Adrianus T. , van der Hijden Jos H. M. T.
Published: October 2002

The space‐time acoustic wave motion generated by an impulsive point source in a solid/fluid configuration with a vertical plane boundary is calculated with the aid of the modified Cagniard method. Two types of sources are considered in detail, viz. (1) a point source of expansion (model for an explosive source), and (2) a point force parallel to the vertical interface (model for a mechanical vibrator). Numerical results are presented for the transmitted scalar traction in the fluid in those regions of space where head wave contributions occur. There is a marked difference in the time response observed for the two types of sources and for the different positions of the receiver in the fluid with respect to the position of the source in the solid. These waveform differences are important when the transmitted wave in the fluid is used to determine experimentally the elastic properties of the solid. Scholte waves are observed only when the source is close to the fluid/solid interface. As compared with the traditional Fourier‐Bessel integral transform method of handling this problem, the computation time with the method presented here is considerably less.
A solution for TM‐mode plane waves incident on a two‐dimensional inhomogeneity
Authors: Lee K. H. , Morrison H. F.
Published: October 2002

Quantitative interpretation of magnetotelluric (MT) surveys depends at present on the availability of an efficient forward modeling algorithm. To date, two major numerical techniques have been used to obtain the scattered fields from buried inhomogeneities in plane‐wave fields: methods solving the governing differential equation which generally uses a finite‐element or finite‐difference approach, and methods which solve an integral‐equation formulation of the problem. For two‐dimensional (2-D) inhomogeneities a solution for incident fields with the electric field parallel to the strike of the inhomogeneity (TE mode solution) was developed by Hohmann (1971) using the integral‐equation approach. For a perfect conductor an integral formulation, for surface scattering currents, for the TM mode (magnetic field parallel to the strike of the inhomogeneity) was developed by Parry (1969). General 2-D solutions in the presence of an arbitrary mode plane wave (mixed TE-TM) were obtained by Ryu (1970), Swift (1971), and Rijo (1977) using either a finite‐element or finite‐difference technique.
On sensitivity of surface‐to‐borehole resistivity measurements to the attitude and the depth to center of a three‐dimensional spheroid
Authors: Yang F. W. , Ward S. H.
Published: October 2002

Borehole‐to‐surface and surface‐to‐borehole resistivity measurements are versatile but not totally tested methods for detecting anomalies in the vicinity of a borehole. The former method has been discussed by several authors (Alfano, 1962; Merkel, 1971; Merkel and Alexander, 1971; Barnett, 1972; Snyder and Merkel, 1973; Snyder, 1976; Daniels, 1977, 1978, and 1983), but the latter has not received much attention. Morrison (1971) and Daniels (1977) are among the few who have addressed the problem. Each method has its own advantages. Surface‐to‐borehole resistivity measurements are made by placing a current source on the surface and measuring the apparent resistivity in a borehole in which the measuring electrodes are closer to the body than in the borehole‐to‐surface case. Pilot studies presented here suggest that the surface‐to‐borehole method can provide indicators of the attitude and the depth to the center of a body. This paper illustrates a simple method for qualitatively determining the attitude and the depth to the center of a body for a thin three‐dimensional (3-D) conductive oblate body with the surface‐to‐borehole technique. Attitude conveys the orientation of the body— horizontal, vertical dipping toward a borehole, or dipping away from a borehole.
A theory of compressional wave attenuation in noncohesive sediments
Authors: McCann C. , McCann D. M.
Published: October 2002

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.
Dielectric properties of pyrite samples at 1 100 MHz
Authors: Manning Michael J. , Athavale Kumud A.
Published: October 2002

Pyrite occurs in many petroleum reservoirs and significantly affects density and electric well logs even in low concentrations. Ultrahigh‐frequency dielectric measurements also are significantly affected by pyrite. Dielectric properties of core samples containing approximately 50 percent pyrite by volume were measured from 800 to 1 200 MHz ([Formula: see text]). These measurements demonstrate the high, complex dielectric permittivity of pyrite and provide data for calculation of pyrite permittivity at ultrahigh frequencies. The measured complex‐permittivity of water‐saturated pyrite nodules is approximately [Formula: see text] at 1 100 MHz and 25 °C. The measured permittivity of pyrite nodules depends upon the concentration of pyrite and only slightly on saturating‐water salinity. Two geometric mixing models, the complex refractive‐index method (CRIM) and a modified Hanai‐Bruggeman‐Sen (HBS) model, are used to analyze the data. CRIM analysis of water‐saturated and oil‐saturated core data gives inconsistent results because the porosity is poorly connected. HBS, with a variable dielectric exponent, provides more consistent results. [Formula: see text] is the complex permittivity of pyrite at 1 100 MHz and 25 °C determined by applying HBS to laboratory measurements. CRIM‐determined pyrite permittivity is about 50 percent greater in both real and imaginary parts. This high [Formula: see text] has important implications for high‐frequency dielectric well‐logging tools. Signal amplitudes are highly attenuated in formations with large concentrations of pyrite. Where pyrite nodules occur, wave scattering may cause inconsistent data indicative of formation heterogeneity. Low concentration, disseminated pyrite increases the rock “matrix” permittivity. Mineralogical variations, particularly in trace quantities of heavy minerals, are a likely explanation for significant variations in measured matrix permittivities for sandstones. Comparison of pyrite permittivity with available values for the permittivity of rutile, another heavy mineral found in sedimentary rocks, suggests employing pyrite and rutile in artificial sandpack experiments. The real parts of pyrite and rutile permittivities are nearly equal, but the imaginary part of the permittivity of rutile is lower than pyrite by about [Formula: see text]. Experiments with both minerals could test mixing models and the effects of distribution in mixtures of conductive minerals.
On: “Important design considerations for inboard airborne magnetic gradiometers” by C. D. Hardwick (GEOPHYSICS, 49, 2004–2018, November 1984).
Authors: Hood Peter
Published: October 2002

In the above paper, the author states that military‐type magnetic compensators such as the nine‐term compensator produced by Canadian Aviation Electrons (CAE) of Montreal, Quebec may not be suitable for aeromagnetic survey work. In view of his doubts, I wish to assure him that 14 years of usage by the Geological Survey of Canada (GSC) has demonstrated without question that the CAE compensator is efficient for high‐sensitivity aeromagnetic survey work. The GSC first installed a CAE compensator in 1969 on its light, twin‐engine Beechcraft Queenair aircraft, and since that time approximately 450 total field and vertical gradient maps have been produced. Because the device is used for surveys in which the line spacing is commonly 300 m and has been as low as 150 m, any substantial deficiencies in the measurement system would have been readily apparent in the resultant contoured data. These would show as one‐line isolated anomalies and otherwise abnormal contour patterns, etc. Indeed, such effects would be particularly noticeable in the vertical gradient data because the contour interval used in the published maps is only 0.025 γ/m.
Attenuation of waterborne coherent noise by application of hyperbolic velocity filtering during the tau‐p transform
Authors: Noponen Ikka , Keeney Joe
Published: October 2002

By limiting data input to the forward‐inverse tau‐p transform pair, velocity filtering which varies with time and offset can be achieved. The limiting procedure, called hyperbolic velocity filtering, suppresses coherent noise while retaining reflection events. It is based on knowledge of the stacking velocities, but only approximate values are needed. A suitable application for hyperbolic velocity filtering is in hard water‐bottom marine areas where laterally propagating noise, diffracted by shallow scatterers, gives rise to reflection‐like events with high apparent velocity in the CMP gathers. Such diffractions do not, however, generally have reflection‐like moveouts in shot or receiver gathers. Hyperbolic velocity filtering offers moveout discrimination at all offset distances and traveltimes. When it is applied to shot (and receiver) gathers from a hard water‐bottom area such as offshore Florida, a striking reduction of noise occurs in the stacked section. Comparison with similar application of fixed‐limit (f-k) velocity filtering shows the hyperbolic filtering to be more effective for this data set.
Spatial and temporal analysis of electromagnetic survey data
Authors: Garg Nek R. , Keller George V.
Published: October 2002

Development of a relatively straightforward approach to interpretation of electromagnetic survey data when the earth in the vicinity of the survey has a complex geoelectric structure will be necessary before such methods can assume their full role in geophysical exploration. One‐dimensional interpretation methods have been well developed to extract the resistivity‐depth profile from a transient electromagnetic (TEM) sounding when the earth is assumed to be simply layered. Extension of the same methods to more complicated earth structures is difficult because of the tedious calculations involved when three‐dimensional earth structures are examined. An alternate approach could be use of the information contained in the spatial spectra of a set of sounding measurements. In such an approach, it should be possible to obtain a clearer concept of the geoelectric structure by analytic continuation of the electromagnetic field in space, or by heuristic filtering of the field, as is done in various potential field methods in geophysics. To try this concept, a filtering technique developed for treating magnetic data was applied to a set of TEM data acquired in the Snake River plain of Idaho. The results are reasonable, but insufficient control information is available to prove their significance. The effort has demonstrated that such a filtering approach can be done quickly, but it places demands on how the field data are sampled in the space domain.
Observations of wave velocity and attenuation in two‐phase media
Authors: Purnell G. W.
Published: October 2002

The velocity and attenuation of a wave transmitted through a two‐phase material are functions of the material’s composition. In physical model experiments, I used suspensions of grains in a silicone rubber matrix to reduce or avoid uncertainties about framework elastic constants, porosity, and permeability that result from using fluid‐saturated grain frameworks. I varied the composition to produce materials that are useful in physical seismic modeling. In the tested suspensions, ultrasonic P-wave velocity, velocity dispersion, and attenuation all increase with grain concentration and frequency. I compared seven published mathematical models for wave propagation in two‐phase media. One given by Mehta most closely agrees with the P-wave velocities I observed. The agreement is sufficiently close to merit use of Mehta’s model in the design of physical model materials. The observed P-wave attenuation generally increases approximately linearly with frequency. This approximate linearity leads to reliable constant-Q estimates, ranging from 187 to 16 for grain concentrations from 0 to 0.49. I conclude that relative motion between the grains and the rubber matrix contributes most of the observed attenuation at lower concentrations, whereas scattering losses become much more important at higher concentrations and frequencies.
Water‐gun cavity collapse in a compressible liquid
Authors: Krail Paul M.
Published: October 2002

The velocity of the cavity wall is all important in the calculation of the far‐field signature for a water gun firing in the ocean. I use a method of successive approximation to solve Herring’s energy equation for the collapse of a spherical cavity in a compressible liquid. The velocity of the collapse of the cavity wall depends upon the compressibility of the liquid, the amount of residual gas in the cavity, and the amount of acoustic radiation. The compressibility of the liquid has a significant effect on cavity velocity, but it has very little effect on the collapse period. The maximum value of the cavity velocity determines the peak magnitude of the far‐field pressure signature; the pressure signature depends strongly on the amount and rate of residual gas compression. The results from solving Herring’s equation agreed satisfactorily with a numerical solution of the fluid equations of motion. This solution to Herring’s equation includes the compressibility of the liquid, the residual gas compression, and the acoustic radiation, all necessary factors in accurate calculation of the velocity of the cavity wall and thus the far‐field signature.
Maximum entropy analysis of dispersed seismic signals
Authors: Cox K. B. , Mason I. M.
Published: October 2002

Conventional moving‐window analyzers based on Fourier transforms sometimes lack the resolution required to separate each of the modes in a seismic waveguide. It is possible to enhance the resolution of a moving‐window analyzer by using a maximum entropy power spectral estimator to approximate the spectrum of each windowed segment of a trace. Barrodale and Erickson have developed a suitable maximum entropy algorithm which can also be applied to estimating the parameters required in the fast recompression of inseam seismic arrivals. The Barrodale‐Erickson maximum entropy algorithm appears to need a sample rate of approximately ten times the Nyquist rate in order to generate meaningful maximum entropy spectra. The required increase can be achieved in the laboratory by applying an accurate interpolator to field records. Noise captures the maximum entropy spectrum if the input signal‐to‐noise ratio falls much below 10 dB. Use of a maximum entropy spectral analyzer aids in both identifying modes in a waveguide system and estimating the group velocity‐frequency characteristic parameter.
High‐resolution common‐depth‐point reflection profiling:Field acquisition parameter design
Authors: Knapp Ralph W. , Steeples Don W.
Published: October 2002

The results of a seismic reflection profiling exercise are strongly dependent upon parameters used in field recording. The choice of parameters is determined by objectives of the survey, available resources, and geologic locality. Some simple modeling and/or a walkaway noise survey are helpful in choice of field parameters. Filtering data before analog‐to‐digital conversion in the field can help overcome limitations in the dynamic range of the seismograph. Source and geophone arrays can be used to a limited extent in high‐resolution surveys to help attenuate ground roll. Proper planting of geophones can be an important factor in obtaining the flattest spectral response. Various seismic energy sources provide the flattest spectral response. Various seismic energy sources provide different spectral character and varying degrees of convenience and cost.
Seismic reflection investigations of sinkholes beneath Interstate Highway 70 in Kansas
Authors: Steeples Don W. , Knapp Ralph W. , McElwee Carl D.
Published: October 2002

Seismic reflection studies were performed across actively developing sinkholes located astride Interstate Highway 70 in Russell County, Kansas. Results indicate that high‐resolution seismic reflection surveys are useful in the subsurface investigation of some sinkholes. In particular, we were able to delineate the subsurface vertical and horizontal extent of the sinkholes because of the excellent acoustical marker‐bed characteristics of the Stone Corral anhydrite. The seismic reflection evidence presented here, combined with borehole information from 1967, suggest that the Stone Corral anhydrite has been down‐dropped within one of the sinkholes as much as 30 m in 13 years. The seismic reflection method is potentially useful in engineering studies of other sinkholes and karst features. The seismic data presented here were obtained in the presence of relatively heavy highway traffic (i.e., up to a few dozen vehicles per minute) using the MiniSOSIE recording technique.
Migration of common‐shot gathers
Authors: Reshef Moshe , Kosloff Dan
Published: October 2002

Three depth migration methods which operate on common‐shot data are presented. The first migration method maps digitized horizons from the X-T domain to the X-Z domain. Because this method is based on ray tracing, its computation time is short; it is suggested for iterative velocity analysis. The other two migration methods map the entire common‐shot gather into a depth section. The common‐shot migration requires calculation of the arrival time of the direct wave from the source to all the depth points, and is done through a direct solution of the eikonal equation. All three methods are suitable for areas with both lateral and vertical velocity variation.
A novel ground electromagnetic system
Authors: Johnson Ian M. , Doborzynski Zbigniew B.
Published: October 2002

A novel, moving‐source, ground electromagnetic system has been developed. The system, named the “Genie,” has been in routine field use since 1982. The system is based on measurement of the ratio of magnetic field amplitude at two widely separated frequencies. The design is presented and compared with traditional horizontal loop electromagnetic (HLEM) systems. Field survey results show the system is effective in detecting conductors at shallow to intermediate depths in resistive environments. The system is shown to be roughly equivalent in many aspects to conventional HLEM systems with important advantages in areas of moderate to rough terrain.
Errors in depth computation
Authors: Stöckli R. F.
Published: October 2002

Field experience in various locations has shown that an assumption of subsurface isotropy is not always satisfactory. For example, Dunoyer de Segonzac and Laherrere (1959) stated that “Computations using vertical velocities, as derived from well velocity surveys, seemed to yield insufficient depths. On the other hand, the use of horizontal velocity, as derived from refraction traveltime curves, gave far too great depths. Both assumptions were obviously incorrect and it appeared essential to know the actual velocity along refracted oblique raypaths.” Northwood (1967) classified refraction interpretation errors into three main types: (1) those caused by incorrect reading of the data; (2) those caused by incorrect assumptions; and (3) those caused by incorrect geologic interpretation of the velocity layers. This note concerns type (2) errors. Its purpose is to show, in closed form, the errors made when computing the thickness of a layer with the refraction method, as a result of assigning an incorrect anisotropy to such a layer. In short, if a medium is composed of two layers separated by a horizontal interface at depth, and only the refraction traveltime graph is available, the computed depth depends upon the anisotropy assigned to the upper layer.
The Fourier transform of 1/r
Authors: Craig Maurice
Published: October 2002

Potential theory employs the Fourier integral [Formula: see text] where [Formula: see text]. Bhattacharyya (1966) obtained the value [Formula: see text] with the use of Bessel functions; the same argument has been repeated often in the geophysical literature (see Courant, 1961; Fuller, 1971; Lourenço, 1972; Gunn, 1975; Weil, 1976; Nabighian, 1984). The following alternative, short derivation involves only elementary functions and may, therefore, be of interest.
Archaeological prospection: An introduction to the Special Issue
Authors: Wynn Jeffrey C.
Published: October 2002

Archaeological prospection, as the use of geophysical methods in archaeology is known in Europe, is about four decades old (seven decades, if aerial photography of archaeological sites is included). Virtually the entire range of geophysical methods, perhaps excluding only borehole techniques, has found application in the search for archaeological sites unseen or partially known. Pressures by developers, and the public’s growing sensitivity toward the preservation of historic and prehistoric cultural artifacts and sites, has led to an accelerating use of high‐resolution geophysical methods in the archaeological sciences. The archaeogeophysical articles in this Special Issue are reasonably representative of the development of this specialty field of geophysics.
When reflection coefficients are zero
Authors: Levin F. K.
Published: October 2002

At certain angles of incidence, the amplitude of a plane compressional wave reflected from a plane interface separating two solids is zero. Here I consider as a function of incidence angle those combinations of densities, compressional‐wave velocities, and shear‐wave velocities that give rise to a vanishing reflection coefficient.
Application of the maximum‐likelihood method (MLM) for sonic velocity logging
Authors: Hsu Kai , Baggeroer Arthur B.
Published: October 2002

Modern digital sonic tools can record full waveforms using an array of receivers. The recorded waveforms are extremely complicated because wave components overlap in time. Conventional beamforming approaches, such as semblance processing, while robust, sometimes do not resolve the interfering wave components propagating at similar speeds, such as multiple compressional arrivals due to the formation alteration surrounding the borehole. Here the maximum‐likelihood method (MLM), a high‐resolution array processing algorithm, is modified and applied to process borehole array sonic data. Extensive modifications of the original MLM algorithm were necessary because of the transient character of the sonic data and its effect upon the spectral covariance matrix. We applied MLM to several array sonic data sets, including laboratory data, synthetic waveforms, and field data taken by a Schlumberger array sonic tool. MLM’s slowness resolution is demonstrated in resolving a secondary compressional arrival from the primary compressional arrival in an altered formation, and the formation compressional arrival in the presence of a stronger casing arrival in an unbonded cased hole. In comparison with the semblance processing results, the MLM results clearly show a better slowness resolution. However, in the case of a weak formation arrival, the semblance processing tends to enhance and resolve the weak arrival by the semblance normalization procedure, while the MLM, designed to estimate the signal strength, does not. The heavy computational requirement (mainly, many matrix inversions) in the MLM makes it much slower than semblance processing, which may prohibit implementation of the MLM algorithm in a real‐time environment.
Minimization of noise in electromagnetic exploration systems
Authors: McCracken K. G. , Oristaglio M. L. , Hohmann G. W.
Published: October 2002

The noise in electromagnetic (EM) surveys that originates in time‐dependent magnetic fields is quantified as a function of geographic location, season, and polarization. An overall variability of [Formula: see text] is observed. The variance of the observed geophysical data caused by this noise is quantified in terms of the noise bandwidth of the signal‐processing system. While a time‐domain EM (TEM) system has a wide bandwidth for the target (i.e., synchronous) signal, it has a narrow bandwidth for the asynchronous EM noise. A procedure is developed to compute the magnetic moment required to provide a specified ratio of signal to noise (S/N) in the survey data for frequency‐domain EM (FEM) and both step‐ response and impulse‐response TEM. This procedure indicates that magnetic moments in the range [Formula: see text] to [Formula: see text] are necessary for moving transmitter systems, and up to [Formula: see text] for fixed‐loop systems, for both frequency and time domain. A number of models of the overburden are established, and we show that the half‐space response is strongly dependent upon geology and weathering history. A variation of three orders of magnitude in the half‐space response occurs throughout the world. A procedure is defined to calculate the smallest target response detectable in the presence of a specified level of geologic noise. From this response we show that the overburden in the tropical and arid zones of the Earth strongly desensitizes the EM method. This is particularly severe for those styles of mineralization yielding short decay time constants. We conclude it would be impossible to detect targets with time constants <3 ms in substantial portions of the world’s arid zone using EM alone. An overall survey design procedure is defined that determines whether a specified target would be detectable in the presence of the prevailing geologic noise, and the magnetic moment that would be required to detect it in the presence of the anticipated EM noise. The manner in which the primary field corrupts both frequency‐ and time‐domain systems is also analyzed, and we conclude that the TEM method is essentially free of primary field effects, while the simpler forms of FEM can be corrupted by primary field effects which obscure targets with secondary responses that are less than 10 percent of the primary field.
Real data results of Kirchhoff elastic wave migration
Authors: Dai Ting‐Fan , Kuo John T.
Published: October 2002

Although Kirchhoff integral migration has attracted considerable attention for seismic data processing since the early 1970s, it, like all other seismic migration methods, is only applicable to compressional (P) waves. Because of a recent surge of interest in shear (S) waves, Kuo and Dai (1984) developed the Kirchhoff elastic (P and S) wave migration (KEWM) formulation and migration principle for the case of source and receiver noncoincidence. They obtained encouraging results using two‐dimensional (2-D) synthetic surface data from various geometric elastic models, including a dipping layer, a composite dipping and horizontal layer, and two layers over a half‐space.
Fluid pressure response to undrained compression in saturated sedimentary rock
Authors: Green Douglas H. , Wang Herbert F.
Published: October 2002

The pore pressure response of saturated porous rock subjected to undrained compression at low effective stresses are investigated theoretically and experimentally. This behavior is quantified by the undrained pore pressure buildup coefficient, [Formula: see text] where [Formula: see text] is fluid pressure, [Formula: see text] is confining pressure, and [Formula: see text] is the mass of fluid per unit bulk volume. The measured values for B for three sandstones and a dolomite arc near 1.0 at zero effective stress and decrease with increasing effective stress. In one sandstone, B is 0.62 at 13 MPa effective stress. These results agree with the theories of Gassmann (1951) and Bishop (1966), which assume a locally homogeneous solid framework. The decrease of B with increasing effective stress is probably related to crack closure and to high‐compressibility materials within the rock framework. The more general theories of Biot (1955) and Brown and Korringa (1975) introduce an additional parameter, the unjacketed pore compressibility, which can be determined from induced pore pressure results. Values of B close to 1 imply that under appropriate conditions within the crust, zones of low effective pressure characterized by low seismic wave velocity and high wave attenuation could exist. Also, in confined aquifer‐reservoir systems at very low effective stress states, the calculated specific storage coefficient is an order of magnitude larger than if less overpressured conditions prevailed.
Using multiparameter Born theory to obtain certain exact multiparameter inversion goals
Authors: Weglein Arthur B. , Violette Paul B. , Keho Timothy H.
Published: October 2002

Because no exact method exists for multiparameter, multidimensional seismic inversion, approximate methods based on variations of the Born approximation are significant. Artifacts which result from its linear nature limit the usefulness of multiparameter Born inversion. These artifacts can be identified by inferring from the differential equation that portion of the Fourier transformed data that is most consistent with the approximate linear Born relationship. When this portion of the data is inverted, the true parameter changes may be distinguished from linear artifacts.
Vertical seismic profiling depth migration of a salt dome flank
Authors: Whitmore N. D. , Lines Larry R.
Published: October 2002

Vertical seismic profiles (VSPs) can supply information about both velocity and subsurface interface locations. Properly designed VSPs can be used to map steeply dipping interfaces such as salt dome flanks. Mapping subsurface interfaces with VSP data requires careful survey design, appropriate data processing, interval velocity estimation, and reflector mapping. The first of these four ingredients is satisfied, in most cases, by preacquisition modeling. The second is accomplished by careful data processing. Initial velocity estimates are provided by seismic tomography. Velocity‐model refinement is accomplished by a combination of iterative modeling and iterative least‐squares inversion. Finally, the resultant interval velocities are used in depth migration of the processed VSP. These four ingredients have been combined to map a salt dome flank.
Theoretical vertical seismic profiling seismograms
Authors: Suprajitno M. , Greenhalgh S. A.
Published: October 2002

Offset vertical seismic profiling (VSP) theoretical seismograms which include multiples and mode conversions can be computed using a modified “reflectivity” method. In this method, the transformed displacement potentials are first calculated by multiplying the source spectrum by the composite reflectivity function. Integration over wavenumber, followed by inverse Fourier transformation over the frequency range of the signal, yields the synthetic trace. The composite reflectivity function for a buried receiver is derived from Kennett’s matrices (Kennett, 1974, 1979) which are synthesized to form phase‐related reflection and transmission coefficients from a layer stack. Both conventional fixed source‐moving receiver and fixed receiver‐walkaway source (multioffset) VSP geometries can be handled easily. The method can also readily accommodate deviated‐hole VSP. The method is general in that no ray needs to be specified. Because the order of the multiples can be controlled, wraparound problems with the discrete Fourier transform can be avoided. The normal‐incidence VSP seismograms can be rapidly generated as a special case. Several examples illustrate the method. Some classes of laterally varying structures can be approximately handled by restricting the range of ray‐angle integration and by using the principle of superposition.
Linearized inversion of multioffset seismic reflection data in the ω-k domain
Authors: Ikelle Luc T. , Diet Jean Paul , Tarantola Albert
Published: October 2002

In the acoustic approximation, the Earth is described using only density and bulk modulus. Assuming smooth density variations, reflections can be described using a single function—the velocity of compressional waves. If a reference model which is close enough to the actual Earth is known, the problem of estimating the medium velocity from the observed data can be linearized. Using a least‐squares formulation and working in the ω-k domain, the linearized inverse problem for a homogeneous reference medium can be solved by a noniterative algorithm which is economically competitive with prestack migration. Numerical tests with synthetic and real data demonstrate the feasibility and the numerical stability of the method. The numerical results compare well with those obtained by migration of unstacked data, although superior results will only be obtained when the physics of the problem (including elastic versus acoustic effects, three‐dimensional propagation, and accurate source estimation) will realistically be taken into account.
Geophone differencing to attenuate horizontally propagating noise
Authors: Knapp Ralph W.
Published: October 2002

Geophone differencing is a matter of taking the difference of the output response of two geophone elements that are vertically separated by a small distance. The primary purpose of this technique is to attenuate all horizontally propagating energy, such as ground roll, regardless of whether propagation is in line with the shot or out of the plane. The objective is met because horizontally propagating energy is received by the two elements in‐phase and is subtracted out. Vertically propagating energy, however, is slightly phase shifted due to the element separation. Differencing, rather than cancellation, results. The response operator of differencing depends upon several factors: (1) the vertical separation distance of the geophone elements; (2) the propagational velocity in the ground adjacent to and between the elements; (3) the distance of the upper element from the free surface; (4) the reflectivity of the free surface; and (5) the amplitude response of the lower geophone element relative to the response of the upper element. Models show that the best response may be obtained when the upper element is on or very near the free surface, and the other element is at a depth equal to half the shortest expected signal wavelength (highest frequency). Experimental results confirm the expectation that ground roll tends to be in‐phase with depth. In (mild) contrast with the model results, actual data show that best results might be obtained when the geophone elements are as close as possible, because the decay of ground‐roll amplitude depends upon wavelength and depth. Very shallow burial minimizes the amount of decay. How shallow the burial depth can be before it interferes with the reflection signal is unclear, although .9 m is not too shallow. Upcoming compressional (P)-waves are out‐of‐phase and have a reduced amplitude even when the geophone is buried only .9 m. Geophone differencing attenuates ground roll and does not adversely affect upcoming P-waves; it has a gentle high‐pass filtering effect on P-waves.
Plane‐layer prestack inversion in the presence of surface reverberation
Authors: McAulay Alastair D.
Published: October 2002

Experiments with synthetic data have indicated that generalized linear inversion may be used to estimate compressional velocities as a function of depth with high resolution directly from band‐limited, unstacked data. The ocean surface was not included in these experiments. In the presence of strong surface multiples, inversion is expected to take longer and be less accurate, because events from multiple surface reflections overlie primary events and normally have differing moveout. Existing velocity‐analysis techniques rely on the ability of an observer to make the difficult distinction between multiples and primaries. Equations are provided for adding the surface to the inversion procedure. This involves adding the surface effects to the Jacobian matrix as well as to the forward modeling procedure. To speed computation, the addition of the surface effects to the Jacobian matrix is delayed until after the matrix has been multiplied by a vector in the linear‐equation solution. Absorption is added to the inversion to represent the real world more closely and to improve computation speed by reducing sampling requirements. Realistic synthetic band‐limited data with high surface reverberation content were generated from a well‐log velocity profile. The inversion recovered the velocity profile to within 3 percent when a velocity increasing linearly with depth was used as a starting profile. The error in the model‐generated seismogram converges from 100 percent to within 2 percent of the reference data. The positions of interfaces are located more accurately at greater depths than at shallower depths because more sensors are observing deep strata than shallow strata. Convergence is to within 0.1 percent of that of the reference data at the maximum depth. The computation required 25 iterations and a total time of 66 hours on a DEC VAX 11/780. Reducing this time should be possible. In a preliminary study of the effects of noise, additive Gaussian noise was seen to limit the accuracy of the velocity estimate monotonically as the variance of the added noise was increased.
Low‐frequency radiation from point sources in a fluid‐filled borehole
Authors: Lee M. W.
Published: October 2002

Far‐field displacement fields have been derived for an impulsive point force acting on a fluid‐filled borehole wall under the assumption that the borehole diameter is small compared to the wavelength involved. The displacements due to an arbitrary source can be computed easily by combining the solutions for the impulsive sources. In general, the borehole source generates not only longitudinal and vertically polarized shear waves, but also horizontally polarized shear waves. This study also indicates that only the axisymmetric motion around the borehole due to normal stress is affected by the fluid in the borehole. In the long‐wavelength limit, the presence of the fluid does not affect the radiation from tangential sources into the surrounding medium.
Diffraction tomography and multisource holography applied to seismic imaging
Authors: Wu Ru‐Shan , Toksöz M. Nafi
Published: October 2002

Seismic tomography is emerging as an imaging method for determining subsurface structure. When the view‐angle coverage is limited and the scale of the medium inhomogeneities is comparable with the wavelength, as is often true in geophysical applications, the performance of ordinary ray tomography becomes poor. Other tomographic methods are needed to improve the imaging process. Here we study diffraction tomography and multisource holography and evaluate their performances for surface reflection profiling (SRP), vertical seismic profiling (VSP), and cross‐hole measurements. Theoretical formulations are derived for two‐dimensional geometry in terms of line sources along a source line and line receivers along a receiver line. The theory for diffraction tomography is based on the Born or Rytov approximation. The performances of diffraction tomography and multisource holography are evaluated by examining the information coverage in the spatial frequency domain and by numerical examples. Multisource holography, which is similar to Kirchhoff‐type migration, often gives distorted images of the object. This distortion causes long tails of the image in the case of SRP and a strong noise belt in the case of VSP and is due to incomplete and nonuniform coverage of the object spectrum. The filtering operation of diffraction tomography helps in correcting the nonuniform coverage (including duplication) of the object spectrum in the reconstruction process and therefore reduces the distortions. On the other hand, multisource holography is better suited for imaging sharp boundaries with large acoustic impedance contrasts since diffraction tomography is restricted, as presently formulated, to weak inhomogeneities. In addition, multisource holography has the flexibility to be used with an arbitrary number of sources (including a single source). Its sampling interval is not restricted by the Nyquist frequency. Numerical examples show that combined data sets (such as surface reflection data combined with VSP data, or cross‐hole data combined with surface data, etc.) improve the image quality.
Automatic phase correction of common‐midpoint stacked data
Authors: Levy S. , Oldenburg D. W.
Published: October 2002

The residual wavelet on a processed seismic section is often not zero phase despite all efforts to make it so. In this paper we adopt the convolutional model for the processed seismogram, assume that the residual phase shift can be approximated by a frequency‐independent constant, and use the varimax norm to generate an algorithm to estimate the residual phase directly. Application of our algorithm to reflectivities from well logs suggests that it should work in the majority of cases so long as the reflectivity is non‐Gaussian. An application of our algorithm to stacked data enhances the interpretability of the seismic section and leads to an improved match between the recovered relative acoustic impedance and a measured velocity log.
An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures
Authors: Jacobson R. S.
Published: October 2002

Despite many attenuation measurements which indicate a linear functional frequency dependence of absorption or constant [Formula: see text] in sediments, several theories predict no such linear dependence. The primary justification for rejecting a first‐power frequency dependence of attenuation is that it implies that seismic waves cannot propagate causally. Seismic waves must also travel with some velocity dispersion to satisfy causality, yet there is a lack of velocity dispersion measurements in sediments. In‐situ attenuation is caused by two distinct mechanisms: anelastic heating, and scattering due to interbed multiples. Apparent, or scattering, attenuation can produce both frequency‐dependent and non‐frequency‐dependent effects. Accurate measurements of attenuation and velocity dispersion are difficult; it is not surprising that a systematic investigation into the frequency dependence of absorption and velocity has not been made. A reinvestigation into two seismic refraction data sets collected over thickly stratified deep‐sea fans indicates that [Formula: see text] should not be assumed to be independent of frequency. Further, significant frequency‐independent absorption is present, indicating a high degree of apparent attenuation. Phase, or velocity, dispersion was also measured, but the results are more ambiguous than those for attenuation, due to inherent limitations of digital signals. Nevertheless, the absorption and velocity dispersion results are largely compatible, suggesting that if apparent attenuation is observed, then the scattered waves propagate causally.