bluuebunny/crossref_metadata_2025 huggingface dataset:
3-D implicit finite‐difference migration by multiway splitting
Authors: Ristow Dietrich , Rühl Thomas
Published: October 2002

We show that 3-D implicit finite‐difference schemes can be realized by multiway splitting in such a way that the steep dip problem and the problem of numerical anisotropy are overcome. The basic idea is as follows. We approximate the 3-D square root operator by a sequence of 2-D operators in three, four, or six directions to solve the azimuth symmetry problem. Each 2-D square root operator is then approximated by a sequence of implicit 2-D operators to improve steep dip accuracy. This sequence contains some unknown coefficients, which are calculated by a Taylor expansion technique or by an optimization technique. In the Taylor expansion method, the square root and its approximation are expanded into power series. By comparing the terms, the unknown coefficients are calculated. The more 2-D finite‐difference operators for cascading are taken and the more directions for downward continuation are chosen, the more terms from power series can be compared to obtain a higher‐degree migration operator with better circular symmetry. In the second method, optimized coefficients are calculated by an optimization procedure whereby a variation of all unknown coefficients is performed, in such a way that both the sum of all deviations between the correct square root and its approximation and the sum of all deviations from azimuth symmetry are minimized. A mathematical criterion for azimuth symmetry has been defined and incorporated into the opfimization procedure.
Reflection moveout and parameter estimation for horizontal transverse isotropy
Authors: Tsvankin Ilya
Published: October 2002

Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. Here, I present an exact equation for normal‐moveout (NMO) velocities from horizontal reflectors valid for pure modes in HTI media with any strength of anisotropy. The azimuthally dependent P‐wave NMO velocity, which can be obtained from 3-D surveys, is controlled by the principal direction of the anisotropy (crack orientation), the P‐wave vertical velocity, and an effective anisotropic parameter equivalent to Thomsen's coefficient δ. An important parameter of fracture systems that can be constrained by seismic data is the crack density, which is usually estimated through the shear‐wave splitting coefficient γ. The formalism developed here makes it possible to obtain the shear‐wave splitting parameter using the NMO velocities of P and shear waves from horizontal reflectors. Furthermore, γ can be estimated just from the P‐wave NMO velocity in the special case of the vanishing parameter ε, corresponding to thin cracks and negligible equant porosity. Also, P‐wave moveout alone is sufficient to constrain γ if either dipping events are available or the velocity in the symmetry direction is known. Determination of the splitting parameter from P‐wave data requires, however, an estimate of the ratio of the P‐to‐S vertical velocities (either of the split shear waves can be used). Velocities and polarizations in the vertical symmetry plane of HTI media, that contains the symmetry axis, are described by the known equations for vertical transverse isotropy (VTI). Time‐related 2-D P‐wave processing (NMO, DMO, time migration) in this plane is governed by the same two parameters (the NMO velocity from a horizontal reflector and coefficient ε) as in media with a vertical symmetry axis. The analogy between vertical and horizontal transverse isotropy makes it possible to introduce Thomsen parameters of the “equivalent” VTI model, which not only control the azimuthally dependent NMO velocity, but also can be used to reconstruct phase velocity and carry out seismic processing in off‐symmetry planes.
To: “GPR attenuation and its numerical simulation in 2.5‐dimensions,” T. Xu and G. A. McMechan (March‐April 1997 GEOPHYSICS, 62, p. 403–414)
Authors: Xu T. , McMechan G. A.
Published: October 2002

Figure 10 (above) was wrongly identified in columns as a and b. It should have been identified as above showing a through f. Also The caption of Table 2 for this article should have referred to Figure 9 rather than Figure 5, and the caption for Table 3 should have referred to Figure 10 rather than Figure 6.
Audiomagnetotelluric prospecting for groundwater in the Baril coastal area, Piton de la Fournaise Volcano, Reunion Island
Authors: Ritz Michel , Descloitres Marc , Robineau Bernard , Courteaud Michel
Published: October 2002

Surface geophysics has been used for a number of years to solve a variety of major groundwater exploration problems in coastal and island regions. The electrical properties of near‐surface rocks are highly dependent on porosity, degree of saturation, and pore fluid resistivity (Keller and Frischknecht, 1966). Because the resistivity of the formations decreases with increasing salinity of the water content, electrical methods, such as vertical electrical soundings, time‐domain electromagnetic soundings, and audiomagnetotellurics (AMT), are well‐suited for mapping changes in groundwater salinity and, in particular, for detecting a fresh water‐salt water interface.
Hydrophone VSP imaging at a shallow site
Authors: Milligan Paul A. , Rector James W. , Bainer Robert W.
Published: October 2002

We evaluated the capabilities of vertical seismic profiling (VSP) for imaging the complex heterogeneous unconsolidated sedimentary structures at a shallow site. We deployed a 24‐level hydrophone array with 0.5-m level spacing down a preexisting poly vinyl chloride (PVC) cased well. Data acquisition time was quick. Only 15 multioffset shot points using a hammer‐on‐plate source were needed to acquire reflection data between the water table at 3 m and the bedrock at 35 m to produce a depth section image. This image extended 9 m from the receiver well, yielding resolutions between fresh‐water‐bearing sands and impermeable muds and clays of better than 1 m. Depth accuracy of the image was confirmed by good correlation with cone penetrometer logs. We used conventional wavefield separation and VSP-CDP mapping techniques to image the data. Tube waves, created by seismic arrivals at cross‐sectional area changes in the borehole fluid column, were the primary source of coherent noise in the data. The tube‐wave arrival structure was complicated by the hydrophone array, which generated and scattered tube waves at each hydrophone pod. To combat the tube wave interference, we inserted closed‐cell‐foam baffles between elements. The baffles attenuated and slowed the tube waves, and reduced generation and scattering. A comparison between unbaffled and baffled VSP data showed that baffling increased the maximum useful frequency from 300 Hz to over 900 Hz. By contrast, surface shot data recorded at the same site, using buried 40-Hz vertical geophones, exhibited useful frequencies of less than 250 Hz. In addition, coherent noise in surface shot records caused by air waves and first arrivals made it very difficult to identify shallow reflections above 25 m. Reflections from depths as shallow as 10 m were easy to identify in the baffled VSP data.
Improved inversion through use of the null space
Authors: Rowbotham Peter S. , Pratt R. Gerhard
Published: October 2002

Standard least‐squares traveltime inversion techniques tend to produce smoothed estimates of the velocity field. More complete results can be obtained by incorporating into the inversion scheme a priori information about the media to be imaged, derived from well logs, core data, and surface geology. A promising technique for achieving this involves projecting this information onto the null space model singular vectors of the inverse problem and including this projection with the non‐null space contribution in order to produce a solution. The method, demonstrated with both field and synthetic crosshole traveltime data acquired through layered, anisotropic media, successfully produces improved inversion solutions with lower traveltime residuals, layers that are more homogeneous, sharper interfaces, and better correlated anisotropy parameters than solutions obtained with standard techniques.
Modeling of low‐frequency Stoneley‐wave propagation in an irregular borehole
Authors: Tezuka Kazuhiko , Cheng C. H. (Arthur) , Tang X. M.
Published: October 2002

A fast modeling method is formulated for low‐frequency Stoneley‐wave propagation in an irregular borehole. This fast modeling method provides synthetic waveforms which include the effects of two borehole irregularities, diameter changes (washout), and formation property changes. The essential physics of the low‐frequency Stoneley waves are captured with a simple 1-D model. A mass‐balance boundary condition and a propagator matrix are used to express Stoneley‐wave interactions with the borehole irregularities. The accuracy of the proposed method was confirmed through comparison with existing finite‐difference and boundary integral modeling methods that yielded cross‐correlations greater than 0.98. Comparison of synthetic records calculated for an actual borehole with field records showed qualitative agreement in the major reflections because of the washout zones, but showed some disagreements in the reflections caused by the fractures. Since the synthetic records include only information relating to the borehole geometry and the elastic properties of formation, the reflection caused by the fracture will appear only in the field record. These results suggest the possibility of distinguishing Stoneley‐wave reflections caused by fractures from those caused by borehole irregularities. Further, the fast computational speed of this method—over 300 times faster than either boundary integral or finite‐difference methods—makes it quite suitable for field application.
Effects of pore structure and wettability on the electrical resistivity of partially saturated rocks—A network study
Authors: Suman Ravi J. , Knight Rosemary J.
Published: October 2002

A network model of porous media is used to assess the effects of pore structure and matrix wettability on the resistivity of partially saturated rocks. Our focus is the magnitude of the saturation exponent n from Archie's law and the hysteresis in resistivity between drainage and imbibition cycles. Wettability is found to have the dominant effect on resistivity. The network model is used to investigate the role of a wetting film in water‐wet systems, and the behavior of oil‐wet systems. In the presence of a thin wetting film in water‐wet systems, the observed variation in n with saturation is reduced significantly resulting in lower n values and reduced hysteresis. This is attributed to the electrical continuity provided by the film at low‐water saturation between otherwise physically isolated portions of water. Oil‐wet systems, when compared with the water‐wet systems, are found to have higher n values. In addition, the oil‐wet systems exhibit a different form of hysteresis and more pronounced hysteresis. These differences in the resistivity response are attributed to differences in the pore scale distribution of water. The effects of pore structure are assessed by varying pore size distribution and standard deviation of the pore size distribution and considering networks with pore size correlation. The most significant parameter is found to be the pore size correlation. When the sizes of the neighboring pores of the network are correlated positively, the magnitude of n and hysteresis are reduced substantially in both the water‐wet and oil‐wet systems. This is attributed to higher pore accessibility in the correlated networks. The results of the present study emphasize the importance of conducting laboratory measurements on core samples with reservoir fluids and wettability that is representative of the reservoir. Hysteresis in resistivity can be present, particularly in oil‐wet systems, and should be considered in the interpretation of resistivity data.
Dip‐moveout processing by Fourier transform in anisotropic media
Authors: Anderson John E. , Tsvankin Ilya
Published: October 2002

Conventional dip‐moveout (DMO) processing is designed for isotropic media and cannot handle angle‐dependent velocity. We show that Hale's isotropic DMO algorithm remains valid for elliptical anisotropy but may lead to serious errors for nonelliptical models, even if velocity anisotropy is moderate. Here, Hale's constant‐velocity DMO method is extended to anisotropic media. The DMO operator, to be applied to common‐offset data corrected for normal moveout (NMO), is based on the analytic expression for dip‐dependent NMO velocity given by Tsvankin. Since DMO correction in anisotropic media requires knowledge of the velocity field, it should be preceded by an inversion procedure designed to obtain the normal‐moveout velocity as a function of ray parameter. For transversely isotropic models with a vertical symmetry axis (VTI media), P‐wave NMO velocity depends on a single anisotropic coefficient (η) that can be determined from surface reflection data. Impulse responses and synthetic examples for typical VTI media demonstrate the accuracy and efficiency of this DMO technique. Once the inversion step has been completed, the NMO-DMO sequence does not take any more computing time than the genetic Hale method in isotropic media. Our DMO operator is not limited to vertical transverse isotropy as it can be applied in the same fashion in symmetry planes of more complicated anisotropic models such as orthorhombic.
On: “Green's function implementation of common‐offset wave equation migration,” (A. Ehinger, P. Lailly and K. J. Marfurt, November‐December 1996 GEOPHYSICS, 61, p. 1813–1821)
Authors: Wapenaar Kees
Published: October 2002

The paper by Ehinger and co‐authors deals with migration in complex media in which severe multi‐pathing may occur. I wholeheartedly agree with their remark that the use of complete Green's functions is preferred over approximate Green's functions containing first arrivals only.
Integrated reservoir study, Lower Eocene Misoa reservoirs, VLA-6/9/21 Area, Block I, Phase 2, Stage 2, Lagunillas Field, north‐central Lake Maracaibo, Venezuela
Authors: Raeuchle Sandra K. , Ambrose William A. , Akhter M. Saleem , Casas Jhonny , Salamanca Lourdes , Muñoz Pedro , Leon Alfredo
Published: October 2002

Twenty‐eight geologically targeted, field development opportunities, including a variety of deeper pool opportunities that could significantly add to Maraven's (affiliate of PDVSA) reserve base, are identified in Lower Eocene Misoa reservoirs in the Stage 2 Area in Block I in north‐central Lake Maracaibo, Venezuela with the help of integrated geophysical, geological, petrophysical, and engineering analyses. Seismic rms amplitudes are instrumental in detecting and mapping trends of lithofacies and were integrated into stratigraphic models. Amplitude response to net sand thickness is a linear relationship. The amplitude signature also captures hydrocarbon charge as evidenced by bright amplitudes coincident with structural, fault‐bounded culminations. These direct hydrocarbon indicators (DHI) can result from as low as 2% miscible gas fraction within the hydrocarbon column.
Imaging complex geologic structure with single‐arrival Kirchhoff prestack depth migration
Authors: Audebert François , Nichols Dave , Rekdal Thorbjørn , Biondi Biondo , Lumley David E. , Urdaneta Hector
Published: October 2002

We compare various forms of single‐arrival Kirchhoff prestack depth migration to a full‐waveform, finite‐difference migration image, using synthetic seismic data generated from the structurally complex 2-D Marmousi velocity model. First‐arrival‐traveltime Kirchhoff migration produces severe artifacts and image contamination in regions of the depth model where significant reflection energy propagates as late or multiple arrivals in the total reflection wavefield. Kirchhoff migrations using maximum‐energy‐arrival traveltime trajectories significantly improve the image in the complex zone of the Marmousi model, but are not as coherent as the finite‐difference migration image. By carefully incorporating continuous phase estimates with the associated maximum‐energy arrival traveltimes, we obtain single‐arrival Kirchhoff images that are similar in quality to the finite‐difference migration image. Furthermore, maximum‐energy Green's function traveltime and phase values calculated within the seismic frequency band give a Kirchhoff image that is (1) far superior to a first‐arrival—based image, (2) much better than the analogous high‐frequency paraxial‐ray Green's function image, and (3) closely matched in quality to the full‐waveform finite‐difference migration image.
Velocity‐depth ambiguity in the dipping reflector case
Authors: Rathor Brijpal S.
Published: October 2002

Seismic or acoustic wave velocity is a vital parameter for processing and interpretation of seismic data. Various velocity analysis methods, using traveltime moveout of seismic events, have been described in literature. In certain cases, these methods provide ambiguous results. Hence, there is a need to investigate velocity‐depth ambiguity in such cases.
Removal of overburden transmission effects by deterministic deconvolution
Authors: Massier Mark R. F. , Herman Gérard C. , Verschuur Dirk J.
Published: October 2002

Intrabed multiples, either caused by shallow reverberations or the presence of many thin layers, can have a detrimental effect on the signature of deeper reflections. We discuss a method for removing these types of multiples. It can be viewed as a deterministic counterpart of well‐known predictive deconvolution methods and is aimed at estimating the inverse transmission operator of a subsurface region, directly from its reflection response. The method is illustrated by applying it to both synthetic and real data and appears to be able to reduce the effect of transmission intrabed multiples.
Noise reduction in seismic data using Fourier correction coefficient filtering
Authors: Alsdorf Douglas
Published: October 2002

The correlation coefficient between two frequency (or two wave number) componets equals the cosine of their phase‐angle difference. This relation can be exploited to build a filter that separates noise from signal in seismic data in either the F‐X or F-K domain (termed “correlation coefficient filtering”). To implement this filter, seismic data are first divided to form two subsets that are then compared using the cosine function. Signal is defined as the correlative frequencies (or wavelengths) while noncorrelative energy is attributed to noise. Depending on the application, appropriate subsets may consist of (1) groups of adjacent traces or (2) low‐fold stacks created from differing shot gathers. When comparing adjacent traces [i.e., (1)], the correlation coefficient filter combines both phase and dip information and assumes that reflections advance relatively little in time across traces and less than the noise. Correlation coefficient filtering of low‐fold stacks [i.e., (2)] does not depend on dip. Reflections are assumed to be present in both subsets whereas the noise is found only in one data set. Hence, the reflections are correlative and the noise is noncorrelative. In either case, the filter reduces linearly dipping coherent energy, ground roll, and randomly occurring noise bursts while generally maintaining signal integrity. A primary advantage of this filter is its simplicity. It is implemented much like a simple band‐pass filter, thus requiring much less parameterization than alternative noise‐reduction methods.
VSP detection of interbed multiples using inside‐outside corridor stacking
Authors: Burton Andrew , Lines Larry
Published: October 2002

One of the most difficult problems in the exploration of Devonian reefs is the separation of primaries and short period interbed multiples. This is especially true in cases where weak primary reflections from porous reefal carbonates can be easily masked by interbed multiples generated from stronger shale/carbonate reflections above the reef. This problem of primary‐multiple separation is difficult since there are small normal moveout differences between the primary and short‐period multiple reflections, thus stacking might not be as effective at suppressing multiples as one would hope. Also, predictive deconvolution may be ineffective if it is difficult to design an accurate prediction distance for the deconvolution filter. The ineffectiveness of stacking and deconvolution in some cases has caused us to look for other alternatives. A recent paper by Lines (1996) advocates the use of shaping deconvolution and inversion methods that use well log information. Since reliable well log data are not always available, we examine a vertical seismic profiling (VSP) corridor stacking method for multiple identification proposed in Hardage (1983, 154–155) which obviates some of the conventional problems and which does not require well log data. A variation of this concept was applied to long‐period multiple attenuation by Hampson and Mewhort (1983).
1-D inversion of resistivity and induced polarization data for the least number of layers
Authors: Esparza Francisco J. , Gómez‐Treviño Enrique
Published: October 2002

An automatic inverse method has been developed for generating layered earth models from electrical sounding data. The models have the minimum number of layers required to fit a resistivity sounding curve or a combined resistivity and induced polarization sounding. The ground is modeled using a very large number of thin layers to accommodate arbitrary variations. The properties of the layers are optimized using as a constraint the [Formula: see text] norm of the vertical derivative of the resistivity distribution. The use of linear programming leads to piecewise smooth distributions that simulate traditional models made up of a few uniform layers. The process considers from the simplest model of a uniform half‐space to models of many layers, without fixing a priori the number of discontinuities. The solution is sought by iterating a new linear approximation, similar to the classical process of linearization, except that a reference model is not present in either the data vector or the unknown function. For induced polarization soundings, the problem is linear and the solution is obtained in a single iteration, provided an adequate resistivity model is available. The performance of the method is illustrated using numerical experiments and published deep resistivity data from Australia. The method also is applied to combined resistivity and induced polarization soundings from a local groundwater prospect in México.
Gravity inversion of basement relief using approximate equality constraints on depths
Authors: Barbosa Valéria Cristina F. , Silva João B. C. , Medeiros Walter E.
Published: October 2002

We present a gravity interpretation method for estimating the relief of an arbitrary interface separating two homogeneous media. The upper medium is discretized into rectangular, juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated from the gravity anomaly. The density contrast of each prism is assumed to be constant and known. To stabilize the inversion, we introduce two kinds of constraints on the depths. The first one requires proximity between the observed and computed depths at isolated points such as those obtained from boreholes (absolute equality constraint). The second one requires that groups of depths approximately follow an established linear relationship among the depths (relative equality constraint). Both kinds of constraints are imposed in the least‐squares sense. We illustrate the method performance by applying it to a synthetic anomaly produced by a simulated basement relief consisting of four narrow and adjacent structural lows. Only two structural lows produced isolated gravity lows. Nonetheless, the whole basement topography was successfully reconstructed with an average error of 4% of the maximum relief amplitude. In this example, the relative constraints established that the thicknesses of adjacent prisms should be as close as possible to each other (overall relief smoothness). As absolute constraints we used point information about the basement depth at five points. In addition to the overall relief smoothness, other relevant geologic information, such as localized relief smoothness, occurring at structural terraces, for example, can be incorporated by assigning different weights to the relative equality constraints. The method was applied to the gravity anomaly of Recôncavo Basin, Brazil, leading to a sharper definition of the basement features relative to previous gravity interpretations of this area.
Euclid and the art of wavelet estimation, Part II: Robust algorithm and field‐data examples
Authors: Rietsch Eike
Published: October 2002

In this second part of a two‐part work, a more robust algorithm is derived and used for the estimation of the seismic wavelet as the common signal of two or more seismic traces. It is based on the properties of the eigenvectors with zero eigenvalue of a matrix derived in the first part, whose elements are the samples of the autocorrelation functions and crosscorrelation functions of these seismic traces for a number of lags. The noise resistance of this algorithm is illustrated by means of a synthetic‐data example and then demonstrated on field data. In one field‐data example, the so‐called Euclid wavelet is compared with one derived deterministically by means of an impedance log. The other example relates three quite different Euclid wavelets determined in three different time zones on a seismic line to one another by showing that their differences can be explained by absorption.
Methods for estimating the seismic reflection response
Authors: Ursin Bjørn
Published: October 2002

The convolutional model of the seismic trace consists of a seismic pulse convolved with a reflectivity series plus measurement noise. The seismic deconvolution problem is to estimate the reflectivity series, given the data and an estimate of the seismic pulse. The classical solution to this problem is a weighted least‐squares estimate of the reflectivity series, which is optimal when the noise covariance matrix is known and there are no errors in the pulse. The seismic convolutional model has been reformulated, taking into account errors in the pulse and measurement noise, which is taken to be white noise filtered by a finite‐impulse‐response filter. All variables are assumed to be Gaussian, with known a priori mean values and covariance matrices. The unknown parameters may be the reflectivity series, the noise‐filter coefficients, and the white noise variance or, when the noise covariance matrix is known, just the reflectivity series. This results in maximum a posteriori (MAP) and maximum likelihood (ML) estimates of the reflectivity series that take into account uncertainty in the seismic pulse and colored noise. These estimates generally can be computed by solving a nonlinear minimization problem. The constrained total least‐squares (CTLS) estimate of the reflectivity series is found by minimizing a function that contains one less term than does the function that gives the ML estimate. When there is no uncertainty in the pulse and the noise covariance matrix is known all estimates are linear functions of the data corresponding to weighted least squares. The stabilized least‐squares (SLS) estimate of the reflectivity series is a special case of the MAP estimate with a simple statistical model. The problem of estimating the seismic pulse, given seismic data and an estimate of the reflectivity series, is identical to the problem of estimating the reflectivity series, except that the initial conditions in the convolutional model are slightly different.
Potential‐field continuation between irregular surfaces—Remarks on the method by Xia et al.
Authors: Meurers Bruno , Pail Roland
Published: October 2002

Xia et al. (1993) offer an excellent method for potential‐field continuation between irregular surfaces by applying the equivalent source technique. This method has proven to be the fastest and most stable procedure for solving the problem of reducing potential‐field data to a constant datum (e.g., Pail, 1995) as long as no sources exist between observation surface and the equivalent stratum. The authors suggest using special equations for the continuation of magnetic fields. Theoretically this is correct, but neither necessary nor well suited, because of the characteristics of the operator for magnetic fields applied in the wavenumber domain.
Monitoring the width of hydraulic fractures with acoustic waves
Authors: Groenenboom Jeroen , Fokkema Jacob T.
Published: October 2002

During scaled hydraulic fracturing experiments in our laboratory, the fracture growth process is monitored in a time‐lapse experiment with ultrasonic waves. We observe dispersion of compressional waves that have propagated across the hydraulic fracture. This dispersion appears to be related to the width of the hydraulic fracture. This means that we can apply the dispersion measurements to monitor the width of the hydraulic fracture in an indirect manner. For a direct determination of the width, the resolution of the signal is required to distinguish the reflections that are related with two distinct fluid/solid interfaces delimiting the hydraulic fracture from its solid embedding. To make this distinction, the solid/fluid interfaces must be separated at least one eighth of a wavelength and represent sufficient impedance contrast. The applicability of the indirect dispersion measurement method however, extends to a fracture width that is in the order of 1% of the incident wavelength. The time‐lapse ultrasonic measurements allow us to relate the small difference in arrival time and amplitude between two measurements solely to the small changes in the width of the fracture. Additional experimental data show that shear waves are completely shadowed by hydraulic fractures, indicating that there is no acoustic contact mechanism at the fracture interface. Therefore we think it is appropriate to use a thin fluid‐filled layer model for these hydraulic fractures instead of the standard empirically oriented linear slip model. Nevertheless, the thin layer model is consistent with the linear‐slip model, if interpreted correctly. A comparison of width measurements inside the wellbore and width estimates by means of dispersion measurements close to the wellbore shows that the method can be successfully applied, at least under laboratory conditions, and that small changes in the width of the fracture are directly expressed in the dispersion of the transmitted signal. This opens the way for the important new application of width monitoring of hydraulic fractures.
Determination of porosity and formation factor of water‐saturated porous specimens from dielectric dispersion measurements
Authors: Haslund Espen , Nøst Bjarne
Published: October 2002

The porosity and the formation factor of water‐saturated porous glass specimens made from sintered spherical grains are determined from the dielectric dispersion measurements of the specimens. This is done by fitting the Mendelson et al. theory for a water‐saturated porous glass specimen to the experimental data using a bimodal grain shape distribution (spherical and plate‐like) for the glass. The porosity, pore‐water conductivity, concentration of plate‐shaped grains, and their aspect ratio are used as fitting parameters, which are varied to obtain the best fit. The porosity and formation factor obtained by this fitting procedure are very close to the values obtained by separate measurements.
Seismic depth imaging of normal faulting in the southern Death Valley Basin
Authors: Chávez‐Pérez Sergio , Louie John N. , Pullammanappallil Sathish K.
Published: October 2002

Motivated by the need to image faults to test Cenozoic extension models for the Death Valley region of the western basin and range province, an area of strong lateral velocity variations, we examine the geometry of normal faulting in southern Death Valley by seismic depth imaging. We analyze COCORP Death Valley Line 9 to attain an enhanced image of shallow fault structure to 2.5 km depth. Previous work used standard seismic processing to infer normal faults from bed truncations, displacement of horizontal reflectors, and diffractions. We obtain a detailed velocity model by nonlinear optimization of first‐ arrival times picked from shot gathers, examine the unprocessed data for fault reflections, and use a Kirchhoff prestack depth imaging procedure to handle lateral velocity variations and arbitrary dips properly. Fault‐plane reflections reveal the listric true‐depth geometry of the normal fault at the Black Mountains range front in southern Death Valley. This is consistent with the concept of low‐angle extension in this region and strengthens its association with crustal‐scale magmatic plumbing.
Attenuating boundary conditions for numerical modeling of acoustic wave propagation
Authors: Cao Shunhua , Greenhalgh Stewart
Published: October 2002

Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one‐wavelength wide zone. The Neumann‐attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.
Theory of nonstationary linear filtering in the Fourier domain with application to time‐variant filtering
Authors: Margrave Gary F.
Published: October 2002

A general linear theory describes the extension of the convolutional method to nonstationary processes. This theory can apply any linear, nonstationary filter, with arbitrary time and frequency variation, in the time, Fourier, or mixed domains. The filter application equations and the expressions to move the filter between domains are all ordinary Fourier transforms or generalized convolutional integrals. Nonstationary transforms such as the wavelet transform are not required. There are many possible applications of this theory including: the one‐way propagation of waves through complex media, time migration, normal moveout removal, time‐variant filtering, and forward and inverse Q filtering. Two complementary nonstationary filters are developed by generalizing the stationary convolution integral. The first, called nonstationary convolution, corresponds to the linear superposition of scaled impulse responses of a nonstationary filter. The second, called nonstationary combination, does not correspond to such a superposition but is shown to be a linear process capable of achieving arbitrarily abrupt temporal variations in the output frequency spectrum. Both extensions have stationary convolution as a limiting form and, in the discrete case, can be formulated as matrix operations. Fourier transformation shows that both filter types are nonstationary filter integrals in the Fourier domain as well. This result is a generalization of the convolution theorem for stationary signals because, as the filter becomes stationary in one domain, the integral in the other domain collapses to a scalar multiplication. For discrete signals, stationary filters are a matrix multiplication of the input signal spectrum by a diagonal spectral matrix, while nonstationary filters require off‐diagonal terms. For quasi‐stationary filters, a computational advantage is obtained by computing only the significant terms near the diagonal. Unlike stationary theory, a mixed domain of time and frequency is also possible. In this context, the nonstationary filter is applied simultaneously with the transform from time to frequency or the reverse. Nonstationary convolution becomes a generalized forward Fourier integral and nonstationary combination is a generalized inverse Fourier integral.
Overthrust imaging with tomo‐datuming: A case study
Authors: Zhu Xianhuai , Angstman Burke G. , Sixta David P.
Published: October 2002

Through the use of iterative turning‐ray tomography followed by wave‐equation datuming (or tomo‐datuming) and prestack depth migration, we generate accurate prestack images of seismic data in overthrust areas containing both highly variable near‐surface velocities and rough topography. In tomo‐datuming, we downward continue shot records from the topography to a horizontal datum using velocities estimated from tomography. Turning‐ray tomography often provides a more accurate near‐surface velocity model than that from refraction statics. The main advantage of tomo‐datuming over tomo‐statics (tomography plus static corrections) or refraction statics is that instead of applying a vertical time‐shift to the data, tomo‐datuming propagates the recorded wavefield to the new datum. We find that tomo‐datuming better reconstructs diffractions and reflections, subsequently providing better images after migration. In the datuming process, we use a recursive finite‐difference (FD) scheme to extrapolate wavefield without applying the imaging condition, such that lateral velocity variations can be handled properly and approximations in traveltime calculations associated with the raypath distortions near the surface for migration are avoided. We follow the downward continuation step with a conventional Kirchhoff prestack depth migration. This results in better images than those migrated from the topography using the conventional Kirchhoff method with traveltime calculation in the complicated near surface. Since FD datuming is only applied to the shallow part of the section, its cost is much less than the whole volume FD migration. This is attractive because (1) prestack depth migration usually is used iteratively to build a velocity model, so both efficiency and accuracy are important factors to be considered; and (2) tomo‐datuming can improve the signal‐to‐noise (S/N) ratio of prestack gathers, leading to more accurate migration velocity analysis and better images after depth migration. Case studies with synthetic and field data examples show that tomo‐datuming is especially helpful when strong lateral velocity variations are present below the topography.
Shallow, high‐resolution seismic imaging at the Ansil mining camp in the Abitibi greenstone belt
Authors: Perron Gervais , Calvert Andrew J.
Published: October 2002

Volcanic rocks in, and around, the Ansil mining camp host a large number of massive sulfide mineral deposits. A high‐resolution seismic reflection profile was shot across the camp with the objective of mapping the contacts between the different volcanic units at which most of the ore bodies have been found. Numerous exploration boreholes define the geology to a depth of 1600 m and allow a precise comparison with the recorded reflections. Geophysical logs obtained in one deep borehole suggest that reflection coefficients between the andesite‐rhyolite units of the volcanic stratigraphy are around 0.05, but few corresponding reflections can be identified in the seismic data. Those reflections in the surface seismic profile that can be correlated with the subsurface geology originate from diorite sills, at which reflection coefficients are between 0.05 and 0.11. We suggest that reflections are observed from the diorite sills because the sills were intruded as sheets, some along fault planes, resulting in interfaces that extend over an area much greater than the first Fresnel zone. The contacts between the rhyolite‐andesite volcanic units may be highly variable spatially, preventing any strong reflection response, in contrast to the results of 1-D synthetic seismograms calculated from the borehole logs. Thus, the strength of a reflection from a lithological contact in igneous rock is likely to be related as much to the way the contact was created as to the magnitude of any local change in seismic impedance across it. Although it did not prove possible to map the volcanic stratigraphy of the Ansil mining camp, reflections interpreted to be from the disused, 1300-m-deep mine galleries were recorded. The seismic reflection data also indicate that the tonalitic Flavrian pluton, which underlies the volcanics, is an imbricated, tabular body, crosscut by diorite sills. Seismic reflections in the pluton arise from the sills and, possibly, primary magmatic layering.
Geophysical application of a new surface integral equation method for EM modeling
Authors: Liu Eric H. , Lamontagne Yves
Published: October 2002

We describe some 3-D electromagnetic (EM) geophysical applications of a new frequency‐domain iterative surface integral equation (SIE) method. The new method is formulated by applying the scalar Green’s theorem to the three Cartesian components of the magnetic field individually. The boundary conditions are implemented through iterations. The convergence behavior of the iteration is demonstrated explicitly through an example. Frequency‐domain results for a number of simple geophysical models are given. The transient response of one model, obtained via inverse Fourier transform, is shown to be consistent with previously published results. The method is found to be stable for a wide range of conductivity contrasts and capable of giving reasonable descriptions of the EM response from the resistive limit up to the inductive limit.
Removing varying directional trends in aeromagnetic data
Authors: Pilkington Mark , Roest Walter R.
Published: October 2002

Both qualitative and quantitative interpretations of aeromagnetic data can be hindered by the presence of magnetic anomalies caused by mafic dykes. Such anomalies obscure the magnetic signatures due to basement lithology and structure, and their effects will often dominate when automated interpretation methods are applied to gridded data sets. Since dyke swarms are often nonparallel, simple frequency‐domain strike‐sensitive filtering based on a single directional trend is not a viable method for removing their signatures. We use a coordinate transformation to project anomalies of various strikes onto one direction, which is then suppressed using a standard decorrugation method. The resulting grid is subsequently transformed back to the original projection. This approach is illustrated by the removal of the magnetic signature of the Proterozoic Mackenzie dyke swarm occurring in the Slave structural province, Northwest Territories, Canada.
Multiscale seismic imaging of active fault zones for hazard assessment: A case study of the Santa Monica fault zone, Los Angeles, California
Authors: Pratt Thomas L. , Dolan James F. , Odum Jackson K. , Stephenson William J. , Williams Robert A. , Templeton Mary E.
Published: October 2002

High‐resolution seismic reflection profiles at two different scales were acquired across the transpressional Santa Monica Fault of north Los Angeles as part of an integrated hazard assessment of the fault. The seismic data confirm the location of the fault and related shallow faulting seen in a trench to deeper structures known from regional studies. The trench shows a series of near‐vertical strike‐slip faults beneath a topographic scarp inferred to be caused by thrusting on the Santa Monica fault. Analysis of the disruption of soil horizons in the trench indicates multiple earthquakes have occurred on these strike‐slip faults within the past 50 000 years, with the latest being 1000 to 3000 years ago. A 3.8-km-long, high‐resolution seismic reflection profile shows reflector truncations that constrain the shallow portion of the Santa Monica Fault (upper 300 m) to dip northward between 30° and 55°, most likely 30° to 35°, in contrast to the 60° to 70° dip interpreted for the deeper portion of the fault. Prominent, nearly continuous reflectors on the profile are interpreted to be the erosional unconformity between the 1.2 Ma and older Pico Formation and the base of alluvial fan deposits. The unconformity lies at depths of 30–60 m north of the fault and 110–130 m south of the fault, with about 100 m of vertical displacement (180 m of dip‐slip motion on a 30°–35° dipping fault) across the fault since deposition of the upper Pico Formation. The continuity of the uncomformity on the seismic profile constrains the fault to lie in a relatively narrow (50 m) zone, and to project to the surface beneath Ohio Avenue immediately south of the trench. A very high‐resolution seismic profile adjacent to the trench images reflectors in the 15 to 60 m depth range that are arched slightly by folding just north of the fault. A disrupted zone on the profile beneath the south end of the trench is interpreted as being caused by the deeper portions of the trenched strike‐slip faults where they merge with the thrust fault.
Inversion of fracture density from field seismic velocities using artificial neural networks
Authors: Boadu Fred K.
Published: October 2002

The inversion of fracture density from field measured P- and S-wave seismic velocities is performed using a neural network trained with an output from the modified displacement discontinuity fracture model. The basic idea is to use input‐output pairs generated by the fracture model to train the neural network. Once the neural network is trained, inversion of fracture density from field‐measured seismic velocities is performed very quickly. The overall performance of the neural network in the inversion process is assessed by means of a loss function. The results indicate that both sources of field information (P- and S-wave velocities) predict the field fracture density with reasonable accuracy. The performance of the neural network was compared to the prediction from least‐squares fitting. It is shown that the neural network out performs the least‐squares fitting in predicting the field‐fracture density values.
2.5-D true‐amplitude Kirchhoff migration to zero offset in laterally inhomogeneous media
Authors: Tygel Martin , Schleicher Jörg , Hubral Peter , Santos Lúcio T.
Published: October 2002

The proposed new Kirchhoff‐type true‐amplitude migration to zero offset (MZO) for 2.5-D common‐offset reflections in 2-D laterally inhomogeneous layered isotropic earth models does not depend on the reflector curvature. It provides a transformation of a common‐offset seismic section to a simulated zero‐offset section in which both the kinematic and main dynamic effects are accounted for correctly. The process transforms primary common‐offset reflections from arbitrary curved interfaces into their corresponding zero‐offset reflections automatically replacing the geometrical‐spreading factor. In analogy to a weighted Kirchhoff migration scheme, the stacking curve and weight function can be computed by dynamic ray tracing in the macro‐velocity model that is supposed to be available. In addition, we show that an MZO stretches the seismic source pulse by the cosine of the reflection angle of the original offset reflections. The proposed approach quantitatively extends the previous MZO or dip moveout (DMO) schemes to the 2.5-D situation.