bluuebunny/crossref_metadata_2025 huggingface dataset:
1-D layered media: Part 2, Layer‐based waveform inversion
Authors: Jurado Fabrice , Cuer Michel , Richard Vincent
Published: October 2002

We are interested here in the inversion of multioffset data to determine 1-D medium properties. The forward modeling technique accounts for 3-D wave propagation effects. The inversion is performed by minimizing the difference between modeled and reference data using a least‐squares technique. The gradient is computed by the adjoint state technique adapted to the first‐order hyperbolic system and to the Hankel transform. To reduce the number of optimization parameters and to optimize along reflected events from some selected interfaces, we propose a layer‐oriented reparameterization in the full‐waveform inversion. Then we discuss the effect on the inversion results of an incorrect number of layers. The local minima of the least‐squares functional are experimentally investigated and physically interpreted. This sensitivity study has shown that it is necessary to have an accurate initial model for the position of the layer interfaces. In principle, seismic data give access directly to this information. This is why we have formulated the inverse problem in one‐way vertical traveltime as opposed to depth. Using an example, we show that with this parameterization the variation of the least‐ squares misfit function when we change the interval velocity for a given layer tends to a quasi quadratic form. In practice, a layer‐based waveform inversion (LBWI) procedure is proposed to overcome the inherent problem of local minima. The procedure attempts to determine interval velocities, impedance contrasts, and interface positions for a limited number of layers to explain the major seismic events. The LBWI procedure is based on four key elements: traveltime formulation, layer‐based reparameterization, progressive enrichment of the model, and interpretative approach. This procedure is evaluated for a large‐scale acoustic synthetic example.
An elastodynamic inverse scattering method for removing scattered surface waves from field data
Authors: Blonk Bastian , Herman Gerard C. , Drijkoningen Guy G.
Published: October 2002

In an earlier paper, we introduced a 3-D inverse scattering method for removing scattered surface waves from seismic data that was based on a tomographic imaging of the scattered surface waves by a data‐fitting procedure that used as much of the seismic data as possible. After this imaging step, the scattered surface waves can be computed and removed for each separate source‐receiver pair. We now apply the method to two field‐data sets. The method requires a knowledge of the source waveform and shallow propagation characteristics, and these input requirements are estimated from the direct surface wave. We conclude that the method effectively attenuates crossline scattered surface waves without affecting deeper reflections.
Velocity computation from checkshot surveys in deviated wells
Authors: Noponen Ilkka T.
Published: October 2002

When checkshot surveys are done in deviated wells, two source‐receiver geometries are used. In one, the wave source is moved on the earth’s surface in unison with the horizontal movement of the receiver in the well so that the raypath from the source to the receiver is always vertical. This is the source‐over‐receiver approach. In the other approach, called source‐at‐rig, the source is fixed, usually staying in the vicinity of the drilling rig. The source‐over‐receiver method is usually preferred because the source‐at‐ rig method does not measure vertical traveltimes. If velocity varies with depth, the seismic rays from a source at the rig will bend, and a correction to vertical using the common straight‐ray assumption will not produce accurate vertical traveltimes or interval velocity measurements.
On: “Pulse distortion in depth migration,” by M. Tygel, J. Schleicher, and P. Hubral (October 1994 GEOPHYSICS, 59, p. 1561–1569).
Authors: Mohan N. L.
Published: October 2002

I am rather surprised to see “Pulse distortion in depth migration” (Tygel et al., 1994) with no reference of our work (Mohan et al., 1991), which I strongly believe is judgmental in many ways. In fact, the list of references given by Tygel et al. (1994) gives an impression that their work is original. It is indeed quite unfortunate that reviewers, associate editors, and editor did not have our work (Mohan et al., 1991) referenced in their publication appropriately. It may not be out of place to mention that earlier, Brown (1994) also failed to cite our work.
Effects of salt‐related mode conversions on subsalt prospecting
Authors: Ogilvie Jeff S. , Purnell Guy W.
Published: October 2002

Mode conversion of waves during seismic reflection surveys has generally been considered a small phenomenon that could be neglected in data processing and interpretation. However, in subsalt prospecting, the contrast in material properties at the salt/sediment interface is often great enough that significant P‐to‐S and/or S‐to‐P conversion occurs. The resulting converted waves can be both a help and a hinderance for subsalt prospecting. A case history from the Mississippi Canyon area of the Gulf of Mexico demonstrates strong converted‐wave reflections from the base‐of‐salt that complicate the evaluation of a subsalt prospect using 3-D seismic data. Before and after stack, the converted‐wave reflections are evident in 2-D and 3-D surveys across the prospect. Ray‐tracing synthetic common midpoint (CMP) gathers provides some useful insights about the occurrence of these waves, but elastic‐wave‐equation modeling is even more useful. While the latter is more time‐consuming, even in 2-D, it also provides a more realistic simulated seismic survey across the prospect, which helps to reveal how some converted waves survive the processes of CMP stack and migration, and thereby present possible pitfalls to an unwary interpreter. The insights gained from the synthetic‐data study suggest some simple techniques that can assist an interpreter in the 3-D interpretation of subsalt events.
Improved Fourier terrain correction, Part II
Authors: Parker Robert L.
Published: October 2002

Fourier methods for potential fields have always been developed with the simplification that the calculation surface is a level plane. The Fourier approach can be extended to deal with an uneven observation surface. I consider the case of terrain correction for gravity surveys, in which the attraction of a variable‐thickness layer is calculated at points on its upper surface. The main idea is to use a power series in topographic height that is then converted into a series of convolutions. To avoid convergence problems, a cylindrical zone around the observer must be removed from the Fourier treatment and its contribution computed directly. The resultant algorithm is very fast: in an example based on a recent survey, the new method is shown to be more than 300 times faster than a calculation based on summing contributions from a column of material under each topographic grid point.
Simulation of complete seismic surveys for evaluation of experiment design and processing
Authors: Özdenvar Turgut , McMechan George A. , Chaney Preston
Published: October 2002

Synthesis of complete seismic survey data sets allows analysis and optimization of all stages in an acquisition/processing sequence. The characteristics of available survey designs, parameter choices, and processing algorithms may be evaluated prior to field acquisition to produce a composite system in which all stages have compatible performance; this maximizes the cost effectiveness for a given level of accuracy, or for targets with specific characteristics. Data sets synthesized for three salt structures provide representative comparisons of time and depth migration, post‐stack and prestack processing, and illustrate effects of varying recording aperture and shot spacing, iterative focusing analysis, and the interaction of migration algorithms with recording aperture. A final example demonstrates successful simulation of both 2-D acquisition and processing of a real data line over a salt pod in the Gulf of Mexico.
Kinematic inversion of first arrivals of refracted waves—A combined approach
Authors: Shtivelman Vladimir
Published: October 2002

The inversion of first‐arrival times of refracted waves in media with laterally varying parameters can be performed using the refraction tomography technique. Tomographic inversion implemented as a linearized, constrained, least‐squares, iterative scheme requires some a priori information on either refractor depth or velocity above the refractor; however, such information may be unavailable. On the other hand, in many cases a reasonable estimate of the average velocity distribution above the refractor can be obtained by a nontomographic technique such as the generalized reciprocal method (GRM). I propose a combined approach to the inversion problem that uses the advantages of both the refraction tomography and GRM techniques and which does not require additional information not contained in first arrival times. The approach is based upon two assumptions (which prove to be true in most situations). The first is that a reasonable local estimate of refractor velocity can be obtained by tomographic inversion independently of other model parameters, and the second is that the derivative of the velocity analysis function as defined by the GRM, gives a good local approximation of the refractor slowness. The proposed combined inversion scheme can be described as a three‐step procedure. In the first step, the laterally varying refractor velocity is estimated by tomographic inversion. In the second step, local estimation of laterally varying average velocity above the refractor is performed by the GRM on the basis of the previously estimated refractor velocity. In the third step, the estimated values of the average velocity are used as the corresponding constrained initial parameters for tomographic inversion.
AVO correction for scalar waves in the case of a thinly layered reflector overburden
Authors: Widmaier Martin T. , Shapiro Sergei A. , Hubral Peter
Published: October 2002

The reflection response of a seismic target is significantly affected by a thinly layered overburden, which creates velocity anisotropy and a transmission loss by scattering attenuation. These effects must be taken into account when imaging a target reflector and when inverting reflection coefficients. Describing scalar wave (i.e., acoustic wave or SH‐wave) propagation through a stack of thin layers by equivalent‐medium theory provides a simple generalized O’Doherty‐Anstey formula. This formulation is defined by a few statistical parameters that depend on the 1-D random fluctuations of the reflector overburden. The formula has been combined with well‐known target‐oriented and amplitude‐preserving migration/inversion algorithms and amplitude variation with offset (AVO) analysis procedures. The application of these combined procedures is demonstrated for SH‐waves in an elastic thinly‐layered medium. These techniques offer a suitable tool to compensate for the thin‐layer influence on traveltimes and amplitudes of seismic reflection data. The thin‐layer sensitive AVO parameters (zero‐offset amplitude and AVO gradient) of a target reflector can thus be better recovered.
Monte Carlo simulation of wells
Authors: de Groot Paul F. M. , Bril Albertus H. , Floris Frans J. T. , Campbell A. Ewan
Published: October 2002

We present a method to simulate wells, i.e., 1-D stratigraphic profiles with attached physical properties but without spatial information, using a combination of geological knowledge and Monte Carlo statistics. The simulated data is intended to be used in seismic lateral prediction studies. Our algorithm simulates correlated stochastic variables one by one. There are two major advantages in this approach above the conventional way in which all correlated stochastic vectors are drawn simultaneously. The first advantage is that we can steer the algorithm with rules based on geological reasoning. The second advantage is that we can include hard constraints for each of the stochastic variables. If a simulated value does not satisfy these constraints, it can simply be drawn again. The input to the simulation algorithm consists of geological rules, probability density functions, correlations, and hard constraints for the stochastic variables. The variables are attached to the entities of a generic integration framework, which consists of acoustic‐stratigraphic units organized at three scale levels. The simulation algorithm constructs individual wells by selecting entities from the framework. The order in which the entities occur, and the thickness of each entity, is determined by a combination of random draws and specified geological rules. Acoustic properties and optional user‐defined physical properties are attached to the simulated layers by random draws. The acoustic properties are parameterized by top and bottom sonic and density values. The algorithm is capable of simulating acoustic hydrocarbon effects. The algorithm is demonstrated with a simulated example, describing the stratigraphic and physical variations in an oil field with a fluvial‐deltaic labyrinth type reservoir.
Dielectric dispersion of salt‐water—saturated porous glass containing thin glass plates
Authors: Haslund Espen
Published: October 2002

Complex permittivity (i.e., dielectric constant and conductivity) measurements are performed on porous, fused glass bead specimens, and the effect of the presence of glass plates is investigated systematically. Two types of plates are used in this investigation, relatively thick ones made from crushed cover slides and very thin ones made from crushed blown glass bubbles. As a reference, the response of specimens without plates is also measured. After saturating the specimens with conducting water, the effective dielectric function is measured over the frequency range of Maxwell‐Wagner dispersion. The dispersion strength increased with the addition of plates, an effect that is stronger for thinner plates. The dispersion frequency range is larger for thinner plates, but is independent of plate concentration for constant plate thickness. The experimental results are compared with the effective medium theory for the dielectric function of porous media containing plates due to Mendelson and Cohen and to Sen—an extension of the Sen Scala Cohen theory. The theoretical curves are fitted to the experimental points of the real dielectric constant by adjusting the depolarization parameter given by the aspect ratio of the plates. The effect of the plates on the dispersion predicted by the theory is found to be in good agreement with experimental result. The high‐frequency level of the real dielectric constant is almost unaffected by the plates as given by the theory. The low‐frequency level of the conductivity, or the formation factor, is found to vary with plate content, as also predicted by the theory. However, the quantitative difference between the theoretical and the experimental formation factor is generally found to be somewhat larger than the estimated experimental uncertainty. The theory is also fitted to data from the literature on a real rock specimen, and a close fit is obtained, together with encouraging estimates of porosity and formation factor.
An accurate formulation of log‐stretch dip moveout in the frequency‐wavenumber domain
Authors: Zhou Binzhong , Mason Iain M. , Greenhalgh Stewart A.
Published: October 2002

Dip moveout (DMO) processing is a partial prestack migration procedure that has been widely used in seismic data processing. The DMO process has been described in Deregowski (1986), Hale (1991) and Liner (1990). Many different DMO algorithms have been developed over the past decade. These algorithms have been designed to improve either the accuracy or the computational speed of the DMO process. Hale (1984) developed a method for performing DMO via Fourier transforms that is accurate for all reflector dips (assuming constant velocity). Hale’s method is computationally expensive because his DMO operator is temporally nonstationary, but its accuracy and simplicity have made it an industry standard. It has become a benchmark by which results from other DMO algorithms are judged. Of all the methods used to make the frequency‐domain DMO computationally efficient, the technique of logarithmic time stretching, first suggested in Bolondi et al. (1982), is widely used. After logarithmic stretching of the time axis, the DMO operator becomes temporally stationary which enables replacement of the slow temporal Fourier integration with a fast Fourier transform combined with a simple phase shift. Bale and Jakubowicz (1987) presented a log‐stretch DMO operator (hereafter referred to as Bale’s DMO) in the frequency‐wavenumber (F-K) domain without approximations, while Notfors and Godfrey (1987) suggested an approximate version of log‐stretch DMO operator (hereafter referred to as Notfors’s DMO). Surprisingly, Bale’s full log‐stretch DMO operator produces a less satisfactory impulse response than Notfors’s approximate log‐stretch DMO scheme (see Liner, 1990). Liner (1990) attributed this characteristic to the fact that Bale’s DMO derivation implicitly assumes that the Fourier transform frequency in the log‐stretch domain is not time‐dependant. He presented an exact log‐stretch DMO operator (hereafter referred to as Liner’s DMO) which was derived by transforming the time log‐stretched Hale’s (t, x) DMO impulse response into the Fourier domain. Its derivation is relatively complicated, but Liner has shown that his DMO does generate good DMO impulse responses.
A deterministic approach toward isostatic gravity residuals—A case study from South America
Authors: Chapin David A.
Published: October 2002

A new deterministic method for correcting isostatic effects in gravity data sets overcomes the deficiencies of empirically based methods. This technique produces a superior gravity image for South America and has application to other continental‐scale gravity data sets. The basis for the correction is the Airy‐Heiskanen isostatic model, which assumes that surface topography is supported by crustal thickening. The three key parameters, (1) the crustal thickness at sea‐level, (2) the surface reduction density, and (3) the density contrast between the crust and the mantle, are determined directly from the elevation, free‐air gravity, and Bouguer gravity data sets. The surface density parameter of 2.60 g/cc is determined using a new fractal technique. This technique assumes that the topography is fractal. The best value for density is that which minimizes the fractal component caused by topographic effects. The new value is substantially different than the 2.67 g/cc density assumed by many previous workers for most continental‐scale data sets. The crust/mantle density contrast parameter of 0.45 g/cc is determined by comparison between the densities determined from crossplots of the Bouguer values versus elevation. The crustal thickness parameter of 30 km is determined using a spectral method applied to the free‐air gravity. The results of this work are not only an isostatic residual map, but a methodology that cross checks the data for quality control. The final isostatic residual map can be used with confidence for basin evaluation throughout the continent of South America. Basins at high elevations, like the eastern foreland basins of the Andes and the Altiplano Basin, are imaged better by using this method.
On: “Investigating the resolution of IP arrays using inverse theory,” L. P. Beard and A. C. Tripp (September‐October 1995 GEOPHYSICS, p. 1326–1341).
Authors: Arce José E.
Published: October 2002

The authors arrive to a conclusion that is totally in contradiction with a paper published in Geophysical Prospecting, Vol. 21, No. 4 (Dec. 1973), 626–634, by A. Roy and Shikhar C. Jain. It can be argued that one (Beard‐Tripp) is based on speculative data, while the other (Roy‐Jain) is experimental, but the differences are not acceptable. IP users need to clarify this situation.
AVO in North of Paria, Venezuela: Gas methane versus condensate reservoirs
Authors: Regueiro José , Peña Andrés
Published: October 2002

The gas fields of North of Paria, offshore eastern Venezuela, present a unique opportunity for amplitude variations with offset (AVO) characterization of reservoirs containing different fluids: gas‐condensate, gas (methane) and water (brine). AVO studies for two of the wells in the area, one with gas‐condensate and the other with gas (methane) saturated reservoirs, show interesting results. Water sands and a fluid contact (condensate‐water) are present in one of these wells, thus providing a control point on brine‐saturated properties. The reservoirs in the second well consist of sands highly saturated with mathane. Clear differences in AVO response exist between hydrocarbon‐saturated reservoirs and those containing brine. However, it is also interesting that “subtle” but noticeable differences can be interpreted between condensate‐and methane‐saturated sands. These differences are attributed to differences in both in‐situ fluid density and compressibility, and rock frame properties.
A seismic refraction and reflection study across the central San Jacinto Basin, Southern California
Authors: Lee Tien‐Chang , Biehler Shawn , Park Stephen K. , Stephenson William J.
Published: October 2002

The San Jacinto Basin is a northwest‐trending, pull‐apart basin in the San Jacinto fault zone of the San Andreas fault system in southern California. About 24 km long and 2 to 4 km wide, the basin sits on a graben bounded by two strands of the San Jacinto fault zone: the Claremont Fault on the northeast and the Casa Loma Fault on the southwest. We present a case study of shallow structure (less than 1 km) in the central basin. A 2.75-km refraction line running from the northeast to southwest across the regional structural trend reveals a groundwater barrier (Offset I). Another line, bent southward and continued for 1.65-km, shows a crystalline basement offset (Offset III) near an inferred trace of the Casa Loma Fault. Although a basement refractor was not observed along the 2.75-km line, a mismatch between the estimate of its minimum depth and the basement depth determined for the 1.65-km line suggests that an offset in the basement (greater than 260 m) exists around the junction of the two refraction lines (Offset II). By revealing more faults and subtle sedimentary structures, the reflection stack sections confirm the two refraction offsets as faults. Offsets I and III each separate sediments of contrasting structures and, in addition, Offset III disrupts an unconformity. However, the sense and amount of the offset across Offset III contradict what may be expected across the Casa Loma Fault, which has its basinward basement down‐thrown to about 2.5 km in the better defined southeastern part of the graben. The Casa Loma Fault trace has been mislinked in the existing geological maps and the trace should be remapped to Offset II where the reflector disruptions spread over a 400-m wide zone. Our Offset III is an unnamed, concealed fault.
Elastic waves in finely layered sediments: The equivalent medium and generalized O’Doherty‐Anstey formulas
Authors: Shapiro Sergei A. , Hubral Peter
Published: October 2002

We study the influence of elastic 1-D inhomogeneous random media (e.g., finely layered media with variable density and shear and compressional velocities) on the kinematics and dynamics of the transmitted obliquely incident P‐ and SV‐plane waves. Multiple scattering (resulting in localization and spatial dispersion of the elastic wavefield) is the main physical effect controlling the properties of the wavefield in such media. We analyze the wave propagation assuming the fluctuations of velocities and density to be small (of the order of 20% or smaller). We obtain explicit analytic solutions for the attenuation coefficient and phase velocity of the transmitted waves. These solutions are valid for all frequencies. They agree very well with results of numerical modeling. Our theory shows that fine elastic multilayering is characterized by a frequency‐dependent anisotropy. At typical acquisition frequencies this anisotropy differs significantly from the low‐frequency anisotropy described by the well‐known Backus averaging. The increase of the phase velocity with frequency is quantified. It can partly explain the difference between well‐log‐derived velocities and lower frequency seismic velocities [e.g., vertical seismic profiling (VSP) velocities] in terms of localization. The low‐ and high‐frequency asymptotical results for the phase velocity agree with those of Backus averaging and ray approximation, respectively. The theory describes the angle‐dependent attenuation caused by multiple scattering. The proposed formulas are simple enough to be used in many practical applications as, e.g., in an amplitude variation with offset (AVO) analysis. They can be implemented for taking into account the angle dependence of transmission effects, or they can be used in an inversion for statistical parameters of sediments.
Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator
Authors: Smith J. Torquil
Published: October 2002

The preceding paper derives a staggered‐grid, finite‐difference approximation applicable to electromagnetic induction in the Earth. The staggered‐grid, finite‐difference approximation results in a linear system of equations [Formula: see text]x = b, where [Formula: see text] is symmetric but not Hermitian. This is solved using the biconjugate gradient method, preconditioned with a modified, partial Cholesky decomposition of [Formula: see text]. This method takes advantage of the sparsity of [Formula: see text], and converges much more quickly than methods used previously to solve the 3-D induction problem. When simulating a conductivity model at a number of frequencies, the rate of convergence slows as frequency approaches 0. The convergence rate at low frequencies can be improved by an order of magnitude, by alternating the incomplete Cholesky preconditioned biconjugate gradient method with a procedure designed to make the approximate solutions conserve current.
Reducing spurious diffractions in elastic wavefield calculations
Authors: Zeng Xiansong , West Gordon F.
Published: October 2002

A persistent problem in using discrete solution methods for wave propagation calculations arises from the discretization process itself. Since the cell size is finite, a gridded version of a complicated model is necessarily somewhat inaccurate. For instance, when a velocity or density interface in a model is not aligned with the grid, it is usually represented in a “staircase fashion.” The steps in the model then cause spurious diffractions in the calculated wavefield no matter what numerical method is used. In fact, the problem becomes more severe with modern numerical methods such as the Fourier pseudospectral and staggered‐grid, finite‐difference methods, as they allow relatively coarse gridding of the model. To reduce these nonphysical diffractions, techniques based on either a grid of varying spacing (Jastram and Tessmer, 1994) or a curved grid through a mapping (Fornberg, 1988; Nielsen et al., 1994) have been proposed. Muir et al. (1992) introduced some anisotropy into the model using the Schoenberg‐Muir calculus and obtained good results.
Traveltime inversion for the geometry of aquifer lithologies
Authors: Hyndman David W. , Harris Jerry M.
Published: October 2002

Crosswell traveltime tomography can provide detailed descriptions of the geometry and seismic slowness of lithologic zones in aquifers and reservoirs. Traditional tomographic inversions that estimate a smooth slowness field to match traveltime data, provide limited information about the dominant scale of subsurface heterogeneity. We demonstrate an alternative method, called the multiple population inversion (MPI), that co‐inverts traveltimes between multiple well pairs to identify the spatial distribution of a small number of slowness populations. We also compare the MPI with the split inversion method (SIM) that was recently introduced to address the same problem. The lithologies and hydraulic parameters for these populations can then be determined from core data and hydraulic testing. The MPI iteratively assigns pixels to a small number of slowness populations based on the histogram of slowness residuals. By constraining the number of slowness values, this method is less susceptible to inversion artifacts, such as those related to slight variations in ray coverage, and can resolve finer scale sedimentary structures better than methods that smooth the slowness field. We demonstrate the MPI in two dimensions with a synthetic aquifer and in three dimensions with the Kesterson aquifer in the central valley of California. In both cases, the constrained inversion algorithm converges to an equal or smaller average traveltime residual than obtained with unconstrained‐value tomography. The MPI accurately images the dominant lithologies of the synthetic aquifer and provides a geologically reasonable image of the Kesterson aquifer.
3-D two‐point ray tracing for heterogeneous, weakly transversely isotropic media
Authors: Grechka Vladimir Y. , McMechan George A.
Published: October 2002

A two‐point ray‐tracing technique for 3-D smoothly heterogeneous, weakly transversely isotropic media is based on Fermat’s principle and takes advantage of global Chebyshev approximation of both the model and curved rays. This approximation gives explicit relations for derivatives of traveltime with respect to ray parameters and allows use of the rapidly converging conjugate gradient method to compute traveltimes. The method is fast because, for most smoothly heterogeneous media, approximation of rays by only a few polynomials and a few conjugate gradient iterations provide excellent precision in traveltime calculation.
Turning waves and crustal reflection profiling
Authors: Stadtlander Ralf , Brown Larry
Published: October 2002

In the past, steeply dipping features were often recognized on seismic reflection profiles only from indirect evidence such as vertical offsets of cross‐cutting structures. New imaging algorithms, as for example, turning wave migration have had dramatic success in delineating steep, even‐overturned reflectors in sedimentary environments. Evaluation of the applicability of this technology to deep seismic recordings indicates that steep‐dip and turning wave migration will have limited practicality, generally, in the imaging of basement features because of the weak velocity gradients involved and the corollary requirement for large recording offsets. A potential exception arises when the basement structures to be imaged lie beneath a significant thickness of relatively young (i.e., steep velocity gradient) sedimentary cover.
GPR attenuation and its numerical simulation in 2.5 dimensions
Authors: Xu Tong , McMechan George A.
Published: October 2002

Modeling of ground‐penetrating radar (GPR) data in 2.5 dimensions is implemented by superposition of 2-D finite‐difference, time‐domain solutions of Maxwell's equations for different horizontal wavenumbers. Dielectric, magnetic, and conductive losses are included in a single formulation. Attenuations associated with dielectric and magnetic relaxations are introduced by superposition of Debye functions at a set of relaxation frequencies and using memory variables to replace convolutions between the field variables and the decay functions. Better fits to data may always be obtained using the superposition method than by the Cole‐Cole model. Good fits to both loss‐tangent versus frequency data from lab measurements, and to 500 and 900 MHz field GPR profiles of a buried pipe and the surrounding layers, demonstrate the flexibility and viability of the modeling algorithm. Discrepancies between lab and in‐situ measurements may be attributed to scale differences and local variations that make lab samples less representative of the site than the GPR profile.
Parameters controlling sonic velocities in a mixed carbonate‐siliciclastics Permian shelf‐margin (upper San Andres formation, Last Chance Canyon, New Mexico)
Authors: Kenter Jeroen A. M. , Podladchikov F. F. , Reinders Marc , Van der Gaast Sjierk J. , Fouke Bruce W. , Sonnenfeld Mark D.
Published: October 2002

We have measured the acoustic properties and mineralogic composition of 48 rock specimens from mixed carbonate‐siliciclastic outcrops of the Permian upper San Andres formation in Last Chance Canyon, New Mexico. The goals were: (1) identify and model the parameters controlling the sonic velocities; (2) assess the influence of postburial diagenesis on the acoustic velocities. The variation in sonic velocity in the 0 to 25% porosity range is primarily controlled by porosity, and secondly by the ratio of carbonate‐siliciclastic material. Linear multivariate fitting resulted in a velocity‐porosity‐carbonate content transform that accurately predicts sonic velocity at different effective stresses. The slope of the velocity‐porosity transform steepens with increasing carbonate content, which may be explained by the higher velocity of carbonate minerals. Another reason may be the property of carbonate minerals to form more perfect intercrystalline boundaries that improve the transmission properties of acoustic waves and are less sensitive to changes in effective stress. The velocity ratio [Formula: see text] is an excellent tool to discriminate between predominantly calcitic lithologies (ratio between 1.8 and 1.95) and predominantly dolomitic and quartz‐rich lithologies (ratio between 1.65 and 1.8). Gardner's experimental curve overestimates, and the velocity‐porosity transforms by Wyllie and Raymer underestimate, the observed sonic velocities, probably because they do not account for variations in texture, carbonate mineralogy, and pore geometry. Petrographic observations show that postburial diagenesis is minor and does not seem to significanfly affect porosity. Therefore, the outcrop data set can be regarded as a proxy for the subsurface analog. These findings underline the significantly more complex acoustic behavior in mixed carbonate‐siliciclastic sedimentary rocks than in pure siliciclastics where mineralogic composition explains most of the observed relationships between porosity and sonic velocity.
Full waveform inversion of marine reflection data in the plane‐wave domain
Authors: Minkoff Susan E. , Symes William W.
Published: October 2002

Full waveform inversion of a p‐τ marine data set from the Gulf of Mexico provides estimates of the long‐wavelength P‐wave background velocity, anisotropic seismic source, and three high‐frequency elastic parameter reflectivities that explain 70% of the total seismic data and 90% of the data in an interval around the gas sand target. The forward simulator is based on a plane‐wave viscoelastic model for P‐wave propagation and primary reflections in a layered earth. Differential semblance optimization, a variant of output least‐squares inversion, successfully estimates the nonlinear P‐wave background velocity and linear reflectivities. Once an accurate velocity is estimated, output least‐squares inversion reestimates the reflectivities and an anisotropic seismic source simultaneously. The viscoelastic model predicts the amplitude‐versus‐angle trend in the data more accurately than does an elastic model. Simultaneous inversion for reflectivities and source explains substantially more of the actual data than does inversion for reflectivities with fixed source from an air‐gun modeler. The best reflectivity estimates conform to widely accepted lithologic relationships and closely match the filtered well logs.
Bandwidth reduction from location inaccuracies
Authors: Levin Franklyn K.
Published: October 2002

I derive an expression that gives the variance in traveltime for a reflection from a dipping plane resulting from 3-D random errors in the position of a source and receiver. The expression, specialized to common‐midpoint geometry, is confirmed by computer‐generated traveltimes. In general, traveltime errors increase as source‐ to‐receiver separation increases, but for dips larger than 45°, there is a profile direction measured from the dip direction for which the errors are independent of the source‐to‐receiver separation. For profiles nearer dip, the errors decrease as the source‐to‐receiver separation increases.
Determination of anisotropic velocity models from walkaway VSP data acquired in the presence of dip
Authors: Sayers Colin M.
Published: October 2002

Wide‐aperture walkaway vertical seismic profile (VSP) data acquired through transversely isotropic horizontal layers can be used to determine the P phase‐slowness surface, local to a receiver array in a borehole. In the presence of dip, errors in the slowness surface may occur if the medium is assumed to be layered horizontally. If the acquisition plane is oriented parallel to the dip direction, the derived slowness is too large for sources offset from the well in the down‐dip direction and too small for sources offset from the well in the up‐dip direction. For acquisition parallel to the strike of the layers, the recovery of the P phase‐slowness in the vicinity of the receiver array is excellent. It is therefore preferable to orient the walkaway VSP in the strike direction to estimate the anisotropic parameters of the medium in the vicinity of a receiver array. However, this may not be possible. If the dip direction of all layers has the same azimuth, the variation of walkaway traveltimes with azimuth has a simple form. This allows data from a single walkaway VSP extending both sides of a well to be inverted for the local anisotropic P phase‐slowness surface at the receivers even in the presence of dip. If data are acquired at more than one azimuth, the dip direction can be determined.
Hybrid optimization methods for geophysical inversion
Authors: Chunduru Raghu K. , Sen Mrinal K. , Stoffa Paul L.
Published: October 2002

Local and global optimization algorithms are used commonly in geophysical data inversion. Each type of algorithm has unique advantages and disadvantages. Here we propose several methods of combining the two algorithms such that we can overcome their drawbacks and make use of the salient features of the two methods. In particular, we combined a local conjugate gradient (CG) method with a global very fast simulated annealing (VFSA) approach to solve problems of geophysical interests. We conducted a systematic study to find an efficient strategy to combine CG and VFSA optimization schemes and recommend a couple of ways for future implementations. Seven different hybrid algorithms were first tested on a set of field 1-D Schlumberger resistivity sounding data and their performances were compared with stand‐alone genetic algorithm (GA), simulated annealing, and local search algorithms. Almost all of the proposed hybrid algorithms were found to be computationally more efficient than the conventional global optimization approaches. Having found the most efficient of the hybrid approaches we apply them to the problem of seismic velocity analysis using seismograms recorded in the offset‐time domain. Finally, we applied the hybrid algorithm to a 2-D field resistivity profiling data collected over a disseminated sulfide zone at Safford Arizona and compared our hybrid inversion results with the previously published results.
An analytical approach to migration velocity analysis
Authors: Liu Zhenyue
Published: October 2002

Prestack depth migration provides a powerful tool for velocity analysis in complex media. Both prominent approaches to velocity analysis—depth‐focusing analysis and residual‐curvature analysis, rely on approximate formulas to update velocity. Generally, these formulas are derived under the assumptions of horizontal reflector, lateral velocity homogeneity, or small offset. Therefore, the conventional methods for updating velocity lack accuracy and computational efficiency when velocity has large, lateral variations. Here, based on ray theory, I find the analytic representation for the derivative of imaged depths with respect to migration velocity. This derivative function characterizes a general relationship between residual moveout and residual velocity. Using the derivative function and the perturbation method, I derive a new formula to update velocity from residual moveout. In the derivation, I impose no limitation on offset, dip, or velocity distribution. Consequently, I revise the residual‐curvature‐analysis method for velocity estimation in the postmigrated domain. Furthermore, my formula provides sensitivity and error estimation for migration‐based velocity analysis, which is helpful in quantifying the reliability of the estimated velocity. The theory and methodology in this paper have been tested on synthetic data (including the Marmousi data).
Finite‐difference modeling of sonic wavefields with a dipping interface
Authors: Liu Hsui‐lin , Prange Michael , Daube Francois
Published: October 2002

Formation bedding can cause complex wave propagation in a borehole and introduce velocity bias in sonic logs. Because of the lack of symmetry, little is known about sonic wavefields propagating through a dipping bed. In this paper, we investigate effects on the sonic dipole and monopole wavefields across a dipping interface using a 3-D finite‐difference method. For dipole wavefields propagating from a soft to a hard formation across a dipping interface, the transmission is reduced greatly when compared with a horizontal interface. The different transmissions of SV‐ and SH‐waves through the dipping interface result in significant azimuthal amplitude variation and generate large cross‐coupled components. This apparent anisotropy should be taken into account when estimating formation shear anisotropy in a dipping formation. For monopole wavefields, the azimuthal averaging caused by a dipping interface reduces the reflection across an interface. This may affect fracture evaluation using the Stoneley reflection coefficient in a dipping formation.
Some case histories of source discrimination using time‐domain spectral IP
Authors: Seigel Harold O. , Vanhala Heikki , Sheard S. Nicholas
Published: October 2002

It has long been known that induced polarization (IP) transient voltages decay with time at a rate that is dependent strongly on the mean grain size of the metallic conducting particles in the IP source. The Cole‐Cole model provides a three‐parameter representation (M, τ and C) for IP responses. The time‐constant (τ), in particular, has been found to be very useful in resolving IP sources with differing mean particle size. The characterization of IP responses in terms of these parameters has been termed “spectral IP.” These parameters may be determined either through the analysis of the response of the earth to sequential transmission of ac currents of different frequencies (i.e., frequency‐domain IP), or through the analysis of the transient decays resulting from the transmission of interrupted square‐wave currents (i.e., time‐domain IP). The latter approach offers the major convenience of being applicable to data obtained in the course of routine production surveys, with no increase in survey time. In practice, spectral IP parameters are determined most readily from time‐domain transients through the computer matching of the observed data to the best fit in a family of precalculated Cole‐Cole curves. This may be done, off‐line, using a PC, or, in a recent receiver, essentially on‐line, using software imbedded in the receiver. Field case histories from Canada, Finland, and Australia are given to illustrate the application of spectral IP to the resolution of IP sources in the time domain. It is recommended that this approach to the processing and presentation of time‐domain IP data should be applied routinely, as a very cost‐effective enhancement to the exploration value of such data. An additional benefit from this presentation is that it will facilitate a sharing of experimental results with workers in the frequency domain who may also use the spectral IP approach.
Estimation of multiple scattering by iterative inversion, Part I: Theoretical considerations
Authors: Berkhout A. J. , Verschuur D. J.
Published: October 2002

A review has been given of the surface‐related multiple problem by making use of the so‐called feedback model. From the resulting equations it has been concluded that the proposed solution does not require any properties of the subsurface. However, source‐detector and reflectivity properties of the surface need be specified. Those properties have been quantified in a surface operator and this operator is estimated as part of the multiple removal problem. The surface‐related multiple removal algorithm has been formulated in terms of a Neumann series and in terms of an iterative equation. The Neumann formulation requires a nonlinear optimization process for the surface operator; while the iterative formulation needs a number of linear optimizations. The iterative formulation also has the advantage that it can be integrated easily with another multiple removal method. An algorithm for the removal of internal multiples has been proposed as well. This algorithm is an extension of the surface‐related method. Removal of internal multiples requires knowledge of the macro velocity model between the surface and the upper boundary of the multiple generating layer. In part II (also published in this issue) the success of the proposed algorithms has been demonstrated on numerical experiments and field data examples.
Estimation of multiple scattering by iterative inversion, Part II: Practical aspects and examples
Authors: Verschuur D. J. , Berkhout A. J.
Published: October 2002

A surface‐related multiple‐elimination method can be formulated as an iterative procedure: the output of one iteration step is used as input for the next iteration step (part I of this paper). In this paper (part II) it is shown that the procedure can be made very efficient if a good initial estimate of the multiple‐free data set can be provided in the first iteration, and in many situations, the Radon‐based multiple‐elimination method may provide such an estimate. It is also shown that for each iteration, the inverse source wavelet can be accurately estimated by a linear (least‐squares) inversion process. Optionally, source and detector variations and directivity effects can be included, although the examples are given without these options. The iterative multiple elimination process, together with the source wavelet estimation, are illustrated with numerical experiments as well as with field data examples. The results show that the surface‐related multiple‐elimination process is very effective in time gates where the moveout properties of primaries and multiples are very similar (generally deep data), as well as for situations with a complex multiple‐generating system.