bluuebunny/crossref_metadata_2025 huggingface dataset:
Simple data processing procedures for seismic section noise reduction
Authors: Shon Howoong , Yamamoto Tokuo
Published: October 2002

Seismic traces are signals composed of information and noise. In essence, the part of the data set that is noise obscures the information and complicates the processing and interpretation of the seismic traces. Of the two procedures discussed, one is maximum standard deviation for an optimum threshold, and the other is the data transformation by variance. Either or both procedures can be used to enhance signal‐to‐noise (S/N) ratio. The procedures are data processing steps that are applied to each trace. Examples of successful application of the procedures are presented.
Application of high‐resolution seismics in studying reservoir characteristics of hydrocarbon deposits in Hungary
Authors: Albu István , Pápa Antal
Published: October 2002

In preparing for the production of hydrocarbons, there is an increasing demand for surface geophysics. We studied the potential of seismic reflection—and within this, how to increase resolution—when the reservoir is very inhomogeneous and is covered with a thick (∼2 km) young sedimentary sequence of high energy absorption. For high and nearly uniform resolution the lower frequency limit of sweep should be increased to at least 16–18 Hz, in addition to extending the frequency band upward. We carried out measurements over a gas‐capped reservoir made up of Badenian sandstone and a conglomerate of primary and Precambrian metamorphic rocks of secondary porosity, using a sweep from 18–92 Hz. Time sections contain high frequencies, with the upper frequency limit of trace spectra reaching 80 Hz. These time sections enabled us to extrapolate well data laterally. The structure of the reservoir can be mapped and zones barren because of geometric reasons delineated. Not only can rock units of primary and secondary porosity be distinguished but identifiable reflections could be obtained from the boundaries of sandstone and conglomerate beds about 25-m thick in the Badenian sequence. The dynamic features of reflections from the hydrocarbon‐water boundary observed in the region of secondary porosity indicate the grade of tectonization almost independently of pore fluid, and brecciated parts could be distinguished. Velocity anomalies in the Lower Pannonian sequence reveal a 10–18-m thick gas‐bearing sandstone layer. Wells drilled after our studies confirmed our conclusions.
Parametric estimation of phase and group slownesses from sonic logging waveforms
Authors: Hsu Kai , Esmersoy Cengiz
Published: October 2002

Sonic logging waveforms consist of a mixture of nondispersive waves, such as the P‐ and S‐headwaves, and dispersive waves, such as the Stoneley and pseudo‐Rayleigh waves in monopole logging and the flexural wave in dipole logging. Conventionally, slowness dispersion curves of various waves are estimated at each frequency, independent of data at other frequencies. This approach does not account for the fact that slowness dispersion functions in sonic logging are continuous and, in most cases, smooth functions of frequency. We describe a parametric slowness estimation method that uses this property by locally approximating the wavenumber of each wave as a linear function of frequency. This provides a parametric model for the phase and group slownesses of the waves propagating across the receiver array. The estimation of phase and group slownesses is then carried out by minimizing the squared difference between the predicted and observed waveforms. The minimization problem is nonlinear and is solved by an iterative algorithm. Examples using synthetic and field data are shown and the results are compared with those obtained by the conventional Prony method. Based on the comparison, we conclude that the parametric method is better than the conventional Prony method in providing robust and stable slowness estimates.
Exploration in the basalt‐covered areas of the Columbia River Basin, Washington, using electromagnetic array profiling (EMAP)
Authors: Warren R. K. , Srnka L. J.
Published: October 2002

The electromagnetic array profiling (EMAP) exploration method was tested at three basalt‐covered locations on the Columbia Plateau in central Washington state. Three 16 km survey lines were located to intersect test wells drilled by Shell. The data were EMAP filtered, and inverted using a nonlinear 1-D Riccati approach developed for conventional magnetotelluric (MT) processing. Large and small features on the resulting resistivity cross‐sections produced by EMAP filtering near the drill hole closely approximated the electric induction logs. Sedimentary units within the survey area appear to be thin, with some thickening indicated toward the center of the basin. Structuring within the sediments is mild within the limits of the survey, although there is appreciable structure within the Miocene flood basalts on one test line.
Adaptive surface‐related multiple elimination
Authors: Verschuur D. J. , Berkhout A. J. , Wapenaar C. P. A.
Published: October 2002

The major amount of multiple energy in seismic data is related to the large reflectivity of the surface. A method is proposed for the elimination of all surface‐related multiples by means of a process that removes the influence of the surface reflectivity from the data. An important property of the proposed multiple elimination process is that no knowledge of the subsurface is required. On the other hand, the source signature and the surface reflectivity do need to be provided. As a consequence, the proposed process has been implemented adaptively, meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple‐free data equals the inversion residue. Results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion.
Range‐equation weights for AVO
Authors: Duren Richard E.
Published: October 2002

Duren (1991) presented a detailed development of the seismic range equation showing how to calculate a wavelet’s voltage amplitude spectrum and phase spectrum and how to use the resulting wavelets in forming model seismic gathers. These same wavelets can then be used to process model and seismic gathers via prestack deconvolution to reveal a target’s amplitude behavior with offset.
The influence of confining pressure and water saturation on dynamic elastic properties of some Permian coals
Authors: Yu Gang , Vozoff Keeva , Durney David W.
Published: October 2002

Laboratory measurements are described on Permian coals from Wollongong, New South Wales, Australia related to the dependence of ultrasonic P‐ and S‐wave velocities, attenuation, anisotropy and the dynamic elastic moduli on confining pressure, water saturation, and pore pressure. Five independent stiffness constants are used to represent the elastic anisotropy of the specimens as a function of confining pressure and water saturation. The anisotropy is believed to be controlled mainly by the internal structure of the coals, while the pressure dependence of the constants is controlled mainly by randomly oriented cracks. P‐ and S‐wave dispersions were measured on water‐saturated specimens as confining pressures increased from 2 MPa to 40 MPa. The samples represented cores taken both parallel and perpendicular to bedding planes. Velocities along bedding planes are marginally higher than those across bedding planes. This anisotropy is insensitive to confining pressure. Attenuation was also measured, both normal and parallel to bedding planes, on dry and water‐saturated specimens from 2 MPa to 40 MPa confining pressures. The experimental results show that dynamic elastic properties are potential indicators of the states of stress and saturation in coal seams, and provide necessary information for computer modeling and interpreting seismic surveys carried out to assist mine development.
Energy distribution in wavelets and implications on resolving power
Authors: Knapp Ralph W.
Published: October 2002

The suite of a wavelet is defined as being all wavelets that share a common amplitude spectrum and total energy but differ in phase spectra. Within a suite there are also classes of wavelets. A wavelet class has a common amplitude envelope and energy distribution. As such, it includes all wavelets that differ by only a constant‐angle phase shift. Of all wavelets within suite, the zero‐phase wavelet has the minimum energy envelope width; its energy is confined to minimum time dispersion. Therefore, the zero‐phase wavelet has maximum resolving power within the suite. Because a zero‐phase wavelet shares its amplitude envelope with a class of wavelets that differ by only a constant phase shift, all wavelets of the class also have maximum resolving power within the suite. The most familiar of these is the quadrature‐phase wavelet (90‐degree phase shift). Use of the complex trace results in an evaluation of the total energy, both potential and kinetic, of the wavelet signal. Assuming the wavelet signal is the output of a velocity geophone, partial energy represents only kinetic energy. Total energy better represents wavelet energy propagating through the earth. Use of partial energy (real signal only) applies a bias that favors the zero‐phase wavelets with respect to others of its class despite identical energy distribution. This bias is corrected when the wavelet envelope is used in the evaluation rather than wavelet trace amplitude. On a wiggle‐trace seismic section (amplitude display) a zero‐phase wavelet maintains a detectability advantage in the presence of noise because of a slightly greater amplitude; however, the advantage is lost in complex trace sections (energy displays) because both reflection strength and instantaneous frequency are independent of a constant phase shift in the wavelet. These sections are identical whether the wavelet is zero‐phase, quadrature‐phase or any other constant phase value, i.e., a wavelet within the zero‐phase class. (This does not imply that reflection strength sections should replace wiggle trace ones, only that they have advantages in the solution of some problems.)
True‐amplitude imaging and dip moveout
Authors: Black James L. , Schleicher Karl L. , Zhang Lin
Published: October 2002

True‐amplitude seismic imaging produces a three dimensional (3-D) migrated section in which the peak amplitude of each migrated event is proportional to the reflectivity. For a constant‐velocity medium, the standard imaging sequence consisting of spherical‐divergence correction, normal moveout (NMO), dip moveout (DMO), and zero‐offset migration produces a true‐amplitude image if the DMO step is done correctly. There are two equivalent ways to derive the correct amplitude‐preserving DMO. The first is to improve upon Hale’s derivation of F-K DMO by taking the reflection‐point smear properly into account. This yields a new Jacobian that simply replaces the Jacobian in Hale’s method. The second way is to calibrate the filter that appears in integral DMO so as to preserve the amplitude of an arbitrary 3-D dipping reflector. This latter method is based upon the 3-D acoustic wave equation with constant velocity. The resulting filter amounts to a simple modification of existing integral algorithms. The new F-K and integral DMO algorithms resulting from these two approaches turn out to be equivalent, producing identical outputs when implemented in nonaliased fashion. As dip increases, their output become progressively larger than the outputs of either Hale’s F-K method or the integral method generally associated with Deregowski and Rocca. This trend can be observed both on model data and field data. There are two additional results of this analysis, both following from the wave‐equation calibration on an arbitrary 3-D dipping reflector. The first is a proof that the entire imaging sequence (not just the DMO part) is true‐amplitude when the DMO is done correctly. The second result is a handy formula showing exactly how the zero‐phase wavelet on the final migrated image is a stretched version of the zero‐phase deconvolved source wavelet. This result quantitatively expresses the loss of vertical resolution due to dip and offset.
Inversion of seismic reflection traveltimes using a nonlinear optimization scheme
Authors: Pullammanappallil Sathish K. , Louie John N.
Published: October 2002

We present the use of a nonlinear optimization scheme called generalized simulated annealing to invert seismic reflection times for velocities, reflector depths, and lengths. A finite‐difference solution of the eikonal equation computes reflection traveltimes through the velocity model and avoids ray tracing. We test the optimization scheme on synthetic models and compare it with results from a linearized inversion. The synthetic tests illustrate that, unlike linear inversion schemes, the results obtained by the optimization scheme are independent of the initial model. The annealing method has the ability to produce a suite of models that satisfy the data equally well. We make use of this property to determine the uncertainties associated with the model parameters obtained. Synthetic examples demonstrate that allowing the reflector length to vary, along with its position, helps the optimization process obtain a better solution. We put this to use in imaging the Garlock fault, whose geometry at depth is poorly known. We use reflection times picked from shot gathers recorded along COCORP Mojave Line 5 to invert for the Garlock fault and velocities within the Cantil Basin below Fremont Valley, California. The velocities within the basin obtained by our optimization scheme are consistent with earlier studies, though our results suggest that the basin might extend 1–2 km further south. The reconstructed reflector seems to suggest shallowing of the dip of the Garlock fault at depth.
Multiple‐source Werner deconvolution
Authors: Hansen Richard O. , Simmonds Marc
Published: October 2002

A reformulation of the Werner deconvolution algorithm using the analytic signal is extended to multiple source bodies. The extended algorithm involves solving a linear least‐squares problem; the coefficients so obtained determine a complex polynomial whose roots define the locations and depths of the body contacts. The extended algorithm has been used to map the structure of the Cobb offset zone of the Juan de Fuca Ridge from aeromagnetic data; both the top and bottom of the spreading center basalts can be delineated. Connections between the multiple‐source Werner technique and CompuDepth™ are discussed.
Multiple weights in diffraction stack migration
Authors: Tygel M. , Schleicher J. , Hubral P. , Hanitzsch C.
Published: October 2002

Three‐dimensional (3-D) prestack diffraction‐stack migration methods (often called Kirchhoff migration/inversion) play a fundamental role in seismic imaging. In addition to estimating the location of arbitrarily curved reflectors and the angle‐dependent reflection coefficients upon them, they can also be used to provide useful kinematic and dynamic information about the specular reflection ray that connects the source and receiver via the unknown reflecting interface. This is achieved by performing a diffraction stack more than once upon the same seismic data set using identical stacking surfaces but different weights. Some of these weights can be applied simultaneously, i.e., as a weight‐vector. The approach offers the possibility of determining various useful quantities that help to compute and interpret migrated reflections. The vector‐weighted diffraction stack is principally intended to economize the amplitude‐preserving migration that normally would require a large amount of dynamic ray tracing. A simple 2-D synthetic example shows how the method works in principle.
Noise‐discriminating, statistical‐amplitude compensation for AVO analysis
Authors: Rutherford Steven R.
Published: October 2002

Statistical amplitude balancing/compensation techniques are widely used in the industry to prepare seismic data for amplitude variation with offset (AVO) processing and analysis. The intent of such statistical techniques is to compensate the data for the average signal decay with offset such that reflectors that are anomalous with respect to this average decay can be detected and analyzed. Statistical amplitude compensation techniques, however, suffer from a serious flaw when applied to data sets having low signal‐to‐noise ratios (S/N) that vary with offset. An artifact of this flaw is often a suppression of the AVO effects one is trying to detect. When S/N is low and decreases with offset, as is usually the case, the rms amplitude measurements that statistical techniques are based upon become increasingly dominated by noise as offset increases. This can lead to a suppression of the far offsets by the balancing scalars responding to a noise level that is increasing with offset. A noise‐discriminating, statistical‐amplitude compensation technique can be designed that counteracts the detrimental effects of noise. This technique is based on the premise that a common‐midpoint (CMP) ensemble average of crosscorrelations of like offset data is proportional to the average signal amplitude corresponding to that offset. The average signal decay with offset can be estimated with this technique and used to amplitude compensate a data set for AVO analysis. The noise‐discriminating statistical technique performs extremely well on synthetic data. When applied to a Gulf of Mexico data set having poor S/N characteristics, the technique also performs well and offers encouragement that it will be useful in actual practice.
Implementing measured source signatures in a coarse‐grid, finite‐difference modeling scheme
Authors: Landrø Martin , Mittet Rune , Sollie Roger
Published: October 2002

In a marine seismic air‐gun array, each gun location does not necessarily coincide with a node in a finite‐difference grid. Especially for coarse‐grid, finite‐difference modeling, this problem must be handled with care since there might be up to three or four air guns between adjacent grid points. The real sources are represented by fictitious monopole‐ and dipole source functions located at grid nodes. The effective sources are estimated from the extrapolated pressure field at a horizontal surface located below the sources. We find that an array consisting of eight guns separated by a distance of 3 m and located at 7.5 m depth can be approximated by six monopole‐ and dipole source functions distributed on a finite‐difference grid with 10 m spatial sampling. The residual error energy norm between the actual wavefield and the corresponding finite‐difference wavefield observed on a fictitious streamer placed at 95 m depth is less than 0.5 percent.
Estimation of source array signatures
Authors: Amundsen Lasse
Published: October 2002

The signature generated by an array of marine seismic sources is an important input to many seismic processing algorithms. Several methods have been proposed for determining the source signature from a single source or a source array (see e.g., Ziolkowski et al., 1982; Hargreaves, 1984; Loewenthal and Shtivelman, 1989; Carrion et al., 1990; Weglein and Secrest, 1990; Tygel et al., 1991; Landrø and Sollie, 1992, and Amundsen, 1993).
The geometry of reflection
Authors: Worley Shelby C.
Published: October 2002

The two‐dimensional (2-D) reflection path from a dipping plane between an offset source‐receiver combination in a constant velocity medium can be described with several parameters (coordinates, offsets, angles, and lengths). Although there are many parameters, only four independent ones are needed to locally determine the reflection geometry. Given four determining parameters, the evaluations of other ones present problems that range from trivial to formidable. The circumscribed circle about the source, receiver, and specular point turns out to have a number of remarkable properties that are useful for the solution of these problems. The radius of the circle is a useful new auxiliary parameter. Triangles constructed in the circle provide nonintuitive mathematical relationships between angles and lengths. The use of mathematical relations derived from the circle has allowed the creation of formulas to fully recover the reflection geometry in a vast majority of valid sets of four known parameters. This circle provides a powerful tool for the calculation of nondetermining parameters as well as new insight into the geometry of reflection with straight raypaths.
Investigations of magnetic field disturbances at an air force base compass calibration hardstand
Authors: Butler Dwain K. , Kean Thomas B.
Published: October 2002

Investigations were conducted to determine the nature and cause of magnetic field disturbances at the calibration hardstand (compass rose) at an air force base. The disturbances have prevented the normal and routine use of the hardstand since its construction in the mid-1950s, with heightened concern over the problem every 10–12 years. The investigations included the characterization of the horizontal, vertical, and temporal variation of the total magnetic field strength both on and off the hardstand. On the hardstand, the field varies by as much as 1,000 nT over 10 m horizontally and by as much as 600 nT over 2.5 m vertically. Also, on the hardstand, the magnetic field varies extremely erratically with time by 50–60 nT over periods of a few seconds. Off the hardstand, the magnetic field is extremely stable, and varies by less than 10 nT over 10 m horizontally, 2.5 m vertically, and over periods of 10–15 min. The magnetic field “stabilizes” at distances less than 10 m horizontally from the edge of the hardstand. Both on and off the hardstand, the magnetic field variations are independent of the status (on or off) of a nearby instrument landing system (ILS) (approach radar). The results of the magnetic field characterization indicate that the cause of the problem is the hardstand itself. The hardstand concrete was found to have a large bulk magnetic susceptibility, and the concrete aggregate has a permanent magnetization sufficiently large to visibly deflect a compass needle; these factors, coupled with a correlation with the 11-year solar cycle, suffice to explain the magnetic “disturbances” at the hardstand.
Correction of topographic distortions in potential‐field data: A fast and accurate approach
Authors: Xia Jianghai , Sprowl Donald R. , Adkins‐Heljeson Dana
Published: October 2002

The equivalent source concept is used in the wavenumber domain to correct distortions in potential‐field data caused by topographic relief. The equivalent source distribution on a horizontal surface is determined iteratively through forward calculation of the anomaly on the topographic surface. Convergence of the solution is stable and rapid. The accuracy of the Fourier‐based approach is demonstrated by two synthetic examples. For the gravity example, the rms error between the corrected anomaly and the desired anomaly is 0.01 mGal, which is less than 0.5 percent of the maximum synthetic anomaly. For the magnetic example, the rms error is 0.7 nT, which is less than 1 percent of the maximum synthetic anomaly. The efficiency of the approach is shown by application to the gravity and aeromagnetic grids for Kansas. For gravity data, with a maximum elevation change of 500 m reducing to a horizontal datum results in a maximum correction in gravity anomaly amplitude of up to 2.6 mGal. For aeromagnetic data, the method results in a maximum horizontal shift of anomalies of 470 m with a maximum correction in aeromagnetic anomaly amplitudes up to 270 nT.
Electromagnetic field generated by an off‐axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities
Authors: Liu Qing‐Huo
Published: October 2002

We investigate the propagation of electromagnetic waves in a cylindrically layered medium with an arbitrary number of horizontal discontinuities. The dielectric constant, conductivity, and magnetic permeability of the medium are functions of ρ and z only (i.e., independent of the azimuthal angle ϕ), but the field generated by an off‐axis source in this medium is in general a function of ρ, ϕ, and z. This two and a half‐dimensional (2.5-D) problem is often encountered in electromagnetic well logging, as well as in other areas such as optical fiber communications and integrated optics. We show that a coupling exists between the transverse electric (TE) and transverse magnetic (TM) components of the field even in the absence of the horizontal discontinuities, which makes it difficult to solve for the field. We apply an efficient numerical mode‐matching (NMM) algorithm to tackle this 2.5-D problem. This algorithm uses the local reflection and transmission operators developed in the recent work on the diffraction of nonaxisymmetric waves in a cylindrically layered medium with a single horizontal discontinuity. For several special geometries, we compare the numerical results from this NMM algorithm with analytical solutions as well as the earlier numerical results for axisymmetric cases, and found excellent agreement between them. As an application to the geophysical subsurface sensing, we solve several practical problems, and find that a large eccentricity effect can occur in realistic electromagnetic well logging. Moreover, this large eccentricity effect is strongly coupled with thin‐bed effect. Conventional log interpretation methods cannot adequately account for these effects. With the NMM algorithm developed here, all these different effects can be accounted for simultaneously and accurately.
Longitudinal directions in media of arbitrary anisotropy
Authors: Helbig Klaus
Published: October 2002

A longitudinal direction is one in which three pure modes can propagate. It is known that every medium has at least three longitudinal directions. Every axis of symmetry is such a “bound” longitudinal direction, but in most media there are additional “free” longitudinal directions which do not coincide with symmetry directions. In particular, there are longitudinal directions even in triclinic media that possess no symmetry except the point symmetry. The maximum number of distinct longitudinal directions is thirteen. In a longitudinal direction the wave propagation is particularly simple: for the longitudinal mode, wave normal, displacement direction, and ray direction are identical, while for the two transverse modes the deviation of the ray direction from that of the wave normal depends on the type of longitudinal direction and the relative magnitude of a few stiffnesses expressed in a coordinate system aligned with the longitudinal direction. Similarly, the polarization pattern in the vicinity of a longitudinal direction depends strongly on the type of the longitudinal direction and on the relative magnitude of some off‐diagonal stiffnesses. Since the polarization pattern can be observed in suitable vertical seismic profiling (VSP) surveys, it might be inverted to obtain information on elastic parameters that is difficult to obtain by other means. For orthorhombic symmetry, there are always the three bound longitudinal directions coinciding with the axes. In each plane of symmetry a pair of free longitudinal directions can exist, and there can be four symmetrically disposed free longitudinal directions outside the planes of symmetry. Existence and direction of these free directions follows from simple expressions in the elastic stiffnesses.
Determination of Fresnel zones from traveltime measurements
Authors: Hubral Peter , Schleicher Jörg , Tygel Martin , Hanitzsch Ch.
Published: October 2002

For a horizontally stratified (isotropic) earth, the rms‐velocity of a primary reflection is a key parameter for common‐midpoint (CMP) stacking, interval‐velocity computation (by the Dix formula) and true‐amplitude processing (geometrical‐spreading compensation). As shown here, it is also a very desirable parameter to determine the Fresnel zone on the reflector from which the primary zero‐offset reflection results. Hence, the rms‐velocity can contribute to evaluating the resolution of the primary reflection. The situation that applies to a horizontally stratified earth model can be generalized to three‐dimensional (3-D) layered laterally inhomogeneous media. The theory by which Fresnel zones for zero‐offset primary reflections can then be determined purely from a traveltime analysis—without knowing the overburden above the considered reflector—is presented. The concept of a projected Fresnel zone is introduced and a simple method of its construction for zero‐offset primary reflections is described. The projected Fresnel zone provides the image on the earth’s surface (or on the traveltime surface of primary zero‐offset reflections) of that part of the subsurface reflector (i.e., the actual Fresnel zone) that influences the considered reflection. This image is often required for a seismic stratigraphic analysis. Our main aim is therefore to show the seismic interpreter how easy it is to find the projected Fresnel zone of a zero‐offset reflection using nothing more than a standard 3-D CMP traveltime analysis.
The O’Doherty‐Anstey formula and localization of seismic waves
Authors: Shapiro Serguei A. , Zien Holger
Published: October 2002

Angle (or offset) dependent effects of scattering in finely layered media can be observed and analyzed or must be compensated for in vertical seismic profiling data (VSP‐ data), crosshole observations, or seismic amplitude variation with offset (AVO) measurements. Moreover, the adequate description of multiple scattering is important for the study of seismic attenuation in sediments and for the design of inversion procedures.
Multivariate statistical analysis of geophysical data in Nevada
Authors: Vulkan Uzi , Duval Joseph S.
Published: October 2002

Regional magnetic, gravity, and gamma‐ray data in Nevada were analyzed using a multivariate statistical method. The algorithms used are part of the public‐domain Geographical Resource Analysis Support System (GRASS). Twenty‐seven statistical groups (clusters) were found to be the optimum number that best represents the geophysical data. The resulting map of the distribution of these groups shows linear features which define a geophysical trend not previously recognized. This trend is clearly related to the northern Nevada rift and extends from near the northern border of Nevada to the southern part of the State with a northwest‐southeast trend to about 37°N latitude, where a change of direction occurs to a northeast‐southwest trend. Although not spatially coincident, the Roberts Mountains Thrust, the Golconda Thrust, and the 0.706 contour of the [Formula: see text] ratio exhibit similar trends over part of their lengths. The significance of this geophysical trend is uncertain. One possible interpretation is that it corresponds to the central graben of a rift system larger than previously postulated. The classified data were also compared to a digital geologic map, and the results show that, for some areas of the state, mapped geology and specific groups do have a clear relationship. In general, however, mapped geologic units and the groups have no unique relationships.
Minimum uncertainty filters for pulses
Authors: Trantham E. Clark
Published: October 2002

The objective of this paper is to calculate filters with a minimum uncertainty, the product of filter length and bandwidth. The method is applicable to producing minimum uncertainty filters with time or frequency domain constraints on the filter. The calculus of variations is used to derive the conditions that minimize a filter’s uncertainty. The general solution is a linear combination of Hermite functions, where the Hermite functions are summed from low to high order until the filter’s constraints are met. Filters constrained to have zero amplitude at zero hertz have an uncertainty at least three times greater than expected from the uncertainty principle, and the minimum uncertainty filter is a first derivative Gaussian. For the previous filter, the minimum uncertainty high cut filter is a Gaussian function of frequency, but the minimum uncertainty low cut filter is a linear function of frequency.
2-D velocity inversion/imaging of large offset seismic data via the tau‐p domain
Authors: Reiter Edmund C. , Purdy G. Michael , Toksöz M. Nafi
Published: October 2002

We describe a method for determining a two‐dimensional (2-D) velocity field from refraction data that has been decomposed into some function of slowness. The most common decomposition, intercept time‐slowness or [Formula: see text], is used as an intermediate step in an iterative wave field continuation procedure previously applied to one‐dimensional (1-D) velocity inversions. We extend the 1-D approach to 2-D by performing the downward continuation along numerically computed raypaths. This allows a correction to be made for the change in ray parameter induced by 2-D velocity fields. A best fitting velocity model is chosen as a surface defined by critically reflected and refracted energy that has been downward continued into a three dimensional (3-D) space of velocity, offset, and depth. Synthetic data are used to demonstrate how this approach can compensate for the effects of known lateral inhomogeneities while determining an underlying 1-D velocity field. We also use synthetic data to show how multiple refraction lines may be used to determine a general 2-D velocity model. Large offset field data collected with an Ocean Bottom Hydrophone are used to illustrate this technique in an area of significant lateral heterogeneity caused by a sloping seafloor.
On: “The use of the Hartley Transform in geophysical applications” by R. Saatcilar, S. Ergintav, and N. Canitez (November 1990 GEOPHYSICS, p. 1488–1495).
Authors: Rajan N. S.
Published: October 2002

This paper brings us yet another useful and interesting integral transform for geophysical applications. However, the representation of the kernel of the Hartley transform and its inverse [equations (1) and (2)] is inappropriate and confusing. The kernel Cos(ωt) needs to be replaced by Cas(ωt) in these equations.
Gravity interpretation using Fourier transforms and simple geometrical models with exponential density contrast
Authors: Rao D. Bhaskara , Prakash M. J. , Babu N. Ramesh
Published: October 2002

The decrease of density contrast in sedimentary basins can often be approximated by an exponential function. Theoretical Fourier transforms are derived for symmetric trapezoidal, vertical fault, vertical prism, syncline, and anticline models. This is desirable because there are no equivalent closed form solutions in the space domain for these models combined with an exponential density contrast. These transforms exhibit characteristic minima, maxima, and zero values, and hence graphical methods have been developed for interpretation of model parameters. After applying end corrections to improve the discrete transforms of observed gravity data, the transforms are interpreted for model parameters. This method is first tested on two synthetic models, then applied to gravity anomalies over the San Jacinto graben and Los Angeles basin.
Surface‐consistent phase decomposition in the log/Fourier domain
Authors: Cambois Guillaume , Stoffa Paul
Published: October 2002

In the log/Fourier domain, decomposing the amplitude spectra of seismic data into surface‐consistent terms is a linear problem that can be solved, very efficiently, one frequency at a time. However, the nonunique definition of the complex logarithm makes it much more difficult to decompose the phase spectra. The instability of phase unwrapping has previously prevented any attempt to decompose phase spectra in the log/Fourier domain. We develop a fast and robust partial unwrapping algorithm, which makes it possible to efficiently decompose the phase spectra of normal moveout‐corrected (NMO‐) data into surface‐consistent terms, in the log/Fourier domain. The dual recovery of amplitude and phase spectra yields a surface‐consistent deconvolution technique where only the average reflectivity is assumed to be white, and only the average wavelet is required to be minimum‐phase. Each individual deconvolution operator may be mixed‐phase, depending on its estimated phase spectra. For example, surface‐consistent time shifts and phase rotations, as well as any other surface‐consistent phase effects, are included in the phase spectra of the surface‐consistent deconvolution operators. Consequently, static shifts are estimated and removed without ever picking horizons or crosscorrelations.
Determination of the signature of a dynamite source using source scaling, Part 1: Theory
Authors: Ziolkowski Anton
Published: October 2002

It is normally impossible to measure the source signature in land seismic data acquisition with a dynamite source, because it is normally impossible to separate the incident field from the scattered field. Nevertheless, in any serious attempt to invert the seismic data, it is essential to know the source signature; for the dynamite source this is the volume injection function. The problem can be solved by using two different shots at each shot point and relating the source signatures by the source scaling law, which follows from the invariance of the medium parameters with the size of the charge. The volume injection function of the larger shot is an amplified and stretched version of that of the smaller shot, the amplification factor being equal to the ratio of the charge masses and the time stretch factor being equal to the cube‐root of this ratio. At a given receiver, the response to one shot is a convolution of the source signature with the impulse response of the earth, plus noise. The two shots and the scaling law give three independent equations relating the three unknowns: the two source signatures and the impulse response of the earth (plus noise). This theory may be put at risk in a physical experiment which requires a third shot at the same shot point, using a known mass of dynamite, different from the first two. The resulting shot record should be different from the first two and, apart from the noise, should be predictable from them.
Determination of the signature of a dynamite source using source scaling, Part 2: Experiment
Authors: Ziolkowski Anton , Bokhorst Karel
Published: October 2002

In April 1990 we performed an experiment in the Netherlands to test the theory of the determination of the signature of a dynamite source using the scaling law. The theory says that the source signature may be determined from the recorded seismic data using two shots of different charge size at the shotpoint; we used 125 g and 500 g charges. The theory was put at risk with a 250-g test charge at each shotpoint. According to the theory, the test record should be different from the other two and, apart from the noise, should be predictable from them. This experiment was repeated 95 times at approximately 50 m shotpoint intervals, using a 240-channel recording system. The results corroborate the theory within an acceptable error. The second‐derivative of the volume injection function was extracted as the source signature; it varied slightly from shot to shot and was minimum phase. This new method of seismic data acquisition allows the signature of the dynamite source to be obtained from the data, uncontaminated by the earth, and avoids the assumptions that must be made in statistical wavelet estimation methods. If there is good shot‐to‐shot repeatability, the second shot is only needed occasionally for calibration.
2-D phase unwrapping and phase aliasing
Authors: Spagnolini Umberto
Published: October 2002

The phase of complex signals is measured modulo-2π (wrapped phase); continuous‐phase information is obtained by adding properly chosen multiples of 2π shift to the wrapped phase. Unwrapping searches for the 2π combinations that minimize the discontinuity of the unwrapped phase as only the unwrapped phase can be analyzed and interpreted by further processing. The key problem of phase unwrapping is phase aliasing, a condition mainly caused by rapid phase variations. The extension of the one‐dimensional (1-D) phase unwrapping algorithms to a two‐dimensional (2-D) domain by 1-D slicing gives unsatisfactory results even in the presence of low‐phase aliasing, whereas 2-D phase unwrapping deals with the complete problem, overcoming the limitations of 1-D unwrapping. The 2-D unwrapped phase is obtained as the solution of a variational problem that minimizes the differences between the gradients of the wrapped and unwrapped phase. The Euler equation is then integrated using the boundary conditions obtained from the wrapped phase. In addition to determining a unique unwrapped phase, this approach has the advantage that it limits the influence of phase aliasing. It is also more attractive than iterative 1-D unwrapping since it limits the propagation of unwrapping errors. Error propagation in phase unwrapping can strongly influence the result of any phase processing. Examples in this paper apply 2-D phase unwrapping to problems of refraction statics and interferometrical imaging using a remote system (SAR) and demonstrate how limited error propagation allows phase processing.
The relation between seismic P‐ and S‐wave velocity dispersion in saturated rocks
Authors: Mavko Gary , Jizba Diane
Published: October 2002

Seismic velocity dispersionin fluid-saturated rocks appears to be dominated by tow mecahnisms: the large scale mechanism modeled by Biot, and the local flow or squirt mecahnism. The tow mechanisms can be distuinguished by the ratio of P-to S-wave dispersions, or more conbeniently, by the ratio of dynamic bulk to shear compliance dispersions derived from the wave velocities. Our formulation suggests that when local flow denominates, the dispersion of the shear compliance will be approximately 4/15 the dispersion of the compressibility. When the Biot mechanism dominates, the constant of proportionality is much smaller. Our examination of ultrasonic velocities from 40 sandstones and granites shows that most, but not all, of the samples were dominated by local flow dispersion, particularly at effective pressures below 40 MPa.
Seismic offset balancing
Authors: Ross Christopher P. , Beale Paul L.
Published: October 2002

The ability to successfully predict lithology and fluid content from reflection seismic records using AVO techniques is contingent upon accurate pre‐analysis conditioning of the seismic data. However, all too often, residual amplitude effects remain after the many offset‐dependent processing steps are completed. Residual amplitude effects often represent a significant error when compared to the amplitude variation with offset (AVO) response that we are attempting to quantify. We propose a model‐based, offset‐dependent amplitude balancing method that attempts to correct for these residuals and other errors due to sub‐optimal processing. Seismic offset balancing attempts to quantify the relationship between the offset response of back‐ground seismic reflections and corresponding theoretical predictions for average lithologic interfaces thought to cause these background reflections. It is assumed that any deviation from the theoretical response is a result of residual processing phenomenon and/or suboptimal processing, and a simple offsetdependent scaling function is designed to correct for these differences. This function can then be applied to seismic data over both prospective and nonprospective zones within an area where the theoretical values are appropriate and the seismic characteristics are consistent. A conservative application of the above procedure results in an AVO response over both gas sands and wet sands that is much closer to theoretically expected values. A case history from the Gulf of Mexico Flexure Trend is presented as an example to demonstrate the offset balancing technique.
Aeromagnetic anomalies and perspective oil traps in China
Authors: Zhang Yong‐xia
Published: October 2002

Based on analyses of aeromagnetic data from known oil and gas fields in China, aeromagnetic anomalies have been classified according to their genesis into three types: (1) structure‐associated anomalies related to volcanic rock, (2) anomalies related to magnetic basement fault blocks, and (3) structure‐associated anomalies related to weakly magnetic sedimentary strata. The most successful applications of aeromagnetic data for locating favorable oil and gas structures are in the following kinds of areas: (1) areas where basement fault blocks of inhomogeneous lithology and magnetization are developed; (2) areas of weakly magnetic layered strata with a considerable thickness, either effusive or clastic deposits; and (3) areas where magnetic layers have undergone tectonic deformation with faulting and dip angles larger than 30 degrees. For reliable detection of such structures in sedimentary rocks and associated oil and gas traps, an integrated interpretation of geological and geophysical data is necessary.
Scattering attenuation in sediments modeled by ARMA processes—Validation of simple Q models
Authors: Kerner Claudia , Harris Peter E.
Published: October 2002

We investigate the data requirements for a reliable analysis of frequency‐dependent Q caused by scattering in a finely layered geological structure. Numerical wave propagation experiments in stochastic models were performed. We set up autoregressive‐moving average [ARMA(1,1)] models for the reflection coefficients with non‐Gaussian distribution functions and used published parameter sets estimated for sedimentary sequences from real log data. For ARMA models, analytical expressions for the scattering attenuation α and the quality factor Q can be derived from the O’Doherty‐Anstey formula. The aim of this study is to investigate whether scattering attenuation as derived from the O’Doherty‐Anstey formula is measurable with sufficient accuracy with a traditional vertical seismic profile (VSP) configuration in realistic sedimentary sequences, and if so, whether the data can be inverted to yield the statistics of the sediment sequence. The main result is that reliable estimation of scattering attenuation requires VSP data over a considerable depth interval, depending on the magnitude of the attenuation with errors in the estimates increasing inversely as the depth range increases. Extensions of the O’Doherty‐Anstey theory to non‐normal incidence have been given in the literature. We examine the angle dependence of the results using both elastic plane‐wave modeling and acoustic point‐source modeling. For the weak medium variations considered, elastic effects (e.g., mode conversions) and point‐source effects are negligible at angles up to about 25 degrees.
Remote sensing of seismic vibrations by laser Doppler interferometry
Authors: Berni Albert J.
Published: October 2002

The objective of this work is to sense seismic particle motion by recovering the Doppler shift of a laser beam that is directed to various ground spots from a remote location. This paper presents results from two field tests using experimental, laser‐based, data acquisition systems. In the first test, strong ground‐roll vibrations were detected at an 800-m range by reflecting the beam directly from various terrain targets. The weaker, seismic‐reflection events were inundated by a noise associated with propagation of the laser beam through the atmosphere. The second test used a novel optical interferometer that cancelled the turbulence noise. A reflector apparatus is needed at the ground target position to cancel the turbulence effects in this system.