bluuebunny/crossref_metadata_2025 huggingface dataset:
Aliasing in the tau-p transform and the removal of spatially aliased coherent noise
Authors: Turner Greg
Published: October 2002

The tau-p transform is a discretized Radon transform. The choice of discretization parameters is a very important part of performing the transform. Insufficient sampling in the tau direction leads to aliasing problems equivalent to those encountered in any one‐dimensional time series. A simple graphical method illustrates that too coarse sampling in the p direction results in reconstructions containing data duplicated incorrectly at different spatial positions. The spacing of these duplications is dependent on the temporal frequency of the data. Insufficient spatial sampling of the original seismic data causes events to plot at multiple p values in tau-p domain, again dependent on temporal frequency. Therefore, to velocity filter spatially aliased noise efficiently, multiple p values must be filtered. The use of appropriate filters in the p-f domain can substantially improve the noise rejection capabilities of velocity filters on spatially aliased noise while having little effect on desired reflection signals.
On: “A Method to minimize edge effects in two‐dimensional discrete Fourier transforms” by Yanick Ricard and Richard J. Blakely (GEOPHYSICS, 53, 1113–1117, August 1988).
Authors: Sprenke Kenneth F.
Published: October 2002

The authors of this paper have created a very valuable method for approximating the two‐dimensional continuous spectrum by repeatedly rotating a rectangular sampling grid and averaging the resulting spectra. The authors state that their rotational transform “eliminates artifacts associated with the orientation of the rectangular sampling window.” However, I believe that one aspect of their method, the interpolation process, actually creates artifacts:
Measurement of dielectric response of water‐saturated rocks
Authors: Taherian M. R. , Kenyon W. E. , Safinya K. A.
Published: October 2002

We tabulate an extensive set of measurements of the complex permittivity (i.e., dielectric constant and conductivity) of brine saturated rocks in the frequency range 10–1300 MHz. Rather than listing the permittivity at each frequency, we present the parameters of a Cole‐Cole function used to fit the data for each rock sample. We choose the Cole‐Cole function for the following reason. The data sets from 271 rock samples were fitted to the commonly used functions in the literature, i.e., Cole‐Cole, Cole‐Davidson, and power law functions. We found that within experimental errors the fits to both the Cole‐Cole function and the power law represent the frequency dependence of the data better than the Cole‐Davidson function. Further, the Cole‐Cole function fits the data better at the high‐frequency end of our data. This result implies that five parameters of the Cole‐Cole function describe the frequency dependence of the complex permittivity of rock samples in the range 10–1300 MHz within experimental errors.
Electrical and magnetometric fields in a layered earth containing buried electrodes
Authors: Veitch D. , Asten M. W. , van Leeuwen E. H.
Published: October 2002

The number of analytical magnetometric resistivity (MMR) results available for basic earth geometries is limited compared to that of electrical resistivity methods, which is unfortunate since MMR has advantages for certain classes of problems. This paper extends the list of MMR results by deriving the response for the homogeneous half‐space and the multilayered earth. Both are calculated for arbitrary source and receiver positions. We show how the result for the layered earth reduces to that of the half‐space when there is only one layer. Necessary procedures for successful numerical evaluation of results for the layered case are given. Sample borehole logs of electric and magnetic fields for an example of a two‐layer model illustrate an advantage of the magnetic‐field measurement; namely, that it is sensitive to the position of layer boundaries rather than to the position of transmitter electrodes. The algorithm is also applied to interpretation of MMR field data from two boreholes drilled near massive sulfide conductors. The magnetometric influence (or background) due to borehole geometry in an electrically layered earth may be computed and subtracted from the field data, after which it is possible to perform quantitative modeling of the residual MMR anomaly to define the location of ore‐related conductors.
Terrestrial heat‐flow density estimates for the Jeanne D’Arc Basin, offshore eastern Canada
Authors: Correia A. , Jones F. W. , Fricker A.
Published: October 2002

Corrected bottom‐hole temperatures from 35 wells, together with measured and assumed rock thermal conductivities, are used to estimate linear geothermal gradients and effective thermal conductivities in the Jeanne d’Arc Basin in offshore eastern Canada. Heat‐flow density values calculated for each well location indicate that heat‐flow density is slightly higher in the deeper northern part of the basin than in the southern part. It appears that the heat‐flow density distribution is affected by fluid motion within the sediments and not by heat generation or basement topography. Dehydration is suggested as the mechanism that produces the fluid flow pattern that influences the heat‐flow density distribution in the basin, and a simple fluid flow model of the Jeanne d’Arc Basin is presented.
Normal moveout in anisotropic media
Authors: Uren N. F. , Gardner G. H. F. , McDonald J. A.
Published: October 2002

Elliptical anisotropy may be considered a more general case of isotropy, in which the medium has been stretched in one direction (Helbig, 1983; Dellinger and Muir, 1988; Verwest, 1989). As a consequence, certain principles and relationships hold for both isotropy, where wavefronts are circular, and elliptical anisotropy, where the wavefronts are circles which have been stretched in one direction (i.e., ellipses); while they may not hold for the general case of anisotropy, where wavefronts have more complex shapes. Examples are the dip moveout (DMO) relation (Uren et al., 1990) and the method of images (Dellinger and Muir, 1988).
Seismic identification of a karstified reservoir in the Adriatic Sea
Authors: Mendes M. , Beydoun W. , Planchon J. M. , Tarantola A.
Published: October 2002

In this study, an elastic prestack migration/inversion (M/I) scheme was applied to a 2-D seismic line collected in the Adriatic Sea. The objective was to use M/I images to describe a hydrocarbon reservoir, consisting of karstified, brine‐saturated limestones. The M/I technique offers the benefit of extracting maximum information from seismic reflection data to describe, and in some cases characterize, the reservoir target. M/I images are calibrated with well data and represent approximate changes in P- and S-wave impedances across the reservoir. Combining these two images yields a Poisson’s ratio image.
Wave separation and feature extraction of acoustic well‐logging waveforms using Karhunen‐Loeve transformation
Authors: Hsu K.
Published: October 2002

In sonic well logging, a source‐generated wave field is recorded at various points on the axis of a borehole. The recorded waveforms are extremely complicated because various wave components overlap in time and in frequency. I use the Karhunen‐Loeve (KL) transformation, also known as principal‐component analysis, to isolate a particular wave component of interest. The wave features of the primary P, S, and Stoneley waves are extracted by projecting (or transforming) the data into the KL space. The extracted wave features allow us to identify wave responses to different formations. Furthermore, the extracted features can be used as a data compression scheme. To reduce the computational burden, a quick way to obtain the approximations to the first and second eigenvectors, supplemented by a procedure to evaluate their accuracies, is given with the examples. Finally, although the examples appear only for the single‐receiver waveforms, the technique, in principle, has direct extension to arrays of waveforms.
Dipmeter analysis by a Monte Carlo technique
Authors: Schneider W. A. , Whitman W. W.
Published: October 2002

The dipmeter is a borehole tool that can be used to estimate the dip direction and magnitude of subsurface bedding. Typical computer dipmeter analysis utilizes crosscorrelation techniques which can be subject to cycle skipping. A Monte Carlo approach, based upon a method that was successfully applied to determining seismic residual statics, has been developed as an alternative dipmeter analysis method. The technique, which can process either raw or derivative dipmeter data, searches for the best‐fit plane through a depth interval of the data. This plane would approximate a bedding interface intersecting the borehole. Operating on a parameterized forward model, this statistical, iterative algorithm randomly perturbs a local depth shift applied to a dipmeter trace. The algorithm then checks how well that perturbation fits the data by locally stacking the data interval. Random perturbations that improve the solution are always accepted as updates of the parameters. However, random perturbations that degrade the solution are not necessarily rejected. Occasionally, these bad guesses are retained, which gives the algorithm the ability to avoid converging to local minima. Setting the proper initial acceptance‐to‐rejection ratio for bad guesses is important for successful convergence. This ratio is initially large but, after many iterations, is decreased substantially. If this ratio is initially too high, convergence may not occur within reasonable CPU time. If the ratio is initially too low, convergence to a local minimum may result. Testing showed that only a narrow range of initial bad‐guess acceptance‐to‐rejection ratios led to efficient global optimization. For synthetic and real dipmeter data, better results were achieved when processing differentiated dipmeter data than when processing raw dipmeter data.
On: “Comparison of plane‐wave decomposition and slant stacking of point‐source seismic data” by Rakesh Mithal and Emilio E. Vera (GEOPHYSICS, 52, 1631–1638, December 1987)
Authors: McCowan Douglas W.
Published: October 2002

Mithal and Vera give the impression that the correct cylindrically symmetric slant stack (e.g., Chapman, 1981; Harding, 1985; Brysk and McCowan, 1986a) needed to represent point‐source radiation in vertically stratified media is both expensive and unnecessary in ordinary data analysis.
Velocity anisotropy in shale determined from crosshole seismic and vertical seismic profile data
Authors: Winterstein D. F. , Paulsson B. N. P.
Published: October 2002

Crosshole and vertical seismic profile (VST) data made possible accurate characterization of the elastic properties, including noticeable velocity anisotropy, of a near‐surface late Tertiary shale formation. Shear‐wave splitting was obvious in both crosshole and VSP data. In crosshole data, two orthologonally polarrized shear (S) waves arrived 19 ms in the uppermost 246 ft (75 m). Vertically traveling S waves of the VSP separated about 10 ms in the uppermost 300 ft (90 m) but remained at nearly constant separation below that level. A transversely isotropic model, which incorporates a rapid increase in S-wave velocities with depth but slow increase in P-wave velocities, closely fits the data over most of the measured interval. Elastic constants of the transvesely isotropic model show spherical P- and [Formula: see text]wave velocity surfaces but an ellipsoidal [Formula: see text]wave surface with a ratio of major to minor axes of 1.15. The magnitude of this S-wave anisotropy is consistent with and lends credence to S-wave anisotropy magnitudes deduced less directly from data of many sedimentary basins.
Solution of the equations of dynamic elasticity by a Chebychev spectral method
Authors: Kosloff D. , Kessler D. , Filho A. Q. , Tessmer E. , Behle A. , Strahilevitz R.
Published: October 2002

We present a spectral method for solving the two‐dimensional equations of dynamic elasticity, based on a Chebychev expansion in the vertical direction and a Fourier expansion for the horizontal direction. The technique can handle the free‐surface boundary condition more rigorously than the ordinary Fourier method. The algorithm is tested against problems with known analytic solutions, including Lamb’s problem of wave propagation in a uniform elastic half‐space, reflection from a solid‐solid interface, and surface wave propagation in a haft‐space containing a low‐velocity layer. Agreement between the solutions is very good. A fourth example of wave propagation in a laterally heterogeneous structure is also presented. Results indicate that the method is very accurate and only about a factor of two slower than the Fourier method.
Representation of seismic sources in the one‐way wave equations
Authors: Wapenaar C. P. A.
Published: October 2002

One‐way extrapolation of downgoing and upgoing acoustic waves plays an essential role in the current practice of seismic migration (Berkhout, 1985; Stolt and Benson, 1986; Claerbout, 1985; Gardner, 1985). Generally, one‐way wave equations are derived for the source‐free situation. Sources are then represented as boundary conditions for the one‐way extrapolation problem. This approach is valid provided the source representation is done with utmost care. For instance, it is not correct to represent a monopole source by a spatial delta function and to use this as input data for a standard one‐way extrapolation scheme. This yields an erroneous directivity pattern as illustrated below.
Multigrid migration: Reducing the migration aperture but not the migrated dips
Authors: Gray S. H. , Epton M. A.
Published: October 2002

Given a frequency f, CDP interval Δx, and upper‐surface velocity v(0), the spatial Nyquist criterion defines a range of unaliased emergence angles for seismic reflection events. For migration, events outside that range should be discarded beforehand by dip filtering, or the migration operator should be trained to ignore them. In this paper, we express the spatial Nyquist criterion as a limitation on the CDP interval, rather than on emergence angle, which allows Δx to be adjusted as a function of emergence angle, increasing with decreasing emergence angle. We exploit this fact by creating two separate migration grids: a fine grid, with trace spacing Δx, for migrating events with large emergence angles; and a coarse grid, with trace spacing 2Δx, for migrating events with small emergence angles. Combining the two migrations is straightforward. The coarse grid migration, involving one‐half the number of input traces and one‐half the number of output traces, represents a considerable time savings over the small‐emergence‐angle portion of the migration on the original fine grid. The two migrations need not be performed separately, so that overhead associated with migration setup operations need not be paid twice. In fact, a modification of this idea allows the migration to be performed with almost no increase in storage requirements.
Wave‐field separation in two‐dimensional anisotropic media
Authors: Dellinger J. , Etgen J.
Published: October 2002

Until recently, the term “elastic” usually implied two‐dimensional (2-D) and isotropic. In this limited context, the divergence and curl operators have found wide use as wave separation operators. For example, Mora (1987) used them in his inversion method to allow separate correlation of P and S arrivals, although the separation is buried in the math and not obvious. Clayton (1981) used them explicitly in several modeling and inversion methods. Devaney and Oristaglio (1986) used closely related operators to separate P and S arrivals in elastic VSP data.
Source wavelet and its angular spectrum from plan‐wave seismograms
Authors: Carrion Philip M. , Sacramento Selma dos S. , Pestana Reynam da C.
Published: October 2002

In a typical seismic experiment (land or marine), the generated source wavelet is either unknown, or known only approximately. In order to solve many geophysical problems, an accurate wavelet estimation is crucial. This paper demonstrates a fast numerical algorithm which allows not only estimating the source wavelet but also its angular spectrum (radiation pattern) from plane‐wave decomposed seismograms. Surprisingly, literature on this subject is virtually missing, although a nonuniform angular spectrum of the generated wavelet can substantially affect the recorded data. The technique presented here is based on the downward continuation (DC) and reverse‐time extrapolation (RTE) of the recorded data (both pressure and its vertical derivative). The proposed method is iterative: The rate of convergence does not depend on phase characteristics of the generated wavelet. We demonstrate that both the wavelet signature and its angular spectrum can be estimated accurately from plane‐wave seismograms. We also illustrate the technique on a variety of wavelets with different amplitude/phase characteristics.
Large‐scale three‐dimensional seismic models and their interpretive significance
Authors: Mufti Irshad R.
Published: October 2002

Finite‐difference seismic models are commonly set up in 2-D space. Such models must be excited by a line source which leads to different amplitudes than those in the real data commonly generated from a point source. Moreover, there is no provision for any out‐of‐plane events. These problems can be eliminated by using 3-D finite‐difference models. The fundamental strategy in designing efficient 3-D models is to minimize computational work without sacrificing accuracy. This was accomplished by using a (4,2) differencing operator which ensures the accuracy of much larger operators but requires many fewer numerical operations as well as significantly reduced manipulation of data in the computer memory. Such a choice also simplifies the problem of evaluating the wave field near the subsurface boundaries of the model where large operators cannot be used. We also exploited the fact that, unlike the real data, the synthetic data are free from ambient noise; consequently, one can retain sufficient resolution in the results by optimizing the frequency content of the source signal. Further computational efficiency was achieved by using the concept of the exploding reflector which yields zero‐offset seismic sections without the need to evaluate the wave field for individual shot locations. These considerations opened up the possibility of carrying out a complete synthetic 3-D survey on a supercomputer to investigate the seismic response of a large‐scale structure located in Oklahoma. The analysis of results done on a geophysical workstation provides new insight regarding the role of interference and diffraction in the interpretation of seismic data.
Noise elimination by the use of vector resolution
Authors: Wang Hongwei
Published: October 2002

This paper introduces the concept of the Unit Similarity Vector (USV) which is based on the hypothesis that signals on adjacent channels are similar, and then discusses how the amplitude vector formed in a multichannel environment, is resolved into two components—the similarity component and the dissimilarity component. The signal‐to‐noise ratio can be enhanced by compressing the dissimilarity component. Excellent results are obtained using the method with surface seismic data, and satisfactory results are also obtained with three‐component VSP data sets.
Inversion of airborne gravity gradient data, southwestern Oklahoma
Authors: Vasco D. W. , Taylor C.
Published: October 2002

The diagonal elements of the gravity gradient tensor, as recorded by the Bell airborne Gravity Gradient Survey System (GGSS), are used to determine the basement topography in southwestern Oklahoma. This determination is accomplished through a nonlinear inverse procedure based on the conjugate gradient algorithm. The resulting model contains a ridge of shallow basement material (⩽3.0 km deep) trending east‐southeast. This ridge is bounded on the north and the south by basement troughs; the northern trough extends as deep as 10.0 km. The gradient field which results from this model fits most of the GGSS observations within their estimated errors of 12.0 E [Formula: see text]. The model is in general agreement with a set of available oil well depths to the basement and with inferred faults in these igneous rocks. To assess the derived solution, the problem was linearized about the final model and the linear parameter resolution and parameter covariances were computed. Generally, the basement depths are well resolved and the resolution matrix is diagonally dominant. Furthermore, the parameter standard errors are small: 72 parameters out of 98 have errors less than 1.0 km.
Seismic monitoring of water floods?—A petrophysical study
Authors: Wang Zhijing , Hirsche W. Keith , Sedgwick George
Published: October 2002

Seismic velocities were measured in the laboratory on 67 samples as a function of pressure and temperature when saturated with gas and a 35° API = 141.5/(density at 1 atmosphere and 60°F) − 131.5] mineral oil and flooded with pentane and fresh water, respectively, using an ultrasonic pulse transmission method. The rock samples consisted of 39 carbonate cores from eight reservoirs, 22 sandstone cores from six formations, and six unconsolidated samples from three origins. The results show that water flooding increases the compressional velocity [Formula: see text] by more than 5 percent in most of the gas‐saturated cores at effective pressures (overburden pressure minus pore pressure) less than 20 MPa. Such [Formula: see text] increase is less than 5 percent in about half of the carbonate cores and some of the sandstone cores with normal pentane and in all the consolidated cores (both carbonates and sandstones) saturated with the 35° API oil. However, in unconsolidated samples saturated with gas, pentane, or oil, water flooding increases the [Formula: see text] substantially. Both the laboratory results and theoretical analysis show that seismic methods may succeed in monitoring water floods in some reservoirs under certain conditions, while they may fail in others. It is thus important to carry out petrophysical and feasibility studies prior to the implementation of in‐situ seismic monitoring of water‐flood processes.
Fractal stochastic modeling of aeromagnetic data
Authors: Gregotski Mark E. , Jensen Olivia , Arkani‐Hamed Jafar
Published: October 2002

We present a convolutional linear data model for the processing of aeromagnetic data. The model assumes that the data derive from the superposition of a deterministic system function and a stochastic innovation process. The two‐dimensional system function is described by a four‐pass autoregressive (AR) filtering procedure and is radially symmetric. The innovation process represents the distribution of near‐surface magnetic sources and is modeled as a spectrally self‐scaling (i.e., fractal) noise. The appropriate fractal noise is determined by examining aeromagnetic power spectra from various areas of the Canadian Shield. The AR coefficients of the system are determined using an iterative deconvolution procedure. For computational convenience, we make the traditional assumption of a spectrally white innovation, but modify the data prior to its deconvolution by prewhitening the assumed fractal innovation. The recovered system function is then removed from the original data in order to produce the fractal stochastic surface. This deconvolution technique is applied to two aeromagnetic maps from northeastern Ontario, Canada and is shown to be effective in delineating lithologies and enhancing magnetic field anomalies. We propose a particular statistical description of near‐surface magnetic sources for modeling aeromagnetic data in “shield‐type” geologic environments.
MWD resistivity tool response in a layered medium
Authors: Zhou Q. , Hilliker D. J.
Published: October 2002

Numerical solutions for the electromagnetic response of a measurements‐while‐drilling (MWD) resistivity tool in a layered formation are developed. Because of the highly conductive mandrel on which the transmitter and receiver coils are mounted, the geometry of the problem is two‐dimensional. To take advantage of the problem geometry, a boundary integral equation approach is initially applied for accurate evaluation. Then the problem is simplified to one‐dimension by using the image current concept. This solution is equivalent to that of a vertical magnetic dipole in a layered medium, yielding significant savings in computer time. The tool responses calculated from the two methods match each other very closely, and the accuracy of both methods is verified. Correction charts are generated to correct the thin‐bed response for shoulder bed effects.
Transforming a point‐source seismogram into a beam seismogram
Authors: Tygel M. , Leykam A. , Hubral P. , Amorim W. N. , Pestana R.
Published: October 2002

The point‐source seismogram from a horizontally stratified acoustic medium can be transformed by a beam filter into the response of a beam that essentially propagates in the vertical direction. This response, which still obeys the wave equation, naturally enhances the near‐offset traces, thus providing a better illumination of the region below the source.
Northwestern Williston Basin case histories with 3-D seismic data
Authors: Connelly D. L. , Ferris B. J. , Trembly L. D.
Published: October 2002

Two Northwestern Williston Basin field studies illustrate the cost‐effective geological and three‐dimensional seismic methods used to explore for structurally controlled oil reservoirs in the Tule Creek area of northeast Montana. These examples present the geologic and seismic characteristics of a Mississippian Charles C zone pool at Northwest Poplar field and a Devonian Nisku accumulation at Long Creek West field. A classic, upward‐shoaling, nearshore marine carbonate sequence characterizes the reservoir and associated strata in both fields. The Charles C zone pool of Northwest Poplar field is a subtle, tectonically‐controlled accumulation which remained undiscovered and downdip from the large, nearby, well‐known East Poplar field until 1983. Long Creek West field exhibits the subtle character of small closed structures produced by multistage evaporite solution. Three‐dimensional (3-D) seismic techniques best detect such fields of low vertical relief and small areal extent. The significant acquisition costs of multifold, 3-D seismic surveys led us to design, acquire, process, and interpret single‐fold 3-D surveys to disclose these subtle, small structures. Augmented conventional 48-channel vibroseis crews collected the 3-D data. Near‐surface glacial till deposits in the area created residual statics and normal‐moveout problems on the single‐fold data. These processing problems were handled by constraining the statics and normal‐moveout velocity solutions with plausible geologic conditions: the near‐flat attitude of the reflecting beds, and the inferred horizontal simplicity of the earth velocity field. Our geologically constrained processing methods included: single‐event correlation picking, single‐fold, surface‐consistent statics, and velocity interpolation on flattened events. In addition, spatially oriented six‐fold stacking increases the signal‐to‐noise ratio in areas where poor signal quality exists. In the case of Northwest Poplar field, geologic studies and subsequent interpretations involving isochron mapping techniques showed that the absence of Mississippian evaporites and paleostructural thinning produce disruption of evaporite events and interval thinning near the evaporites, respectively. Long Creek West field exhibited the interval thickening below, and the interval thinning above the trap formed by two‐stage evaporite solution. Careful analysis of geologic conditions coupled with single‐fold 3-D methods makes it possible to economically explore for small undiscovered structural traps in a mature exploration area.
Ray tracing in 3-D complex isotropic media: An analysis of the problem
Authors: Virieux Jean , Farra Véronique
Published: October 2002

Procedures for accurate ray tracing in complex three‐dimensional media with interfaces are proposed. The ray tracing equations and the associated paraxial linear equations are solved either by a numerical solver or by an analytical perturbation approach. Interfaces are described with an explicit representation or an implicit representation using B-spline interpolation. For the implicit representation, we exploit two important properties of B-splines, the convex hull and subdivision properties, in order to determine the intersection of the ray with the interface. At the free surface where the recording system is located, a sampling strategy is proposed: limits of branches at caustics, shadow zones, and medium boundaries are detected for a fixed azimuth while the take‐off angle is automatically adjusted in order to have a roughly homogeneous spacing between end points of the rays. The same strategy is also possible for a fixed take‐off angle. The assumed continuity of the traveltime surface between two adjacent azimuths enables one to obtain the initial condition of a ray arriving at any station located on the portion of surface delimited by these two azimuths. This procedure allows for the classification of rays arriving at a given station as we show on different synthetic examples.
Why don’t we measure seismic signatures?
Authors: Ziolkowski A.
Published: October 2002

There are three related problems with our approach to signature deconvolution. First, there is a confusion among geophysicists about the basis of the convolutional model itself, which leads to doubts about the value of measurements of the source signature. Secondly, it is not generally recognized that statistical methods of wavelet estimation are unreliable. Thirdly, many explorationists are unaware that it is practical in many cases to make meaningful measurements of the source signature. The convolutional model of the reflection seismogram applies only for a point source, and is the convolution of the source signature with the impulse response of the earth, of Green’s function, which contains all possible arrivals, including reflections, refractions, multiples and diffractions. Stabilized deconvolution of the data with a known band‐limited signature is straightforward. The signature can be obtained by independent measurements, as described in the literature. The recovery of the elastic layer parameters from the band‐limited impulse response of the earth, after removal of the source signature by deconvolution, is the problem of inversion, and is not discussed in this paper. The theory of wave propagation does not support the commonly held view that a reflection seismogram can be regarded as a convolution of a wavelet with the series of normal‐incidence primary reflection coefficients. This is true of both prestack and poststack data. Poststack seismic inversion schemes, based on this model, that use well logs to extract the wavelet for predicting lateral variations in lithology away from the wells, rely on the wavelet to be laterally invariant. Even if there is perfect shot‐to‐shot repeatability, this model must yield a different wavelet at every well, and therefore the extracted wavelet does vary laterally. These schemes are therefore self‐contradictory and, in the worst cases, their results are likely to be worthless. Published methods for determining the source signature from measurements for the land vibrator, marine seismic source arrays, and dynamite on land are summarized. None of these methods appears to be in use. A Vibroseis example is included to show that the signal transmitted into the ground by the vibrators does not closely resemble the predetermined sweep, as is normally assumed. The transmitted signal could be determined in processing from measurements of the vibrator behaviour that are made in production for vibrator control, if only these measurements were recorded. Normally they are not. Instead of using measurements to determine the signature, the exploration industry relies on wavelet estimation methods that depend on both a model and statistical assumptions that have no theoretical justification.
Measurement of borehole seismic noise with hydrophones
Authors: Chouzenoux C.
Published: October 2002

High sensitivity hydrophones are needed to detect borehole pressure noise in the 1 kHz frequency band. Measurements conducted at various sites show that seismic noise level in borehole drops rapidly as frequency increases (−12 dB per octave). In a quiet environment, the measured rms pressure noise level is 2 mPa around 1 kHz; a crosswell system working in this frequency range will take full advantage of low seismic noise level. Moreover, part of borehole seismic noise propagates as tube waves so that noise reduction is expected by array filtering techniques. In case of a noisy environment such as producing pumps near the receiving well, special attention should be paid to pumping activity within a range of 150 m.
Pore geometry and pressure dependence of the transport properties in sandstones
Authors: Bernabe Y.
Published: October 2002

The model of the pore geometry of sandstones proposed in this paper is based on three‐dimensional qualitative observations of the pore structure of sandstones reported in the literature. Three categories of pores can be distinguished: large spherical pores at four‐grain vertices (or nodal pores); tube‐like throats at three‐grain edges; and narrow sheet‐like throats at two‐grain faces. As a first step, the model is limited to rocks with a low clay content and, therefore, pores and throats are supposed to be free of clay. In this model, the sheet‐like and tube‐like throats are in parallel and, because of their different shapes, respond differently to pressure. The transport properties can thus be split into two parts: a strongly pressure dependent part associated with the sheet‐like throats and an approximately constant part associated with the tube‐like throats and the equidimensional nodal pores. Following these remarks, a scheme to estimate the volume fraction of each category of pores using the pressure dependence of the transport properties and a simple capillary model is developed. This approach was applied to data from the literature and appeared to succeed and fail when it was expected to (however, one exception was noted). For 15 of the 27 sandstones considered, the volume fraction and the size of the throats and pores predicted agreed in order of magnitude with microstructure data gathered in the literature. For several of the 12 remaining sandstones, independent microstructure data showed that basic assumptions of the model were not satisfied. Eight of these sandstones were associated with high clay content, and it was speculated that the last four might contain semimacroscopic fissures.
Linear aspects of tomographic velocity analysis
Authors: Stork C. , Clayton R. W.
Published: October 2002

Prestack velocity analysis in areas of complex structure is a coupled migration and transmission inversion problem that can be analyzed from a tomographic perspective. By making as few a priori assumptions about the solution as possible in parameterizing the inverse problem, generalized tomographic velocity analysis is applicable to a wide range of geologic cases. Constraints modify the method to the unique characteristics of each application. The ray trace/traveltime formulation for tomography, as proposed by Bishop et al. (1985), provides a conceptual tool for presenting features that are important to automated prestack velocity analysis in complex structure, such as (1) the coupling of the velocity field to the reflector positions, (2) the nonuniform coverage of the model by the data, (3) the ability to perform a controlled inversion of large matrices over a wide eigenvalue range, and (4) the implementation of constraints in the inversion. These features may impact other automated prestack velocity analysis methods for reflection seismology.
Could the processed seismic wavelet be simpler than we think?
Authors: Neidell N. S.
Published: October 2002

J. P. Lindsey, (1988) in a clearly written short piece, opens an old question which concerns the analytic properties of seismic wavelets. This well conceived study concludes that most of the roots of a seismic wavelet as expressed by its z transform representation lie on or are very near the unit circle. The present discussion does not seek to characterize the form of all seismic wavelets, but only many if not most of those which have been processed with deconvolutions or “inversion” type operators to have reduced length, broadened bandwidth, and some desirable phase property. For such wavelets, despite the diversity by which they are obtained, remarkably simple operations having very few parameters can be extremely effective. As a case in point, constant‐phase rotations appear to carry such wavelets to zero‐phase symmetric form to a very good approximation. I start with empirical attributes which appear to characterize most processed seismic wavelets. Such wavelets tend to be of 40–100 ms duration with a smooth and unimodal amplitude spectrum of “peak” or “central” frequency between 15 and 30 Hz. The amplitude spectrum itself is further largely concentrated at frequencies between 5 and 55 Hz. A z transform root structure having essentially all of its roots only on the unit circle and on the real axis seems able to characterize all of the observed attributes rather well. This structure will be termed the band‐limiting root approximation (BLRA) and describes the attributes I seek to explain which are not as readily understood from alternative descriptions of the wavelets. Since the class of wavelets we address is obtained by a variety of means, and because the differences in character are at best subtle according to interpretive criteria, my justification is heuristic. The BLRA wavelet structure can be represented with remarkably few parameters (typically fewer than five). Of these few parameters, two relate to the frequency distribution. Such a formalism should be exceptionally useful for designing seismic techniques which seek to extract interpretive information based on properties of the wavelet.
Thin‐layer fracture density
Authors: Spencer T. W. , Chi H. C.
Published: October 2002

Vertically propagating shear waves reflected from a thin reservoir permeated by a single oriented system of open vertical fractures contain information about the fracture density. The outer perimeter of the hodogram constructed from shear waves polarized in the fast and slow directions in the natural coordinate system is approximately elliptical. The polarization is defined as the angle which the major axis of the ellipse makes with the natural coordinate. Over a range of layer thickness which extends well above and below the tuning frequency, the polarization does not deviate from its value for an infinitely thick layer, [Formula: see text], by more than a few degrees. [Formula: see text] and [Formula: see text] are the reflection coefficients in the fast and slow directions. [Formula: see text] is independent of the fracture density, but ψ, [Formula: see text], and the anisotropy η all depend on the fracture density. [Formula: see text], [Formula: see text], and η are related by [Formula: see text]. Analysis of the constant‐anisotropy hyperbolas derived from this equation reveals conditions under which ψ is extremely sensitive to variations in anisotropy. As η increases by 20 percent, the change in ψ approaches 135 degrees for small negative [Formula: see text] and 45 degrees for small positive [Formula: see text]. The ellipse is also characterized by an aspect ratio which is significantly different from zero over a range of layer thickness that extends above and below the tuning frequency. Aspect ratio versus polarization (ARP) curves can be constructed from multi component field data. Each curve is constructed for fixed [Formula: see text] and [Formula: see text] (the two‐way traveltime across the layer for the fast polarization). [Formula: see text] and [Formula: see text] are independent of lateral changes in fracture density. Consequently, points on ARP curves correspond to different values of the anisotropy. If [Formula: see text] is known from well measurements, [Formula: see text] can be determined and a value of anisotropy assigned to each point where there is a field measurement.
A simple approach to improve the S/N ratio for TEM data using multiple receivers
Authors: Stephan A. , Strack K.‐M.
Published: October 2002

Since electromagnetic (EM) techniques are very sensitive to cultural noise, many cases exist where standard processing techniques do not yield satisfactory signal‐to‐noise ratios (S/N). For EM surveys in areas with coherent regional EM noise we have developed a local noise compensation (LNC) technique. This technique, for transient EM methods, uses several mobile receivers referenced to a nearby (local) base station. LNC is applied as a prestack processing technique, and it is intended for multichannel systems with close receiver spacings. The main premise for LNC is that the regional noise is highly correlated over a region around the base station and that any other, more localized, noise is small. These assumptions must be tested at the beginning of the survey. The base station remains fixed with measurements being recorded continuously. Meanwhile, measurements are made at various other mobile stations in the zone of coherent noise. During the subsequent signal processing and removal of the transient signal, the actual noise at the base station is calculated as a function of time. Then, this noise is subtracted from the time series measured at the mobile sites. The method results in improvements in data quality, in depth of investigation and in productivity. Field tests carried out in Germany demonstrate results in an environment where the initial test showed that the necessary assumptions were not satisfied, although improvements in the S/N of the single records were obtained. Field tests in the Peoples Republic of China show a successful application of the technique, whereby the length of the usable signal was increased by a factor of about ten.
On: “Temperature dependence of the electrical resistivity of water‐saturated rocks” by F. J. Llera, M. Sato, K. Nakatsuka, and H. Yokoyama (GEOPHYSICS, 56, 576–585, May 1990)
Authors: Evans Hilton B.
Published: October 2002

Perhaps I missed something in this paper by Llera et al., but the data presented in their Table 1, their saturating fluid resistivity and Archie’s relationship [their equation (1)] do not seem to be consistent. For example, the authors give the saturating solution resistivity [Formula: see text] to be 70 Ω⋅m at 20° C, which is about 60 Ω⋅m at 30° C using the plots of Figure 4, p. 580; and on p. 582, the authors suggest a value of m = 2.0 for the cementation exponent. Sample 1 in Table 1 gives the rock resistivity (ρϕ) at 30° C to be 30 Ω⋅m and the porosity (ϕ) is 4.5 percent; then, using the Archie relationship, we would expect one of the following if a = 1.0.
Processing via spectral modeling
Authors: Rosa A. L. R. , Ulrych T. J.
Published: October 2002

The widespread occurrence of subtle trap accumulations offshore Brazil has led to the need for the development of a high resolution processing scheme that helps the delineation of these features. The process consists of three stages, the first of which is deterministic and stochastic deconvolution. The second stage is the deconvolution of the residual wavelet by means of spectral modeling. The last stage consists of the correction of the color of the reflectivity function using a model developed for the area. An important conclusion that is drawn from the model is that the acoustic impedance is not white. Rather it is as red as the corresponding reflectivity is blue. Successful results from the application of the proposed technique to real data indicate that the color compensation is of second order importance as compared with the first two stages of the proposed scheme.
Shear‐wave polarizations and subsurface stress directions at Lost Hills field
Authors: Winterstein D. F. , Meadows M. A.
Published: October 2002

2 × 2 S-wave data matrix, accomplished by computationally rotating sources and receivers. Although polarization directions obtained by assuming a homogeneous subsurface were moderately consistent with depth, considerable improvement in consistency resulted from analytically stripping off a thin near‐surface layer whose fast S-wave polarization direction was about N 6°E. S-wave birefringence for vertical travel averaged 3 percent in two zones, 200–700 ft and 1200–2100 ft (60–210 m and 370–640 m), which had closely similar S-wave polarizations. Between those zones, the polarization direction changed and the birefringence magnitude was not well defined. S-wave polarizations from two concentric rings of offset VSPs were consistent in azimuth with one another and with polarizations of the near offset VSP. This consistency argues strongly for the robustness of the S-wave polarization technique as applied in this area. The S-wave polarization pattern in offset data fits a model of vertical cracks striking N 55°E in a weakly transversely isotropic matrix, where the infinite‐fold symmetry axis of the matrix is tilted 10 degrees from the vertical towards N 70°E. Such a model is of monoclinic symmetry.
Inversion modeling of gravity with prismatic mass bodies
Authors: Lee Tieng‐Chang , Biehler Shawn
Published: October 2002

A combined method for forward and inverse modeling of gravity data is presented. Based on the Fourier transform of Poisson’s equation, the forward modeling is suitable for observation points above, within, and below causative masses with any prescribed density distribution. The inversion is linearized in the spatial domain by superimposing numerous prismatic bodies, each having constant but different density, and fixed geometry. Our inversion algorithm adopts a sampling window to reduce memory storage and computations. Testing, with synthetic and field data, demonstrates that a successful inversion can be obtained from crudely estimated a priori density distributions and uncertainties. Lateral variations in density are well resolved but depth resolution often requires better constrained a priori information. Under various a priori conditions, our modeling indicates that sediment density tends to vary exponentially with depth in the San Jacinto basin, southern California.
Can we perform statistical deconvolution by polynomial factorization?
Authors: Ziolkowski Anton , Slob Evert
Published: October 2002

We investigate the possibility of finding the source signature from multichannel seismic data by factorization of the Z-transforms of the seismic traces. In the convolutional model of the data, the source signature is the same from trace to trace within a shot gather, while the impulse response of the earth varies. In the noise‐free case, the roots of the Z-transform of the wavelet are the same from trace to trace, while the roots of the Z-transform of the impulse response of the earth must move from trace to trace. It follows that the roots of the wavelet can be found by the invariance of their positions. We demonstrate this using a simple wedge model. No assumptions about the length of the wavelet or the statistical properties of the impulse response of the earth are required. It is shown that this idea cannot work on real seismic data. There are two difficulties which we regard as insuperable. First, even without noise, a seismic trace cannot be regarded as a complete convolution, because the data are always truncated. This causes the factorization to be inexact: the wavelet roots move from trace to trace and are indistinguishable from the roots of the earth’s impulse response. Second, the addition of a small amount of noise alters the root pattern unpredictably from trace to trace and the roots of the wavelet are again indistinguishable from the roots of the earth’s impulse response. We conclude that it is impossible to identify and extract the true source signature from real seismic data using no assumptions about the statistical properties of the impulse response of the earth. We propose that the signature should be measured.