bluuebunny/crossref_metadata_2025 huggingface dataset:
On: “Approximating subsurface structure in areas of severe subsea erosion — A nonprocessing technique” by F. W. Lishman, and M. N. Christos (GEOPHYSICS, 54, 1397–1409, November 1989).
Authors: Blyth C. J.
Published: October 2002

Two important questions were addressed in this paper. Firstly, how to construct an accurate model of a sea floor canyon — its topography and associated seismic velocities. Secondly, how the effects of such canyons can be accounted for in obtaining depths to subcanyon reflections using conventionally processed seismic data. An answer to the first question is required not only for deriving depths from conventional data but is equally required of the various canyon‐solving data processing methods listed in the paper (p. 1397). The second question is important, as the authors say, to provide a quick and inexpensive reconnaissance method of mapping structures in depth with reasonable accuracy.
Deconvolution of a directional marine source
Authors: Krail Paul M. , Shin Y.
Published: October 2002

A single source firing below the surface of the ocean, because of the surface reflection, has directionality. Directionality is defined as variation of amplitude with angle. Conceptually the radiation field of such a source may be treated as due to a vertical dipole of finite length. A formulation for transforming data recorded with a dipole wavelet to that of a monopole or plane‐wave wavelet is derived in this study. We have found that the cylindrical τ-p transform allows the removal of the source waveform and amplitude variation in the data due to the dipole and observed on the offset‐time record. The spherical wave field of a vertical dipole can be expanded in a conical bundle of plane waves. Accordingly, the recorded seismic data are transformed into a conical bundle of plane waves by the cylindrical τ-p transform. In this form the directionality effects of the vertical dipole are removed from the data. The formulation derived here was implemented in discrete form. A model study was conducted using synthetic dipole data and the results show the transformation to a monopole.
Mapping of Quaternary sediments in northeastern Ontario using ground electromagnetic methods
Authors: Palacky G. J. , Stephens L. E.
Published: October 2002

Since 1985, the Geological Survey of Canada has been evaluating the suitability of electromagnetic (EM) methods for Quaternary geologic mapping. Initially, a variety of ground EM instruments were tested at the Val Gagné, Ontario, site. The multifrequency horizontal‐loop equipment (APEX MaxMin I) was selected for transect surveys in the Kapuskasing‐Timmins area. After interpretation of ground EM results, 70 holes were drilled in the area using Rotasonic equipment. A correlation of drilling logs and geophysical data shows that clay, till, and sand have distinct EM responses. A constrained inversion of the ground EM data, in which drilling information was used to fix the layer thicknesses, yielded resistivity estimates for sediments encountered in boreholes. The following average resistivities were obtained: clay, 47 Ω⋅m; till, 123 Ω⋅m; sand, 251 Ω⋅m; the respective standard deviations were 7, 35, and 70 Ω⋅m. Resistivities of clays and tills were also determined in the laboratory on drill core samples. The results of the study indicate that resistivities of Quaternary sediments in northeastern Ontario are sufficiently stable to justify using EM methods for their identification. When layering is not too complex, inversion of EM data can be used to determine overburden thickness. For some applications, for which only qualitative scanning of bedrock topography is required (detection of bedrock valleys), ground EM techniques are a cost‐effective alternative to more accurate, but more expensive, seismic methods.
On: “Variable‐depth magnetization mapping: Application to the Athabasca basin, northern Alberta and Saskatchewan, Canada” by Mark Pilkington (GEOPHYSICS, 54, 1164–1179, September 1989)
Authors: Brod R. Jerry
Published: October 2002

The thrust of Pilkington’s paper is that a frequency‐domain approach to variable‐depth magnetization mapping is superior to a space‐domain approach and has been “shown to improve the geologic mapping capability over total‐field data.” He states that “apparent susceptivility or magnetization‐mapping methods have proven useful in improving the resolving power of total‐field magnetic data, leading to a more precise delineation of geologic boundaries and providing a map of susceptibility‐magnetization levels that can be related directly to rock properties.” He accepts the premise that northern Saskatchewan can be divided into domains on the basis of structure and lithology and that these “lithostructural domains can be distinguished on the basis of aeromagnetic character.”
Prestack amplitude analysis methodology and application to seismic bright spots in the Po Valley, Italy
Authors: Mazzotti Alfredo
Published: October 2002

The amplitude‐versus‐offset (AVO) characteristics of three separate bright spots on the same seismic section are analyzed. One of the bright spots results from a water‐bearing gravel layer, and the others correspond to gas‐saturated sandy beds. The amplitude analysis includes reflections from the entire range of incidence angles available from the survey; for the shallower amplitude anomaly, these angles reached values up to 66°. Extension of the analysis to longer offsets is aimed at detecting possible critical‐angle phenomena in order to reduce the uncertainty when the zero‐offset reflection’s polarity is unknown. The reflection from the gravel layer has this property. Its amplitude exhibits an initial decrease followed by a sudden rise in the AVO trend due to critical reflection and head waves. The gas‐related anomalies have a much different AVO characteristic, one in which the amplitude increases with offset distance. Two seismic events located above the bright spots were also investigated to further verify the validity of the seismic amplitude processing. The AVO trends of the three bright spots and of the two reference levels were compared with analogous trends of synthetic seismograms that were computed from models derived from borehole data.
Hole geometry and anisotropic effects on tube‐wave propagation: A quasi‐static study
Authors: Nicoletis L. M. A. , Bamberger A. , Quiblier J. A. , Joly P. , Kern M.
Published: October 2002

Tube‐wave characteristics, namely velocity and polarization, are affected by borehole anomalies related to nonhydrostatic tectonic stress. The anomalies we consider are borehole ellipticity, azimuthal anisotropy as modeled by a rotated transversely isotropic medium, and borehole breakouts as modeled by local heterogeneities in elastic properties. The low‐frequency tube‐wave velocity is obtained by a variational approach to a plane‐strain, static‐equilbrium problem. We solve the problem with hole ellipticity analytically and the problem with azimuthal anisotropy numerically by a finite‐element method. The results show that weak ellipticity has a negligible effect on the tube‐wave velocity: a relative variation of 10 percent in the main diameters of the hole produces a perturbation of only 0.5 percent in the velocity. However, localized damage to the hole can reduce tube‐wave velocity significantly. Furthermore, for tube‐wave polarization, it is unrealistic to obtain deviations from the radial direction greater than 15 degrees, which makes it difficult to obtain any valuable information on the stress directions from the tube wave.
Hyperbolic traveltime analysis of first arrivals in an azimuthally anisotropic medium: A physical modeling study
Authors: Ebrom D. A. , Tatham R. H. , Sekharan K. K. , McDonald J. A. , Gardner G. H. F.
Published: October 2002

Wave propagation in a fractured medium is modeled physically using layers of Plexiglas with thin films of water, held under moderate uniaxial confining pressure. The system exhibits anisotropy comparable to that of measured earth materials; i.e., shear‐wave splitting to waves with 3 percent velocity differences and P-wave directional anisotropy of at least 20 percent. SV polarizations demonstrate the concept of the shear‐wave window with the conversion of an SV body wave to an internal head wave with P-wave velocity, a head wave which is present in both the fractured medium and the control solid (unfractured) medium. For an azimuthally anisotropic medium, moveout curves are hyperbolic for a surface line oriented parallel to the fractures but are nonhyperbolic for a line oriented perpendicular to the fractures. Q anisotropy is observed in the system, with strongest attenuation on propagation paths perpendicular to the fractures.
Gravimetric terrain corrections by triangular‐element method
Authors: Zhou X. , Zhong B. , Li X.
Published: October 2002

Terrain corrections for gravity data are a critical concern in rugged topography, because the magnitude of the corrections may be large relative to the anomalies of interest. The terrain‐correction process, however, is very tedious. At present, rectangular prism and fan‐shaped prism methods are commonly used for the corrections; but these methods assume elements have horizontal tops, an assumption which does not reflect true topography, especially near the station. A triangular‐element method which allows dipping surfaces has been developed using a Gaussian formulation to improve the correction process. This method involves a simple formula employing a surface rather than a volume integral for computing the terrain corrections with high accuracy.
Two‐dimensional mapping of sea‐ice keels with airborne electromagnetics
Authors: Liu Guimin , Becker Alex
Published: October 2002

Airborne electromagnetic (AEM) equipment can be used to sense sea ice thickness by interpreting the AEM data to obtain the distance from the towed bird that holds the EM system to the ice/seawater interface. The ice thickness itself is obtained by subtracting from that quantity the distance from the bird to the upper ice surface, as determined by a laser altimeter. To interpret AEM data acquired over sea‐ice keels, we first solve the forward problem using an integral equation approach to the Neumann boundary‐value problem. In this approach, we assume that sea ice is an insulator and that seawater is a perfect conductor. When the ice keel is two‐dimensional, the pertinent equations can be transformed into the wavenumber domain along the strike direction, resulting in the rapid numerical computation of the AEM response. By compiling numerical‐model results, we constructed an interpretation chart that relates the parameters of the observed AEM response anomaly to the geometric variables of the ice keel. The strike length of the ice keel should be about three times the bird height above the Ice‐water interface, so that the assumption of two‐dimensionality holds. The use of the chart has been verified by interpreting field AEM data.
Background restoration of dip‐filtered data
Authors: Hornbostel S. C. , Bishop G. W.
Published: October 2002

Coherent linear scattering noise frequently corrupts stacked seismic data (Larner et al., 1983). In general, data may be thought of as having three parts: coherent signal, coherent noise, and incoherent background noise. Coherent noise is often attacked with prestack or poststack dip filtering, which also affects the incoherent background noise. Specifically, when coherent noise is dip filtered, the same dips are filtered out of the background noise as well.
Three‐dimensional gravity or magnetic constrained depth inversion with lateral and vertical variation of contrast
Authors: Chenot D. , Debeglia N.
Published: October 2002

Depth‐mapping inversion of gravity or magnetic fields generally assumes that anomalies originate from a main density or magnetization contrast interface. This particular inversion takes into account inhomogeneous density or magnetization distributions reflecting sediment compaction and basement heterogeneities: above the interface, the density can be approximated by an exponential function, and below it, an intrabasement contrast map can be used. The inversion also integrates local depth constraints from wells or seismic data, as well as general constraints set on the geometry and the contrast of the interface. After field transformations, spectral analysis and constraints help to define a starting model characterized mainly by the interface mean depth and the mean parameter contrast between the two media. The depth adjustment is completed iteratively under constraints using a space‐domain formulation derived from the Bouguer‐slab approximation. The interface model effect is computed in the wavenumber domain. A model data example shows the accuracy of the inversion and illustrates the role of the constraints. In a field example of a basin area where constraints can be derived from numerous well data, successive inversions of gravity data result in an isodepth map of the basement. The compatibility of the map with local depth constraints from wells is obtained by taking into account density heterogeneities related to known lithologic variations in the basement.
An automated method for the interpretation of magnetic vertical‐gradient anomalies
Authors: Keating Pierre B. , Pilkington Mark
Published: October 2002

The use of airborne magnetic vertical‐gradient surveys is increasing. Interpretation, however, is mostly used qualitatively as an aid to geologic mapping. Presently, quantitative interpretation techniques are based on the analysis of isolated anomalies. In this paper, we develop a numerical method for interpreting the magnetic vertical‐gradient anomalies of dipping dikes and planar geologic contacts. The method is based on a linearization of the equations describing these anomalies. The solution can be used to interpret isolated anomalies or whole profiles in a Werner‐style deconvolution. Using data from the Val d’Or mining area (Canada), we have calculated magnetic models to test the interpretation technique. Magnetic vertical‐gradient profiles calculated from the interpreted models closely match the observed data.
Magnetic forward models of Cement oil field, Oklahoma, based on rock magnetic, geochemical, and petrologic constraints
Authors: Reynolds R. L. , Webring M. , Grauch V. J. S. , Tuttle M.
Published: October 2002

Magnetic forward models of the Cement oil field, Oklahoma, were generated to assess the possibility that ferrimagnetic pyrrhotite related to hydrocarbon seepage in the upper 1 km of Permian strata contributes to aeromagnetic anomalies at Cement. Six bodies having different magnetizations were constructed for the magnetic models, based on geology and on petrologic and geochemical results, supplemented by rock magnetic measurements of shallow‐core and outcrop samples. The column of rock through which hydrocarbons have passed is divided into three sulfide zones on the basis of pyrrhotite content, and the column is capped by a 30 m thick zone that contains ferric oxide minerals formed mainly from oxidized pyrite. Red beds unaffected by sulfidization, as well as a zone of rock depleted in hematite but lacking sulfide, surround sulfidic zones. The synthetic magnetic profiles are controlled mainly by pyrrhotite‐bearing strata at depths of 200–500 m. The magnetizations of these bodies are calculated from: (1) petrographic estimates of pyrrhotite content relative to pyrite; (2) content of sulfide sulfur determined from chemical analysis; and (3) values for the magnetic susceptibility of monoclinic pyrrhotite. Total magnetizations of the bodies of highest pyrrhotite content range from about [Formula: see text] to [Formula: see text] in the present field direction and yield magnetic anomalies (at 120 m altitude) having amplitudes of less than 1 nT to ∼6 to 7 nT, respectively. Such amplitudes are much lower than those (as high as 60 nT) reported from the original total‐field survey over the Cement field. Numerous assumptions were made in the generation of the models, and thus the results neither prove nor disprove the existence of aeromagnetic anomalies related to hydrocarbon seepage at Cement. Nevertheless, the results suggest that pyrrhotite, formed via hydrocarbon reactions and within a range of concentrations estimated at Cement, is capable of causing magnetic anomalies.
Model studies of shallow common‐offset seismic data
Authors: Wilson Thomas H.
Published: October 2002

For simplicity, optimum‐window common‐offset data‐acquisition procedures are frequently employed to collect near‐surface, high‐resolution, seismic reflection data. However, because of large incidence angles, interpretations of the data often cannot be evaluated accurately using zero‐offset simulations alone. Common‐offset hammer seismic data collected in the central Appalachian plateau province of West Virginia are examined in this paper. Synthetic shot records using a minimum‐phase wavelet estimated from the data and subsurface acoustic properties derived from full‐waveform and other geophysical logs are used to simulate the offset seismic response of near‐surface, coal‐bearing Pennsylvanian aged rocks. Zoeppritz equations are used to model amplitudes. This study indicates that offset simulations may be required to determine the origins of events observed at a given offset. Offset simulations also help determine whether amplitude variations with offset have a significant effect on the appearance of events observed at the optimum offset. The offset seismic response is significantly different from the zero‐offset response for reflections arising from depths less than about two‐thirds of the offset distance; for greater depths, zero‐offset simulations adequately approximate the offset response.
Amplitude preservation equations for dip moveout
Authors: Gardner G. H. F. , Forel David
Published: October 2002

Kinematic equations for a velocity‐independent dip moveout (DMO) transformation were given by Forel and Gardner [1988, equations (1) and (2)]. An augmented set of equations is derived in this note which specifies one way in which a physical meaning for the amplitude can be preserved through DMO.
SH waves from point sources in anisotropic inhomogeneous media
Authors: Ben‐Menahem Ari
Published: October 2002

During the past decade, there has been renewed interest in seismic wave propagation in anisotropic media. Traveltime analyses of improved shear‐wave data gave evidence for shear‐wave splitting consistent with azimuthal isotropy (or transverse isotropy with vertical axis of symmetry) in both sedimentary rocks and the earth's deep mantle (Jones and Wang, 1981; Crampin, 1985; Winterstein, 1986). Numerical solutions to line sources in a half‐space (Kraut, 1963) and asymptotic plane‐wave theory in multilayered media (e.g., Garmany, 1988) were set up; however, a source‐amplitude theory is lacking, without which no sound physical understanding of the problem can be achieved. In the present note, I endeavor to demonstrate how simple analytical solutions are able to illuminate the intricate interrelations between inhomogeneity and anisotropy.
Gravity anomaly separation by Wiener filtering
Authors: Pawlowski R. S. , Hansen R. O.
Published: October 2002

We introduce a gravity anomaly separation method based on frequency‐domain Wiener filtering. Gravity anomaly separation can be effected by such wavelength filtering when the gravity response from the geologic feature of interest (the signal) dominates one region (or spectral band) of the observed gravity field’s power spectrum. The Wiener filter is preferable to a conventional band‐pass filter because geologic information from the study area can be incorporated to a greater extent in specifying the filter’s transfer function. Our method differs from previous Wiener filtering schemes in that it provides, through direct modeling of known geology (e.g., outcrop and borehole data), a more objective estimate of the signal power spectrum required for defining the transfer function of the filter. We illustrate the technique first with synthetic data, and then with a field example from the southern Paradox basin. The Paradox basin example reveals the limitation inherent to all wavelength filtering which results from spectral overlap between the gravity signal and the spectral contributions of other geologic sources. In the study area, significant spectral overlap occurs between the gravity effects of sources in the Precambrian basement and the gravity signal arising from the density contrast across the Mississippian‐Pennsylvanian interface.
General theory and comparative anatomy of dip moveout
Authors: Liner Christopher L.
Published: October 2002

It is possible to derive a general formula for constant‐velocity, two‐dimensional dip moveout (DMO). This serves to unify the many published forms of DMO. Known results for common‐offset and shot profile DMO are special cases of the general formula. The analysis is based on the dip‐corrected NMO equation, and thus is a kinematic DMO theory. Using a logarithmic stretch of the time axis, efficient fast Fourier transform (FFT) common‐offset DMO algorithms can be derived. In the published versions, log variables are introduced into the NMO equation. It can be shown that the resulting impulse response departs from the DMO ellipse, which means that some dips have been improperly handled. A new log‐stretch formulation (exact log DMO) which preserves the DMO ellipse can be derived by starting with the analytic impulse response, rather than the NMO equation. Tests on field data indicate that exact log DMO handles shallow, steeply dipping events in agreement with Hale’s DMO, while the other log‐stretch algorithms degrade these events. In situations where constant‐velocity DMO is viable, exact log DMO can be used to create a Hale‐quality image at FFT speed.
Frequency‐domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging
Authors: Pratt R. Gerhard
Published: October 2002

The migration, imaging, or inversion of wide‐aperture cross‐hole data depends on the ability to model wave propagation in complex media for multiple source positions. Computational costs can be considerably reduced in frequency‐domain imaging by modeling the frequency‐domain steady‐state equations, rather than the time‐domain equations of motion. I develop a frequency‐domain approach in this note that is competitive with time‐domain modeling when solutions for multiple sources are required or when only a limited number of frequency components of the solution are required.
Processing, correlating, and interpreting converted shear waves from borehole data in southern Alberta
Authors: Geis W. T. , Stewart R. R. , Jones M. J. , Katapodis P. E.
Published: October 2002

Borehole measurements coupled with phase information from Zoeppritz equation modeling has assisted in accurate correlation between a VSP converted S-wave section and both the surface and VSP P-wave sections from southern Alberta. For the most part, both the character and polarities of the sections agree; however, there are some differences. Some reflections are stronger and more distinct on the S-wave section than on the P-wave section. Spectral analysis of the time‐domain upgoing P-wave and S-wave energy shows that the frequency content of the S-waves is comparable to the P-waves. Thus, the slower velocity S-waves have a shorter wavelenght and provide better vertical resolution of some interfaces. Other upgoing S-wave modes can interfere with the P‐SV mode and contribute to the differences between the P- and S-wave sections. The match between P-wave and S-wave velocities ([Formula: see text] and [Formula: see text]), determined from VSP traveltime inversion and the full‐waveform sonic log, is best in the Paleozoic carbonate section; there is some discrepancy in Cretaceous sandstone intervals. A basal salt unit in the Paleozoic Beaverhill Lake formation has a VSP‐determined [Formula: see text] ratio of 1.97, suggesting that salt can be distinguished from carbonates using both P-wave and S-wave velocity information in this region.
Static corrections from shallow‐reflection surveys
Authors: Steeples D. W. , Miller R. D. , Black R. A.
Published: October 2002

Shallow seismic reflection surveys can assist in determination of velocity and/or thickness variations in near‐surface layers. Static corrections to seismic reflection data compensate for velocity and thickness variations within the “weathered zone.” An uncompensated weathered‐layer thickness variation on the order of 1 m across the length of a geophone array can distort the spectrum of the signal and result in aberrations on final stacked data. P-wave velocities in areas where the weathered zone is composed of unconsolidated materials can be substantially less than the velocity of sound in air. Weathered‐layer thickness variation of 1 m in these low‐velocity materials could result in a static anomaly in excess of 3 ms. Shallow‐reflection data from the Texas panhandle illustrate a real geologic situation with sufficient variability in the near surface to significantly affect seismic signal reflected from depths commonly targeted by conventional reflection surveys. Synthetic data approximating a conventional reflection survey combined with a weathered‐layer model generated from shallow‐reflection data show the possible dramatic static effects of alluvium. Shallow high‐resolution reflection surveys can be used both to determine the severity of intra‐array statics and to assist in the design of a filter to remove much of the distortion such statics cause on deeper reflection data. The static effects of unconsolidated materials can be even more dramatic on S-wave reflection surveys than on comparable P-wave surveys.
Decomposition into minimum and maximum phase components
Authors: Eisner E. , Hampson G.
Published: October 2002

In this paper we give a new solution to the problem of factoring p′(t) = a(t) * b(−t) * δ(t−τ) into its maximum‐phase, minimum‐phase, and pure‐delay components. Our method is based on the “winding number” and the solution of three Toeplitz systems of equations. First we use the winding number from complex analysis to estimate the pure‐delay component, which we subsequently remove using [Formula: see text]. Then we solve the symmetrical Toeplitz system of equations, considering only t ⩾ 0, [Formula: see text] to get [Formula: see text]. Finally, we similarly solve the two asymmetrical Toeplitz systems of equations, [Formula: see text] for a(t) and [Formula: see text] for b(t). The practical effectiveness of the method is confirmed by application to a synthetic waveform and to an air‐gun signature. When stabilization of the Toeplitz solution is required, we find that it is important to be frugal with the addition of white noise. The computation of the winding number is robust.
Estimates of virgin rock temperature derived from BHT measurements: Bias and error
Authors: Hermanrud C. , Cao S. , Lerche I.
Published: October 2002

Virgin rock temperatures are important to hydrocarbon exploration, as these temperatures are necessary for the computation of source rock temperatures, and for hydrocarbon generation computations. Several methods have been developed for determination of virgin rock temperatures from maximum temperatures recorded during logging in the past decades. This paper describes an investigation where the calculated virgin rock temperatures from several different methods were examined for bias and accuracy using 18 different measurement series at the Oseberg field. The temperatures were corrected for different depths of burial, and then compared with each other and with drill stem test (DST) measurements to investigate the inaccuracy of the methods. The most advanced methods gave values close to the DST temperatures on average, but with standard deviations as high as 9° C. The less advanced models (like the Horner plot method) have systematically too low virgin rock temperatures (by about 8° C) for the Oseberg field, with standard deviations of 8° C. The errors in calculated virgin rock temperatures are large enough to completely alter predictions of hydrocarbon generation in an area. The large errors are attributed to poor quality data and to physical effects that are not properly taken into account in the temperature calculations. Improved sampling of temperature data can probably reduce the errors to some extent.
A new system for acquisition and processing of very high‐resolution seismic reflection data
Authors: Lericolais G. , Allenou J. P. , Berné S. , Morvan P.
Published: October 2002

A new digital seismic data acquisition system and accompanying software have been developed by Ifremer to replace the analog equipment commonly used in very high‐resolution (less than 1 m) shallow marine seismic reflection surveys. The acquisition part, based on a Hewlett‐Packard 9000 microcomputer, is capable of sampling rates of up to 15 kHz for one channel. Signal processing and image processing can be performed either during the survey by the acquisition computer or after the survey with a software system that runs on a Sun workstation. The system has been developed for the specific requirements of coastal studies; understanding of the sediment layers in such studies requires a vertical resolution of around 1 m in the top 10 m of sediment. This system has been successfully used for the study of subtidal sand waves off the Cherbourg peninsula (France). The results, which revealed the internal structure of sand waves from about 3 m to 8 m high, correlated well with synthetic seismograms that were created using data from core studies of the survey area.
Transient electromagnetic responses of surficial, polarizable patches
Authors: Hohmann G. W. , Newman G. A.
Published: October 2002

Abnormal decay curves that are depressed or change sign often are observed in coincident‐loop and central‐loop transient electromagnetic (TEM) measurements, particularly in areas of conductive overburden. With the publication of papers by Smith and West (1989a, b) and Flis et al. (1989), the phenomenon, which is due to induced polarization (IP) in near‐surface, weakly polarizable material such as clay, is well understood.
The spectrum of GPS measurement errors and the accuracy of airborne gravity measurements
Authors: Bower D. R. , Kouba J. , Beach R. J.
Published: October 2002

Recent observations (Georgiadou and Kleusberg, 1987; Kleusberg et al., 1989) suggest that errors in GPS carrier phase observations at frequencies within the gravity passband of airborne gravity systems may be due mainly to multipath interference. Further, the power spectral density (PSD) of these errors has been found to fall off rapidly with increase in frequency throughout the anticipated gravity passband, in the manner of a red spectrum rather than a white (which remains constant). It is shown that this implies a much greater allowable error in GPS‐derived altitude reference than would be the case if the PSD of altitude errors (1) was white, (2) had the same shape as that of typical aircraft vertical motion, or (3) was dominated by a sinusoidal wave located near the high frequency limit of the gravity passband. This enhances the feasibility of airborne gravity for regional scale surveys and perhaps explains why actual measurements have been better than predicted. For example, given a uniform [Formula: see text] distribution of spectral noise power and a speed to grid‐width ratio of 60 per hour, an rms altitude error as large as 12 cm will still allow the computation of acceleration correction with an accuracy of 2 mGal. For the same conditions, the allowable rms altitude error given a white distribution of spectral noise power is 1.5 cm.
Recommended standard for seismic (/radar) data files in the personal computer environment
Authors: Pullan S. E.
Published: October 2002

This paper is the result of the work of a subcommittee of SEG’s Engineering and Groundwater Geophysics Committee. It recommends a data file format for raw or processed shallow seismic or digital radar data in the small computer environment. It is recommended that this format be known as the SEG-2 format.
A least‐squares minimization approach to invert gravity data
Authors: Abdelrahman E. M. , Bayoumi A. I. , El‐Araby H. M.
Published: October 2002

The interpretation of gravity data often involves initial steps to eliminate or attenuate unwanted field components in order to isolate the desired anomaly (e.g., residual‐regional separations). These initial filtering operations include, for example, the radial weights methods (Griffin, 1949; Elkins, 1951; Abdelrahman et al., 1990), the fast Fourier transform methods (Bhattacharyya, 1965; Clarke, 1969; Meskó, 1969, 1984, Botezatu, 1970), the rational approximation techniques (Agarwal and Lal, 1971) and recursion filters (Bhattacharyya, 1976), and the bicubic spline approximation techniques (Bhattacharyya, 1969; Inoue, 1986). The derived local gravity anomalies are then geologically interpreted to derive depth estimates, often without properly accounting for the uncertainties introduced by the filtering process. When filters are applied to observed data, the filters often cause serious distortions in the shape of the gravity anomalies (Hammer, 1977). Thus the filtered gravity anomalies generally yield unreliable geologic interpretations (Rao and Radhakrishnamurthy, 1965; Hammer, 1977; Abdelrahman et al., 1985, 1989.
Amplitude‐versus‐offset measurement errors in a finely layered medium
Authors: Swan Herbert W.
Published: October 2002

Recently Spratt (1987) showed how amplitude‐versus‐offset analysis (AVO) can be sensitive to small residual velocity errors. However, even when the velocity is determined perfectly, serious AVO distortions remain due to normal‐moveout stretch, differential tuning as a function of offset, spherical divergence, and source and receiver directivity patterns. I have found that all of these errors can be expanded in a Taylor series about the zero‐offset event time, assuming it is much larger than the wavelet width. The first term of this series represents the residual velocity error term found by Spratt, while the second term encompasses the remaining effects mentioned. In practice, either term can be larger than the underlying amplitude variations being estimated. For example, Ricker wavelet stretch leads to a peak AVO error which is 61 percent of the peak zero‐offset reflectivity, even though the velocity field is uniform and correct. This result is independent of the wavelet frequency, and the range of incidence angles used in the analysis. Positive gradients in moveout velocity amplify this error, while narrowband filtering of the data prior to AVO analysis greatly widens its temporal extent. Aligning a particular event with static shifts instead of normal‐moveout correction can eliminate stretch, but not differential tuning error, in a finely layered target zone whose wavelets overlap.
Effects of averaging and sampling on the statistics of reflection coefficients
Authors: Hsu K. , Burridge R.
Published: October 2002

The reflection coefficients derived from sonic and density logs are frequently used in seismic exploration. Even though they measure the in‐situ formation slowness and density, sonic and density tools do not measure the exact, continuous formation properties but locally averaged properties sampled at discrete depth points. Furthermore, the logs are frequently reinterpolated to form a Goupillaud medium for many applications such as synthetic seismogram computation. Both the logging tools and the Goupillaud interpolation introduce averaging and sampling effects into the reflection coefficients and significantly alter the autocorrelation of the reflection coefficient sequence. Analytical formulas are derived to show how the autocorrelation is altered and to calculate how the autocorrelation depends on the averaging and sampling intervals. Essentially, these effects impose sincsquared envelopes on the power spectrum of the reflection coefficient sequence and alias high‐frequency components to low‐frequency components in the spectral domain. These findings are verified using synthetic and real examples.
On: “Experimental studies on downhole seismic sources” by S. T. Chen, E. A. Eriksen, and M. A. Miller (GEOPHYSICS, 55, 1645–51, December 1990)
Authors: Levin F. K.
Published: October 2002

Recording on the surface with a source in wells near Friendswood, Texas and Sego Canyon, Utah, Chen et al. found that log‐log plots of the amplitude of the direct arrival against distance yielded straight lines with slopes of −2.14. A 1958 paper by the Ralph Lynn and me (Levin and Lynn, 1958) included log‐log plots of first arrival amplitudes against traveltimes for eight wells, mostly wells in western United States. We obtained straight lines with average slopes of −2.38 and −2.26. By present standards, our wells were shallow and velocities did not vary greatly within a well. In view of the limited accuracy explosive, nonreproducible sources and paper records allowed, our result confirm those of Chen et al.
Induced polarization of shaly sands: Salinity domain modeling by double embedding of the effective medium theory
Authors: Samstag F. J. , Morgan F. D.
Published: October 2002

A modeling technique is proposed that assumes a typical shaly sand to be a three‐phase porous mixture: water, quartz, and clay. The complex conductivity of such a mixture can be modeled with an equation containing only the complex conductivity of each constituent and the geometry of the pore structure. The effective medium theory provides the basis for such a model. The model typically handles two phases at a time, but one of the phases can be considered as a submixture and then the model is simply applied again after the first inversion to determine the properties of the submixture. In the first inversion, the two phases are water and matrix. For the second inversion, the matrix conductivities are modeled by a mixture of quartz and clay. The present work relies on a published data set of 19 samples, with measurements as a function of salinity taken at constant frequency (Vinegar and Waxman, 1984). The proposed technique fit this data better than the Vinegar‐Waxman model which requires more variables. Moreover, this “double embedding” procedure yields realistic values for clay conductivity, clay dielectric constant, and fractional volume of clay.
3-D depth migration via McClellan transformations
Authors: Hale Dave
Published: October 2002

Three‐dimensional seismic wavefields may be extrapolated in depth, one frequency at a time, by two‐dimensional convolution with a circularly symmetric, frequency‐ and velocity‐dependent filter. This depth extrapolation, performed for each frequency independently, lies at the heart of 3-D finite‐difference depth migration. The computational efficiency of 3-D depth migration depends directly on the efficiency of this depth extrapolation. McClellan transformations provide an efficient method for both designing and implementing two‐dimensional digital filters that have a particular form of symmetry, such as the circularly symmetric depth extrapolation filters used in 3-D depth migration. Given the coefficients of one‐dimensional, frequency‐ and velocity‐dependent filters used to accomplish 2-D depth migration, McClellan transformations lead to a simple and efficient algorithm for 3-D depth migration. 3-D depth migration via McClellan transformations is simple because the coefficients of two‐dimensional depth extrapolation filters are never explicitly computed or stored; only the coefficients of the corresponding one‐dimensional filter are required. The algorithm is computationally efficient because the cost of applying the two‐dimensional extrapolation filter via McClellan transformations increases only linearly with the number of coefficients N in the corresponding one‐dimensional filter. This efficiency is not intuitively obvious, because the cost of convolution with a two‐dimensional filter is generally proportional to [Formula: see text]. Computational efficiency is particularly important for 3-D depth migration, for which long extrapolation filters (large N) may be required for accurate imaging of steep reflectors.
Exact results for generalized Gassmann’s equations in composite porous media with two constituents
Authors: Berryman James G. , Milton Graeme W.
Published: October 2002

Wave propagation in fluid‐filled porous media is goverened by Bilot's equations of poroelasticity. Gassmann's relation gives an exact formula for the poroelastic parameters when the porous contains only one type of solid constituent. The present paper generalizes Gassmann's relation and derives exact formulas for two elastic parameters needed to describe wave propagation in a conglomerate of two porous phases. The parameters were first introduced by Brown and Korringa when they derived a generalized form of Gassmann's equation for conglomerates. These elastic parameters are the bulk modulus [Formula: see text] associated with changes in the overall volume of the conglomerate and the bulk modulus [Formula: see text] associated with the pore volume when the fluid pressure [Formula: see text] and confining pressure (p) are increased, keeping the differential pressure [Formula: see text] fixed. These moduli are properties of the composite solid frame (drained of fluid) and are shown here to be completely determined in terms of the bulk moduli associated with the two solid constituents, the bulk moduli of the drained conglomerate and the drained phases, and the porosities in each phase. The pore structure of each phase is assumed uniform and smaller than the grain size in the conglomerate. The relations found are completely independent of the pore microstructure and provide a means of analyzing experimental data. The key idea leading to the exact results is this: Whenever two scalar fields (in our problem [Formula: see text] and [Formula: see text]) can be independently varied in a linear composite containing only two constituents, there exists a special value γ of the increment ratio for these two fields corresponding to an overall expansion or contraction of the medium with no change of relative shape. This fact guarantees that a set of consistency relations exists among the constituent moduli and the effective moduli, which then determines all but one of the effective constants. Thus, [Formula: see text] and [Formula: see text] are determined in terms of the drained frame modulus K and the constituents’ moduli. Because the composite is linear, the coefficients found for the special value of the increment ratio are also the exact coefficients for an arbitrary ratio. Since modulus K is commonly measured while the other two are not, these exact relations provide a significant advance in our ability to predict the response of porous materials to pressure changes. It is also shown that additional results (such as rigorous bounds on the parameters) may be easily obtained by exploiting an analogy between the equations of thermoelasticity and those of poroelasticity. The method used to derive these results may also be used to find exact expressions for three component composite porous materials when thermoelastic constants of the components and the composite are known.
2-D Bayesian deconvolution
Authors: Lavielle Marc
Published: October 2002

Inverse problems can be solved in different ways. One way is to define natural criteria of good recovery and build an objective function to be minimized. If, instead, we prefer a Bayesian approach, inversion can be formulated as an estimation problem where a priori information is introduced and the a posteriori distribution of the unobserved variables is maximized. When this distribution is a Gibbs distribution, these two methods are equivalent. Furthermore, global optimization of the objective function can be performed with a Monte Carlo technique, in spite of the presence of numerous local minima. Application to multitrace deconvolution is proposed. In traditional 1-D deconvolution, a set of uni‐dimensional processes models the seismic data, while a Markov random field is used for 2-D deconvolution. In fact, the introduction of a neighborhood system permits one to model the layer structure that exists in the earth and to obtain solutions that present lateral coherency. Moreover, optimization of an appropriated objective function by simulated annealing allows one to control the fit with the input data as well as the spatial distribution of the reflectors. Extension to 3-D deconvolution is straightforward.
Spatial prediction filtering in the t-x and f-x domains
Authors: Hornbostel Scott
Published: October 2002

The predictability of seismic signals from nearby traces can be a powerful tool for reducing random or locally coherent noise. The choice of algorithm to reduce noise for a given application is a function of the data signal and noise characteristics. When the signal and noise are relatively consistent over a given design window, an f-x domain Wiener‐filter approach can be used. For cases in which the data are time‐ or space‐varying, a new approach using 2-D adaptive filtering in the t-x domain can be very effective. In either of these approaches, a prediction trace‐gap can often be successfully used to remove locally coherent noise when lateral signal changes are not too rapid.
Theory of a 2.5-D acoustic wave equation for constant density media
Authors: Liner Christopher L.
Published: October 2002

The theory of 2.5-dimensional (2.5-D) wave propagation (Bleistein, 1986) allows efficient computation of 3-D wavefields in c(x, z) acoustic media when the source and receivers lie in a common y-plane (assumed to be y = 0 in this paper). It is really a method of efficiently computing an inplane 3-D wavefield in media with one symmetry axis. The idea is to raytrace the wavefield in the (x, z)-plane while allowing for out‐of‐plane spreading. In this way 3-D amplitude decay is honored without 3-D ray tracing. This theory has its conceptual origin in work by Ursin (1978) and Hubral (1978). Bleistein (1986) gives an excellent overview and detailed reference to earlier work.
The Fresnel zone for P-SV waves
Authors: Eaton David W. S. , Stewart Robert R. , Harrison Mark P.
Published: October 2002

Mode‐converted (P-SV) reflections in field data contain information about an area on the reflecting boundary, rather than a single point. For unmigrated data, the total area contributing to the observed reflection amplitude is approximated by the Fresnel zone. We derive formulas for the P-SV Fresnel‐zone radius for both surface and VSP geometries. In the surface case, the Fresnel radius can be expressed in a form similar to that of the P-P case by substitution of the P-SV single‐layer migration velocity. Numerical modeling shows that the relative changes in size and shape of the P-SV Fresnel zone as a function of offset are not large and are comparable to the P-P case. For a given depth and frequency, the P-SV Fresnel radius is smaller than the P-P Fresnel radius by a factor of about 0.8; hence the lateral resolution of converted‐wave (P-SV) data may be somewhat better than the P-P data. Two sample calculations using field data are presented. For the VSP example, the P-SV Fresnel radius (184 m) is smaller than the corresponding P-P Fresnel radius (231 m), but for the surface example the two are similar (315 m and 295 m, respectively), because of differences in the frequency contents of the reflected P and SV waveforms.
The output of predictive deconvolution
Authors: Ulrych T. J. , Matsuoka T.
Published: October 2002

The method of predictive deconvolution, with prediction distance greater than unity, is widely used in the oil industry to eliminate multiple reflections from seismic reflection data. When the prediction distance is unity the method corresponds to autoregressive modeling. In this case the output of the deconvolution becomes the reflectivity series of the subsurface for a minimum‐phase wavelet. For prediction distances greater than unity, prediction filters are related recursively (Ulrych et al., 1973). We show that another interesting relationship exists between the autoregressive prediction error operator and the prediction error operator with arbitrary prediction distance. This relationship can be used to investigate the output of predictive deconvolution applied to nonminimum‐phase wavelets. As a consequence, we can show that predictive deconvolution and the phase correction method for Vibroseis data (Ristow and Jurczyk, 1975) are nearly identical.