bluuebunny/crossref_metadata_2025 huggingface dataset:
3-D elastic modeling with surface topography by a Chebychev spectral method
Authors: Tessmer E. , Kosloff D.
Published: October 2002

The 3-D numerical Chebychev modeling scheme accounts for surface topography. The method is based on spectral derivative operators. Spatial differencing in horizontal directions is performed by the Fourier method, whereas vertical derivatives are carried out by a Chebychev method that allows for the incorporation of boundary conditions into the numerical scheme. The method is based on the velocity‐stress formulation. The implementation of surface topography is done by mapping a rectangular grid onto a curved grid. Boundary conditions are applied by means of characteristic variables. The study of surface effects of seismic wave propagation in the presence of surface topography is important, since nonray effects such as diffractions and scattering at rough surfaces must be considered. Several examples show this. The 3-D modeling alogrithm can serve as a tool for understanding these phenomena since it computes the full wavefield.
A physical model of shear‐wave propagation in a transversely isotropic solid
Authors: Chang Chih‐Hsiung , Gardner G. H. F. , McDonald John A.
Published: October 2002

It is now understood that seismic anisotropy is a comparatively common phenomenon in sedimentary layers. The elastic properties of most sedimentary rocks have been shown to be anisotropic. (Anisotropy means that the physical property of the material is a function of the measuring direction). Seismologists are generally concerned with velocity variation with the direction of propagation.
AVO in transversely Isotropic media—An overview
Authors: Blangy J. P.
Published: October 2002

The amplitude variation with offset (AVO) responses of elastic transversely isotropic media are sensitive to contrasts in both of Thomsen’s anisotropic parameters δ and ε. The equation describing P-P reflections indicates that the smaller the contrasts in isotropic properties (compressional velocity, shear velocity, and density) and the larger the contrasts in δ and ε across an interface of reflection, the greater the effects of anisotropy on the AVO signature. Contrasts in δ are most important under small‐to‐medium angles of incidence as previously described by Banik (1987), while contrasts in ε can have a strong influence on amplitudes for the larger angles of incidence commonly encountered in exploration (20 degrees and beyond). Consequently, using Rutherford and Williams’ AVO classification of isotropic gas sands, type I gas sands overlain by a transversely isotropic (TI) shale exhibit a larger decrease in AVO than if the shale had been isotropic, and type III gas sands overlain by a transversely isotropic (TI) shale exhibit a larger increase in AVO than if the shale had been isotropic. Furthermore, it is possible for a “type III” isotropic water sand to exhibit an “unexpected) increase in AVO if the overlying shale is sufficiently anisotropic. More quantitative AVO interpretations in TI media require considerations of viscoelastic TI in addition to elastic TI and lead to complicated integrated earth models. However, when elastic and viscoelastic TI have the same axis of symmetry in a shale overlying an isotropic sand, both elastic and viscoelastic TI affect the overall AVO response in the same direction by constructively increasing/decreasing the isotropic component of the AVO response. Continued efforts in this area will lead to more realistic reservoir models and hopefully answer some of the unexplained pitfalls in AVO interpretation.
Factor analysis of ambiguity in geophysics
Authors: Fraiha Simone G. C. , Silva João B. C.
Published: October 2002

We present an empirical ambiguity analysis method based on a finite number of acceptable solutions that are representative of the ambiguity region. These solutions are submitted to a Q‐mode factor analysis that indicates which parameters are ambiguous and their ambiguity range. We illustrate, with a synthetic nonlinear example, that our method is more effective than singular value decomposition analysis in producing an average trend of the ambiguity region. It requires less restrictive hypotheses and is more robust than analytical methods of ambiguity analysis, in the sense of being applicable to a broader class of problems.
AVO modeling and the locally converted shear wave
Authors: Simmons James L. , Backus Milo M.
Published: October 2002

The locally converted shear wave is often neglected in ray‐trace modeling when reproduction of the AVO response of potential hydrocarbon reservoirs is attempted. Primaries‐only ray‐trace modeling in which the Zoeppritz equations describe the reflection amplitudes is most common. The locally converted shear waves, however, often have a first‐order effect on the seismic response. This fact does not appear to be widely recognized, or else the implications are not well understood. Primaries‐only Zoeppritz modeling can be very misleading. Interference between the converted waves and the primary reflections from the base of the layers becomes increasingly important as layer thicknesses decrease. This interference often produces a seismogram that is very different from one produced under the primaries‐only Zoeppritz assumption. For primaries‐only modeling of thin layers, synthetic seismograms obtained by use of a linearized approximation to the Zoeppritz equations to describe the reflection coefficients are more accurate than those obtained by use of the exact Zoeppritz reflection coefficients. A real‐data example consisting of an assemblage of very thin layers has recently been discussed in the literature. Inferences as to the true earth properties based on the predicted amplitude variation with offset are in error because the primaries‐only assumption is invalid. For one of the models, primaries‐only modeling predicts an amplitude increase of approximately a factor of three from the near trace to the far trace. Reflectivity modeling predicts an amplitude decrease with offset. The O’Doherty‐Anstey effect suggests that transmission loss for primary reflections should not be included in normal‐incidence synthetic seismograms if the short‐period reverberations are not also included. The same principle holds for prestack modeling. Similarly, the Zoeppritz equations should not be used for synthetic seismograms without including the locally converted shear wave.
Source signature determination from ministreamer data
Authors: Landrø Martin , Langhammer Jan , Sollie Roger , Amundsen Losse , Berg Eivind
Published: October 2002

Two methods for estimating the pressure wavefield generated by a marine airp‐gun array are tested. Data have been acquired at a ministreamer located below the source array. Effective source signatures for each air gun are estimated. In the first method a nonlinear inversion algorithm is used, where the forward modeling scheme is based upon a physical modeling of the air bubble generated by each air gun. In the second method a linear inversion method is used, with the assumption that the physics in the problem can be described by the acoustic wave equation with explosive point sources as the driving term. From the estimated effective source signatures, far‐field signatures have been calculated for both methods and compared with measured far‐field signatures. The error energy between the measured and estimated far‐field signatures was approximately 8 percent for both methods.
Frame moduli of unconsolidated sands and sandstones
Authors: Spencer James W. , Cates Michael E. , Thompson Don D.
Published: October 2002

In this study, we investigate the elastic moduli of the empty grain framework (the “frame” moduli) in unconsolidated sands and consolidated sandstones. The work was done to improve the interpretation of seismic amplitude anomalies and amplitude variations with offset (AVO) associated with hydrocarbon reservoirs. We developed a laboratory apparatus to measure the frame Poisson’s ratio and Young’s modulus of unconsolidated sands at seismic frequencies (0.2 to 155 Hz) in samples approximately 11 cm long. We used ultrasonic pulse velocity measurements to measure the frame moduli of consolidated sandstones. We found that the correlation coefficient between the frame Poisson’s ratio [Formula: see text] and the mineral Poisson’s ratio [Formula: see text] is 0.84 in consolidated sandstones and only 0.28 in unconsolidated sands. The range of [Formula: see text] values in unconsolidated sands is 0.115 to 0.237 (mean = 0.187, standard deviation = 0.030), and [Formula: see text] cannot be estimated without core or log analyses. Frame moduli analyses of core samples can be used to calibrate the interpretation of seismic amplitude anomalies and AVO effects. For use in areas without core or log analyses, we developed an empirical relation that can be used to estimate [Formula: see text] in unconsolidated sands and sandstones from [Formula: see text] and the frame P‐wave modulus.
Imaging the permeability structure of a limestone aquifer by crosswell acoustic tomography
Authors: Yamamoto Tokuo , Nye Thomas , Kuru Murat
Published: October 2002

A narrow‐band pseudorandom binary sequence (PRBS) code was used to generate an acoustic pulse that approximates a single laser‐like frequency. Measurements of crosswell tomography under a Florida limestone aquifer were made using four different PRBS frequencies: 250, 1 000, 2 000, and 3 000 Hz. Velocity images created by different PRBS frequencies showed different velocity values in the permeable layers but no velocity difference in the impermeable layers. For selected source‐receiver pairs across these layers, crosswell experiments were conducted with more PRBS frequencies ranging from 200 to 5 000 Hz. Pulse propagation calculations using a layered elastic model indicate that the velocity‐frequency dispersion is not a result of geometrical dispersion. The original procedure to extract porosity, permeability, and shear strength from seismic velocity images has been extended to the more general case of mixed lithified and unlithified sediments. The velocity‐frequency dispersion data for the limestone layer were compared with the Biot theory and the Biot‐squirt flow (BISQ) theory. The permeability value of the cavity‐filled limestone layer inferred from BISQ theory is 200 darcies, whereas the average permeability measured from pumping tests was 331 darcies.
Least‐squares deconvolution of apparent resistivity pseudosections
Authors: Loke M. H. , Barker R. D.
Published: October 2002

A fast technique for the inversion of data from resistivity tomography surveys has been developed. This technique is based on the smoothness‐constrained, least‐squares method, and it produces a 2-D subsurface model that is free of distortions in the apparent resistivity pseudosection caused by the electrode array geometry used. A homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. Tests with a variety of models and data from field surveys show that this technique is insensitive to random noise, provided a sufficiently large damping factor is used, and that it can resolve structures that cause overlapping anomalies in the pseudosection. On a 33 MHz 80486DX microcomputer, it takes about 5 s to process a single data set.
An integration of aeromagnetic and electrical resistivity methods in dam site investigation
Authors: Aina Adebayo , Olorunfemi Martins O. , Ojo John S.
Published: October 2002

Aeromagnetic map and electrical resistivity sounding data obtained along eight traverses were examined at two sites across the Katsina‐Ala River. The principal goals of this exercise were to define depths to the bedrock, bedrock relief, geologic structures, define the nature of the superficial deposit, and select probable minor and major axes for hydroelectric power dams. The aeromagnetic map shows that the basement rocks trend roughly northeast‐southwest, which correlates with the strike of foliation measurements made on rock outcrops along the river channel. A network of cross cutting lineaments, suspected to be faults/fractures that trend approximately northeast/southwest and northwest/southeast, was also delineated from the magnetic map. The depths to the bedrock estimated from resistivity depth sounding data at site I generally vary from 1–53.1 m. Depths to the bedrock estimated at site II range from 1.9–19.5 m. The superficial deposit varies from clay to sandy clay, to clayey sand (with boulders in places), and to sand and laterite. The bedrock relief is relatively flat and gently undulates along most of the traverses, with an overall dip towards the river channel. Traverses E-F or I‐J at site I and K-L at site II are probable dam axes. These traverses are characterized by relatively thin overburden thicknesses and rock heads dipping toward the river channel, thereby reducing the likelihood of water seepages from the flanks of the proposed dam axes.
Permeability prediction with artificial neural network modeling in the Venture gas field, offshore eastern Canada
Authors: Huang Zehui , Shimeld John , Williamson Mark , Katsube John
Published: October 2002

Estimating permeability from well log information in uncored borehole intervals is an important yet difficult task encountered in many earth science disciplines. Most commonly, permeability is estimated from various well log curves using either empirical relationships or some form of multiple linear regression (MLR). More sophisticated, multiple nonlinear regression (MNLR) techniques are not as common because of difficulties associated with choosing an appropriate mathematical model and with analyzing the sensitivity of the chosen model to the various input variables. However, the recent development of a class of nonlinear optimization techniques known as artificial neural networks (ANNs) does much to overcome these difficulties. We use a back‐propagation ANN (BP-ANN) to model the interrelationships between spatial position, six different well logs, and permeability. Data from four wells in the Venture gas field (offshore eastern Canada) are organized into training and supervising data sets for BP-ANN modeling. Data from a fifth well in the same field are retained as an independent data set for testing. When applied to this test data, the trained BP-ANN produces permeability values that compare well with measured values in the cored intervals. Permeability profiles calculated with the trained BP-ANN exhibit numerous low permeability horizons that are correlatable between the wells at Venture. These horizons likely represent important, intra‐reservoir barriers to fluid migration that are significant for future reservoir production plans at Venture. For discussion, we also derive predictive equations using conventional statistical methods (i.e., MLR, and MNLR) with the same data set used for BP-ANN modeling. These examples highlight the efficacy of BP-ANNs as a means of obtaining multivariate, nonlinear models for difficult problems such as permeability estimation.
P‐wave signatures and notation for transversely isotropic media: An overview
Authors: Tsvankin Ilya
Published: October 2002

Progress in seismic inversion and processing in anisotropic media depends on our ability to relate different seismic signatures to the anisotropic parameters. While the conventional notation (stiffness coefficients) is suitable for forward modeling, it is inconvenient in developing analytic insight into the influence of anisotropy on wave propagation. Here, a consistent description of P‐wave signatures in transversely isotropic (TI) media with arbitrary strength of the anisotropy is given in terms of Thomsen notation. The influence of transverse isotropy on P‐wave propagation is shown to be practically independent of the vertical S‐wave velocity [Formula: see text], even in models with strong velocity variations. Therefore, the contribution of transverse isotropy to P‐wave kinematic and dynamic signatures is controlled by just two anisotropic parameters, ε and δ, with the vertical velocity [Formula: see text] being a scaling coefficient in homogeneous models. The distortions of reflection moveouts and amplitudes are not necessarily correlated with the magnitude of velocity anisotropy. The influence of transverse isotropy on P‐wave normal‐moveout (NMO) velocity in a horizontally layered medium, on small‐angle reflection coefficient, and on point‐force radiation in the symmetry direction is entirely determined by the parameter δ. Another group of signatures of interest in reflection seisimology—the dip‐dependence of NMO velocity, magnitude of nonhyperbolic moveout, time‐migration impulse response, and the radiation pattern near vertical—is dependent on both anisotropic parameters (ε and δ) and is primarily governed by the difference between ε and δ. Since P‐wave signatures are so sensitive to the value of ε − δ, application of the elliptical‐anisotropy approximation (ε = δ) in P‐wave processing may lead to significant errors. Many analytic expressions given in the paper remain valid in transversely isotropic media with a tilted symmetry axis. Moreover, the equation for NMO velocity from dipping reflectors, as well as the nonhyperbolic moveout equation, can be used in symmetry planes of any anisotropic media (e.g., orthorhombic).
The effects of noise on Occam’s inversion of resistivity tomography data
Authors: LaBrecque Douglas J. , Miletto Michela , Daily William , Ramirez Aberlardo , Owen Earle
Published: October 2002

An Occam’s inversion algorithm for crosshole resistivity data that uses a finite‐element method forward solution is discussed. For the inverse algorithm, the earth is discretized into a series of parameter blocks, each containing one or more elements. The Occam’s inversion finds the smoothest 2-D model for which the Chi‐squared statistic equals an a priori value. Synthetic model data are used to show the effects of noise and noise estimates on the resulting 2-D resistivity images. Resolution of the images decreases with increasing noise. The reconstructions are underdetermined so that at low noise levels the images converge to an asymptotic image, not the true geoelectrical section. If the estimated standard deviation is too low, the algorithm cannot achieve an adequate data fit, the resulting image becomes rough, and irregular artifacts start to appear. When the estimated standard deviation is larger than the correct value, the resolution decreases substantially (the image is too smooth). The same effects are demonstrated for field data from a site near Livermore, California. However, when the correct noise values are known, the Occam’s results are independent of the discretization used. A case history of monitoring at an enhanced oil recovery site is used to illustrate problems in comparing successive images over time from a site where the noise level changes. In this case, changes in image resolution can be misinterpreted as actual geoelectrical changes. One solution to this problem is to perform smoothest, but non‐Occam’s, inversion on later data sets using parameters found from the background data set.
Inversion versus migration: A new perspective to an old discussion
Authors: Wapenaar C. P. A.
Published: October 2002

Seismic imaging techniques can be subdivided into inversion and migration. The object functions for inversion and migration are, respectively, the medium contrast parameters and reflectivity. In this paper, the relationship between inversion and migration is approached by analyzing the underlying representations (the forward models). It appears that the “two‐way representation” (which underlies inversion) as well as the “one‐way representation” (which underlies migration) can both be expressed in terms of a volume integral over the appropriate object function. In their linearized form, these representations account for primaries only. In this case, the one‐way representation in terms of reflectivity is the most accurate of the two, which implies that proper migration is more accurate than linearized inversion. Internal multiples can be taken into account by the nonlinear representations. As an alternative, however, the “generalized primary representation” is introduced. In its explicit form, this one‐way representation is linear in the reflectivity (opposed to linearized). Nonlinear effects are implicitly accounted for by the generalized primary propagators. The generalized primary representation is a suitable basis for true amplitude migration, taking the angle‐dependent dispersive effects of fine layering into account.
3-D ground‐penetrating radar applied to fracture imaging in gneiss
Authors: Grasmueck Mark
Published: October 2002

Three‐dimensional, ground‐penetrating radar (georadar) techniques suitable for geological engineering applications have been developed and tested. Initial experiments were conducted on the floor of a quarry in southern Switzerland from which ornamental gneissic rock is extracted. During a brief two‐day period, constant‐offset georadar data were recorded over a [Formula: see text] area with a grid cell size of 0.1 m × 0.2 m. Georadar velocities were estimated from the results of expanding spread surveys. All georadar data and associated geometry files were recorded automatically in seismic industry formats. The experimental georadar data set was processed, image‐enhanced, and interpreted using [Formula: see text] seismic reflection software operating on a workstation. Arbitrary vertical sections, time slices, [Formula: see text] images, and animated movies in which the observer “travels” through the entire data volume were constructed from the resultant migrated georadar data. Semi‐automatic tracking routines allowed continuous subhorizontal reflections to a maximum depth of 30 m to be mapped through the rock mass. These reflections, which are characterized by negative polarity onsets, are probably caused by a system of ubiquitous water‐filled fractures, 2–4 cm thick. Volumes of rock bounded by the subhorizontal fractures were estimated from isopach maps and rock quality was assessed on the basis of root‐mean‐square (rms) amplitudes of reflections. An extension of a steep‐dipping fault exposed on a nearby quarry wall was best delineated on maps representing the horizontal gradients of reflection times. To synthesize in a single figure the principal geological results of the study, picked reflection times were presented in the form of shaded relief surfaces, in which remarkably vivid structural details of the subhorizontal fractures and intersecting near‐vertical fault could be discerned. It is concluded that 3-D georadar methods have the potential to resolve a wide range of engineering and environmental problems.
Measurement of seismic attenuation from high‐resolution crosshole data
Authors: Neep J. P. , Sams M. S. , Worthington M. H. , O’Hara‐Dhand K. A.
Published: October 2002

High‐resolution crosshole seismic data have been acquired at the Imperial College borehole test site in Northumberland, England. Raypaths between source and receiver were horizontal and parallel to plane layered beds of sandstone, mudstone, and limestone. Shots were fired at 25 cm intervals between the depths of 50 and 72 m. Estimates of the total attenuation using the spectral ratio and centroid frequency shift methods show Q values that correlate well with the frequency content of the first arrivals. Synthetic modeling studies with and without intrinsic attenuation show that the contribution of scattering attenuation is significant and must be accounted for to recover the intrinsic Q values used in the modeling. At some depths, there appears to be an increase in the frequency content of the compressional wave with distance, implying a negative scattering Q. Snapshots of the wave as it travels across the velocity structure at this depth show that the high frequencies are preserved in the wavefield and the low frequencies are scattered to other depths. Intrinsic Q values of less than 20 were obtained at all depths. Within experimental error, there is no evidence to suggest any significant variation of attenuation with lithology. This is consistent with estimates of attenuation from core samples. However, there is a significant difference in the median of Q estimates from the crosshole and core data.
Multifrequency viscoacoustic modeling and inversion
Authors: Liao Qingbo , McMechan George A.
Published: October 2002

Modeling and inversion for seismic wavefields that include the attenuation and phase dispersion effects of Q can be implemented in the space‐frequency domain. The viscoacoustic wave equation is solved by the moment method. Absorbing boundary conditions are implemented by reducing Q and adjusting the complex velocity (to reduce Q‐dependent reflectivity) in a zone around the edges of the model grid. Nonlinear inversion is performed using iterative linearized inversions. The residual wavefield at a single frequency is back projected, using an anticausal Green’s function, along the viscoacoustic wavepath in an estimate of the model, to get updated velocity and Q distributions. The model obtained from data at one frequency becomes input to inversion at the next higher frequency. Velocity and Q are inverted simultaneously as they are interdependent. Both modeling and inversion algorithms are successfully tested with synthetic examples; data at two or three frequencies are sufficient to produce reliable images from noise‐free synthetic data.
Fracture density estimates in glaciogenic deposits from P‐wave velocity reductions
Authors: Karaman Abdullah , Carpenter Philip J.
Published: October 2002

Subsidence‐induced fracturing of glaciogenic deposits over coal mines in the southern Illinois basin alters hydraulic properties of drift aquifers and exposes these aquifers to surface contaminants. In this study, refraction tomography surveys were used in conjunction with a generalized form of a seismic fracture density model to estimate the vertical and lateral extent of fracturing in a 12-m thick overburden of loess, clay, glacial till, and outwash above a longwall coal mine at 90 m depth. This generalized model accurately predicted fracture trends and densities from azimuthal P‐wave velocity variations over unsaturated single‐ and dual‐parallel fractures exposed at the surface. These fractures extended at least 6 m and exhibited 10–15 cm apertures at the surface. The pre‐ and postsubsidence velocity ratios were converted into fracture densities that exhibited qualitative agreement with the observed surface and inferred subsurface fracture distribution. Velocity reductions as large as 25% were imaged over the static tension zone of the mine where fracturing may extend to depths of 10–15 m. Finally, the seismically derived fracture density estimates were plotted as a function of subsidence‐induced drawdown across the panel to estimate the average specific storage of the sand and gravel lower drift aquifer. This value was at least 20 times higher than the presubsidence (unfractured) specific storage for the same aquifer.
Point‐source τ‐p transform: A review and comparison of computational methods
Authors: Wang Yanghua , Houseman Gregory A.
Published: October 2002

The τ‐p transformation of reflection seismic data excited by a point source requires a cylindrical slant stack, which includes compensation for the phase shift and geometrical spreading associated with cylindrical geometry. Using a simple test model, we review and compare the different computational methods used for the cylindrical slant stack. The two major method types are the Bessel‐Fourier transform (BFT) method and a set of methods (TD2D, TDX, TDTC and TDTS) based on time‐domain convolution. The stack integral in each of these approaches can be separated into two parts, with the part corresponding to the contribution of incoming waves being negligible for large ray parameter p. Neglecting the latter term for large p generally avoid a major problem caused by aliasing between time and space domains. The TDTS method introduced here has the advantage of being expressed in terms of a conventional 2-D slant stack (weighted by offset x) plus a correction term. This formulation facilitates a quantitative comparison of the 3-D cylindrical slant stack with a 2-D slant stack. The TDTS method compares favorably with the TD2D method, in which the cylindrical slant stack is expressed as a weighted integral of the 2-D slant stacks. TDTS avoids the singular weighting function needed in the integral for the TD2D method, and therefore has less problems with numerical noise. For all of the methods considered, the accuracy of the map transformation is limited by the spatial and temporal resolution of the test data set. Some corrections to previously published methods are also provided.
Velocity dispersion: A tool for characterizing reservoir rocks
Authors: Brown Raymon L. , Seifer Dirk
Published: October 2002

Apparent discrepancies between velocity measurements made with different frequencies in a formation at the Gypsy test site are explained in terms of elastic scattering and intrinsic attenuation. The elastic scattering component of the dispersion (38%) in a marine interval above the Gypsy sandstone is estimated via simple models constructed from well log information. Any dispersion above the predicted value for elastic scattering in this interval is assigned to intrinsic attenuation (62%). Using the vertical measurements in the well, the marine interval directly above the Gypsy sandstone has an estimated intrinsic [Formula: see text] and an effective Q because of the scattering of [Formula: see text]. The total Q of the combined mechanisms is 32. The dispersion of the vertical measurements through the heterogeneous sands and shales of the Gypsy formation can be explained using an intrinsic [Formula: see text] and neglecting the effects of scattering. The horizontal observations require a more detailed modeling effort to unravel the relative roles of path and volume effects, elastic scattering, attenuation, and intrinsic anisotropy. Thin layers barely resolvable on the sonic logs play a significant role in modifying the cross‐well response. Potentially, the dispersion can be a key to mapping reservoir properties using crosswell and surface seismic data.
Imaging complex structures with semirecursive Kirchhoff migration
Authors: Bevc Dimitri
Published: October 2002

I present a semirecursive Kirchhoff migration algorithm that is capable of obtaining accurate images of complex structures by combining wave‐equation datuming and Kirchhoff migration. The method is successful because breaking up the complex velocity structure into small depth regions allows traveltimes to be calculated in regions where the computation is well‐behaved and where the computation corresponds to energetic arrivals. The traveltimes computed in such a region are used first for imaging and second for downward continuation of the entire survey (shots and receivers) to the boundary of the next region. This process results in images comparable to those obtained by shot‐profile migration, but at reduced computational cost. Because traveltimes are computed for small depth domains, the adverse effects of caustics, headwaves, and multiple arrivals do not develop. In principle, this method requires only the same number of traveltime calculations as a standard migration. Tests on the Marmousi data set produce excellent results.
Electromagnetic conductivities of rock cores: Theory and analog results
Authors: Yang Y. P. , Emerson D. W.
Published: October 2002

Measurement theory developed for a laboratory investigation of electromagnetic characteristics of conductive and magnetic rocks agreed with experiments performed on synthetic conductive samples using a multifrequency coil‐bridge system in the 10 kHz to 4 MHz range. The theoretical analysis also provides a basic and useful method for the study of inductive [electromagnetic (EM)] conductivity and magnetic susceptibility spectra from conductive and/or magnetic samples. The skin effect, an important consequence of eddy current behavior, affects EM measurements and can be recognized by varying the energizing frequency. Investigations of the EM respses of 104 synthetic cores, of five types, revealed that textural effects, i.e., the structure, arrangement, and particle size of the conducting elements exerted a large influence on results. These analog cores contained a range of conductors, including copper wires, graphite powder, aluminum particles, and magnetite‐ilmenite grains, set in a matrix of insulating plaster or wax, representing models of layered, stringer, disseminated, network, massive, and magnetite‐rich mineralizations. For a heterogeneous sample, the laboratory‐measured EM conductivity depends strongly on the structure and orientation of the conducting materials and usually differs from the galvanic conductivity. For a sample with insulated conducting particles, the measured EM conductivity decreases with the increasing square of the sample diameter. This indicates that EM field methods may not respond well to disseminated targets with dispersed conducting minerals even at high concentrations. A mechanism attributed to magnetic loss produced unrealistically high apparent conductivities for magnetite‐bearing samples, especially at low frequencies (f < 100 kHz). For a conductive magnetite sample (σ >1 S/m), the effect of magnetic loss can be eliminated at high frequencies (f > 400 kHz ), and the ohmic conductivity of the magnetite sample can then be estimated.
Mixed‐phase deconvolution
Authors: Porsani Milton J. , Ursin Bjorn
Published: October 2002

We describe a new algorithm for mixed‐phase deconvolution. It is valid only for pulses whose Z-transform has no zeros on the unit circle. That is, the amplitude spectrum cannot be zero for any frequency. Using the Z-transform of a discrete‐time signal, and assuming that the signal has α zeros inside the unit circle, the inverse of its minimum‐delay component may be estimated by solving the extended Yule‐Walker (EYW) system of equations with the lag α of the autocorrelation function (ACF) on diagonal of the coefficient matrix. This property of the solution of EYW equations is exploited to derive mixed‐phase inverse filters and their corresponding mixed‐phase pulses. For different values of α, a suite of inverse filters is generated using the same ACF. To choose the best decomposition and its corresponding mixed‐phase inverse filter, we have used the value of α which gives the maximum value of the Lp norm of the filtered signal. The optimal value of α does not seem to be very sensitive to the choice of norm as long as p > 2. In the numerical examples, we have used p = 5. The mixed‐phase deconvolution filter performs better than minimum‐phase deconvolution on the synthetic and real data examples shown.
Multiple suppression using a local coherence filter
Authors: Houston Louis M.
Published: October 2002

Generally, when velocity filters are applied to prestack seismic data, they can suppress long‐period multiples, but they can also deteriorate the primary amplitudes. Since the apparent velocity differences between primaries and multiples can be negligible within the near‐offset regions of data gathers, a velocity filter will be ineffective in these regions, tending to remove or distort primary signal. The normal solution to this problem is to mute or remove near‐offset data, but this approach is detrimental to low‐fold data. In this paper, we derive a filter that can be used to address the problem by responding to average apparent velocity differences rather than to instantaneous apparent velocity differences between primaries and multiples. The filter, called a local coherence filter, is essentially a finite‐difference operator whose step size is equivalent to a spatial prediction distance. Within the local coherence filter’s small application window, an NMO-corrected multiple is predictable while an overcorrected primary is not predictable. The step size of its difference operator gives the filter the ability to discriminate between primaries and long‐period multiples in regions of a data gather where velocity filters fail. This paper derives the local coherence filter and compares it to the f-k filter in both model and real‐data applications. Results demonstrate that the local coherence filter is more effective in suppressing long‐period multiples without distorting the primary reflections.
On: “Magnetic interpretation using the 3-D analytic signal” (Walter R. Roest, Jacob Verhoef, and Mark Pilkington, GEOPHYSICS, 57, 116–125)
Authors: Lin‐ping Huang , Zhi‐ning Guan
Published: October 2002

Over the last decades increasing interest has been expressed for determining boundaries and depths by using the analytic signal. The basic concepts of the analytic signal in 2-D case for magnetic data were extensively discussed by Nabighian (1972, 1974). Roest et al. (1992) discussed a new method for magnetic interpretation based on the generalization of analytic signal concept to 3-D. They considered that the analytic signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field, and source magnetization directions and locations of these maxima thus determine the outlines of magnetic sources. Afterward, Hsu et al. (1996) adopted a high‐resolution technique (also related to analytic signal) to image geologic boundaries such as contacts and faults. The outlines of the geologic boundaries can be determined by tracing the maximum amplitudes of an enhanced analytic signal composed of the nth‐order vertical derivative values of two horizontal gradients and one vertical gradient.
Precision analysis of first‐break times in grid models
Authors: Gruber Thomas , Greenhalgh Stewart A.
Published: October 2002

Rectangular grid velocity models and their derivatives are widely used in geophysical inversion techniques. Specifically, seismic tomographic reconstruction techniques, whether they be based on raypath methods (Bregman et al., 1989; Moser, 1991; Schneider et al., 1992; Cao and Greenhalgh, 1993; Zhou, 1993) or full wave equation methods (Vidale, 1990; Qin and Schuster, 1993; Cao and Greenhalgh, 1994) for calculating synthetic arrival times, involve propagation through a grid model. Likewise, migration of seismic reflection data, using asymptotic ray theory or finite difference/pseudospectral methods (Stolt and Benson, 1986; Zhe and Greenhalgh, 1997) involve assigning traveltimes to upward and downward propagating waves at every grid point in the model. The traveltimes in both cases depend on the grid specification. However, the precision level of such numerical models and their dependence on the model parameters is often unknown. In this paper, we describe a two‐dimensional velocity model and derive an error bound for first‐break times calculated with such a model. The analysis provides clear guidelines for grid specifications.
High‐resolution shallow‐seismic experiments in sand, Part II: Velocities in shallow unconsolidated sand
Authors: Bachrach Ran , Dvorkin Jack , Nur Amos
Published: October 2002

We conducted a shallow high‐resolution seismic reflection and refraction experiment on a sandy beach. The depth of investigation was about 2 m. We interpret the data using the Hertz‐Mindlin contact theory combined with Gassmann’s equation. These were used to obtain the vertical velocity profile. Then the profile was computed from seismic data using the turning‐rays approximation. The normal moveout (NMO) velocity at the depth of 2 m matches the velocity profile. As a result, we developed a method to invert measured velocity from first arrivals, i.e., velocity versus distance into velocity versus depth using only one adjustable parameter. This parameter contains all the information about the internal structure and elasticity of the sand. The lowest velocity observed was about 40 m/s. It is noteworthy that the theoretical lower bound for velocity in dry sand with air is as low as 13 m/s. We find that modeling sand as a quartz sphere pack does not quantitatively agree with the measured data. However, the theoretical functional form proves to be useful for the inversion.
Ground‐penetratinng radar reflection profiling of groundwater and bedrock in an area of discontinuous permafrost
Authors: Arcone Steven A. , Lawson Daniel E. , Delaney Allan J. , Strasser Jeffrey C. , Strasser Jodie D.
Published: October 2002

We have used ground‐penetrating radar to profile the depth of permafrost, to groundwater beneath permafrost, and to bedrock within permafrost in alluvial sediments of interior Alaska. We used well log data to aid the interpretations and to calculate dielectric permittivities for frozen and unfrozen materials. Interfaces between unfrozen and frozen sediments above permafrost were best resolved with wavelet bandwidths centered at and above 100 MHz. The resolution also required consideration of antenna configuration, season, and surface conditions. Depths to subpermafrost groundwater were profiled where it was in continuous contact with the bottom of the permafrost, except near transitions to unfrozen zones, where the contact appeared to dip steeply. The complexity of the responses to intrapermafrost bedrock, detected at a maximum depth of 47 m, appears to distinguish these events from those of subpermafrost saturated sediments. The relative dielectric permittivity ranged between 4.4 and 8.3 for the permafrost, and between 12 and 45 for partially to fully saturated, unfrozen silts and sands. Scattering losses are evident from intrapermafrost diffractions and from the improved penetration achieved by lowering the midband radar frequency from 100 to 50 MHz.
Optimization and sensitivity analysis of seismic depth migrations from Hibernia Field
Authors: Kelly Irene , Lines Larry R.
Published: October 2002

Accurate imaging of seismic reflectors with depth migration requires accurate velocity models. In frontier areas with few well constraints, velocity estimation generally involves the use of methods such as normal moveout analysis, seismic traveltime tomography, or iterative prestack depth migration. These techniques can be effective, but may also be expensive or time‐consuming. In situations where we have information on formation tops from a series of wells which intersect seismic reflectors, we use a least‐squares optimization method to estimate velocity models. This method produces velocity models that optimize depth migrations in terms of well constraints by using least‐squares inversion to match the depth migration images to formation tops. The well log information is used to optimize poststack migration, thereby eliminating some of the time and expense of velocity analysis. In addition to applying an inversion method which optimizes depth migration in terms of formation tops, we can use a sensitivity analysis method of “most‐squares inversion” to explore a range of velocity models which provide mathematically acceptable solutions. This sensitivity analysis quantifies the expected result that our velocity estimates are generally less reliable for thin beds than for thick beds. The proposed optimization method is shown to be successful on synthetic and real data cases from the Hibernia Field of offshore Newfoundland.
Multichannel blind deconvolution of seismic signals
Authors: Kaaresen Kjetil F. , Taxt Tofinn
Published: October 2002

A new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given. To remove the inherent ambiguity in this blind deconvolution problem, we introduce relevant a priori information. Our major assumption is sparseness of the reflectivity, which corresponds to a layered‐earth model. This allows nonminimum‐phase wavelets to be recovered reliably and closely spaced reflectors to be resolved. To combine a priori knowledge and data, we use a Bayesian framework and derive a maximum a posteriori estimate. Computing this estimate is a difficult optimization problem solved by a suboptimal iterative procedure. The procedure alternates steps of wavelet estimation and reflectivity estimation. The first step only requires a simple least‐squares fit, while the second step is solved by the iterated window maximization algorithm proposed by Kaaresen. This enables better efficiency and optimality than established alternatives. The resulting optimization method can easily handle multichannel models with only a moderate increase of the computational load. Lateral continuity of the reflectors is achieved by modeling local dependencies between neighboring traces. Major improvements in both wavelet and reflectivity estimates are obtained by taking the wavelet to be invariant across several traces. The practicality of the algorithm is demonstrated on synthetic and real seismic data. An application to multivariate well‐log segmentation is also given.
Wavelet estimation from marine pressure measurements
Authors: Osen Are , Secrest Bruce G. , Amundsen Lasse , Reitan Arne
Published: October 2002

A new and alternative procedure for the deterministic estimation of the seismic source time function (wavelet) is proposed. This paper follows a series of reports on source signature estimation, requiring neither statistical assumptions on the signature nor any knowledge about the earth below the receivers. The proposed estimation method, which in principle is exact, uses conventional recordings of the pressure on a surface below the source and recordings of the pressure at one or more locations above the receiver surface. The derivation of the method is based on the Kirchhoff‐Helmholtz integral equation. The formulation ensures that the scattered energy is filtered from the wavelet estimation, enabling the wavelet to be detected from the direct pressure field. Along with the derivation, we present a numerical example.
Estimating depth of investigation in dc resistivity and IP surveys
Authors: Oldenburg Douglas W. , Li Yaoguo
Published: October 2002

In this paper, the term “depth of investigation” refers generically to the depth below which surface data are insensitive to the value of the physical property of the earth. Estimates of this depth for dc resistivity and induced polarization (IP) surveys are essential when interpreting models obtained from any inversion because structure beneath that depth should not be interpreted geologically. We advocate carrying out a limited exploration of model space to generate a few models that have minimum structure and that differ substantially from the final model used for interpretation. Visual assessment of these models often provides answers about existence of deeper structures. Differences between the models can be quantified into a depth of investigation (DOI) index that can be displayed with the model used for interpretation. An explicit algorithm for evaluating the DOI is presented. The DOI curves are somewhat dependent upon the parameters used to generate the different models, but the results are robust enough to provide the user with a first‐order estimate of a depth region below which the earth structure is no longer constrained by the data. This prevents overinterpretation of the inversion results. The DOI analysis reaffirms the generally accepted conclusions that different electrode array geometries have different depths of penetration. However, the differences between the inverted models for different electrode arrays are far less than differences in the pseudosection images. Field data from the Century deposit are inverted and presented with their DOI index.