bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonuniform fast Fourier transform
Authors: Duijndam A. J. W. , Schonewille M. A.
Published: October 2002

The nonuniform discrete Fourier transform (NDFT) can be computed with a fast algorithm, referred to as the nonuniform fast Fourier transform (NFFT). In L dimensions, the NFFT requires [Formula: see text] operations, where M𝓁 is the number of Fourier components along dimension 𝓁, N is the number of irregularly spaced samples, and ε is the required accuracy. This is a dramatic improvement over the [Formula: see text] operations required for the direct evaluation (NDFT). The performance of the NFFT depends on the lowpass filter used in the algorithm. A truncated Gauss pulse, proposed in the literature, is optimized. A newly proposed filter, a Gauss pulse tapered with a Hanning window, performs better than the truncated Gauss pulse and the B-spline, also proposed in the literature. For small filter length, a numerically optimized filter shows the best results. Numerical experiments for 1-D and 2-D implementations confirm the theoretically predicted accuracy and efficiency properties of the algorithm.
On: “Wavelets, well ties, and the search for subtle stratigraphic traps,” (A. Ziolkowski, J. R. Underhill, and R. G. K. Johnston, GEOPHYSICS, 63, 297–313)
Authors: White Roy E.
Published: October 2002

This paper by Ziolkowski, Underhill, and Johnson (abbreviated below to ZUJ) opens by speaking of problems in tying seismic data to wells that have not been addressed properly. Yet it fails to present any solid evidence of the problems it claims to address and shows no clear awareness of the state of the art. The paper’s arguments are sustained only by ignoring important distinctions, degrees of approximation, necessary trade‐offs in processing, and quantitative analysis.
New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry
Authors: Druskin Vladimir L. , Knizhnerman L. A. , Lee Ping
Published: October 2002

Traditional resistivity tools are designed to function in vertical wells. In horizontal well environments, the interpretation of resistivity logs becomes much more difficult because of the nature of 3-D effects such as highly deviated bed boundaries and invasion. The ability to model these 3-D effects numerically can greatly facilitate the understanding of tool response in different formation geometries. Three‐dimensional modeling of induction tools requires solving Maxwell’s equations in a discrete setting, either finite element or finite difference. The solutions of resulting discretized equations are computationally expensive, typically on the order of 30 to 60 minutes per log point on a workstation. This is unacceptable if the 3-D modeling code is to be used in interpreting induction logs. In this paper we propose a new approach for solutions to Maxwell’s equations. The new method is based on the spectral Lanczos decomposition method (SLDM) with Krylov subspaces generated from the inverse powers of the Maxwell operator. This new approach significantly speeds up the convergence of standard SLDM for the solution of Maxwell’s equations while retaining the advantages of standard SLDM such as the ability of solving for multiple frequencies and eliminate completely spurious modes. The cost of evaluating powers of the matrix inverse of the stiffness operator is effectively equivalent to the cost of solving a scalar Poisson’s equation. This is achieved by a decomposition of the stiffness operator into the curl‐free and divergence‐free projections. The solution of the projections can be computed by discrete Fourier transforms (DFT) and preconditioned conjugate gradient iterations. The convergence rate of the new method improves as frequency decreases, which makes it more attractive for low‐frequency applications. We apply the new solution technique to model induction logging in geophysical prospecting applications, giving rise to two orders of magnitude convergence improvement over the standard Krylov subspace approach and more than an order of magnitude speed‐up in terms of overall execution time. This makes it feasible to routinely use 3-D modeling for model‐based interpretation, a breakthrough in induction logging and interpretation.
Frequency analysis of time‐domain reflectometry (TDR) with application to dielectric spectroscopy of soil constituents
Authors: Friel Richard , Or Dani
Published: October 2002

Standard analyses of time‐domain reflectometry (TDR) waveforms in environmental sciences use traveltime along waveguides and reflection amplitude to infer water content and bulk electrical conductivity, respectively. TDR waveforms contain additional information on the frequency‐dependent dielectric permittivity of media, which can be extracted through transformation of TDR waveforms into the frequency domain. The primary objective of this study was to provide a more complete picture of TDR responses in the frequency domain and to improve estimation of dielectric properties. The frequency content of TDR waveforms interacting with various constituents was measured and compared with predictions based on known dielectric properties and waveguide geometries. The study highlights the dominant role of the S11 scatter function, which describes how a TDR signal is modified by media properties and probe configuration. Scatter functions derived from transformed TDR waveforms into the frequency domain were used for estimation of frequency‐dependent dielectric properties of wet soils. The main results were (1) a more complete picture of TDR waveforms in the frequency domain; (2) estimation and use of scatter functions for TDR‐based dielectric permittivity estimation; and (3) highlights of potential usefulness and limitations of a commonly used TDR cable tester (Tektronix 1502B) and waveguide design for estimation of frequency‐dependent dielectric properties of porous media.
Resistivity and percolation study of preferential flow in vadose zone at Bokhorst, Germany
Authors: al Hagrey S. A. , Michaelsen Johannes
Published: October 2002

Traditional nondestructive resistivity techniques have been applied in combination with tracer displacement and conventional soil moisture recording methods [i.e., buried tensiometer and time domain reflectometry (TDR)] for studying flow processes at an arable site in Bokhorst, Germany. Three water infiltration experiments were carried out using tap water spiked with a nonreactive tracer at different concentrations. The study aimed at exploring the capabilities of these combined techniques for tracing the preferential movement of water in the uppermost 1.5 m of the highly heterogeneous vadose zone. The results illustrate that the applied tensiometer and TDR techniques can detect the relatively fast flow process at their position points and thus only tentatively trace the preferential flow. The additional application of the resistivity method can trace the preferential flow paths continuously along the plane of measurements. The results of the individual applied methods complement and confirm each other.
3-D moveout velocity analysis and parameter estimation for orthorhombic media
Authors: Grechka Vladimir , Tsvankin Ilya
Published: October 2002

Orthorhombic symmetry describes several azimuthally anisotropic models typical for fractured formations, such as those containing two orthogonal crack systems or parallel vertical cracks in a VTI (transversely isotropic with a vertical symmetry axis) background. Here, we present a methodology for inverting multiazimuth P-wave reflection traveltimes for the parameters of vertically inhomogeneous orthorhombic media. Our approach is based on the general analytic representation of normal‐moveout (NMO) velocity as an ellipse in the horizontal plane. A minimum of three differently oriented common‐midpoint (CMP) lines (or a “wideazimuth” 3-D survey) is needed to reconstruct the ellipse and thus obtain NMO velocity in any azimuthal direction. Then, the orientation and the semiaxes of the NMO ellipse, which are dependent on both anisotropy and heterogeneity, can be inverted for the medium parameters. Our analytic and numerical study shows that for the model of a homogeneous orthorhombic layer above a dipping reflector, the exact P-wave NMO velocity is determined by the symmetry‐plane orientation and five parameters: the NMO velocities from a horizontal reflector measured in the symmetry planes [[Formula: see text]] and three anisotropic coefficients η(1,2,3)introduced by analogy with the Alkhalifah‐Tsvankin parameter η for VTI media. The importance of the medium parameterization in terms of the η coefficients goes well beyond the NMO-velocity function. By generating migration impulse responses, we demonstrate that the parameters [Formula: see text] and η(1,2,3)are sufficient to perform all time processing steps (normal‐moveout and dip‐moveout corrections, prestack and poststack time migration) in orthorhombic models. The velocities [Formula: see text] and the orientation of the vertical symmetry planes can be found using the azimuthally dependent NMO velocity from a horizontal reflector. Then the NMO ellipse of at least one dipping event is additionally needed to obtain the coefficients η(1,2,3)that control the dip dependence of normal moveout. We discuss the stability of the inversion procedure and specify the constraints on the dip and azimuth of the reflector; for instance, for all three η coefficients to be resolved individually, the dip plane of the reflector should not coincide with either of the symmetry planes. To carry out parameter estimation in vertically inhomogeneous orthorhombic media, we apply the generalized Dix equation of Grechka, Tsvankin and Cohen, which operates with the matrices responsible for interval NMO ellipses rather than with the NMO velocities themselves. Our algorithm is designed to find the interval values of [Formula: see text] and η(1,2,3)using moveout from horizontal and dipping reflectors measured at different vertical times (i.e., only surface P-wave data are needed). Application to a synthetic multiazimuth P-wave data set over a layered orthorhombic medium with depth‐varying orientation of the symmetry planes verifies the accuracy of the inversion method.
Removal of water‐layer multiples from multicomponent sea‐bottom data
Authors: Osen Are , Amundsen Lasse , Reitan Arne
Published: October 2002

A method for suppressing water‐layer multiples in multicomponent sea‐floor measurements is presented. The multiple suppression technique utilizes the concept of wavefield separation into upgoing and downgoing modes just below the sea floor for eliminating the sea‐floor ghost, the sea‐surface ghost, and the accompanying water‐layer reverberations. The theory applies to each of the recorded components: pressure, vertical velocity, and horizontal velocities. The fundamental physical principle for the multiple suppression technique rests on identifying these multiples as downgoing waves just below the sea floor, while the primaries of interest arriving from the subsurface are upgoing waves. White presented this realization for the pressure component three decades ago; hence, the theory for the velocity field is an extension of the theory. In this paper, the theory is derived for an experiment with a marine source in the water layer above a locally flat, elastic sea floor with known elastic parameters. The method is otherwise multidimensional and operates on a shot‐to‐shot basis; hence, it is computationally fast. Aside from this, we show that this demultiple method removes the strongest multiples in sea‐floor data without knowledge of the source wavelet. Synthetic and real data examples are provided to illustrate the application of the algorithms to the pressure, in‐line velocity, and vertical velocity components. The numerical tests show that strong multiples have been attenuated on the pressure and the velocity recordings, producing promising results.
A recipe for stability of finite‐difference wave‐equation computations
Authors: Lines Larry R. , Slawinski Raphael , Bording R. Phillip
Published: October 2002

Finite‐difference solutions to the wave equation are pervasive in the modeling of seismic wave propagation (Kelly and Marfurt, 1990) and in seismic imaging (Bording and Lines, 1997). That is, they are useful for the forward problem (modeling) and the inverse problem (migration). In computational solutions to the wave equation, it is necessary to be aware of conditions for numerical stability. In this short note, we examine a convenient recipe for insuring stability in our finite‐difference solutions to the wave equation. The stability analysis for finite‐difference solutions of partial differential equations is handled using a method originally developed by Von Neumann and described by Press et al. (1986, p. 827–830).
The wavelet transform in aeromagnetic processing
Authors: Ridsdill‐Smith T. A. , Dentith M. C.
Published: October 2002

The discrete wavelet transform (DWT) provides an effective and efficient alternative to traditional Fourier and spatial‐convolution processing techniques in the enhancement of aeromagnetic data. Standard operators such as horizontal and vertical derivatives, integrals of any order, and the Hilbert transform can be diagonalized in the wavelet domain, leading to an efficient algorithm. The DWT preserves the spatial localization of the components of the signal, allowing for intelligent discrimination between noise and signal in a given frequency range. This, for example, allows for more accurate calculation of higher order derivatives from noisy signals than is possible with conventional techniques. Additional accuracy can be gained by using a cycle‐spinning algorithm to minimize local artifacts from the DWT denoising procedure.
Filtering coherent noise during prestack depth migration
Authors: Duquet Bertrand , Marfurt Kurt J.
Published: October 2002

We can often suppress short‐period multiples by predictive deconvolution. We can often suppress coherent noise with significantly different moveout by time‐invariant dip filtering on common‐shot, common‐receiver or NMO-corrected common‐midpoint gathers. Unfortunately, even time variant dip filtering on NMO-corrected data breaks down in the presence of strong lateral velocity variation where the underlying NMO correction breaks down. Underattenuated multiples, converted waves, and diffracted head waves can significantly impede and/or degrade prestack migration‐driven velocity analysis and amplitude variation with offset analysis as well as the quality of the final stacked image. Generalization of time‐variant dip filtering based on conventional NMO corrections of common‐midpoint gathers also breaks down for less conventional data processing situations where we wish to enhance data having nonhyperbolic moveout, such as converted wave energy or long‐offset P-wave reflections in structurally deformed anisotropic media. We present a methodology that defines a depth‐variant velocity filter based on an approximation to the true velocity/depth structure of the earth developed by the interpreter/processor during the normal course of their prestack imaging work flow. Velocity filtering in the depth domain requires the design and calibration of two new least‐squares transforms: a constrained least‐squares common offset Kirchhoff depth migration transform and a transform in residual migration‐velocity moveout space. Each of these new least‐squares transforms can be considered to be generalizations of the well‐known discrete Radon transform commonly used in the oil and gas exploration industry.
An analysis of deconvolution: Modeling reflectivity by fractionally integrated noise
Authors: Saggaf M. M. , Toksöz M. Nafi
Published: October 2002

Reflection coefficients are observed in nature to have stochastic behavior that departs significantly from the white‐noise model. Conventional deconvolution methods, however, assume reflectivity to be a white‐noise process. In this paper we analyze the deconvolution process, study the implications of the assumption of white noise, and show that the conventional operator can recover only the white component of reflectivity. A new stochastic model, fractionally integrated noise, is proposed for modeling reflectivity—a model that more closely approximates its spectral character and that encompasses white noise as a special case. We discuss different techniques to generalize the conventional deconvolution method based on the new model in order to handle reflectivity that is not white and compare the results of the conventional and generalized filters using data derived from well logs.
Azimuthal variation inP-wave signatures due to fluid flow
Authors: MacBeth Colin
Published: October 2002

The favored dominant mechanism for attenuation in the upper crust at seismic frequencies is intracrack fluid flow. In cracked media, the azimuthal attenuation of the P-wave amplitudes arising from such flow is predicted to be quite substantial. The consequence of this variation in azimuth is a modification in the amplitude behavior of the base event from a cracked reservoir due to transmission through the attenuative layer. Indeed, the effect is of sufficient strength to exacerbate, diminish, or reverse variations that arise solely due to the reflectivity coefficient. Thus, although this attenuation is always greatest perpendicular to the crack strike, the direction of the dimming or brightening of the base reservoir event will depend upon the exact attenuation law and the crack properties. The combination of these factors contributes to a wave behavior that can provide a more adequate discrimination between conditions of brine and oil fill than an interpretation assuming the reflection coefficient alone. Unfortunately, regions of commonality do remain, and the distinction between fills is still only apparent for particular reservoir and crack conditions. The attenuated amplitudes are large enough to be seen at small offsets and may possibly account for the significant azimuthal variations in the P-wave signatures observed in field data.
3-D moveout inversion in azimuthally anisotropic media with lateral velocity variation: Theory and a case study
Authors: Grechka Vladimir , Tsvankin Ilya
Published: October 2002

Reflection moveout recorded over an azimuthally anisotropic medium (e.g., caused by vertical or dipping fractures) varies with the azimuth of the source‐receiver line. Normal‐moveout (NMO) velocity, responsible for the reflection traveltimes on conventional‐length spreads, forms an elliptical curve in the horizontal plane. While this result remains valid in the presence of arbitrary anisotropy and heterogeneity, the inversion of the NMO ellipse for the medium parameters has been discussed so far only for horizontally homogeneous models above a horizontal or dipping reflector. Here, we develop an analytic moveout correction for weak lateral velocity variation in horizontally layered azimuthally anisotropic media. The correction term is proportional to the curvature of the zero‐offset traveltime surface at the common midpoint and, therefore, can be estimated from surface seismic data. After the influence of lateral velocity variation on the effective NMO ellipses has been stripped, the generalized Dix equation can be used to compute the interval ellipses and evaluate the magnitude of azimuthal anisotropy (measured by P-wave NMO velocity) within the layer of interest. This methodology was applied to a 3-D “wide‐azimuth” data set acquired over a fractured reservoir in the Powder River Basin, Wyoming. The processing sequence included 3-D semblance analysis (based on the elliptical NMO equation) for a grid of common‐midpoint “supergathers,” spatial smoothing of the effective NMO ellipses and zero‐offset traveltimes, correction for lateral velocity variation, and generalized Dix differentiation. Our estimates of depth‐varying fracture trends in the survey area, based on the interval P-wave NMO ellipses, are in good agreement with the results of outcrop and borehole measurements and the rotational analysis of four‐ component S-wave data.
Reply by the authors to the discussion by M. Zhdanov
Authors: Guo, Yanping , Ko, Harvey W. , White David M.
Published: October 2002

The work described in our paper is an inverse source problem using a back propagation approach to reconstruct the field distribution below the surface based on surface field measurements. The algorithm we developed is consistent with quasi‐static diffusion field conditions and uses spatial transforms to reconstruct the below surface image. The result is an efficient method of identifying the location and orientation of underground objects within the near field of excitation coils on the surface.
Transformation of VLF data into apparent resistivities and phases
Authors: Gharibi Mehran , Pedersen Laust B.
Published: October 2002

In the VLF method, the ratio between the vertical and the horizontal magnetic field or the total magnetic field anomaly is measured to detect localized changes in electrical conductivity contrasts. Although the VLF technique has probably been the most popular electromagnetic (EM) tool for mapping near‐surface geological structures in a large scale for the past few decades because of the low cost and speed with which surveys can be carried out, the measurements themselves do not give a direct estimate of electrical conductivity. A fast iterative method has been developed to estimate the impedance or apparent resistivity and phases from measurements of the magnetic components at the surface of a 2-D geological structure. From Maxwell’s equations in E-polarization, a relation was derived between the horizontal and vertical components of the magnetic field. A full solution has been obtained by making use of the fact that the secondary horizontal and vertical magnetic fields are of internal origin and form a Hilbert transform pair. Synthetic and real VLF data have been used to evaluate the performance and limitation of the method. Using synthetic and real data, one can achieve a full recovery of the E-polarization impedance as long as the length of the profile is sufficiently long. A number of precautions must be taken to ensure reliable estimation of impedance results.
The whiteness hypothesis: Reflectivity, inversion, chaos, and Enders
Authors: Ulrych Tadeusz J.
Published: October 2002

The earth’s reflectivity is one of the principal targets of seismic exploration for oil and gas. It exhibits some fascinating properties. It is blue. It is fractal. In all probability, it reflects the output of a chaotic generator. I examine some of these characteristics here. Specifically, I look at the statistical properties of a canonical chaotic model, and I examine the effect of multiples on the statistical properties of seismograms generated from primary reflectivities. This article is a tribute to Enders Robinson. He is a pioneer who has inspired many. He inspires many to this day. I am one of them.
An improved method of determining near‐surfaceQ
Authors: Jeng Yih , Tsai Jing‐Yih , Chen Song‐Hong
Published: October 2002

We performed field measurements using the modified method of spectral ratios to estimate shallow seismic Q. Three component seismograms from artificial sources were recorded to determine [Formula: see text] and [Formula: see text] in the unconsolidated sedimentary layer at the experimental site. This modified spectral ratio method was assumed to be frequency dependent, and the amplitude ratios then were plotted against the arrival‐time difference of any two receivers for one particular frequency. The slope of the regression line in the log‐amplitude‐time space yields a Q for each frequency. Results show that Q is a function of frequency in the frequency range (below 300 Hz) we tested. A simple mathematical derivation with experimental data strongly suggests that the Q of shallow seismic waves is frequency dependent. Corrections for geometric spreading are used; however, the original and corrected Qs show no significant difference in our data, and therefore the geometric factor may be ignored in this problem. The conventional frequency‐independent spectral ratio method is easier and faster to apply, but it gives less stable results than this modified method. The unstable Q is attributed to geometric amplification effects in the conventional frequency‐independent spectral ratio method. The source factor can have an effect on the estimates of Q; however, different seismic sources give about the same Q over the dominant frequency band. We established the frequency function by assuming a simple power law regression model, where [Formula: see text] and k ≪ 1 in [Formula: see text]. This may confirm that the weathered unconsolidated layer is saturated partially, and [Formula: see text] stresses that attenuation in our study is physically a local compressional mechanism.
Signal and noise separation: Art and science
Authors: Ulrych Tadeusz J. , Sacchi Mauricio D. , Graul J. Michael
Published: October 2002

The separation of signal and noise is a central issue in seismic data processing. The noise is both random and coherent in nature, the coherent part often masquerading as signal. In this tutorial, we present some approaches to signal isolation, in which stacking is a central concept. Our methodology is to transform the data to a domain where noise and signal are separable, a goal that we attain by means of inversion. We illustrate our ideas with some of our favorite transformations: wavelets, eigenvectors, and Radon transforms. We end with the notion of risk, baseball, and the Stein estimator.
LaCoste & Romberg gravity meter: System analysis and instrumental errors
Authors: Ander Mark E. , Summers Tom , Gruchalla Michael E.
Published: October 2002

Although the LaCoste & Romberg (L&R) gravity sensor can be used with great care to collect 1-μGal data, the sensor has a thermodynamic noise limit of 0.012 μGal—about two orders of magnitude below the present measurement precision. Hence, thermodynamic noise is not the limiting factor, and there is significant room for improvement by bringing the other perturbing influences under adequate control. We do not see any fundamental instrumental limitations to substantially improving measurement accuracy at least down to 0.1 μGal. We have improved the noise level, stability, and reliability of the L&R borehole gravity meter sensor, with the goal of reducing the total system noise to below 1 μGal. In the process of these improvements, we made several fundamental observations about noise sources within the L&R sensor, particularly related to thermal noise, electronic noise, sources of mechanical and electrical rectification errors, temporal mass variations, and instrument tares and drift. It has always been assumed that the effective proof mass of the L&R sensor did not change over the time scale of a gravity survey. From our experiments we conclude that this assumption is incorrect below about 10 μGal. Large instrumental errors are produced by temporal proof‐mass variations over time scales of a survey, resulting from contamination and migration of dust, oil, and other volatiles inside the sensor. The results are drift and tares, for it takes only 0.01 μg of dust or oil transferred to the proof mass to offset the gravity reading by 1 μGal.
Multiple attenuation in the parabolic τ-pdomain using wavefront characteristics of multiple generating primaries
Authors: Landa Evgeny , Belfer Igor , Keydar Shemer
Published: October 2002

The problem of multiple attenuation has been solved only partially. One of the most common methods of attenuating multiples is an approach based on the Radon transform. It is commonly accepted that the parabolic Radon transform method is only able to attenuate multiples with significant moveouts. We propose a new 2-D method for attenuation of both surface‐related and interbed multiples in the parabolic τ-p domain. The method is based on the prediction of a multiple model from the wavefront characteristics of the primary events. Multiple prediction comprises the following steps: 1) For a given multiple code, the angles of emergence and the radii of wavefront curvatures are estimated for primary reflections for each receiver in the common‐shotpoint gather. 2) The intermediate points which compose a specified multiple event are determined for each shot‐receiver pair. 3) Traveltimes of the multiples are calculated. Wavefields within time windows around the predicted traveltime curves may be considered as multiple model traces which we use for multiple attenuation process. Using the predicted multiple traveltimes, we can define the area in the τ-p domain which contains the main energy of the multiple event. Resolution improvement of the parabolic Radon operator can be achieved through a simple multiplication of each sample in the τ-p space by a nonlinear semblance function. In this work, we follow the idea of defining the multiple reject areas automatically by comparing the energy of the multiple model and the original input data in the τ-p space. We illustrate the usefulness of this algorithm for the attenuation of multiples on both synthetic and real data.
Application of the Wiener‐Hopf technique to the calculation of the diffraction of a cylindrical wave by a soft half‐plane embedded in a fluid half‐space
Authors: Tan Tik Hing
Published: October 2002

Wavelets currently are estimated directly from the data by statistical means or, for marine data, by direct measurement with deep hydrophones. The first method, based on statistical arguments, uses the convolution model of seismic traces as the starting point. In addition, it also assumes whiteness of the earth’s reflectivity series and the minimum‐phase character of the wavelet. The second method does not work very well for shallow seas because of interference with reflections by the seafloor. In a companion paper, an algorithm for the estimation of wavelets of marine sources has been presented. The algorithm starts from the reduced wave equation to describe the measured field and an auxiliary field. Physically, the auxiliary field, also known as the Green’s function, is the wavefield configuration of a line source and a soft half‐plane in a fluid half‐space. The calculation of this Green’s function is the subject of this paper.
3-D traveltime computation using second‐order ENO scheme
Authors: Kim Seongjai , Cook Richard
Published: October 2002

We consider a second‐order finite difference scheme to solve the eikonal equation. Upwind differences are requisite to sharply resolve discontinuities in the traveltime derivatives, whereas centered differences improve the accuracy of the computed traveltime. A second‐order upwind essentially non‐oscillatory (ENO) scheme satisfies these requirements. It is implemented with a dynamic down ’n’ out (DNO) marching, an expanding box approach. To overcome the instability of such an expanding box scheme, the algorithm incorporates an efficient post sweeping (PS), a correction‐by‐iteration method. Near the source, an efficient and accurate mesh‐refinement initialization scheme is suggested for the DNO marching. The resulting algorithm, ENO-DNO-PS, turns out to be unconditionally stable, of second‐order accuracy, and efficient; for various synthetic and real velocity models having large contrasts, two PS iterations produce traveltimes accurate enough to complete the computation.
Some remarks on nonlinear amplitude versus scattering angle‐azimuth inversion in anisotropic media
Authors: Neves Fernando A. , de Hoop Maarten V.
Published: October 2002

A feasibility study for inverting reflection coefficients for a single‐interface model consisting of a shale overlying a fractured sand is presented. To characterize the medium contact from amplitude versus scattering angles (AVA) behavior associated with the reflection from a particular interface, in view of the anisotropy, wide‐angle scattering data are required. However, wide‐angle scattering turns the inverse problem into an essentially nonlinear one. The inverse problem is hence analyzed with a global optimization procedure—a genetic algorithm with constraints. The key to making a genetic algorithm work for our AVA inverse problem appears to be a proper parameterization of the direct scattering problem and introducing a parameter hierarchy. These reduce the complexity of the misfit function occurring in the optimization procedure and let this function become convex over a relatively large range of medium parameter values. We illustrate how well our approach performs with a single‐interface example representing a shale/fractured‐sandstone contact. In this example, we assume the overburden, i.e., the shale, to be known; we allow the data to be contaminated with noise.
The echo of a fault or fracture
Authors: Haugen Geir U. , Schoenberg Michael A.
Published: October 2002

The seismic response of single faults, joints, or fractures of large planar extent is analyzed. These are modeled as nonwelded interfaces. In spite of the large range of scale, all are assumed to behave according to linear slip theory. Such a model has been considered theoretically and experimentally before. The aim of this paper is to give a physical interpretation to such a linear slip interface; to provide simple analytical formulae for the scattering response, even when the fracture is embedded in an anisotropic background medium; and to relate the properties of this scattering response, in the isotropic case, to the physical features of the fracture. The analysis shows that the reflectivity and transmissivity of the fracture depend on slowness along the fracture and on frequency. The frequency dependence arises from the fact that, even though the fracture is assumed to be an interface of zero thickness, it still has at least two characteristic widths that provide the length scales necessary for scattering dependence on wavelength. For isotropic media, the PP and SS reflections generally decrease in amplitude with increasing slowness along the fracture. At certain slowness values, they reach minima before starting to increase for still larger slownesses. The slowness value of these minima reveals the fracture compliances, from which inferences about the physical properties of the fracture may be drawn. Both forward modeling of the acoustic response of a fracture and the estimation of fracture properties from acoustic scattering data can benefit from the type of analysis presented here. The range of such problems extends from the scattering of earthquake‐generated seismic energy by major faults in the earth, through reservoir fracture characterization from single‐well sonic imaging, to the characterization of flaws or poorly bonded surfaces in ultrasonic nondestructive testing.
Imaging shallow objects and heterogeneities with scattered guided waves
Authors: Herman Gérard C. , Milligan Paul A. , Huggins Robert J. , Rector J. W.
Published: October 2002

Current surface seismic reflection techniques based on the common‐midpoint (CMP) reflection stacking method cannot be readily used to image small objects in the first few meters of a weathered layer. We discuss a seismic imaging method to detect such objects; it uses the first‐arrival (guided) wave, scattered by shallow heterogeneities and converted into scattered Rayleigh waves. These guided waves and Rayleigh waves are dominant in the shallow weathered layer and therefore might be suitable for shallow object imaging. We applied this method to a field data set and found that we could certainly image meter‐size objects up to about 3 m off to the side of a survey line consisting of vertical geophones. There are indications that cross‐line horizontal geophone data could be used to identify shallow objects up to 10 m offline in the same region.
Reconstruction of 3-D seismic signals irregularly sampled along two spatial coordinates
Authors: Hindriks Kees , Duijndam Adri J. W.
Published: October 2002

Seismic signals are often irregularly sampled along spatial coordinates, leading to suboptimal processing and imaging results. Least‐squares estimation of Fourier components is used for the reconstruction of band‐limited seismic signals that are irregularly sampled along two spatial coordinates. A simple and efficient diagonal weighting scheme, based on the areas surrounding the spatial samples, takes the properties of the noise (signal outside the bandwidth) into account in an approximate sense. Diagonal stabilization based on the energies of the signal and the noise ensures robust estimation. Reconstruction by temporal frequency component allows the specification of varying bandwidth in two dimensions, depending on the minimum apparent velocity. This parameterization improves the reconstruction capability for lower temporal frequencies. The shape of the spatial aperture affects the method of sampling the Fourier domain. Taking into account this property, a larger bandwidth can be recovered. The properties of the least‐squares estimator allow a very efficient implementation which, when using a conjugate gradient algorithm, requires a modest number of 2-D fast Fourier transforms per temporal frequency. The method shows signicant improvement over the conventionally used binning and stacking method on both synthetic and real data. The method can be applied to any subset of seismic data with two varying spatial coordinates.
Weighted average seismic attributes
Authors: Barnes Arthur E.
Published: October 2002

Local weighted averaging of instantaneous seismic attributes improves their interpretability by removing spikes and reducing rapid and confusing variations. Averaging in a window weighted by the instantaneous power produces a local measure that equals a Fourier spectral average, facilitating quantitative analysis. Local 1-D frequency and bandwidth are scalars, but local 2-D and 3-D seismic attributes derive from average vector wavenumbers, which may require velocity information. The direction of the average vector wavenumber provides average dip and azimuth, and its magnitude provides a measure of average wavelength or frequency. A related measure of bandwidth is a scalar in all dimensions; it includes contributions from both instantaneous bandwidth and the variance of instantaneous frequency or wavenumber. It quantifies data similarity.
Bottom‐simulating reflectors: Seismic velocities and AVO effects
Authors: Carcione José M. , Tinivella Umberta
Published: October 2002

We obtain the wave velocities of ice‐ and gas hydrate‐bearing sediments as a function of concentration and temperature. Unlike previous theories based on simple slowness and/or moduli averaging or two‐phase models, we use a Biot‐type three‐phase theory that considers the existence of two solids (grain and ice or clathrate) and a liquid (water), and a porous matrix containing gas and water. For consolidated Berea sandstone, the theory underestimates the value of the compressional velocity below 0°C. Including grain‐ice interactions and grain cementation yields a good fit to the experimental data. Strictly speaking, water proportion and temperature are closely related. Fitting the wave velocity at a given temperature allows the prediction of the velocity throughout the range of temperatures, provided that the average pore radius and its standard deviation are known. The reflection coefficients are computed with a viscoelastic single‐phase constitutive model. The analysis is carried out for the top and bottom of a free‐gas zone beneath a gas hydrate‐bearing sediment and overlying a sediment fully saturated with water. Assuming that the bottom‐simulating reflector is caused solely by an interface separating cemented gas hydrate‐ and free gas‐bearing sediments, we conclude that (1) for a given gas saturation, it is difficult to evaluate the amount of gas hydrate at low concentrations. However, low and high concentrations of hydrate can be distinguished, since they give positive and negative anomalies, respectively. (2) Saturation of free gas can be determined from the reflection amplitude, but not from the type of anomaly. (3) The P to S reflection coefficient is a good indicator of high amounts of free gas and gas hydrate. On the other hand, the amplitude‐variation‐with‐offset curves are always positive for uncemented sediments.
Electrical imaging of engineered hydraulic barriers
Authors: Daily William , Ramirez Abelardo L.
Published: October 2002

Electrical resistance tomography (ERT) was used to image the full‐scale test emplacement of a thin‐wall grout barrier installed by high‐pressure jetting and a thick‐wall polymer barrier installed by low‐pressure permeation injection. Both case studies compared images of electrical resistivity before and after barrier installation. Barrier materials were imaged as anomalies which were more electrically conducting than the native sandy soils at the test sites. Although the spatial resolution of the ERT was insufficient to resolve flaws smaller than a reconstruction voxel (50 cm on a side), the images did show the spatial extent of the barrier materials and therefore the general shape of the structures. To verify barrier performance, ERT was also used to monitor a flood test of a thin‐wall grout barrier. Electrical resistivity changes were imaged as a saltwater tracer moved through the barrier at locations which were later found to be defects in a wall or the joining of two walls.
Robust estimation of the band‐limited inductive‐limit response from impulse‐response TEM measurements taken during the transmitter switch‐off and the transmitter off‐time: Theory and an example from Voisey’s Bay, Labrador, Canada
Authors: Smith Richard S. , Balch S. J.
Published: October 2002

Modern transient electromagnetic systems are able to take measurements in the transmitter on‐time. Integrating measurements taken during the transmitter switch‐off and those collected in the transmitter off‐time yield an estimate of the primary field plus the secondary inductive‐limit response. If the transmitter loop position is known and the position and orientation of the receiver dipoles are known, it is possible to calculate the primary field. When the theoretical primary field is subtracted from the measured inductive‐limit‐plus‐primary response, the inductive‐limit response can be isolated. An anomalous inductive‐limit response is a diagnostic feature of highly conductive ore bodies. On‐ and off‐time PROTEM data collected in a drill hole proximal to the Reid Brook Zone (one of the Voisey’s Bay deposits in Labrador, Canada) shows a strong inductive‐limit anomaly corresponding to an off‐hole conductor. A drill hole targeted to test this conductor intersected 20.4 m of mineralization, including 8.25 m of massive sulfide.
Limited‐aperture migration
Authors: Sun Jianguo
Published: October 2002

I establish a general theory on the true‐amplitude migration with limited aperture. The key point of this theory is to find the true‐amplitude weight function, eliminating the contribution from the boundary of the migration aperture, or edge effect. I show that the true‐amplitude weight function is a singular generalized function defined by the migration aperture. If it is used without regularization, the singular weight function reduces a diffraction stack to the distribution of the amplitude at a given traveltime to every point along a corresponding isochron. After regularization, I obtain a formula for the true‐amplitude weight function as a weak solution having the same global properties as the fundamental solution to the governing equation derived here. In comparison with other published weight functions that disregard migration aperture, this theory contains a taper function that makes the obtained weight function suitable for the migration with limited aperture. If the migration aperture goes to infinity, my weight function reduces to the one cited in the literature. Furthermore, I present a theoretical guideline for designing both the taper function and the migration aperture. Specifically, an optimal migration aperture should be larger than or equal to the region confined by the outer boundary of the second transformed Fresnel zone. The exact size of the optimal migration aperture is obtained when an equation describing the global property of the true‐amplitude weight function is satisfied. Using the true‐amplitude weight function developed, together with a first‐order perturbation of the traveltime surfaces of point‐diffracted rays, I also obtain an asymptotic formula for the depth‐migrated image. According to the formula, diffraction stack results in frequency scaling in the depth domain. This frequency scaling gives physical insight into the problem of pulse stretching in depth migration. If the formula is expanded into a Taylor series and if the Taylor series is truncated at its linear term, the formula published in the literature can be derived. Therefore, this paper also presents a general theory on the depth‐migrated image.
Focusing aspects of the hyperbolic Radon transform
Authors: Bickel Samuel H.
Published: October 2002

The parabolic approximation does not accurately model residual moveout for long‐offset marine data. Consequently the focusing power of the parabolic Radon transform is degraded. Maeland (1998) analyzes this problem by deriving the envelope of hyperbolic events in the (τ, q) domain. This note extends Maeland’s analysis to the hyperbolic Radon transform (τ, p) domain.
On: “3-D traveltime compuation using the fast marching method” (J. A. Sethian and A. M. Popovici, GEOPHYSICS, 64, 516–523).
Authors: Qin Fuhao
Published: October 2002

The Sethian and Popovici paper “3-D traveltime computation using the fast marching method” that appeared in Geophysics, Vol. 64, 516–523, discussed a method to solve the eikonal equation for first arrival traveltimes which was called the “fast marching” method. The method, as the authors demonstrated, is very fast and stable. However, their method is very similar to the method discussed by F. Qin et al. (1992), entitled “Finite difference solution of the eikonal equation along expanding wavefronts,” Geophysics, Vol. 57, 478–487. F. Qin et al. first proposed the “expanding wavefront” method for solving eikonal equation in the 60th Ann. Internat. Mtg. of the SEG in 1990.
On: “3-D instantaneous frequency used as a coherency/continuity parameter to interpret reservoir compartment boundaries across an area of complex turbidite deposition,” (B. A. Hardage et al., GEOPHYSICS, Vol. 63, 1520–1531)
Authors: Barnes Arthur E.
Published: October 2002

Hardage et al. are to be commended for a thoughtful and valuable study on instantaneous frequency applied to reservoir characterization. Of particular note is the observation that anomalous instantaneous frequencies often correspond to lower seismic coherency and form interpretable patterns. This observation has an interesting background.
3-D electromagnetic modeling and nonlinear inversion
Authors: Xie Ganquan , Li Jianhua , Majer Ernest L. , Zuo Daxin , Oristaglio Michael L.
Published: October 2002

We describe a new algorithm for 3-D electromagnetic inversion that uses global integral and local differential equations for both the forward and inverse problems. The coupled integral and differential equations are discretized by the finite element method and solved on a parallel computer using domain decomposition. The structure of the algorithm allows efficient solution of large 3-D inverse problems. Tests on both synthetic and field data show that the algorithm converges reliably and efficiently and gives high‐resolution conductivity images.