bluuebunny/crossref_metadata_2025 huggingface dataset:
Geophysical inversion using approximate equality constraints
Authors: Medeiros Walter E. , Silva João B. C.
Published: October 2002

Current inversion methods estimating a physical property on a grid use two kinds of constraints: (1) absolute constraints requiring that the solution vector be close to a prespecified vector as, for example, proximity to the null vector in the ridge regression, and (2) relative constraints requiring that the elements of the solution vector be close to each other as, for example, smoothness imposed by methods requiring that spatial derivatives of the physical property be continuous. Using just absolute constraints may produce a biased solution conflicting with some true geological attributes of the source. On the other hand, using just relative constraints may be insufficient to stabilize the inversion. We present a stable inversion method incorporating absolute constraints only at points where the physical property is known as, for example, outcroppings and boreholes. Elsewhere, relative constraints are introduced according to a linear relationship for the spatial distribution of the physical property. The proposed method is analogous to an interpolation method applied to the physical property distribution: the interpolating function must satisfy some property, like continuity, and pass through the data. The proposed method is versatile in incorporating not only factual, but also indirect information such as continuity, symmetry, and trends. In addition, it may be applied both to linear and nonlinear problems. The relevant results obtained from applying the method to synthetic potential‐field data were: (1) ability to produce reliable mappings of the basement relief of a sedimentary basin (from gravity data) and of an areal distribution of magnetization, using only smoothness constraints and restricted surface and borehole information; (2) operational simplicity because of the solution insensitivity to the damping parameter. The method is also applied to the Bouguer anomaly over San Jacinto Graben, California, producing results consistent with previous interpretations.
Inversion of seismic refraction data using genetic algorithms
Authors: Boschetti Fabio , Dentith Mike C. , List Ron D.
Published: October 2002

The use of genetic algorithms in geophysical inverse problems is a relatively recent development and offers many advantages in dealing with the nonlinearity inherent in such applications. However, in their application to specific problems, as with all algorithms, problems of implementation arise. After extensive numerical tests, we implemented a genetic algorithm to efficiently invert several sets of synthetic seismic refraction data. In particular, we aimed at overcoming one of the main problems in the application of genetic algorithms to geophysical problems: i.e., high dimensionality. The addition of a pseudo‐subspace method to the genetic algorithm, whereby the complexity and dimensionality of a problem is progressively increased during the inversion, improves the convergence of the process. The method allows the region of the solution space containing the global minimum to be quickly found. The use of local optimization methods at the last stage of the search further improves the quality of the inversion. The genetic algorithm has been tested on a field data set to determine the structure and base of the weathered layer (regolith) overlaying a basement of granite and greenstones in an Archaean terrain of Western Australia.
Green’s function implementation of common‐offset, wave‐equation migration
Authors: Ehinger Andreas , Lailly Patrick , Marfurt Kurt J.
Published: October 2002

Common‐offset migration is extremely important in the context of migration velocity analysis (MVA) since it generates geologically interpretable migrated images. However, only a wave‐equation‐based migration handles multipathing of energy in contrast to the popular Kirchhoff migration with first‐arrival traveltimes. We have combined the superior treatment of multipathing of energy by wave‐equation‐based migration with the advantages of the common‐offset domain for MVA by implementing wave‐equation migration algorithms via the use of finite‐difference Green’s functions. With this technique, we are able to apply wave‐equation migration in measurement configurations that are usually considered to be of the realm of Kirchhoff migration. In particular, wave‐equation migration of common offset sections becomes feasible. The application of our wave‐equation, common‐offset migration algorithm to the Marmousi data set confirms the large increase in interpretability of individual migrated sections, for about twice the cost of standard wave‐equation common‐shot migration. Our implementation of wave‐equation migration via the Green’s functions is based on wavefield extrapolation via paraxial one‐way wave equations. For these equations, theoretical results allow us to perform exact inverse extrapolation of wavefields.
Efficient one‐pass 3-D time migration
Authors: Brzostowski Matthew A. , Snyder Fred F. C. , Smith Patrick J.
Published: October 2002

An efficient one‐pass 3-D time migration algorithm is introduced as an alternative to Ristow’s splitting approach. This algorithm extends Black and Leong’s [Formula: see text] approach with a time‐dependent Stolt stretch operation called dilation. Migration using [Formula: see text] dilation consists of a single pass over the 3-D data volume after [Formula: see text] slices are formed with each [Formula: see text] slice downward continued independently. A number of downward continuation algorithms based upon the 3-D wave equation may be used. Dilation accommodates any lateral variations in velocity before the 3-D data volume is decomposed into [Formula: see text] slices via a Fourier transform. An inverse dilation operation is performed after the downward‐continuation operation and after the data volume have been inverse Fourier transformed subsequently along the [Formula: see text] direction. Migration using the [Formula: see text] approach yields a one‐pass 3-D time migration algorithm that is practical and efficient where the medium velocity is smoothly varying.
A numerical free‐surface condition for elastic/viscoelastic finite‐difference modeling in the presence of topography
Authors: Robertsson Johan O. A.
Published: October 2002

An accurate free‐surface boundary condition is important for solving a wide variety of seismic modeling problems. In particular, for earthquake site studies or shallow environmental investigations the surface of the earth may have a significant impact on the outcome of simulations. Computations based on several elastic/viscoelastic flat horizontal free‐surface conditions are compared and benchmarked against an analytical solution. An accurate and simple condition is found and then generalized to allow for irregular free surfaces. This new method is simple to implement in conventional staggered finite‐difference schemes, is computationally efficient and enables modeling of highly irregular topography. The accuracy of the method is investigated and criteria for sampling of the wavefield are derived.
Incorporating pore geometry and fluid pressure communication into modeling the elastic behavior of porous rocks
Authors: Endres Anthony L. , Knight Rosemary J.
Published: October 2002

Inclusion‐based formulations allow an explicit description of pore geometry by viewing porous rocks as a solid matrix with embedded inclusions representing individual pores. The assumption commonly used in these formulations that there is no fluid pressure communication between pores is reasonable for liquid‐filled rocks measured at high frequencies; however, complete fluid pressure communication should occur throughout the pore space at low frequencies. A generalized framework is presented for incorporating complete fluid pressure communication into inclusion‐based formulations, permitting elastic behavior of porous rocks at high and low frequencies to be described in terms of a single model. This study extends previous work by describing the pore space in terms of a continuous distribution of shapes and allowing different forms of inclusion interactions to be specified. The effects of fluid pressure communication on the elastic moduli of porous media are explored by using simple models and are found to consist of two fundamental elements. One is associated with the cubical dilatation and governs the effective bulk modulus. Its magnitude is a function of the range of pore shapes present. The other is due to the extensional part of the deviatoric strain components and affects the effective shear modulus. This element is dependent on pore orientation, as well as pore shape. Using sandstone and granite models, an inclusion‐based formulation shows that large differences between high‐ and low‐frequency elastic moduli can occur for porous rocks. An analysis of experimental elastic wave velocity data reveals behavior similar to that predicted by the models. Quantities analogous to the open and closed system moduli of Gassmann‐Biot poroelastic theory are defined in terms of inclusion‐based formulations that incorporate complete fluid pressure communication. It was found that the poroelastic relationships between the open and closed system moduli are replicated by a large class of inclusion‐based formulations. This connection permits explicit incorporation of pore geometry information into the otherwise empirically determined macroscopic parameters of the Gassmann‐Biot poroelastic theory.
Imaging in 3-D DMO, Part I: Geometrical optics models
Authors: Collins Charles L.
Published: October 2002

Systematic azimuthal variation in the input data for 3-D dip moveout (3DDMO) can compromise the illumination of the subsurface, produce imaging artifacts, and cause amplitude variation in the output 3DDMO traces. A simple graphical method allows easy visualization of the subsurface illumination at a dip moveout (DMO) output location for any set of input data. The same method permits selection or construction of sets of input data that illuminate all subsurface reflectors with no redundancy.
Fast computation of the 3-D Radon transform
Authors: Cools Ottilie F. , Herman Gérard C. , van der Welden Raphic M. , Kets Frans B.
Published: October 2002

Radon transforms can be used to decompose seismic shot records into sets of plane waves and, as such, are a useful processing tool. Haneveld and Herman (1990) discussed a fast algorithm for the numerical evaluation of both the forward and inverse 2-D Radon transforms. They showed that, by rewriting the transform as a convolution, the computation time is proportional to [Formula: see text], instead of [Formula: see text] (where N denotes the number of input and output traces). In the present paper, we describe a similar method for the computation of the 3-D Radon transform for the case of rotational symmetry (see also Mallick and Frazer, 1987; McCowan and Brysk, 1989). With the aid of asymptotic techniques, the 3-D Radon transform is recast into a form similar to the 2-D Radon transform after which similar acceleration techniques are used. We have implemented and tested the fast transform on synthetic as well as on real data and found that the computation time of the fast 3-D Radon transform is indeed proportional to [Formula: see text].
Transformation of the resistivity anomalies from archaeological sites by inversion filtering
Authors: Tsokas Gregory N. , Tsourlos Panagiotis
Published: October 2002

The resistivity profiling anomalies that are produced using various arrays are deconvolved by the use of inversion filters. The filters are computed by inverting the effect produced by a simple basic model. The forward computations of the effect of the basic model and all other models used are performed by means of a finite‐element modeling scheme. The filters are designed in such a way that the output is a spike centered over the buried body. Tests with synthetic and real data are presented, which justify the use of the scheme. The scheme is particularly useful in archaeological geophysics where it is important that the presentation of the measured fields are in a form that resembles the result we would have obtained if an excavation had taken place.
Multiseparation, multisystem electromagnetic depth sounding‐An extension for unification
Authors: Das Umesh C.
Published: October 2002

A recent definition of controlled‐source electromagnetic apparent resistivity has been adopted, and it is shown that this definition is unique. It produces a single apparent resistivity value by transforming any of the given combinations of the mutual coupling ratios measured by five different source‐receiver configurations, namely, horizontal coplanar loops (HCP), vertical coplanar loops (VCP), vertical coaxial loops (VCA), electric dipole source and horizontal receiver loop (EDL), and central loop (in‐loop) configurations. Synthetic field data for the commercially available MaxMin system, which can be operated with HCP, VCP, and VCA configurations, are fabricated and they are transformed to apparent resistivities. An analysis of apparent resistivity curves so obtained reveals the requirements of the ranges of frequencies and transmitter‐receiver separations needed for given exploration depth. A concise analysis of the effect of the random noise errors in the MaxMin data on stability of apparent resistivity is carried out. From this analysis, it is expected that apparent resistivities from field measurements will be stable, even when the measurements are corrupted with random noises.
Optimum negative response of a coincident‐loop electromagnetic system above a polarizable half‐space
Authors: El‐Kaliouby Hesham M. , El‐Diwany Essam A. , Hussain Safwat A. , Hashish Essam A. , Bayoumi Abdel Rahim
Published: October 2002

The loop radius of the coincident‐loop system above a polarizable half‐space has a significant effect on the magnitude of the negative response and its time of occurrence. Computations are made to study this phenomenon for various values of the electrical parameters of the ground, which is described by a Cole‐Cole model. An optimum loop radius is found to exist, which leads to the largest peak of the negative response. It is found that for values of the frequency parameter (c) larger than 0.5, the largest peak of the negative response occurs at a time nearly equal to the Cole‐Cole time constant. Empirical formulas are deduced relating both the optimum loop radius and the largest peak of the negative response to the electrical parameters of the polarizable half‐space. The above phenomena may be used as a simple and effective guide for the detection of a polarizable target and estimating its electrical parameters.
Automatic 3-D interpretation of potential field data using analytic signal derivatives
Authors: Debeglia Nicole , Corpel Jacques
Published: October 2002

A new method has been developed for the automatic and general interpretation of gravity and magnetic data. This technique, based on the analysis of 3-D analytic signal derivatives, involves as few assumptions as possible on the magnetization or density properties and on the geometry of the structures. It is therefore particularly well suited to preliminary interpretation and model initialization. Processing the derivatives of the analytic signal amplitude, instead of the original analytic signal amplitude, gives a more efficient separation of anomalies caused by close structures. Moreover, gravity and magnetic data can be taken into account by the same procedure merely through using the gravity vertical gradient. The main advantage of derivatives, however, is that any source geometry can be considered as the sum of only two types of model: contact and thin‐dike models. In a first step, depths are estimated using a double interpretation of the analytic signal amplitude function for these two basic models. Second, the most suitable solution is defined at each estimation location through analysis of the vertical and horizontal gradients. Practical implementation of the method involves accurate frequency‐domain algorithms for computing derivatives with an automatic control of noise effects by appropriate filtering and upward continuation operations. Tests on theoretical magnetic fields give good depth evaluations for derivative orders ranging from 0 to 3. For actual magnetic data with borehole controls, the first and second derivatives seem to provide the most satisfactory depth estimations.
Computation of Cole‐Cole parameters from IP data
Authors: Yuval  , Oldenburg Douglas W.
Published: October 2002

We develop a process to estimate Cole‐Cole parameters from time‐domain induced polarization (IP) surveys carried out over a nonuniform earth. The recovery of parameters takes the following steps. We first divide the earth into rectangular cells and assume that the Cole‐Cole decay parameters [Formula: see text] and c constant in each cell. Apparent chargeability data measured at times [Formula: see text] after the cessation of the input current are inverted using a 2-D inversion algorithm to recover the intrinsic chargeability structure [Formula: see text] for k = 1, L, where L is the number of time channels measured. When carrying out this inversion, it is necessary to introduce a normalization criterion so that the inversion outputs from the different time channels can be meshingfully combined. The L chargeability structures provide L estimates of the chargeability decay curve for each cell. The desired intrinsic Cole‐Cole parameters are recovered from these decay curves using a very fast simulated annealing (VFSA) algorithm. Application of the process in all cells provides interpretation maps of [Formula: see text], τ(x,z), and c(x, z). Our analysis is demonstrated on a synthetic example and is implemented on a field data set. The application of the process to field data yields reasonable results.
Data‐matrix asymmetry and polarization changes from multicomponent surface seismics
Authors: Li Xiang‐Yang , MacBeth Colin
Published: October 2002

We present methods for interpreting data‐matrix asymmetry and polarization changes with depth from multicomponent surface seismics. There are two main sources of data matrix asymmetry in four component shear‐wave seismics: that arising from the acquisition geometry caused by source and receiver misorientation, misalignment, imbalance, and cross‐coupling, and that arising from the medium caused by variations in the geological structure, lithology, or stress. The asymmetry caused by acquisition geometry is more significant than that from the medium. Two asymmetry indices are used to quantify these medium and acquisition asymmetries separately. Their behavior may be used to identify the origin of the asymmetry. The asymmetry caused by the medium is studied by deriving approximate normal‐incidence, plane‐wave reflection coefficients for an interface separating two anisotropic media with differenfly oriented symmetry axes. The degree of asymmetry in the reflectivity is proportional to the product of the degree of anisotropy in the layers above and below the reflector, and is thus small for most realistic cases. Consequently, the reflection coefficients can be approximated by a similarity transform of the principal reflection coefficients using the expected polarization difference. These equations can then be used to formulate a singular‐value decomposition (SVD) in the time‐domain to recover both the principal reflectivity and the changes of polarizations with depth. Applications to field data in south Texas reveal the potential of the technique, and zones of polarization changes in the Austin Chalk are identified that may be correlated with fracture swarms.
Use of ground‐penetrating radar for 3-D sedimentological characterization of clastic reservoir analogs
Authors: McMechan George A. , Gaynor Gerard C. , Szerbiak Robert B.
Published: October 2002

Clastic reservoir analogs based on 2-D outcrop studies provide valuable definitions of geometric and petrophysical heterogeneities at interwell scales. Integration of 3-D ground‐penetrating radar (GPR) surveys with sedimentological and stratigraphic data provides information on the internal heterogeneities of sedimentary sequences at scales that allow dissection of the 3-D anatomy of clastic depositional systems. Two 3-D GPR data volumes were acquired in the Ferron sandstone of east‐central Utah. The data show prominent lenticular features, a variety of lithologies, and structural elements such as channels and shale drapes that match well with those seen at the same stratigraphic levels in adjacent cliff faces.
Elastic wave equation traveltime and waveform inversion of crosswell data
Authors: Zhou Changxi , Schuster Gerard T. , Hassanzadeh Sia , Harris Jerry M.
Published: October 2002

A method is presented for reconstructing P‐ and S‐velocity distributions from elastic traveltimes and waveforms. The input data consist of crosswell hydrophone records generated by a piezoelectric borehole source. Borehole effects are partially accounted for by using a low‐frequency Green's function to simulate the pressure generated in the fluid‐filled receiver well. The tube waves in the borehole are ignored, on the assumption that they can be removed from the field data by median filtering. In addition, the source‐radiation pattern is partially taken into account by inverting for the equivalent stress components acting on the earth at the source location. The elastic wave equation traveltime and waveform inversion (WTW) method is applied to both synthetic crosswell data and the McElroy field crosswell data. As predicted by theory, results show that elastic WTW tomograms provide a sharper interface image than delineated in the traveltime tomograms. The spatial resolution of the McElroy traveltime tomogram is about 20 m compared to about 3 m and 1.5 m, respectively, for the associated P‐ and S‐velocity WTW tomograms. From these tomograms, detailed porosity maps of the interwell geology are constructed. There is a very good correlation between the P‐velocity tomograms and the P‐velocity log profiles, and there is a good correlation between the smooth parts of the S‐velocity tomogram and the S‐velocity logs. Unfortunately, the high‐wavenumber parts of the S‐velocity tomograms do not correlate well with the high‐wavenumber parts of the S‐velocity logs. We believe this problem is partly caused by not taking into account attenuation effects in the WTW algorithm.
Application of the recursive‐approaching signal filter (RASF) to VSP data processing
Authors: Sun Chuanwen , Rabinowitz Philip D. , Griswold Norman C.
Published: October 2002

The recursive‐approaching signal filter (RASF) is a newly developed filtering technique that combines many advantages of linear, nonlinear, and adaptive filters. It passes step functions without altering them and removes many types of noise, such as Gaussian and Laplacian distributed noise. When applied to VSP data processing, the RASF emphasizes those abrupt discontinuities that originate or terminate at discrete depth points and effectively accomplishes the separation of upgoing and downgoing wave modes. The RASF may be transformed into a desired filter by simply changing a parameter to achieve the maximum usefulness of VSP field data. In the tests with the synthetic VSP modeling data corrupted by white Gaussian noise and real VSP data, the RASF compares favorably to f-k velocity and median filtering methods in removing noise, preserving step functions, and computational simplicity.
Application of optical‐fiber temperature logging—An example in a sedimentary environment
Authors: Förster Andrea , Schrötter J. , Merriam D. F. , Blackwell David D.
Published: October 2002

Continuous‐temperature depth logs, especially when recorded in boreholes under thermal equilibrium conditions, provide detailed information of the subsurface thermal structure, which is necessary for the determination of reliable heat‐flow and rock thermal properties. In conjunction with independent thermal‐conductivity determinations, thermal logging data also allow the separation of heat conduction effects from thermal convection effects by fluid flow driven by various pressure differences such as pore fluid pressure. The Earth's thermal field is related intimately to geothermal resources and hydrocarbon resources. Therefore, the characterization of temperature in the subsurface and its relationship to lithology is of critical importance.
Gibbs statistics in crosswell and reflection tomography: Inversion of noisy data
Authors: Carrion Philip M. , Puledda Salvatore , Comelli Paolo
Published: October 2002

In this paper, we examine Gibbs's potential taken as a Cauchy function. This function depends on one parameter and can be useful in inserting a priori information in terms of chosen directions in Gibbs inversion. The results presented in this paper, show the possibility of using Gibbs's statistics for obtaining tomograms of superior quality compared with conventional methods using uncorrelated Gaussian least‐squares optimization. Although Gibbs's statistics give images of higher quality when compared to conventional methods, the geophysical literature on Gibbs's algorithms is quite scanty. For example, Carrion et al. (personal communication) have determined the results of the 3-D Gibbs inversion in processing crosswell data. Carrion et al. (1993) have discussed a hybrid method based on the constrained traveltime inversion when “hard” bounds were driven by Gibbs's statistics. One major problem of crosswell geotomography is incomplete data coverage. A lack of information in the angular spectrum leads to smearing in directions of predominant wave vectors. For example, in crosswell tomography, smearing will occur predominantly in the horizontal direction.
Kinematic interpretation in the prestack depth‐migrated domain
Authors: Apostoiu‐Marin Irina , Ehinger Andreas
Published: October 2002

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.
Seismic stratigraphy and oil recovery potential of tide‐dominated depositional sequences in the Lower Misoa Formation (Lower Eocene), LL-652 Area, Lagunillas Field, Lake Maracaibo, Venezuela
Authors: Ambrose William A. , Ferrer Eulise R.
Published: October 2002

Structurally complex, heterogeneous, estuarine‐delta and tide‐dominated shelf reservoirs in the Lower Misoa Formation (Lower Eocene C Members) in the LL-652 Area of Lagunillas Field in the Maracaibo Basin, Venezuela, had produced 135 million stock‐tank barrels (MMSTB) of oil as of 1993 but have a low recovery efficiency of 22 percent. In an 18-month joint study, the Bureau of Economic Geology (BEG) and Lagoven, S. A., demonstrated that these reservoirs will contain more than 900 MMSTB of unrecovered mobile oil at the end of primary recovery operations at the current 80‐acre well spacing. Two‐dimensional seismic, core, geophysical log, and production data were integrated to improve estimates of hydrocarbon reserves and to identify potential areas for secondary‐recovery projects in Lower Eocene reservoirs in the LL-652 Area. Maps of hydrocarbon pore volume (SoPhih) and remaining oil were derived from improved petrophysical characterization and production apportioning to specific reservoir horizons by permeability feet (kh). These maps indicate that most remaining oil lies in the poorly developed and structurally complicated north part of the field and where narrow [less than 2000 ft (<610 m) wide], high‐SoPhih belts are intersected by sealing and partly sealing reverse faults. The original‐oil‐in‐place resource base of the C Members in the LL-652 area increased by 867 MMSTB (60%) to 2318.2 MMSTB, mainly in the C-3-X and C-4-X Members, by identifying additional reservoir areas and improving quantification of porosity and other petrophysical parameters. Extended development on the current 80-acre [1968-ft (600-m)] well pattern will increase reserves from 127 to 302 MMSTB. However, 116 MMSTB, in addition to the 302 MMSTB, can be produced from 102 geologically based infill wells strategically targeted to tap areas of high remaining oil saturation in narrow sandstone bodies poorly contacted at the current well spacing. Horizontal and inclined wells in steeply dipping strata can capture additional volumes of poorly contacted mobile oil.
Reconditioning inverse problems using the genetic algorithm and revised parameterization
Authors: Curtis Andrew , Snieder Roel
Published: October 2002

The better conditioned an inverse problem is, the more independent pieces of information may be transferred from the data to the model solution, and the less independent prior information must be added to resolve trade offs. We present a practical measure of conditioning that may be calculated swiftly even for large inverse problems. By minimizing this measure, a genetic algorithm can be used to find a model parameterization that gives the best conditioned inverse problem. We illustrate the method by finding an optimal, irregular cell parameterization for a cross‐borehole tomographic example with a given source‐receiver geometry. Using the final parameterization, the inverse problem is almost a factor of three better conditioned than that using an average random parameterization. In addition, this method requires little additional programming when solving a linearized inverse problem. Hence, the improvement in conditioning and corresponding increase in independent information available for the model solution essentially come for free.
Flooding the topography: Wave‐equation datuming of land data with rugged acquisition topography
Authors: Bevc Dimitri
Published: October 2002

Wave‐equation datuming overcomes some of the problems that seismic data recorded on rugged surface topography present in routine image processing. The main problems are that (1) standard, optimized migration and processing algorithms assume data are recorded on a flat surface, and that (2) the static correction applied routinely to compensate for topography is inaccurate for waves that do not propagate vertically. Wave‐based processes such as stacking, dip‐moveout correction, normal‐moveout correction, velocity analysis, and migration after static shift can be severely affected by the nonhyperbolic character of the reflections. To alleviate these problems, I apply wave‐equation datuming early in the processing flow to upward continue the data to a flat datum, above the highest topography. This is what I refer to as “flooding the topography.” This approach does not require detailed a priori knowledge of the near‐surface velocity, and it streamlines subsequent processing because the data are regridded onto a regularly sampled datum. Wave‐equation datuming unravels the distortions caused by rugged topography, and unlike the static shift method, it does not adversely effect subsequent wave‐based processing. The image obtained after wave‐equation datuming exhibits better reflector continuity and more accurately represents the true structural image than the image obtained after static shift.
3-D AVO analysis and modeling applied to fracture detection in coalbed methane reservoirs
Authors: Ramos Antonio C. B. , Davis Thomas L.
Published: October 2002

Over the years, amplitude variation with‐offset (AVO) analysis has been used successfully to predict reservoir properties and fluid contents, in some cases allowing the spatial location of gas‐water and gas‐oil contacts. In this paper, we show that a 3-D AVO technique also can be used to characterize fractured reservoirs, allowing spatial location of crack density variations. The Cedar Hill Field in the San Juan Basin, New Mexico, produces methane from the fractured coalbeds of the Fruitland Formation. The presence of fracturing is critical to methane production because of the absence of matrix permeability in the coals. To help characterize this coalbed reservoir, a 3-D, multicomponent seismic survey was acquired in this field. In this study, prestack P‐wave amplitude data from the multicomponent data set are used to delineate zones of large Poisson's ratio contrasts (or high crack densities) in the coalbed methane reservoir, while source‐receiver azimuth sorting is used to detect preferential directions of azimuthal anisotropy caused by the fracturing system of coal. Two modeling techniques (using ray tracing and reflectivity methods) predict the effects of fractured coal‐seam zones on angle‐dependent P‐wave reflectivity. Synthetic common‐midpoint (CMP) gathers are generated for a horizontally layered earth model that uses elastic parameters derived from sonic and density log measurements. Fracture density variations in coalbeds are simulated by anisotropic modeling. The large acoustic impedance contrasts associated with the sandstone‐coal interfaces dominate the P‐wave reflectivity response. They far outweigh the effects of contrasts in anisotropic parameters for the computed models. Seismic AVO analysis of nine macrobins obtained from the 3-D volume confirms model predictions. Areas with large AVO intercepts indicate low‐velocity coals, possibly related to zones of stress relief. Areas with large AVO gradients identify coal zones of large Poisson's ratio contrasts and therefore high fracture densities in the coalbed methane reservoir. The 3-D AVO product and Poisson's variation maps combine these responses, producing a picture of the reservoir that includes its degree of fracturing and its possible stress condition. Source‐receiver azimuth sorting is used to detect preferential directions of azimuthal anisotropy caused by the fracturing system of coal.
Poroelastic Backus averaging for anisotropic layered fluid‐ and gas‐saturated sediments
Authors: Gelinsky Stephan , Shapiro Sergei A.
Published: October 2002

A homogeneous anisotropic effective‐medium model for saturated thinly layered sediments is introduced. It is obtained by averaging over many layers with different poroelastic moduli and different saturating fluids. For a medium consisting of a stack of vertically fractured horizontal layers, this effective medium is orthorhombic. We derive the poroelastic constants that define such media in the long‐wavelength limit as well as the effective large‐scale permeability tensor. The permeability shows strong anisotropy for large porosity fluctuations. We observe pronounced effects that do not exist in purely elastic media. At very low frequencies, seismic waves cause interlayer flow of pore fluid across interfaces from more compliant into stiffer layers. For higher frequencies, the layers behave as if they are sealed, and no fluid flow occurs. The effective‐medium velocities of the quasi‐compressional waves are higher in the no‐flow than in the quasi‐static limit. Both are lower than the high‐frequency, i.e., ray‐theory limit. Partial saturation affects the anisotropy of wave propagation. In the no‐flow limit, gas that is accumulated primarily in the stiffer layers reduces the seismic anisotropy; gas that is trapped mainly in layers with a more compliant frame tends to increase the anisotropy. In the quasi‐static limit, local flow keeps the anisotropy constant independent of partial saturation effects. For dry rock, no‐flow and quasi‐static velocities are the same, and the anisotropy caused by layering is controlled only by fluctuations of the layer shear moduli. If the shear stiffness of all layers is the same and only the compressive stiffness or saturation varies, only the ray‐theory velocity exhibits anisotropy.
Extraction of geological information from acoustic well‐logging waveforms using time‐frequency wavelets
Authors: Saito Naoki , Coifman Ronald R.
Published: October 2002

Recently developed classification and regression methods are applied to extract geological information from acoustic well‐logging waveforms. First, acoustic waveforms are classified into the ones propagated through sandstones and the ones propagated through shale using the local discriminant basis (LDB) method. Next, the volume fractions of minerals are estimated (e.g., quartz and gas) at each depth using the local regression basis (LRB) method. These methods first analyze the waveforms by decomposing them into a redundant set of time‐frequency wavelets, i.e., the orthogonal wiggle traces localized in both time and frequency. Then, they automatically extract the local waveform features useful for such classification and estimation or regression. Finally, these features are fed into conventional classifiers or predictors. Because these extracted features are localized in time and frequency, they allow intuitive interpretation. Using the field data set, we found that it was possible to classify the waveforms without error into sandstone and shale classes using the LDB method. It was more difficult, however, to estimate the volume fractions, in particular, that of gas, from the extracted waveform features. We also compared the performance of the LRB method with the prediction based on the commonly used ratio of compressional and shear‐wave velocities, [Formula: see text], and found that our method performed better than the [Formula: see text] method.
A convenient expression for the NMO velocity function in terms of ray parameter
Authors: Cohen Jack K.
Published: October 2002

Tsvankin (1995) derived an expression for the normal‐moveout (NMO) velocity from horizontal or dipping reflectors that is valid in symmetry planes of anisotropic media. This equation is written in terms of the phase velocity and its derivatives with respect to the phase angle with vertical. The phase angle, however, is not a seismic observable, while the ray parameter p is. Indeed, Alkhalifah and Tsvankin (1995) pointed out the importance of representing the NMO velocity function as a function of ray parameter and obtained a number of significant results via an indirect use of this variable. Subsequently, Cohen (1997) directly transformed the Tsvankin expression for the moveout velocity obtaining an expression involving the phase velocity expressed as a function of ray parameter. Applying this result to the normal moveout of P-waves in transversely isotropic media with a vertical symmetry axis (VTI media), he was able to get various approximations for the ray‐parameter form of the moveout function and thus give additional analytic insight into the success of the velocity‐analysis methodology Alkhalifah and Tsvankin.
Evaluating EM waveforms by singular‐value decomposition of exponential basis functions
Authors: Stolz Edward M. , Macnae James
Published: October 2002

Exponential basis functions preconvolved with the system waveform are used to convert measured transient decays to an ideal frequency‐domain response that can be modeled more easily than arbitrary waveform data. Singular‐value decomposition (SVD) of the basis functions are used to assess which specific EM waveform provides superior resolution of a range of exponential time constants that can be related to earth conductivities. The pulse shape, pulse length, transient sampling scheme, noise levels, and primary field removal used in practical EM systems all affect the resolution of time constants. Step response systems are more diagnostic of long time constants, and hence good conductors, than impulse response systems. The limited bandwidth of airborne EM systems compared with ground systems is improved when the response is sampled during the transmitter on time and gives better resolution of short time constants or fast decays.
Optimized inversion of borehole temperature data
Authors: Cooper Gordon R. J. , Jones Michael Q. W.
Published: October 2002

A comparison is made between the effectiveness of the inversion of borehole temperature data (for the purpose of climate reconstruction) by the least‐squares (L2) technique and the minimization of the absolute difference between the observed and calculated data (L1) technique. The L1 technique is found to require approximately half the number of iterations to reach the practically achievable minimum error compared to the L2 technique. The choice of which technique to use depends on the statistics of the difference between the observed and calculated data, and it can be advantageous to switch techniques during the inversion process. The inversion damping is also adjusted during the course of the inversion, based on the rate of change of the difference between the observed and calculated data. The aim is to get the best fit of the model to the data while minimising the model size, in the minimum number of iterations. A method of adjusting the damping to achieve this is suggested.
Resolution in seismic imaging: Is it all a matter of perspective?
Authors: Levin Stewart A.
Published: October 2002

Classical wave‐equation migration of seismic data combines both acoustic wave propagation and an imaging condition to produce a subsurface section. Integral methods implicitly combine high‐frequency ray asymptotics of the wave equation with a ray‐dependent imaging condition. The inherent limits on subsurface resolution imposed by acoustic‐wave generation (e.g., source bandwidth), subsurface propagation (e.g., attenuation), and recording (e.g., receiver arrays and aperture) have been studied extensively. This article studies how (or whether) the choice of imaging condition affects resolution. We will see in particular that the phenomenon of migration wavelet stretch, wherein the vertical resolution of steeply dipping reflectors is preferentially lowered by migration, is neither an artifact of an imaging condition nor a reduction of resolution on steeply dipping reflectors. In fact, we will discover that in seismic imaging of prestack data, steeply dipping reflectors are ultimately better resolved than horizontal beds. Finally, the concept of “superresolution” from seismic inversion, a generalization of thin‐bed tuning analysis, is explored and explicated with a simple example of multiple reflections.
Some remarks on surface multiple attenuation
Authors: Dragoset William H. , Jeričević Željko
Published: October 2002

The surface multiple attenuation algorithm discussed in this paper is a prestack inversion of a surface‐recorded, 2-D wavefield that aims to remove all orders of all surface multiples present within the wavefield. Although the algorithm requires no assumptions or modeling regarding the positions and reflection coefficients of the multiple‐causing reflectors, it does require complete internal physical consistency between primary and multiple events—something that exists only in ideal 2-D data sets. In field data sets the physical consistency between primaries and multiples is disturbed by phenomena such as variations in the acquisition wavelet, cable feathering, cross‐line dip, a finite near offset, and unequal or too coarse spatial sampling in source and receiver coordinates. Careful survey design can minimize the impact of those phenomena on surface multiple attenuation. If it is not too large, trace extrapolation can solve the finite near‐offset problem. Minor adjustments to the algorithm allow processing of data for which the source and receiver intervals differ by an integer multiple, although for those and other acquisition geometries, trace interpolation may be preferred. In the f-x domain, surface multiple attenuation can be formulated as an equation whose straightforward solution involves the inversion of a large matrix that is a function of the acquisition wavelet. Since that wavelet is generally unknown, solving this matrix equation becomes an optimization problem. Many matrix inversions are needed to estimate the acquisition wavelet that leads to the best multiple suppression, rendering the straightforward solution to the surface multiple attenuation equation quite costly. We offer two alternative approaches. In our first approach we compute an eigenvalue decomposition of the large matrix, allowing the equation to be recast so that the wavelet dependency appears in a diagonal matrix for which repetitive inversion is trivial. In our second approach we begin by using the surface multiple attenuation algorithm with a fixed, approximately correct wavelet to compute the surface multiple wavefield. We then filter the predicted multiples adaptively to match the actual multiples in the original wavefield and subtract these filtered multiples from the original wavefield. The second approach is relatively inexpensive and to some extent can cope with physical inconsistencies between primaries and multiples caused by field data set imperfections.
Optimal 3-D traveltime tomography
Authors: Eppstein Margaret J. , Dougherty David E.
Published: October 2002

We propose a practical new method for 3-D traveltime tomography. The method combines an efficient approximation to the extended Kalman filter for rapid, accurate, nonlinear tomography, with the concept of data‐driven zonation, in which the dimensionality and geometry of the parameterization are dynamically determined using cluster analysis and region merging by random field union. The Bayesian filter uses geostatistics as it recursively incorporates measurements in an optimal (minimum‐variance) manner. Geologic knowledge is introduced through a priori estimates of the parameter field and its spatial covariance. Conditional estimates of the parameter number, geometry, value, and covariance are evolved. An initial decomposition of the 3-D domain into 2-D slices, the simplified filter design, and the data‐driven reduction in parameter dimensionality, all contribute to make the method computationally feasible for large 3-D domains. The method is verified by the inversion of crosswell seismic traveltimes to 3-D estimates of seismic slowness in four synthetic heterogeneous domains. Starting with homogeneous, fully distributed slowness fields, and no knowledge of the true covariance structure, the method is able to accurately and efficiently resolve the structure and values of markedly different domains.
On: “Straightforward inversion of vertical electrical sounding data,” (Pravin K. Gupta, Sri Niwas, and Vinod Gaur, GEOPHYSICS, 62, 775–785)
Authors: Omnes Gildas
Published: October 2002

Reading the paper by Pravin K. Gupta, Sri Niwas, and Vinod Gaur in Geophysics, I came to the opinion that, although the proposed algorithm is interesting and may inspire interpreters of electrical data in the future, a number of misleading and even contradictory statements are present in the text. Here are two examples.