bluuebunny/crossref_metadata_2025 huggingface dataset:
Velocity analysis using nonhyperbolic moveout in transversely isotropic media
Authors: Alkhalifah Tariq
Published: October 2002

P‐wave reflections from horizontal interfaces in transversely isotropic (TI) media have nonhyperbolic moveout. It has been shown that such moveout as well as all time‐related processing in TI media with a vertical symmetry axis (VTI media) depends on only two parameters, [Formula: see text] and η. These two parameters can be estimated from the dip‐moveout behavior of P‐wave surface seismic data. Alternatively, one could use the nonhyperbolic moveout for parameter estimation. The quality of resulting estimates depends largely on the departure of the moveout from hyperbolic and its sensitivity to the estimated parameters. The size of the nonhyperbolic moveout in TI media is dependent primarily on the anisotropy parameter η. An “effective” version of this parameter provides a useful measure of the nonhyperbolic moveout even in v(z) isotropic media. Moreover, effective η, [Formula: see text], is used to show that the nonhyperbolic moveout associated with typical TI media (e.g., shales, with η ≃ 0.1) is larger than that associated with typical v(z) isotropic media. The departure of the moveout from hyperbolic is increased when typical anisotropy is combined with vertical heterogeneity. Larger offset‐to‐depth ratios (X/D) provide more nonhyperbolic information and, therefore, increased stability and resolution in the inversion for [Formula: see text]. The X/D values (e.g., X/D > 1.5) needed for obtaining stability and resolution are within conventional acquisition limits, especially for shallow targets. Although estimation of η using nonhyperbolic moveouts is not as stable as using the dip‐moveout method of Alkhalifah and Tsvankin, particularly in the absence of large offsets, it does offer some flexibility. It can be applied in the absence of dipping reflectors and also may be used to estimate lateral η variations. Application of the nonhyperbolic inversion to data from offshore Africa demonstrates its usefulness, especially in estimating lateral and vertical variations in η.
An example of seismic time picking by third‐order bicoherence
Authors: Yung S. K. , Ikelle Luc T.
Published: October 2002

Conventional seismic time‐delay estimation relies on the crosscorrelation that quantifies the similarities between two measurements in the second‐order time domain. When the noise correlation in the measurements is considerable, the correlation peak can be substantially distorted, resulting in imprecise and even biased estimation of the time delay. The synthetic data computed by Ikelle et al. (1993) and Ikelle and Yung (1994) in their studies of wave propagation through random media provide a good example of data with considerable noise correlation. In picking the arrival times in this data set, we found that the crosscorrelation technique suffers both from the severely restricted signal bandwidth and from the presence of coda. Here we present an alternative approach involving high‐resolution nonparametric time‐delay estimation in the third‐order domain.
Transverse isotropy versus lateral heterogeneity in the inversion ofP-wave reflection traveltimes
Authors: Grechka Vladimir Y.
Published: October 2002

Nonelliptic transverse isotropy may cause pronounced nonhyperbolic moveout of long‐spread P-wave reflection data. Lateral heterogeneity may alter the moveout in much the same way, and one can expect that a given P-wave reflection moveout may be interpreted equally well in terms of parameters of homogeneous transversely isotropic (TI) or laterally heterogeneous (LH) isotropic models. Here, the common‐midpoint (CMP) moveout of a P-wave reflected from a horizontal interface beneath a weakly laterally heterogeneous medium that is also weakly transversely isotropic is represented analytically in the form similar to that in homogeneous TI media. Both the normal‐moveout (NMO) velocity and the quartic moveout coefficient contain derivatives of the zero‐ offset traveltime t0and the NMO velocity Vnmowith respect to the lateral coordinate. Despite the presence of heterogeneity, nonhyperbolic velocity analysis can be performed in the same way as in homogeneous TI models. If all parameters of the medium are linear functions of the lateral coordinate, heterogeneity does not influence the results of inversion for the anisotropic parameter η. However, to find η in the case of general lateral heterogeneity, the second derivative of Vnmoand the fourth derivative of t0are needed. Since these high‐order derivatives are calculated from the data measured at discrete points by numerical differentiation, stability of η estimation is further reduced as compared to that in homogeneous TI media. Consequently, the trade‐off between anisotropy and heterogeneity significantly complicates the inversion of P-wave reflection traveltimes, even in the simplest model of a single plane layer.
A unified method for 2-D and 3-D refraction statics
Authors: Taner M. Turhan , Wagner Donald E. , Baysal Edip , Lu Lee
Published: October 2002

Most of the seismic data processing procedures are divided into 2-D, 2.5-D, crooked lines or 3-D versions dictated by the differences in the shot and receiver configurations. In this paper, we introduce a tomographic approach that overcomes these geometrical difficulties and provides stable statics solutions from picked first‐break times. We also show that the first‐break picks contain both the short and the long wavelength surface statics. The solutions are obtained by solving a set of generalized surface‐consistent delay‐time equations using the method of weighted least squares and conjugate gradient. While iterating, each first‐break pick is evaluated to ensure its consistency with the least‐squares solution. Based on consistency, we weight the traveltime picks and use them in the next iteration. These weights also serve as an indicator of anomalous picks to the user. We show that long wavelength solutions leave large residual errors in the least‐squares solutions. We also use the expected length of the Fresnel zone to differentiate between short and long wavelength static solutions. After removing the influence of long wavelength statics, we apply short wavelength statics to reduce the residual errors further. We demonstrate the validity of our unified method by applying it to actual data examples. The removal of both long and short wavelength statics improves the initial data set that produces a more consistent set of velocities and leaves only the short wavelength residual reflection statics, which are generally less than quarter wavelet period delays. This removes the most probable cause of the leg jump contamination and poor velocity estimates from the residual statics computations, especially from the 3-D data.
On: “Suppression of sea‐floor‐scattered energy using a dip‐moveout approach—Application to the mid‐ocean ridge environment” by G. M. Kent, I. I. Kim, A. J. Harding, R. S. Detrick, and J. A. Orcutt (May‐June 1996 GEOPHYSICS, 61, 821–834)
Authors: Calvert A. J.
Published: October 2002

In their paper, Kent et al. (1996) present an excellent case history of the use of dip moveout (DMO) and velocity‐filtering in the common midpoint (CMP) domain for the suppression of out‐of‐plane arrivals scattered from a deep sea‐floor. However, they imply that as a result of a “small offset approximation” the use of DMO in this way is limited to surveys recorded in water depths of at least a few kilometers with conventional streamer offsets. This is incorrect. I argue here that the application of DMO will reduce to water velocity the stacking velocity of arrivals scattered from the upper surface of the seafloor without any restriction on water depth. Furthermore, I argue that this use of DMO is simply an example of the equivalence between 2-D and 3-D DMO for marine surveys where all source‐receiver azimuths are equal, and that no “small offset approximation” is required. I first present a counter‐example to the claim of Kent et al. (1996) that seafloor scattering cannot be suppressed using DMO in shallow water, and then consider in more detail their argument for the application of DMO to out‐of‐plane scattering. In the discussion that follows, I only consider DMO in the context of a constant velocity medium.
New aspects of through‐casing resistivity theory
Authors: Singer Bension Sh. , Strack Kurt‐M.
Published: October 2002

A closed‐form solution for a basic model of the through‐casing resistivity measurement is found. The solution reveals fundamental characteristics of the measurement and the dependence of these characteristics on the parameters of the casing and formation. We start our consideration with an analysis of the current distribution in the vicinity of a single electrode energizing the casing. This analysis shows that the distribution becomes axially symmetrical at a distance of just a few radii from the injection point. As a consequence, the number and the physical location of the electrodes used to inject electric current become unimportant if the measurement electrodes are not placed too close to the sensing electrodes. We also derive a closed‐form solution for the distribution of the current flowing in a homogeneous casing embedded in a homogeneous formation. This consideration results in an expression specifying the so‐called characteristic length. The electric field potential is analyzed as a function of the vertical and radial distances from the current injection electrode. Explicit closed‐form expressions are derived for the electric potential distribution at a distance that is greater or less than the characteristic length. A transition from a cylindrical to spherical pattern of the current flow occurs at a radial distance controlled by the characteristic length. This phenomenon bounds the “current tube” resistance. An analytical result is also found for the casing surrounded with a homogeneous cement sheath. The concept of the characteristic length is related closely to the geometrical factor of the through‐casing resistivity measurement. It follows from our solution that the geometrical factor displays a significant dependence on the resistivity of the formation and the parameters of the casing. This dependence should be taken into account in the quantitative interpretation of through‐casing resistivity logs.
Salt dissolution and surface subsidence in central Kansas: A seismic investigation of the anthropogenic and natural origin models
Authors: Anderson Neil L. , Martinez Alex , Hopkins John F. , Carr Timothy R.
Published: October 2002

Gradual subsidence in the Punkin Center study area, northeast Reno County, Kansas, has resulted in ponding of surface waters, abandonment of at least one oil well, and damage to county roads. Because the Punkin Center area is within the Burrton oil field and is underlain by the Hutchinson Salt Member, surface subsidence historically has been attributed to salt dissolution of anthropogenic origin. Subsidence that occurred significant distances from any known well sites has been attributed to unrecorded abandoned wells or complex asymmetric patterns of salt dissolution that originated at a drillhole. To ascertain the validity of the widely accepted anthropogenic salt‐dissolution model, a 4-km seismic reflection profile was acquired along an east‐west‐oriented county road adjacent to an abandoned oil well. The expectation was that the residual Hutchinson Salt Member would be anomalously thin where maximum recorded surface subsidence occurred and thicker elsewhere. Contrary to expectations, the residual Hutchinson Salt Member is relatively thick (20–30 m) below areas of significant recent surface subsidence. There is no evidence of recent surface subsidence at those locations along the seismic profile where the rock salt has been totally leached. At these sites dissolution and subsidence is interpreted to predate European settlement in Kansas and to be of natural origin. The presence of dissolution and subsidence features related to natural processes has implications for developing an understanding of the potentially complex relationship between anthropogenic activities and pre‐existing geologic conditions. Sinkhole development is apparently a natural and expected process along an irregular salt dissolution front. The geometry of this front may be influenced strongly by geologic factors (e.g., fracture patterns and facies distribution). The results are that not all modern sinkhole development has a clear‐cut anthropogenic cause, and the potential for adverse impact resulting from anthropogenic activities will be influenced strongly by pre‐existing geologic conditions. Efficient management decisions along the dissolution front related to well location and well‐site practices should take into account natural processes that previously have and will continue to have an effect on salt dissolution and surface subsidence.
Separation of regional and residual magnetic field data
Authors: Li Yaoguo , Oldenburg Douglas W.
Published: October 2002

We present a method for separating regional and residual magnetic fields using a 3-D magnetic inversion algorithm. The separation is achieved by inverting the observed magnetic data from a large area to construct a regional susceptibility distribution. The magnetic field produced by the regional susceptibility model is then used as the regional field, and the residual data are obtained by simple subtraction. The advantages of this method of separation are that it introduces little distortion to the shape of the extracted anomaly and that it is not affected significantly by factors such as topography and the overlap of power spectra of regional and residual fields. The proposed method is tested using a synthetic example having varying relative positions between the local and regional sources and then using a field data set from Australia. Results show that the residual field extracted using this method enables good recovery of target susceptibility distribution from inversions.
Estimation of unbiased delays
Authors: Taner M. Turhan , Koehler Fulton
Published: October 2002

A large number of exploration processing procedures need the solution to the problem stated as, “Given a set of seismic traces, determine the common element.” This element could be the seismic wavelet, as in a set of common‐shot traces or as in a set of stack traces that need to be matched with synthetic seismograms. It could also be a pilot trace representing a noise‐free estimate of traces in a common‐depth‐point (CDP) gather to be used during an automatic time and phase statics computation. Most present computations use iteratively improved estimates of one sort or another. They assume that initial estimates are close enough to ensure that subsequent steps will produce more accurate results. The problem, of course, is the accuracy of the first unbiased estimation: when it fails, the rest becomes uncertain. In this paper we introduce a method that provides a robust solution to the problem of finding the common element. We also show that the method may be used to estimate both common wavelets and pilot traces conveniently with error correction facilities.
Derivative analysis of SP anomalies
Authors: Abdelrahman El‐Sayed Mohamed , Ammar Ahmed Abu Baker , Hassanein Hamdy Ismail , Hafez Mahfooz Abdelmottaleb
Published: October 2002

Numerical second horizontal derivative self‐potential (SP) anomalies obtained from SP data using filters of successive window lengths (graticule spacings) can be used to determine the shape and depth of a buried structure. For a fixed window length, the depth is determined using a simple formula for each shape factor. The computed depths are plotted against the shape factors on a graph. All points for a fixed window length are connected by a continuous curve (window curve). The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. The method is applied to theoretical data with and without random noise and tested on a field example from Turkey.
Resolving seismic anisotropy: Sparse matrix methods for geophysical inverse problems
Authors: Vasco Don W. , Peterson John E. , Majer Ernest L.
Published: October 2002

Two techniques for the singular value decomposition (SVD) of large sparse matrices are directly applicable to geophysical inverse problems: subspace iteration and the Lanczos method. Both methods require very little in‐core storage and efficiently compute a set of singular values and singular vectors. A comparison of the singular value and vector estimates of these iterative approaches with the results of a conventional in‐core SVD algorithm demonstrates their accuracy. Hence, it is possible to conduct an assessment of inversion results for larger sparse inverse problems such as those arising in seismic tomography. As an example, we examine the resolution matrix associated with a crosswell seismic inversion of first arrival times for lateral variations in anisotropy. The application to a set of first arrival times from a crosswell survey at the Grimsel Laboratory emphasizes the utility of including anisotropy in a traveltime inversion. The isotropic component of the estimated velocity structure appears to be well constrained even when anisotropy is included in the inversion. In the case of the Grimsel experiment, we are able to resolve a fracture zone, in agreement with borehole fracture intersections. Elements of the resolution matrix reveal moderate averaging among anisotropy coefficients as well as between anisotropy coefficients and source‐receiver static terms. The information on anisotropy, such as the directions of maximum velocity, appears sensitive to lateral variations in velocity and must be interpreted with some caution.
Shallow seismic reflection study of a glaciated valley
Authors: Büker Frank , Green Alan G. , Horstmeyer Heinrich
Published: October 2002

Shallow seismic reflection data were recorded along two long (>1.6 km) intersecting profiles in the glaciated Suhre Valley of northern Switzerland. Appropriate choice of source and receiver parameters resulted in a high‐fold (36–48) data set with common midpoints every 1.25 m. As for many shallow seismic reflection data sets, upper portions of the shot gathers were contaminated with high‐amplitude, source‐generated noise (e.g., direct, refracted, guided, surface, and airwaves). Spectral balancing was effective in significantly increasing the strength of the reflected signals relative to the source‐generated noise, and application of carefully selected top mutes ensured guided phases were not misprocessed and misinterpreted as reflections. Resultant processed sections were characterized by distributions of distinct seismic reflection patterns or facies that were bounded by quasi‐continuous reflection zones. The uppermost reflection zone at 20 to 50 ms (∼15 to ∼40 m depth) originated from a boundary between glaciolacustrine clays/silts and underlying glacial sands/gravels (till) deposits. Of particular importance was the discovery that the deepest part of the valley floor appeared on the seismic section at traveltimes >180 ms (∼200 m), approximately twice as deep as expected. Constrained by information from boreholes adjacent to the profiles, the various seismic units were interpreted in terms of unconsolidated glacial, glaciofluvial, and glaciolacustrine sediments deposited during two principal phases of glaciation (Riss at >100 000 and Würm at ∼18 000 years before present).
Land streamer for shallow seismic data acquisition: Evaluation of gimbal‐mounted geophones
Authors: van der Veen Michiel , Green Alan G.
Published: October 2002

To increase the speed and efficiency of shallow seismic data recording and thereby decrease acquisition costs, the concept of a towed land streamer containing self‐orienting, gimbal‐mounted geophones is being evaluated. Our initial experiments at two locations within Switzerland demonstrate that good coupling with the ground may be achieved when the gimbal‐mounted vertical geophones are contained in heavy (∼1 kg) casings and pulled along a very shallow (2–3 cm deep) furrow. Such a furrow may be created by mounting a heavy wheel on the towing vehicle. Placing the geophones in even heavier casings may provide the necessary good coupling with the ground, negating the need for the furrow. Shot gathers and stacked sections recorded with the gimbal‐mounted geophones are practically indistinguishable from those recorded with conventional spike geophones. The principal advantage of this approach is that significantly fewer field personnel (only two or three) are required than for conventional shallow seismic surveying. When fully operational, the new acquisition system should be faster and less expensive for a wide variety of engineering and environmental applications.
On: “A quasi‐Monte Carlo approach to 3-D migration: Theory,” (Y. Sun, G. T. Schuster, and K. Sikorski, GEOPHYSICS, 62, 918–928)
Authors: Vermeer Gijs J. O.
Published: October 2002

Sun et al. discuss the fact that random coarse sampling produces less serious artifacts in migration than regular coarse sampling. This is an interesting phenomenon which also applies to stacking: for high‐fold data, regular offset sampling produces the best result, whereas for low‐fold data random offset sampling is better.
Effects of attenuation and anisotropy on reflection amplitude versus offset
Authors: Carcione José M. , Helle Hans B. , Zhao Tong
Published: October 2002

To investigate the effects that attenuation and anisotropy have on reflection coefficients, we consider a homogeneous and viscoelastic wave incident on an interface between two transversely isotropic and lossy media with the symmetry axis perpendicular to the interface. Analysis of P P and P S reflection coefficients shows that anisotropy should be taken into account in amplitude variation with offset (AVO) studies involving shales. Different anisotropic characteristics may reverse the reflection trend and substantially influence the position of the critical angle versus offset. The analysis of a shale‐chalk interface indicates that when the critical distance is close to the near offsets, the AVO response is substantially affected by the presence of dissipation. In a second example, we compute reflection coefficients and synthetic seismograms for a limestone/black shale interface with different rheological properties of the underlying shale. This case shows reversal of the reflection trend with increasing offset and compensation between the anisotropic and anelastic effects.
Dithering of absorbers for efficient finite‐difference modeling of viscoelastic wave propagation
Authors: Zeng Xiansong , West Gordon F.
Published: October 2002

Viscoelastic modeling traditionally uses multiple relaxation mechanisms (absorbers) per wave type in each cell of the numerical grid. We show that one absorber per cell suffices when the absorbers of different relaxation frequencies and absorption strengths are dithered in a supercell, i.e., a very small area of several nearby cells. The relaxation frequencies used in a supercell can be preselected to cover the bandwidth required in the modeling and distributed locally in a random manner to minimize numerical scattering. The absorption strengths, however, must be found iteratively to yield an average absorption that matches the desired medium over the bandwidth. We have tested the dithered‐absorber method for modeling a variety of 2-D media using a staggered‐grid finite‐difference scheme. For a uniform medium, our result agrees well with the exact analytic solution. For inhomogeneous models, the dithered‐absorber solution agrees well with the finite‐difference solution computed with five absorbers per cell. The computer time and memory requirements of the dithered‐absorber method are only ≈60% and ≈40% of those with five absorbers per cell. In all cases, random numerical scattering is very small—typically less than similar types of error because of model discretization.
Composite boundary‐valued solution of the 2.5-D Green’s function for arbitrary acoustic media
Authors: Zhou Bing , Greenhalgh Stewart A.
Published: October 2002

Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Fréchet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of [Formula: see text] at each frequency can be determined rationally from the critical wavenumber value of the medium around the source. Furthermore, it shows that the frequency‐domain solution is not improved continuously by increasing the number of [Formula: see text] samples because of the complicated nature of the wavefield. Both experiments show that the proposed method is effective and flexible for computing the 2.5-D Green’s function for arbitrary acoustic media.
Fractal behavior and detectibility limits of geophysical surveys
Authors: Dimri V. P.
Published: October 2002

The detectibility limits of a large‐scale geophysical measuring network (such as arrays of seismometers for seismic hazard assessment, arrays of air guns and vibrators in seismic profiling, and station spacing in gravity, magnetic, magnetotelluric, and other geophysical surveys for exploration of oil, minerals, and groundwater) depends on the fractal dimension of the network and the anomaly (Lovejoy et al., 1986; Korvin, 1992). The geophysical anomaly resulting from the fractal nature of sources (Turcotte, 1992) [such as length of fault (Okubo and Aki, 1987; Robertson et al., 1995), velocity inhomogeneities (Sato, 1988), nonrandom distribution of density (Thorarinsson and Magnusson, 1990) and susceptibility (Pilkington and Todoeschuck, 1993; Pilkington et al., 1994; Maus and Dimri, 1994, 1995, 1996), reflectivity (Todoeschuck et al., 1990; Dimri, 1992), etc.] cannot be accurately measured unless its fractal dimension does not exceed the difference of the 2-D Euclidean and fractal dimension of the network (Lovejoy et al., 1986; Korvin, 1992).
Depth to magnetic source using the generalized analytic signal
Authors: Hsu Shu‐Kun , Coppens Dorothée , Shyu Chuen‐Tien
Published: October 2002

The advantage of using analytic signal techniques to determine magnetic parameters from magnetic anomalies is the independence of magnetization direction. In addition, using the amplitude ratio method to determine depths to magnetic sources can avoid tedious operations with several characteristic points and reduce interference effects. A drawback of this method, however, is the assumption that near‐surface structures can be characterized adequately by step models. To improve mapping resolution, we have extended the amplitude ratio method to allow both step‐like and dike‐like structures. A criterion is constructed that discriminates between maxima from dike‐like or step‐like structures and significantly improves near‐surface structural mapping. This avoids a bias in geological interpretation caused by the original assumption that all structures can be characterized by step models. Synthetic data and real data acquired offshore northern Taiwan demonstrate the effectiveness of this method.
Preconditioning of full‐waveform inversion in viscoacoustic media
Authors: Causse Emmanuel , Mittet Rune , Ursin Bjørn
Published: October 2002

Intrinsic absorption in the earth affects the amplitude and phase spectra of the seismic wavefields and records, and may degrade significantly the results of acoustic full‐waveform inversion. Amplitude distortion affects the strength of the scatterers and decreases the resolution. Phase distortion may result in mislocated interfaces. We show that viscoacoustic gradient‐based inversion algorithms (e.g., steepest descent or conjugate gradients) compensate for the effects of phase distortion, but not for the effects of amplitude distortion. To solve this problem at a reasonable numerical cost, we have designed two new forms of preconditioning derived from an analysis of the inverse Hessian operator. The first type of preconditioning is a frequency‐dependent compensation for dispersion and attenuation, which involves two extra modeling steps with inverse absorption (amplification) at each iteration. The second type only corrects the strength of the recovered scatterers, and requires two extra modeling steps at the first iteration only. The new preconditioning methods have been incorporated into a finite‐difference inversion scheme for viscoacoustic media. Numerical tests on noise‐free synthetic data illustrate and support the theory.
Traveltime prediction and suppression of 3-D multiples
Authors: Ross Warren S. , Yu Yang , Gasparotto Fernanda A.
Published: October 2002

We analyze the characteristics and suppression of multiples generated in three dimensions. We derive expressions for the traveltime of peg‐leg multiples generated by two dipping planes. Using this theory, we demonstrate that multiples generated in three dimensions may have traveltimes substantially different from 2-D multiples. For a case studied of 3° cross‐line dip, second‐order water‐bottom and peg‐leg multiples arrive on the order of 10 ms earlier than they would in two dimensions. For fifth‐order multiples, this difference is as high as 65 ms. These 2-D/3-D time differences grow to many hundreds of milliseconds for 10° of cross‐line dip. We confirm the presence of the cross‐line dip effect in field data containing salt‐related multiples. Using dips estimated from a 3-D interpretation of a top‐salt horizon, we further demonstrate that the theory can accurately predict traveltimes for such multiples. Finally, based on the theory, we present an algorithm for suppressing 3-D multiples when cross‐line dip can be estimated, validating the algorithm using model and field data.
Applying finite element analysis to the memory variable formulation of wave propagation in anelastic media
Authors: Kay Ian , Krebes E. S.
Published: October 2002

Finite‐element methods are applied to solution of seismic wave motion in linear viscoelastic media using the memory variable formalism. The displacements are represented as a superposition of a set of basis functions. It is shown that if memory variables are represented using the spatial derivatives of those basis functions, rather than the basis functions themselves, the equations to be solved are simpler and require less computer memory. Using this formulation, results for SH waves in one and two dimensions are calculated using a simple explicit finite‐element‐in‐space/finite‐difference‐in‐time scheme. These results agree with those found with a “method of lines” solution. Results in a homogeneous medium also agree with the frequency domain solutions of Kjartansson’s constant-Q method.
Airborne resistivity data leveling
Authors: Huang Haoping , Fraser Douglas C.
Published: October 2002

Helicopter‐borne frequency‐domain electromagnetic (EM) data are used routinely to produce resistivity maps for geologic mapping, mineral exploration, and environmental investigations. The integrity of the resistivity data depends in large part on the leveling procedures. Poor resistivity leveling procedures may, in fact, generate false features as well as eliminate real ones. Resistivity leveling is performed on gridded data obtained by transformation of the leveled EM channel data. The leveling of EM channel data is often imperfect, which is why the resistivity grids need to be leveled. We present techniques for removing the various types of resistivity leveling errors which may exist. A semi‐automated leveling technique uses pseudo tie‐lines to remove the broad flight‐based leveling errors and any high‐magnitude line‐based errors. An automated leveling technique employs a combination of 1-D and 2-D nonlinear filters to reject the rest of the leveling errors including both long‐and short‐wavelength leveling errors. These methods have proven to be useful for DIGHEM helicopter EM survey data. However, caution needs to be exercised when using the automated technique because it cannot distinguish between geological features parallel to the flight lines and leveling errors of the same wavelength. Resistivity leveling is not totally objective since there are no absolutes to the measured frequency‐domain EM data. The fundamental integrity of the EM data depends on calibration and the estimate of the EM zero levels. Zero level errors can be troublesome because there is no means by which the primary field can be determined absolutely and therefore subtracted to yield an absolute measure of the earth’s response. The transform of incorrectly zero‐leveled EM channels will yield resistivity leveling errors. Although resistivity grids can be leveled empirically to provide an esthetically pleasing map, this is insufficient because the leveling must also be consistent across all frequencies to allow resistivity to be portrayed in section. Generally, when the resistivity looks correct in plan and section, it is assumed to be correct.
3-D inversion of gravity and magnetic data with depth resolution
Authors: Fedi Maurizio , Rapolla Antonio
Published: October 2002

Magnetization and density models with depth resolution are obtained by solving an inverse problem based on a 3-D set of potential field data. Such a data set is built from information on vertical and horizontal variations of the magnetic or gravity field. The a priori information consists of delimiting a source region and subdividing it in a set of blocks. In this case, the information related to a set of field data along the vertical direction is not generally redundant and is decisive in giving a depth resolution to the gravity and magnetic methods. Because of this depth resolution, which derives solely from the potential field data, an unconstrained and joint inversion of a multiobservation‐level data set is shown to provide surprising results for error‐free synthetic data. On the contrary, a single‐observation level data inversion produces an incorrect and too shallow model. Hence, a good depth resolution is likely to occur for the gravity and magnetic methods when based on the information along the vertical direction. This is also evidenced by an analysis of the kernel function versus the field altitude level and by a singular value analysis of the inversion operators for both the single and multilevel cases. Errors connected to numerical upward continuation do not affect the quality of the solution, provided that the data set extent is larger than that of the anomaly field. Application of the method to a 3-D magnetic data set relative to Vesuvius indicates that the method may significantly improve interpretation of potential fields.
A noise‐optimized objective method for predictive deconvolution
Authors: Hornbostel Scott C.
Published: October 2002

Predictive deconvolution filters are designed to remove as much predictable energy as possible from the input data. It is generally understood that temporally correlated geology can cause problems for these filters. It is perhaps less well appreciated that uncorrelated random noise can also severely affect filter performance. The root of these problems is in the objective function being minimized; in addition to minimizing predictable multiple energy, the filter is attempting to simultaneously minimize the temporally correlated geology and the random‐noise energy. Instead of minimizing the input trace energy, an alternative objective function for minimization can be defined that is the result of a linear operator acting on the input data. Ideally this alternative objective function contains only the targeted noise (e.g., multiples). The linear operator that creates this objective function is designated as the “noise‐optimized objective” (NOO) operator. The filter that minimizes this new objective function is the NOO filter. Useful NOO operators for multiple suppression are those that maximize multiple energy and/or minimize primary or random noise energy in the data. Examples of such linear operators include stacking, bandpass filtering, dip filtering, and muting or scaling. Simply scaling down the primary‐containing portion of the objective function can address the problematic removal of correlated geology. Stacking can also be a useful NOO operator. By minimizing the predictable energy on a stacked trace, the prestack filters are less affected by random noise. The NOO stacking method differs from a standard poststack filter design because the filters are designed to be applied prestack. Further, this method differs from a standard prestack prediction filter because it minimizes the predictable energy on the stacked trace. The standard prestack filter has reduced multiple suppression because the filter must compromise between minimizing the multiple energy and minimizing the random noise energy. Minimizing the impact of random noise can be quite important in prediction filtering. At a signal‐to‐random‐noise ratio of one, for example, half the multiple remains after filtering. This random noise‐related degradation might help to explain the common observation that prediction filters tend to leave multiple energy in the data. A time‐varying gap implementation of a stacking NOO filter addresses these random noise effects while also addressing data aperiodicity issues.
Variogram analysis of helicopter magnetic data to identify paleochannels of the Omaruru River, Namibia
Authors: Maus Stefan , Sengpiel K. P. , Röttger B. , Siemon B. , Tordiffe E. A. W.
Published: October 2002

The geomagnetic field over sedimentary basins is very sensitive to variations in basement depth. Therefore, magnetic surveys are widely used to map basement topography in petroleum and groundwater exploration. We propose variogram analysis as a more accurate alternative to power spectral methods. Data variograms are computed from aeromagnetic flight‐line data. To estimate depth, the data variograms are compared with model variograms for a range of source depths. We use the exact space domain counterparts of a fractal power spectral model as model variograms. To demonstrate the utility of this method for groundwater exploration, we map the basement topography of the Omaruru Alluvial Plains in Namibia. A comparison with electromagnetic (EM) resistivities and drilling information confirms the high accuracy—but also the limitations—of variogram analysis depth. Variogram analysis makes maximum use of short‐wavelength contributions to the magnetic signal, which is the key to the resolution of shallow basement topography. Moreover, by using a realistic source model and avoiding extensive data preconditioning and the transform to wavenumber domain, variogram analysis is likely to provide improved magnetic depth estimates even for deep basins.
Coarse‐layer stripping of vertically variable azimuthal anisotropy from shear‐wave data
Authors: Thomsen Leon , Tsvankin Ilya , Mueller Michael C.
Published: October 2002

Alford rotation analysis of 2C × 2C shear‐wave data (two source components, two receiver components) for azimuthal anisotropy is valid only when the orientation of that azimuthal anisotropy is invariant with depth. The Winterstein and Meadows method of layer stripping vertical seismic profiling (VSP) data relaxes this restriction for coarse‐layer variation of the orientation of the anisotropy. Here we present a tensor generalization of the conventional convolutional model of scalar wave propagation and use it to derive generalizations of Winterstein and Meadows layer stripping, valid for 2C × 2C data and for the restricted 2C-only case, in the VSP and reflection contexts. In the 2C × 2C VSP application, the result reduces to that of Winterstein and Meadows in the case where both fast and slow shear modes have the same attenuation and dispersion; otherwise, a balancing of mode spectra and amplitudes is required. The 2C × 2C reflection result differs from the 2C × 2C VSP result since two applications of the mode‐balancing and mode‐advance operations are required (since the waves travel up as well as down). Application to a synthetic data set confirms these results. The 2C × 2C reflection algorithm enables the exploration for sweet spots of high fracture intensity ahead of the bit without the restrictive assumption that the anisotropy orientation is depth invariant.
Azimuth‐dependent tuning of seismic waves reflected from fractured reservoirs
Authors: Schoenberg Michael A. , Dean Simon , Sayers Colin M.
Published: October 2002

Reservoirs with thickness less than the seismic wavelength can still contain significant amounts of hydrocarbons. Such layers exhibit a tuning effect which involves the interference of reflected waves from the top and bottom of the reservoir. Natural fractures in such reservoirs can play an important role in determining fluid flow, which makes the density and orientation of fractures of great interest. In the presence of one or more sets of aligned vertical fractures, the amplitude of reflected waves at nonzero offset varies with azimuth; hence, the tuning effect will vary with azimuth. For wavelengths much greater than typical fracture spacing, equivalent medium theory allows such a vertically fractured layer to be modeled as a monoclinic layer with a plane of mirror symmetry parallel to the layer. The variation in reflection and transmission coefficients with incidence and azimuthal angle for a thin vertically fractured layer can be expressed in terms of the horizontal slowness, automatically accounting for the change of angle with azimuth for rays propagating through the layer and for the tuning effect which occurs for layers with thickness of the order of the wavelength. For low enough frequency (or equivalently, thin enough layers), approximate expressions for the reflection and transmission coefficient matrices and transmitted amplitudes are derived. These expressions demonstrate explicitly that all reflected pulses and all converted transmitted pulses have the same shape as the time derivative of the incident pulse, whereas for thicker layers, distinct reflections from the top and bottom of the layer are evident, particularly for small angles of incidence. When these reflections interfere, significant changes in pulse shape with azimuth are found which result from differences in the azimuthal variation of reflection coefficient from the top and bottom of the layer due to propagation effects in the layer.
Analysis of multiazimuthal VSP data for anisotropy and AVO
Authors: Leaney W. Scott , Sayers Colin M. , Miller Douglas E.
Published: October 2002

Multioffset vertical seismic profile (VSP) experiments, commonly referred to as walkaways, enable anisotropy to be measured reliably in the field. The results can be fed into modeling programs to study the impact of anisotropy on velocity analysis, migration, and amplitude versus offset (AVO). Properly designed multioffset VSPs can also provide the target AVO response measured under optimum conditions, since the wavelet is recorded just above the reflectors of interest with minimal reflection point dispersal. In this paper, the multioffset VSP technique is extended to include multioffset azimuths, and a multiazimuthal multiple VSP data set acquired over a carbonate reservoir is analyzed for P-wave anisotropy and AVO. Direct arrival times down to the overlying shale and reflection times and amplitudes from the carbonate are analyzed. Data analysis involves a three‐term fit to account for nonhyperbolic moveout, dip, and azimuthal anisotropy. Results indicate that the overlying shale is transversely isotropic with a vertical axis of symmetry (VTI), while the carbonate shows 4–5% azimuthal anisotropy in traveltimes. The fast direction is consistent with the maximum horizontal stress orientation determined from break‐out logs and is also consistent with the strike of major faults. AVO analysis of the reflection from the top of the carbonate layer shows a critical angle reduction in the fast direction and maximum gradient in the slow direction. This agrees with modeling and indicates a greater amplitude sensitivity in the slow direction—the direction perpendicular to fracture strike. In principle, 3-D surveys should have wide azimuthal coverage to characterize fractured reservoirs. If this is not possible, it is important to have azimuthal line coverage in the minimum horizontal stress direction to optimize the use of AVO for fractured reservoir characterization. This direction can be obtained from multiazimuthal walkaways using the azimuthal P-wave analysis techniques presented.
On: “3-D localization of buried objects by nearfield electromagnetic holography” (Y. Guo, H. W. Ko, and D. M. White, GEOPHYSICS, 63, 3, 880–889).
Authors: Zhdanov Michael
Published: October 2002

The authors present a method of localizing underground objects with low‐frequency electromagnetic field based on ideas of electromagnetic holography. Though I do strongly support this method and practical results presented in the paper, I should note that the authors neglected in their paper to reference the previous publications on this subject, where the basic principles, ideas, methods, and term “electromagnetic holography” have been already introduced and developed as applied to low‐frequency electromagnetic field underground imaging.
Experimental studies of electrokinetic conversions in fluid‐saturated borehole models
Authors: Zhu Zhenya , Haartsen Matthijs W. , Toksöz M. Nafi
Published: October 2002

Experimental and theoretical studies show that there are electromagnetic (EM) fields generated by seismic waves with two kinds of conversion mechanisms in a fluid‐saturated, porous medium. Within a homogeneous formation, the seismic wave generates a seismoelectric field that exists only in the area disturbed by the seismic wave and whose apparent velocity is that of the seismic wave. At an interface between differing formation properties, the generated seismoelectric wave is a propagating EM wave that can be detected everywhere. An electrode, used as a receiver on the ground surface, can detect the propagating EM wave generated at an interface, but cannot detect the seismoelectric field generated in a homogeneous formation. When the electrode is in a borehole and close to a porous formation, it can detect both the EM waves and the seismoelectric field. In this paper, electrokinetic measurements are performed with borehole models made of natural rocks or artificial materials. Experimental results show that the Stoneley wave and other acoustic modes, excited by a monopole source in the borehole models, generate seismoelectric fields in fluid‐saturated formations. The electric components of the seismoelectric fields can be detected by an electrode in the borehole or on the borehole wall. The amplitude and frequency of the seismoelectric fields are related not only to the seismic wave, but also to formation properties such as permeability, conductivity, etc. Comparison between the waveforms of the seismoelectric signals and acoustic logging waves suggests that seismoelectric well logging may explore the different properties of the formation. Electroseismic measurements are also performed with these borehole models. The electric pulse through the electrode in the borehole or on the borehole wall induces Stoneley waves in fluid‐saturated models that can be received by a monopole transducer in the same borehole. These measurement methods (seismoelectric logging or electroseismic logging) might directly apply to well logging to investigate formation properties related to the pore fluid flow.