bluuebunny/crossref_metadata_2025 huggingface dataset:
Absorbing boundary conditions and surface waves
Authors: Sochacki James , Kubichek Robert , George John , Fletcher W. R. , Smithson Scott
Published: October 2002

One of the major problems in numerically simulating waves traveling in the Earth is that an artificial boundary must be introduced to produce unique solutions. To eliminate the spurious reflections introduced by this artificial boundary, we use a damping expression based on analogies to shock absorbers. This method can reduce the amplitude of the reflected wave to any pre‐specified value and is successful for waves at any angle of incidence. The method can eliminate unwanted reflections from the surface, reflections at the corners of the model, and waves reflected off an interface that strike the artificial boundary. Many of the boundary conditions currently used in the numerical solution of waves are approximations to perfectly absorbing boundary conditions and depend upon the angle of incidence of the incoming wave at the artificial boundary. Stability problems often occur with these boundary conditions. The method we use at the artificial boundary allows use of stable Dirichlet or von Neumann conditions. Since the surface motion is easily measured when the waves are induced by normal seismic techniques, approximations of surface waves are needed to obtain information on Rayleigh waves. An implicit finite‐difference scheme that is relatively easy to incorporate into existing numerical simulators is used to obtain the surface data for the forward finite‐difference approximations.
Carbonate porosity from S/P traveltime ratios
Authors: Robertson James D.
Published: October 2002

A twenty‐mile S‐wave seismic line was acquired on the northeastern shelf of the Anadarko basin by the 1977–1978 Conoco P‐Wave/S‐Wave Group Shoot. The resolution of the S‐wave section is at least as good as the resolution of a coincident P‐wave section acquired in 1975. The top and bottom of a collection of Paleozoic carbonates called the Hunton group can be identified on both sets of data. P and S traveltimes and traveltime ratios delineate lateral variations in the thickness and average porosity of the Hunton. Where the pore space is saturated with liquid, a systematic increase in average porosity from less than 2 percent to about 11 percent correlates with an increase in the S/P traveltime ratio from 1.84 to 1.96. The ratio decreases to values between 1.65 and 1.80 at two places along the line, probably indicating that the pore space is partially gas‐saturated at these locations. The data are consistent with the seismic response of a petrophysical model of the Hunton in which a majority of the pore shapes are elongated rather than round.
Multiple‐shot processing of array sonic waveforms
Authors: Hsu Kai , Chang Shu‐Kong
Published: October 2002

Signal processing techniques are needed to estimate the slownesses (inverses of velocities) of compressional, shear, and Stoneley waves from array sonic waveforms recorded by array sonic tools. Existing processing techniques process entire array waveforms, assuming that each wave component has linear moveout (a constant velocity) across the array. The results show poor vertical resolution if the formation spanned by the array aperture is not homogeneous. Multiple‐shot processing is a technique to improve the vertical resolution of slowness logs. The algorithm incorporates redundant information from the multiplicity of overlapping tool locations. Specifically, the method includes four steps: (1) subarrays are selected from full arrays associated with shots from successive sources; (2) subarray waveforms are processed using the semblance statistic; (3) the semblance statistic is projected onto the slowness axis; and (4) the projected semblances of all selected subarrays are combined and the slownesses of the wave components are estimated from the combined statistic. The technique improves the vertical resolution of slowness logs because the subarrays are shorter than the full array. It also increases the accuracy of estimates of slowness because more data are used in the processing. This procedure is applicable to common‐shot subarrays as well as to common‐receiver subarrays. Combining common‐shot and common‐receiver results provides two additional advantages, namely, borehole compensation and measurement enhancement.
Direct inversion of time‐domain electromagnetic data
Authors: Nekut A. G.
Published: October 2002

This note describes a simple method for converting transient electromagnetic (EM) sounding data into profiles of conductivity versus depth, based on an approximate image representation for the decaying induced ground currents. The method can provide one‐dimensional (1-D) inversion for any kind of time‐domain EM sounding data; the discussion here is limited to the case of central‐loop sounding. In particular, I apply the inversion to some time‐derivative central‐loop sounding data and demonstrate that essentially the same interpretation of the geoelectric section is obtained with the simple image method as is obtained using traditional iterative least‐squares fitting to layered models. This simple inverse can be computed much more quickly than an iterative least‐squares inverse, making it possible to estimate the geoelectric section concomitant with data acquisition.
Experimental investigation of interference from other seismic crews
Authors: Lynn Walt , Doyle Mark , Larner Ken , Marschall Richard
Published: October 2002

In a study of the contamination of reflection seismic data by interfering noise from other seismic crews, controlled experiments were performed in the Gulf of Mexico and the North Sea. In each experiment, a survey ship traversed a line several times collecting both data free of and data contaminated by interfering crew noise. In the Gulf of Mexico experiment, the “noise” ship followed a prescribed course about 11 km from the survey ship. In the North Sea experiment, the noise ship was positioned at stationary locations 10 and 40 km broadside to the survey line. Recorded interference noise in both experiments had peak amplitudes well above the 0.5 to 1.5 Pa (5 to 15 μbar) limit beyond which crews typically must agree on time‐sharing. Despite recorded crew noise that was three to eight times higher than levels typically considered acceptable, the conventionally processed common‐midpoint stack of the contaminated Gulf of Mexico data shows only slight evidence of the interference noise; in contrast, the North Sea stack is severely contaminated by crew noise as early as 1 s. However, when each unstacked trace is scaled by time‐varying weights that vary inversely with the local power in the trace, the crew noise is no longer visible in the contaminated stack of either data set. Trace‐weight normalization in this process is designed to ensure that stacked signal amplitudes are generally preserved. A simulated line wherein the actual Gulf of Mexico data are contaminated by crew noise five times stronger than that recorded in the field [yielding effective peak noise values of 7.5 to 20 Pa (75 to 200 μbar)] also shows no evidence of crew noise after inverse‐power weighted stacking. When data processing includes conventional stacking, we recommend that the specified tolerable amount of crew noise be based upon the root‐mean‐square amplitude of the crew noise computed over an entire record. With burst suppression techniques, such as inverse power‐weighted stacking, we recommend that the specified level be based upon the duration of the strong‐amplitude burst as well. With both criteria, field specifications can be chosen that remain conservative while tolerating considerably more crew‐interference noise than in the past. Issues of the influence of crew noise on the analysis of prestack data remain for future study.
Modeling of borehole resistivity measurements using infinite electrical grids
Authors: Zemanian A. H. , Anderson B.
Published: October 2002

An infinite electrical resistive grid generated by a finite‐difference approximation to Poisson’s equation in cylindrical coordinates with no azimuthal variation has been used to model borehole resistivity measurements. The medium surrounding the borehole is infinite in extent and its resistivity varies only in the radial direction. As a result, the branch resistance values of the infinite grid also vary only in the radial direction. A continued fraction of Laurent operators determines the node voltages along the borehole’s surface. Use of an operational calculus based upon the finite Fourier transformation converts the continued fraction into a readily computed form. This yields new formulas for apparent resistivity, given various resistivity measuring arrays and a resistivity profile in the radial direction. In contrast to classical methods, the need to match boundary conditions at the interface of a cylindrically layered earth is eliminated, so that the procedure is just as easily applied to a continuous resistivity profile as it is to a stepped profile. Moreover, the method is computationally fast by virtue of the fast Fourier transform algorithm and the avoidance of boundary‐condition matching. The speed and versatility of this model make it useful for studying the effects of complex invasion on the response of resistivity tools.
Entropy interpretation of maximum‐likelihood deconvolution
Authors: Giannakis Georgios B. , Mendel Jerry M.
Published: October 2002

Entropy concepts are embodied in the maximum‐likelihood deconvolution (MLD) method, just as they are in minimum‐entropy (MED) methods. MLD asymptotically minimizes Shannon’s entropy of the reflectivity sequence (which, in MLD, is modeled as a Bernoulli‐Gaussian random sequence). Study of maximum‐ likelihood detection and estimation of the reflectivity sequence reveals that MLD is embodied in the general framework of the “adaptive” MED methods. Comparisons based on similarities and differences between MLD and various existing MED techniques show that MLD is robust due to explicit inclusion of noise in its statistical model.
Electromagnetic induction in an inhomogeneous conductive thin sheet
Authors: Smith Richard S. , West G. F.
Published: October 2002

Distinguishing between the electromagnetic (EM) response of a subsurface conductor and the EM response of an overburden whose conductivity and/or thickness varies laterally requires a capability to calculate the EM response of both types of conductor. While methods for calculating the response of some simple subsurface conductors such as dipping rectangular sheets are already available, methods for computing the response of an irregular overburden are not common. Using Price’s analysis, we have formulated two numerical techniques for calculating the response of a laterally varying overburden which is thin and flat, and which lies on a perfectly resistive subspace. The first technique is a frequency‐domain method in which a large matrix equation is solved to find the horizontal‐wavenumber components of the secondary vertical magnetic field. The method is best suited to calculating the response of the overburden when the EM source and receiver are located above the sheet, such as in airborne EM systems. Helicopter EM profiles calculated using this technique have been checked against a simple scale model. The second method calculates the time‐domain step response of the overburden by time‐stepping the vertical component of the magnetic field. The method is suitable for calculating the response of the overburden when the EM source is a large transmitter loop close to the overburden. Using the time‐domain method to investigate the response of simple conductance structures illustrates that the zero crossing of the vertical magnetic field moves more slowly across conductive regions than across resistive regions. This is because the rate of decay of the vertical field in a region varies in proportion to the resistance of the region. A response profile from a UTEM survey shows a response that could be interpreted as due to a dipping subsurface conductor. This response has been modeled using the time‐domain method, and a geologically acceptable pattern of lateral variations in the overburden conductance yields a response close to the measured EM response. Thus, a subsurface conductor need not lie below the profile line to explain the response.
Natural‐field and very low‐frequency tipper profile interpretation of contacts
Authors: Labson Victor F. , Becker Alex
Published: October 2002

Anomalous vertical magnetic field (tipper) profiles acquired using natural or very low‐frequency (VLF) radio transmitter sources can be interpreted simply and rapidly for a number of geologic settings. The relations between computed numerical models, and outcropping dipping and buried vertical contacts are presented here in a series of interpretation charts. Use of the tipper phase in the analysis minimizes the effect of transmitter azimuth in the VLF case. Two examples illustrate the application to field data. An audiofrequency natural‐field tipper profile over a conductive bed in a north‐central Washington State metasedimentary sequence demonstrates the interpretation procedure for a dipping contact. VLF profiles over covered basement faults in Ontario demonstrate the application for a buried vertical contact. In both cases the quick results are in agreement with the much more laborious trial‐and‐error matching to two‐dimensional models.
Formation resistivity factors for a compressible solid‐brine mixture
Authors: McLachlan D. S. , Button M. B. , Adams S. R. , Gorringe V. M. , Kneen J. D. , Muoe J. , Wedepohl E.
Published: October 2002

Formation resistivity factors were measured as a function of porosity for various rubber‐brine mixtures under uniaxial compression. Electrical measurements were made parallel and transverse to the direction of compression for regular crystal lattices (FCC and CsCl) and various random packings. Porosities from about 0.35 to as low as 0.03 were obtained. The formation factors ranged from about 5 to nearly 1 000. A new, effective media formula qualitatively, or in some cases even semiquantitatively, describes the results. The results agree reasonably well with calculations made on a model system, which the rubber‐brine mixture approximates. These calculations show, and the results from the rubber‐brine mixture confirm, a critical porosity below which the system is insulating.
Aeromagnetic images: Fresh insight to the buried basement, Rolla quadrangle, southeast Missouri
Authors: Cordell Lindrith , Knepper Daniel H.
Published: October 2002

Aeromagnetic data from the Rolla 1° × 2° quadrangle, Missouri, displayed as a small‐scale, grey‐tone image, provide a lucid picture of basement features beneath sedimentary‐rock cover. Late‐stage “tin” granite plutons of the Proterozoic St. Francois magmatic terrane are clearly delineated. The plutons average about 11 km in diameter and occupy a significant fraction (12 percent) of the area surveyed. Gravity data require that certain plutons are at least 3 km thick. Most of the plutons are fat ovals in plan view and show no flattening trend or structural alignment. The ensemble indicates significant extension in an orthorhombic stress field, with the minimum compressional stress being vertical. Exposed St. Francois terrane volcanic rocks show a characteristic intricate pattern in the magnetic signature. This pattern is more widespread than the subsurface distribution of volcanic rocks indicated by drilling and likely also incorporates areas of St. Francois batholith granite. The horseshoe‐shaped trend of the southeast Missouri lead deposits may be crudely aligned with the edge of this intricately patterned unit. Small, very high‐amplitude magnetic anomalies occur over the well known magnetite‐bearing deposits of the region. The magnetic background for all these features is probably provided by extensive areas of the Butler‐Hill type biotite granite, characterized by large tracts of low magnetic intensity and a cobblestone‐like pattern of ring‐shaped, weak magnetic highs. Few of the many regional faults, calderas, ring complexes, and lineaments previously interpreted from geologic, geophysical, and remote sensing data are expressed in the aeromagnetic image.
Magnetotelluric strike rules
Authors: Zhang P. , Roberts R. G. , Pedersen L. B.
Published: October 2002

The distortion of the magnetotelluric impedance tensor by complex “near‐surface” structure leads to leakage between the elements of the tensor. The magnetotelluric impedance tensor for our principal model, which has both a local and a regional strike, can be written in the long‐period limit as a sum of the regional, undistorted impedance and a perturbed impedance. The latter can be written as a product of a local distortion (which can be regarded as thin‐sheet distortion in the long‐period range) tensor and the regional impedance. Local and regional strikes are found by rotating the impedance tensor into directions in which diagonal elements are proportional and column elements are proportional, respectively. The regional impedance tensor is calculated assuming that the strikes are uniquely defined. An example from a crystalline area with well conducting fracture zones illustrates the model concepts. A weighted least‐squares procedure is used for the estimation of distortion parameters.
On: “Crone pulse electromagnetic response of a conducting thin horizontal sheet—Theory and application,” by S. S. Rai (GEOPHYSICS, 50, 1350–1354, August 1985).
Authors: Bartel David C.
Published: October 2002

Rai uses a simple formula for the step response of a conducting, horizontal thin sheet in the time domain and applies it to the Crone pulse electromagnetic (PEM) system. He also uses this formulation to interpret some field results. The idea of an infinite, horizontal, conductive thin sheet is valid in some cases for both ground and airborne EM systems. However, I disagree with some of the derivations of the thin‐sheet equation as presented in the subject paper. The applicability of the study is not questioned; but the interpretation of the field example may be different.
On: “Deconvolution of noisy seismic data—A method for prestack wavelet extraction,” by B. J. Newman (GEOPHYSICS, 51, 34-44, January 1986).
Authors: Hutchinson D. R.
Published: October 2002

I read Newman’s article published in the January 1986 Geophysics and was interested by his ideas for noise prediction. Newman referred to the paper which Brian Link and I presented at the SEG convention in Atlanta, and although I am glad that Newman mentioned our talk, there is a serious error in this reference.
Vp/Vs in unconsolidated oil sands: Shear from Stoneley
Authors: Hornby Brian E. , Murphy William F.
Published: October 2002

The SDT-A sonic tool was tested in a borehole in the Orinoco heavy oil belt, eastern Venezuela. The sonically slow reservoir consists of unconsolidated quartz sand interbedded with shale. Full‐waveform analysis yields both compressional and shear slownesses. We calculated the shear‐wave slowness from the Stoneley slowness; compressional and Stoneley slownesses were determined using modified semblance techniques. The compressional velocity is relatively fast in the heavy oil pay zone compared to the remainder of the well. Heavy oil (8 API) possesses a finite rigidity at sonic frequencies, and the rigidity of the hydrocarbon adds to the stiffness of the poorly consolidated sand. The sand would not otherwise yield such a high velocity. Compressional and shear velocities of samples from eight whole cores were measured in the laboratory, and the core velocities were found to be consistent with the logs. Especially encouraging is the agreement of the laboratory shear with the shear log derived from Stoneley. The ratio of the compressional‐to‐shear velocities, [Formula: see text], is sensitive to fluid saturation and rock fabric. The oil sands have a [Formula: see text] of less than 2.5. The shales in the well have a [Formula: see text] of greater than 2.5. We found that water‐saturated formations are governed by Biot’s theory, while oil sands are better described by scattering theory. A third arrival has been identified as a leaky compressional mode trapped in the borehole. The velocity of the mode is dominated by the slowness of the borehole mud.
Estimating slowness dispersion from arrays of sonic logging waveforms
Authors: Lang S. W. , Kurkjian A. L. , McClellan J. H. , Morris C. F. , Parks T. W.
Published: October 2002

Acoustic wave propagation in a fluid‐filled borehole is affected by the type of rock which surrounds the hole. More specifically, the slowness dispersion of the various body‐wave and borehole modes depends to some extent on the properties of the rock. We have developed a technique for estimating the dispersion relations from data acquired by full‐waveform digital sonic array well‐logging tools. The technique is an extension of earlier work and is based on a variation of the well‐known Prony method of exponential modeling to estimate the spatial wavenumbers at each temporal frequency. This variation, known as the forward‐backward method of linear prediction, models the spatial propagation by purely real‐valued wavenumbers. The Prony exponential model is derived from the physics of borehole acoustics under the assumption that the formation does not vary in the axial or azimuthal dimensions across the aperture of the receiver array, but can vary arbitrarily in the radial dimension. The exponential model fits the arrivals of body waves (i.e., head waves) well, because the body waves are dominated by a pole rather than a branch point. Examples of this processing applied to synthetic waveforms, laboratory scale‐model data, and field data illustrate the power of the technique and verify its ability to recover dispersion relations from sonic array data. The interpretation of the estimated dispersion in terms of rock properties is not discussed.
The generalized one‐dimensional synthetic seismogram
Authors: Gutowski P. R. , Treitel S.
Published: October 2002

The normal‐incidence synthetic seismogram for an elastic and horizontally stratified medium has been thoroughly studied for a relatively restricted number of source and receiver locations. Most existing treatments are concerned with the special case in which the source as well as the receiver are situated at the surface; few attempts have dealt with completely arbitrary source and receiver geometries. Here we examine arbitrary geometries with the aid of the layer matrix approach, in which upgoing and downgoing wave motion at each interface is expressed in terms of z-transform polynomials. Such an approach brings to light a number of physically important relations that the model satisfies. For example, the synthetic seismograms generally have the familiar autoregressive‐moving average (ARMA) structure for the surface‐source, surface‐receiver case. For particular combinations of reflection coefficients, however, the seismograms reduce to purely autoregressive (AR) representations. In all cases, we work out the delay properties that the respective autoregressive and moving average components must obey. The present solutions are easily reduced to a useful form for practical computation. One application of particular current interest is the simulation of vertical seismic profiling (VSP) surveys, where we have extended the theoretical treatment to include expressions for the derivatives of the seismograms with respect to the reflection coefficients. The resulting time series, which we call Jacobograms, are indicative of the sensitivity of the seismogram to the various reflection coefficients and are thus diagnostic of the model’s behavior.
A Kalman filter approach to susceptibility mapping
Authors: Pilkington Mark , Crossley D. J.
Published: October 2002

The linear inverse problem in magnetic interpretation arises when the distribution of magnetization or susceptibility is sought in a source region which is divided into blocks. The solution is usually achieved by deconvolution or matrix methods. Here we develop a simple, state‐variable model of the magnetic field generating process in which the subsurface is divided into a number of vertical prisms with infinite depth extent. The magnetization in each prism is assumed to be a linear combination of adjacent prisms plus a random component. The discrete Kalman filter is used to obtain estimates of the magnetization distribution. Tests on synthetic data show the method compares favorably with conventional deconvolution techniques. The approach has been applied to part of the Abitibi green‐stone belt and has proven effective in delineating the major lithologies there.
Results of a controlled‐source audiofrequency magnetotelluric survey at the Puhimau thermal area, Kilauea Volcano, Hawaii
Authors: Bartel L. C. , Jacobson R. D.
Published: October 2002

The Puhimau thermal area in the Volcanoes National Park, Hawaii, has attracted interest because it represents an area with anomalously high heat flow and the heat source may be a shallow magma body. At Puhimau a variety of geophysical data, including heat‐flow measurements, have been acquired. The self‐potential data suggest that the heat source is a result of a magma intrusion which plunges steeply northward. The heat‐flow data can be explained in terms of a shallow, relatively thick magma intrusion with a solidification rate sufficient to supply the surficial heat flow for the period of time since the appearance of the thermal area in 1936. In February of 1984, we performed a controlled‐source audiofrequency magnetotelluric (CSAMT) electromagnetic geophysical survey at the Puhimau thermal area to investigate the electrical nature of the thermal anomaly and estimate the depth to any hot water and/or remaining molten magma. The CSAMT survey consisted of several lines of stations where two orthogonal primary‐field transmitting antennas were used. A technique was developed to correct near‐field CSAMT apparent resistivities to plane‐wave values so that plane‐wave analysis techniques could be applied. Plane‐wave 2-D finite‐difference calculations are used to interpret the field data. The results are consistent with the interpretation that the conducting anomaly is a long, thick, dike‐like feature and within this conducting anomaly there is an excellent conductor (approximately 5 Ω ⋅ m) at a depth of approximately 200 m which may be magma or hot, mineralized water. Above this conductor is a zone 40 times less conductive which probably represents an area with less than 100 percent water saturation. The dike‐like structure is connected to a conducting (approximately 5 Ω ⋅ m) basal layer at a depth of 350 m.
Prestack Kirchhoff inversion of common‐offset data
Authors: Sullivan Michael F. , Cohen Jack K.
Published: October 2002

In trying to resolve complex geologic structures, the pitfalls in employing the CDP method become evident. Additionally, stacking multioffset traces corrupts the amplitudes necessary for stratigraphic analysis. In order to preserve whatever structural and amplitude information is in the data, prestack processing should be performed. Given common‐offset data and the velocity above a reflector, prestack acoustic Kirchhoff inversion resolves the location of the interface. When amplitude information has been preserved in the data, the method additionally calculates the reflection coefficient at each interface point. For band‐limited seismic data, the inversion operator produces a sinc‐like picture of the reflector, with the peak amplitude of this band‐limited singular function equal to the angularly dependent reflection coefficient. The inversion development is based upon high‐frequency Kirchhoff data which are inserted into a general 3-D inversion operator. Asymptotically evaluating the four resulting integrals by the method of four‐dimensional stationary phase permits an inversion amplitude function to be chosen so that the inversion operator produces a singular function of support on the reflector, weighted by the reflection coefficient. Specializing the three‐dimensional inversion operator to two and one‐half dimensions allows for processing of single lines of common‐offset data. Synthetic examples illustrate the accuracy of the method for constant‐velocity Kirchhoff data, as well as the problems in applying constant‐velocity data to multivelocity models.
On: “Multicomponent seismic studies using complex trace analysis” by R. M. René, L. Fitter, P. M. Forsyth, K. Y. Kim, D. J. Murray, J. K. Walters, and J. D. Westerman (GEOPHYSICS, 51, 1235–1251, June 1986).
Authors: Evans B. J.
Published: October 2002

I congratulate René on his application of complex trace analysis to three‐component studies. Clearly, his work is a great advance in the understanding and classification of surface waves. However, one glaring failure he made is apparent from the outset—that is, the failure to account for the recording impulse response.
Image processing of aeromagnetic data and integration with Landsat images for improved structural interpretation
Authors: Kowalik W. S. , Glenn W. E.
Published: October 2002

Digital image processing of aeromagnetic data from three mineral prospects significantly improved the existing structural interpretations that were made from contour maps of the aeromagnetic data. Useful image‐processing techniques include (1) presentation as small‐scale, gray‐level images, (2) local contrast enhancement, (3) artificial illumination, and (4) directional filtering. Digital processing also enables direct comparison between Landsat data and aeromagnetic data. Interpretations were improved by the study of the integrated data sets. Images of aeromagnetic data from one prospect in a Precambrian granite‐greenstone terrane show major folds and faults that were not previously recognized from contour maps of the aeromagnetic data. A Landsat Multispectral Scanner (MSS) image shows the subtle surface expression of two folds. The newly identified structures point to additional prospective ground in the search for volcanogenic massive sulfide deposits in the area. Aeromagnetic data from a second prospect are complicated by a young, north‐south striking, strongly magnetic, diabase dike swarm. Directional filtering and artificial illumination of the aeromagnetic data effectively remove the response of the dikes and enhance the earlier structural and lithologic features. The combined interpretation of illuminated aeromagnetic and registered Landsat Thematic Mapper (TM) images for a third prospect added several significant faults that were previously unrecognized from separate interpretations of contour maps of aeromagnetic data and the Landsat image.
Wave‐equation trace interpolation
Authors: Ronen Joshua
Published: October 2002

Spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero‐offset experiment, and the data are seismic data after normal moveout (NMO). The formulation of the (linear) relation between the data and the model is based on the wave equation and on Fourier analysis of aliasing. A processing sequence in which one treats missing data as zero data and performs partial migration before stacking is equivalent to application of the transpose of the operator that actually needs to be inverted. The inverse of that operator cannot be uniquely determined, but it can be estimated using spatial spectral balancing in a conjugate‐gradient iterative scheme. The first iteration is conventional processing (including prestack partial migration). As shown in a field data example in which severe spatial aliasing was simulated, a few more iterations are necessary to achieve significantly better results.
Direct time‐domain calculation of the transient response for a rectangular loop over a two‐layer medium
Authors: Goldman Mark M. , Fitterman David V.
Published: October 2002

The time derivative of the vertical magnetic field due to an electric dipole on the surface of a two‐layer half‐space is computed directly in the time domain by applying the residue theorem to the analytic field expressions. The second layer must be either insulating [Formula: see text] or perfectly conducting [Formula: see text]. The first case can be used to estimate the response of a conductive overburden for mining exploration problems. The second case is useful in explaining the overshoot seen in transient sounding voltage apparent‐resistivity curves when a conductive basement underlies a resistive first layer. In the late stage, the time derivative of the vertical magnetic field decays as [Formula: see text] and the late‐stage apparent resistivity increases as t for [Formula: see text], while for [Formula: see text], these quantities behave as [Formula: see text] and [Formula: see text], respectively, where [Formula: see text], [Formula: see text], is the first‐layer conductivity, [Formula: see text] is the first‐layer thickness, and [Formula: see text]. The electric dipole expressions are integrated to obtain solutions for rectangular loops. Numerical results for a rectangular loop on a layer over an insulating basement (overburden case) show that the overburden response is initially positive inside the loop and negative outside the loop. At later times, the response outside the loop becomes positive. The thinner the overburden layer, the greater the maximum response.
Beam stacking: A generalized preprocessing technique
Authors: Raz Shalom
Published: October 2002

Gaussian beams are well understood frequency‐ domain entities combining the directional properties of plane waves with an effectively finite region of support. These outstanding properties are retained not only on a prescribed observation plane, but throughout the propagation path. A preprocessing sequence aimed at transforming raw seismic data into beam stacks is proposed. That is, time‐harmonic Gaussian beams are synthesized, replacing the plane waves generated by conventional slant‐stacking procedures. The suggested scheme is characterized by an open parameter, essentially the beam width, whose selection is critical to ultimate success. Specific criteria for choosing this parameter can be given. In the limits of zero and infinite beam widths, beam stacks degenerate to the original raw data and to the conventional slant stacks, respectively. Although beam stacking is basically a frequency‐domain procedure, a transformation into the time domain, using frequency constituents within selected bands, may be accomplished without losing finite spatial support. Advantages of choosing beam‐stacked data as a starting point for subsequent inversion may be cited on two levels. The intrinsic property of finite spatial support overcomes edge effects. In addition, the degree of localization achieved by beam stacking may point the way to new approaches to seismic imaging.
Particle displacements on the wall of a borehole from incident plane waves
Authors: Lee M. W.
Published: October 2002

Particle displacements from incident plane waves at the wall of a fluid‐filled borehole are formulated by applying the seismic reciprocity theorem to far‐field displacement fields. Such displacement fields are due to point forces acting on a fluid‐filled borehole under the assumption of long wavelengths. The displacement fields are analyzed to examine the effect of the borehole on seismic wave propagation, particularly for vertical seismic profiling (VSP) measurements. When the shortest wavelength of interest is approximately 25 times longer than the borehole’s diameter, the scattered displacements are proportional to the first power of incident frequency and borehole diameter. The maximum scattered energy occurs when an incident P‐wave propagates perpendicular to the borehole. Borehole effects on VSP measurements, such as waveform distortion, amplitude variation, and time delay, have been analyzed using the concept of a transfer function. When the shortest wavelength of interest is about 40 times longer than the borehole’s diameter, borehole effects on VSP measurements using a wall‐locking geophone are negligible.
Processing of wide‐angle Vibroseis data
Authors: Wenzel F.
Published: October 2002

In 1984 seismic wide‐angle Vibroseis experiments across the Rhine‐graben in Eastern France/Southwest Germany were carried out as a joint French/German venture. Signals generated by French vibrators were recorded at the eastern flank of the graben in the Black Forest. With a 200 channel array spread along 16 km (group spacing: 80 m), data were recorded at offsets between 66 and 82 km. The data are characterized by a low signal‐to‐noise ratio (S/N) and distortions of seismic phases caused by strong topographic variations. For wide‐angle records, conventional static corrections based on the assumption of vertical travelpaths are no longer appropriate. Ray parameter‐dependent time delays should be used in order to correctly eliminate topographic and near‐surface influences on the data. In addition, delineation of reflector segments requires an increase in S/N. A two‐dimensional filter based on forward and inverse slant stacking was designed to handle the time delay and S/N problems simultaneously. Stacking along a suite of ray parameters allows the use of static corrections which depend on the angle of emergence of the seismic arrivals. Weighting data by their coherence emphasizes spatially correlatable phases. Both procedures significantly increase S/N.
Hydraulic fracture evaluation with multiple radioactive tracers
Authors: Pemper Richard R. , Flecker Michael J. , McWhirter Vernie C. , Oliver Donald W.
Published: October 2002

For many years, wireline tracer surveys have been used to determine the height of fractures created during hydraulic stimulation procedures. A recent advancement in fracture evaluation technology has been to tag different stages of a fracture operation with multiple radioactive tracers, providing the capability to discern between created and propped fracture heights in one or more zones of interest. In this research, a wireline instrumentation and data analysis system is implemented to identify and separate the individual yields from multiple radioactive tracers, with an additional feature that determines whether the tracer material is inside of the borehole or distributed throughout the created fracture zone. A single postfracture pass of the logging instrument is used to accumulate gamma ray spectra at each 7.6 cm interval along a borehole. A weighted least‐squares spectrum unfolding algorithm calculates the radioactive intensities as a function of depth, while the peak‐to‐Compton down‐scatter ratio determines the proximity of the tracer material to the wellbore. Field examples illustrate the effectiveness of the system for the evaluation of multistage fracture operations.
On: “Three‐dimensional imaging of steeply dipping structure near the San Andreas fault, Parkfield, California” by John N. Louie, Robert W. Clayton, and Ronan J. LeBras, (GEOPHYSICS, 53, 176–185, February 1988).
Authors: McBride J. H.
Published: October 2002

Louie et al. (1988) apply to COCORP survey data a prestack migration process, which they describe, to image better reflections associated with structure in the upper 5 km of the San Andreas fault zone near Parkfield, California. They demonstrate the usefulness of this approach in an area along the survey where, as they point out, the CMP-stacking process may be particularly troublesome. While the authors were sensitive to the extreme lateral heterogeneities in and about the fault zone, the crooked survey line, and the complex terrain in which the survey was mounted (McBride and Brown, 1986), I suspect they were nevertheless a little too zealous in discounting, in this case, the value of conventional stacking applied and interpreted judiciously. Moreover, Louie et al. imply that their approach yields previously unobtained results; however, this is not the case.
A hydrophone vertical seismic profiling experiment
Authors: Marzetta Thomas L. , Orton Marion , Krampe Alfred , Johnston Lucian K. , Wuenschel Paul C.
Published: October 2002

To reduce the cost of VSP data acquisition, it is necessary to record the VSP signal from a vertical array of geophones for a single operation of the source. Until a vertical array of clamped three‐component geophones is available, it seems logical to evaluate the capabilities of a vertical array of hydrophones, which is much easier to fabricate. It is well known that elastic waves in the solid couple to pressure waves in the borehole fluid. It is also well known that this coupling excites in the borehole fluid energy known as tube‐wave noise that dominates the borehole pressure signal after the first arrival. (The borehole acts as a waveguide.) In this paper we test the effectiveness of velocity filtering of the borehole pressure signal to attenuate the slowly propagating tube‐wave noise and enhance the faster propagating body‐wave signals. Our initial test satisfactorily extracted from the hydrophone array data a strong reflected event that was also observed in the conventional clamped geophone VSP taken in the same borehole. We were not as successful in recovering subsequent weaker reflected signals from the hydrophone data, because of the strong incoherent ambient tube‐wave noise. This incoherency resulted from instrumental limitations that allowed us to record, for each shot, only three of the twelve hydrophone channels available in the vertical array.
An analysis of statistical average velocities in a horizontally layered earth
Authors: Byun Bok S. , Tran Hung V. , Carter Melvan D.
Published: October 2002

For a medium consisting of two lithologic components, we analyze relationships among various velocity statistics that have appeared in the literature. We then address the problem of using stacking velocities to estimate the lithologic content.
On: “The critical reflection theorem” by J. T. Fokkema and A. Ziolkowski (GEOPHYSICS, 52, 965–972, July 1987).
Authors: Walden Andrew , White Roy
Published: October 2002

In this paper, Fokkema and Ziolkowski consider precritical and postcritical incidence and resulting implications for the reflection response of the earth. The ideas are interesting and thought provoking, but their inferences with regard to the whiteness assumption in standard deconvolution are misleading. We will endeavor to show why.
Local phase velocity from complex seismic data
Authors: Scheuer Tim Ellis , Oldenburg D. W.
Published: October 2002

We propose a new method that uses the concepts of complex trace analysis for the automatic estimation of local phase velocity. A complex seismic record is obtained from a real seismic record by extending complex trace analysis into higher dimensions. Phase velocity is estimated from the complex data by finding trajectories of constant phase. In two dimensions, phase velocity calculation reduces to a ratio of instantaneous frequency and wavenumber, and thus provides a measure of the dominant plane‐wave component at each point in the seismic record. The algorithm is simple to implement, and computational requirements are small, partly due to a new method for computing instantaneous frequency and wavenumber which greatly simplifies these calculations for 2-D and 3-D complex records. In addition, our approach has the advantage that no a priori velocity input is needed; however, optimum stability is achieved when a limited range of dipping events is considered. Preconditioning the record with an appropriate velocity filter helps reduce the detrimental effects of crossing events, spatial aliasing, and random noise contamination.
Normal moveout revisited: Inhomogeneous media and curved interfaces
Authors: de Bazelaire Eric
Published: October 2002

The equation of normal moveout, [Formula: see text], is valid for a reflection from the base of a single homogeneous and isotropic bed, but is only an approximation in the real world of multilayered, inhomogeneous media and curved interfaces. Using the theory of geometrical optics, we can find another second‐order equation which represents hyperbolas that are also symmetrical about the time axis. However, the centers of these hyperbolas do not coincide with the center of coordinates, but are shifted along the time axis. The equation describing this second type of hyperbola is [Formula: see text], where [Formula: see text] is the time of focusing depth and [Formula: see text], the velocity of the input medium. This equation is not only more accurate than the usual normal moveout, but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the [Formula: see text] analysis. This procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity section. [Formula: see text] analysis can also be used to build a stacked section without any manual picking of velocities. The same concepts can be extended to the section after stack, allowing recognition of the geometrical patterns of the reflectors.
Source wavelet estimation by upward extrapolation
Authors: Shtivelman V. , Loewenthal D.
Published: October 2002

A new deterministic technique for wavelet estimation and deconvolution of seismic traces was recently introduced. This impedance‐type technique was developed for a marine environment where both the source and the receivers are located inside a homogeneous layer of water. In this work, an extension of the theory of source wavelet estimation is proposed. As in previous publications, this method is based on extrapolation of the wave field measured at depth, upward to the free surface. The extrapolation is performed by using the finite‐difference approximation to the full inhomogeneous wave equation. The extrapolation results in a wavelet which generally includes ghosts and can be used for source signature deconvolution and deghosting. The method needs two closely spaced receivers and is applicable for arbitrary locations of the source and the receivers in one‐dimensional multilayered models, provided the source is above the receivers; furthermore, it can be applied to both marine and land data. Application of the proposed method to a number of synthetic models shows that it gives a good estimate of the source wavelet.
Robust deconvolution by modified Wiener filtering
Authors: Walden A. T.
Published: October 2002

Deconvolution in the presence of additive noise is a well known problem for which there exists a Wiener filter which spectrally whitens while also suppressing the noise. A simple variant of this standard Wiener filter incorporates a parameter p which is intended to allow further weight to be given to noise suppression. This filter is often called a modified Wiener filter. To design such a filter, one must know the frequency characteristics of the wavelet precisely, plus the spectra of the input and additive noise. Typically, some appropriate estimate of the frequency function of the wavelet is taken, and the modified Wiener filter is designed from that estimate. A more realistic practical viewpoint is to think of the estimated wavelet response as one of a set of possible frequency response functions. By using statistical information obtained during wavelet estimation, a value of p can be chosen which gives a modified Wiener filter equivalent to a statistically robust deconvolution filter. Here “robust” means that the error criterion which defines the deconvolution filter allows for the set of possible wavelet frequency functions. Two different error criteria are considered: (1) the minimization of the average mean‐squared error, and (2) the minimization of the maximum mean‐squared error. Deconvolution using an estimated wavelet can thus be made robust to wavelet uncertainties in an easily followed technique.