bluuebunny/crossref_metadata_2025 huggingface dataset:
Iterative asymptotic inversion in the acoustic approximation
Authors: Lambaré Gilles , Virieux Jean , Madariaga Raul , Jin Side
Published: October 2002

We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations. There is no need to retrace rays, and the same ray quantities are used in the iterations. For this reason our method is very fast and efficient. The results of the inversion demonstrate that iterations improve the spatial resolution of the model images since they mainly contribute to the increase in the short wavelength contents of the final image. A synthetic example with one‐dimensional (1-D) velocity background illustrates the main features of the inversion method. An example with two‐dimensional (2-D) heterogeneous background demonstrates our ability to handle multiple arrivals and a nearly perfect reconstruction of a flat horizon once the perturbations above it are known. Finally, we consider a seismic section taken from the Oseberg oil field in the North Sea off Norway. We show that the iterative asymptotic inversion is a reasonable and accurate alternative to methods based on finite differences. We also demonstrate that we are able to handle an important amount of data with presently available computers.
Elastic wave propagation in composite media
Authors: Lamb William J. , Zhu Xianhuai , McMechan George A. , Greenberg Matt L. , Castagna John P.
Published: October 2002

Numerical simulation can be a useful tool for studying composite media. It is not limited by weak or single scattering assumptions, and it requires only constituent properties and an arrangement of constituents as input. For solid/solid media with octagonal cylindrical inclusions and for typical values of constituent moduli, composite moduli are accurately predicted by two‐dimensional (2-D) analogs of Kuster‐Toksöz formulas. For solid/solid media there is a small but discernable difference between responses of square and those of octagonal inclusions. Coherent reflections are produced by a coherent wave incident at a change in concentration of inclusions, if the contrast between material properties of the matrix and those of the inclusions is sufficient to produce significant scattering, and if the size of scatterers is sufficiently small and their concentration sufficiently large so there is constructive interference between waves originating at adjacent scatterers.
Amplitude preprocessing of single and multicomponent seismic data
Authors: Wapenaar C. P. A. , Verschuur D. J. , Herrmann P.
Published: October 2002

Whenever the data acquisition is restricted to line surveys rather than areal surveys, seismic processing is necessarily in two dimensions. In this paper it is argued that two‐dimensional (2-D) processing is preferably applied after transforming the point source responses into line source responses. The effect of this transformation is a correction of the amplitudes in the data. For single‐component acoustic data as well as for multicomponent elastic data a line source response is nothing but a superposition of point source responses. Hence, in principle a line source response can be synthesized by integrating point source responses along the desired line source axis. In practice, however, this integration cannot be carried out due to the incompleteness of the data. It is shown that the integration along the source axis can be replaced by an integration along the receiver axis. The underlying assumption is that the wavefields exhibit a certain type of cylindrical symmetry. For horizontally layered acoustic and elastic media this assumption is fully satisfied. For 2-D inhomogeneous media this assumption is approximately satisfied, provided the data are sorted in CMP gathers. Having transformed the point source responses into line source responses, the results may be considered as “true amplitude” 2-D data. Hence, proceeding with existing 2-D seismic processing techniques is then justified.
Seismic modeling in viscoelastic media
Authors: Carcione José M.
Published: October 2002

Anelasticity is usually caused by a large number of physical mechanisms which can be modeled by different microstructural theories. A general way to take all these mechanisms into account is to use a phenomenologic model. Such a model which is consistent with the properties of anelastic media can be represented mechanically by a combination of springs and dash‐pots. A suitable system can be constructed by the parallel connection of several standard linear elements and is referred to as the general standard linear solid rheology. Two relaxation functions that describe the dilatational and shear dissipation mechanisms of the medium are needed. This model properly describes the short and long term behaviors of materials with memory and is the basis for describing viscoelastic wave propagation. This work presents two‐dimensional (2-D) and three‐dimensional (3-D) forward modeling in linear viscoelastic media. The theory implements Boltzmann’s superposition principle based on a spectrum of relaxation mechanisms in the time‐domain equation of motion by the introduction of the memory variables. The algorithm uses a polynomial interpolation of the evolution operator for time integration and the Fourier pseudospectral method for computation of the spatial derivatives. This scheme has spectral accuracy for band‐limited functions with no temporal or spatial dispersion, a very important fact in anelastic wave propagation. Examples are given of how to pose typical problems of viscoelastic forward modeling for geophysical problems in two and three dimensions. A model separating an elastic medium of a viscoelastic medium with similar elastic moduli but different attenuations shows that the interface generates appreciable reflected energy. A second example computes the response of a single interface in the presence of highly dissipative sandstone lenses, properly simulating the anelasticity of direct and converted P‐ and S‐waves. A common‐shot reflection survey over a gas cap reservoir indicates that attenuation significantly affects the bright spot response. 3-D viscoelastic modeling requires twice the memory storage of 3-D viscoacoustic modeling when one dissipation mechanism is used for each wave mode. Simulation in a 3-D homogeneous viscoelastic medium shows how the anelastic characteristics of the different modes can be controlled independently. The result of this simulation is compared to the analytical solution indicating sufficient accuracy for many applications.
First‐break refraction event picking and seismic data trace editing using neural networks
Authors: McCormack Michael D. , Zaucha David E. , Dushek Dennis W.
Published: October 2002

Interactive seismic processing systems for editing noisy seismic traces and picking first‐break refraction events have been developed using a neural network learning algorithm. We employ a backpropagation neural network (BNN) paradigm modified to improve the convergence rate of the BNN. The BNN is interactively “trained” to edit seismic data or pick first breaks by a human processor who judiciously selects and presents to the network examples of trace edits or refraction picks. The network then iteratively adjusts a set of internal weights until it can accurately duplicate the examples provided by the user. After the training session is completed, the BNN system can then process new data sets in a manner that mimics the human processor. Synthetic modeling studies indicate that the BNN uses many of the same subjective criteria that humans employ in editing and picking seismic data sets. Automated trace editing and first‐break picking based on the modified BNN paradigm achieve 90 to 98 percent agreement with manual methods for seismic data of moderate to good quality. Productivity increases over manual editing, and picking techniques range from 60 percent for two‐dimensional (2-D) data sets and up to 800 percent for three‐dimensional (3-D) data sets. Neural network‐based seismic processing can provide consistent and high quality results with substantial improvements in processing efficiency.
Relation of thorium‐normalized surface and aerial radiometric data to subsurface petroleum accumulations
Authors: Saunders Donald F. , Burson K. Ray , Branch Jim F. , Thompson C. Keith
Published: October 2002

A new exploration method has been developed using surface and aerial gamma‐ray spectral measurements in prospecting for petroleum in stratigraphic and structural traps. Formerly troublesome lithologic and environmental variables are suppressed by correcting potassium and uranium readings using a new process of thorium normalization. Normalized potassium shows characteristic low concentrations above petroleum deposits. Normalized uranium shows higher values than normalized potassium over petroleum and generally lower values elsewhere. We attribute these anomalies to effects of microbial consumption of microseeping light hydrocarbons. Studies of National Uranium Resource Evaluation (NURE) Program aerial, gamma‐ray, spectral data covering portions of six states have shown characteristic normalized potassium and uranium anomalies above 72.7 percent of 706 oil and gas fields. Additionally, an average of 27 similar untested anomalies were found for each 1000 square mi (2600 square km) covered. Similar aerial gamma‐ray spectral data are available over large portions of potential petroleum areas of the U.S. including Alaska and Australia. Preliminary tests in two basins in Australia showed positive correlation between radiometrically favorable areas and known oil and gas regions. Ground‐based, gamma‐ray, spectral measurements found the same types of potassium and uranium anomalies over all twelve fields evaluated. Since 1988, our research of surface radiometric data coupled with soil gas hydrocarbon and soil magnetic susceptibility surveys has resulted in discovery of four oil and gas fields in Concho County, Texas.
Dip‐moveout error in transversely isotropic media with linear velocity variation in depth
Authors: Larner Ken L.
Published: October 2002

Levin modeled the moveout, within common‐midpoint (CMP) gathers, of reflections from plane‐dipping reflectors beneath homogeneous, transversely isotropic media. For some media, when the axis of symmetry for the anisotropy was vertical, he found departures in stacking velocity from predictions based upon the familiar cosine‐of‐dip correction for isotropic media. Here, I do similar tests, again with transversely isotropic models with vertical axis of symmetry, but now allowing the medium velocity to vary linearly with depth. Results for the same four anisotropic media studied by Levin show behavior of dip‐corrected stacking velocity with reflector dip that, for all velocity gradients considered, differs little from that for the counterpart homogeneous media. As with isotropic media, traveltimes in an inhomogeneous, transversely isotropic medium can be modeled adequately with a homogeneous model with vertical velocity equal to the vertical rms velocity of the inhomogeneous medium. In practice, dip‐moveout (DMO) is based on the assumption that either the medium is homogeneous or its velocity varies with depth, but in both cases isotropy is assumed. It turns out that for only one of the transversely isotropic media considered here—shale‐limestone—would v(z) DMO fail to give an adequate correction within CMP gathers. For the shale‐limestone, fortuitously the constant‐velocity DMO gives a better moveout correction than does the v(z) DMO.
A versatile shotgun source for engineering and groundwater seismic surveys
Authors: Parker James C. , Pelton John R. , Dougherty Martin E.
Published: October 2002

We describe an electrical seismic gun that is capable of firing 8-gauge blank black powder shells in a water‐filled borehole under relatively high hydrostatic pressures. The new seismic gun is a modified version of the electrical shotgun source for engineering seismic surveys introduced by Pullan and MacAulay (1987). Our modifications seal the firing circuit and 8-gauge shell against water entry so underwater detonation will occur reliably at depths to at least 80 m (0.9 MPa atmospheric pressure). Source energy is controlled by varying the size of the black powder load in the shell from 50 grains to 500 grains (10 kJ to 100 kJ). Although our seismic gun may be used in any seismic application suitable for modest explosive charges, it was initially developed as a versatile source for use in seismic investigations of the shallow subsurface (primarily engineering and groundwater studies). As of this writing, the gun has been used for optimum offset and CMP high‐resolution seismic reflection profiling, engineering refraction surveys, fixed‐source and variable‐source noise tests, and vertical traveltime measurements in water wells. Other potential uses include VSP and borehole‐to‐surface or borehole‐to‐borehole seismic tomography.
Differential‐equation‐based seismic data filtering
Authors: Li Jianchao , Larner Ken
Published: October 2002

Suppressing noise and enhancing useful seismic signal by filtering is one of the important tasks of seismic data processing. Conventional filtering methods are implemented through either the convolution operation or various mathematical transforms. We describe a methodology for studying and implementing filters, which, unlike conventional filtering methods, is based on solving differential equations in the time and space domain. We call this differential‐equation‐based filtering (DEBF). DEBF does not require that seismic data be stationary, so filtering parameters can vary with every time and space point. Examples with two‐dimensional (2-D) synthetic and field seismic data demonstrate that the DEBF method accomplishes the desired time‐ and space‐varying temporal and move‐out filtering at lower cost than conventional frequency‐wavenumber‐domain filtering. The computational advantage in 3-D would be much greater.
Nonlinear inversion of resistivity sounding data
Authors: Sen Mrinal K. , Bhattacharya Bimalendu B. , Stoffa Paul L.
Published: October 2002

The resistivity interpretation problem involves the estimation of resistivity as a function of depth from the apparent resistivity values measured in the field as a function of electrode separation. This is commonly done either by curve matching using master curves or by more formal linearized inversion methods. The problems with linearized inversion schemes are fairly well known; they require that the starting model be close to the true solution. In this paper, we report the results from the application of a nonlinear global optimization method known as simulated annealing (SA) in the direct interpretation of resistivity sounding data. This method does not require a good starting model but is computationally more expensive. We used the heat bath algorithm of simulated annealing in which the mean square error (difference between observed and synthetic data) is used as the energy function that we attempt to minimize. Samples are drawn from the Gibbs probability distribution while the control parameter the temperature is slowly lowered, finally resulting in models that are very close to the globally optimal solutions. This method is also described in the framework of Bayesian statistics in which the Gibbs distribution is identified as the a posteriori probability density function in model space. Computation of the true posterior distribution requires computation of the energy function at each point in model space. However, a fairly good estimate of the most significant portion(s) of the function can be obtained from simulated annealing run in a reasonable computation time. This can be achieved by making several repeat runs of SA, each time starting with a new random number seed so that the most significant portion of the model space is adequately sampled. Once the posterior density function is known, many measures of dispersion can be made. In particular, we compute a mean model and the a posteriori covariance matrix. We have applied this method successfully to synthetic and field data. The resulting correlation covariance matrices indicate how the model parameters affect one another and are very useful in relating geology to the resulting resisitivity values.
Measure for the resolving power and bias effect in the nonlinear inverse analysis of geophysical potential fields
Authors: Pan Guocheng
Published: October 2002

Several measures are proposed for the power of resolution and the bias effect of nonlinearity in the inverse analysis of geophysical potential fields. They are the power of complete resolution for the entire system of both data and parameters, the power of partial resolution for individual data prediction and parameter estimation, and the bias for the effect of linearization of a nonlinear function. Relations between the measures for the resolution power and bias are derived. The tradeoff relations between the resolving power and estimation variance are also demonstrated. All these measures are tested on a synthetic gravity data set. A two‐dimensional (2-D) forward gravity model is employed to demonstrate the use of the measures proposed in this study. The selection of the reference depth [Formula: see text] and the number of nonzero eigenvalues (q) is highlighted based on the 2-D prism forward model. The “best” [Formula: see text] is that value that produces the least curvature in the plot of singular values versus q. The choice of q is considered “best” when it meets most of the critical requirements (e.g., small bias and high resolving power) and then satisfies secondary important needs (e.g., estimation variance).
On: “Ultrasonic velocity and anisotropy of hydrocarbon source rocks” by L. Vernik and A. Nur (May 1992 GEOPHYSICS, p. 727‐735)
Authors: Eaton David W.
Published: October 2002

Vernik and Nur have reported anisotropy parameters for the Bakken formation determined from ultrasonic measurements. Their paper showed that the Bakken shale is strongly anisotropic, exhibiting transverse isotropy with a vertical symmetry axis. A significant part of their conclusions were devoted to the apparently small values of Thomsen’s (1986) δ parameter for this rock, which is defined in terms of stiffness coefficients as [Formula: see text]For seismic exploration, δ is perhaps the most important of Thomsen’s three anisotropy parameters, since it influences both the P‐wave moveout velocity and the AVO slope near zero offset (Thomsen, 1986; Banik, 1987). However, as pointed out by Banik (1987), the numerical value of δ is highly sensitive to small errors in the elastic stiffnesses. Moreover, the magnitude of [Formula: see text], one of the required stiffness coefficients in (1), depends on the choice of phase or group velocity to interpret the measurements, as explained below.
Vertical open fractures and shear‐wave velocities derived from VSPs, full waveform acoustic logs, and televiewer data
Authors: Lefeuvre Frédéric , Turpening Roger , Caravana Carol , Born Andrea , Nicoletis Laurence
Published: October 2002

Fracture or stress‐related shear‐wave birefringence (or azimuthal anisotropy) from vertical seismic profiles (VSPs) is commonly observed today, but no attempt is made to fit the observations with observed in‐situ fractures and velocities. With data from a hard rock (limestones, dolomites, and anhydrites) region of Michigan, fast and slow shear‐wave velocities have been derived from a nine‐component zero offset VSP and compared to shear‐wave velocities from two full waveform acoustic logs. To represent the shear‐wave birefringence that affects the shear wave’s vertical propagation, a propagator matrix technique is used allowing a local measurement independent of the overburden layers. The picked times obtained by using a correlation technique have been corrected in the birefringent regions before we compute the fast and slow velocities. Although there are some differences between the three velocity sets, there is a good fit between the velocities from the shear‐wave VSP and those from the two logs. We suspect the formations showing birefringence to be vertically fractured. To support this, we examine the behavior of the Stoneley wave on the full waveform acoustic logs in the formations. In addition, we analyze the borehole televiewer data from a nearby well. There is a good fit between the fractures seen from the VSP data and those seen from the borehole.
Westhazel General Petroleums Pool: Case history of a salt‐dissolution trap in west‐central Saskatchewan, Canada
Authors: Anderson Neil L. , Cederwall Dale A.
Published: October 2002

The Westhazel General Petroleums (GP) Pool of west‐central Saskatchewan, Canada, produces from the GP member of the Lower Cretaceous Mannville Group. This reservoir is structurally closed across the updip, eastern dissolutional edge of the underlying Middle Devonian rock salt of the Leofnard Member, Prairie Formation. The leaching of these salts occurred in post‐Mannville time in the Westhazel area and caused the regional southwest dip of the General Petroleums member to be locally reversed. The Westhazel GP Pool, from a geophysical perspective, is characteristic of many of the shallow Lower Cretaceous pools situated along the dissolutional edge of the Prairie salt. The thin, 10 m reservoir facies at Westhazel does not exhibit a diagnostic signature on either seismic or gravity data. Rather, it is the updip edge of the salt across which the reservoir is closed that can be mapped using geophysical techniques. On seismic data, the dissolutional edge of the Prairie salt is characterized by: (1) a subtle decrease in the amplitude and lateral coherency of the underlying Winnipegosis event; (2) a gradual thinning of key encompassing Paleozoic intervals; (3) dip reversal along the Beaverhill Lake (Late Devonian) event; (4) dip reversal along the Mannville (Lower Cretaceous) event; and (5) time‐structural “push down” of Lower Cretaceous and underlying reflections in areas of recent salt dissolution. On the gravity profile, the edge of the salt is manifested as a 1.5 mGal anomaly. The interpretation of both geophysical data sets is consistent with available geologic control.
Elastic waves through a simulated fractured medium
Authors: Hsu Chaur‐Jian , Schoenberg Michael
Published: October 2002

Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelengths much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, we inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describe the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.
Some effects of velocity variation on AVO and its interpretation
Authors: Xu Yu , Gardner G. H. F. , McDonald J. A.
Published: October 2002

In recent years interest has increased in the interpretation of the amplitude variation of reflected signals as a function of offset (AVO). A more meaningful relationship for interpreting reflection coefficients at the target horizon is amplitude variation with incident angle (AVA). The challenge is to convert from AVO to AVA. The effects of velocity variation in the overburden on amplitude variation with offset (AVO) and on the final inversion of AVO data into velocity, density, and Poisson’s ratio can be significant. Examples are given here for subsurface medium with a vertical velocity gradient range of [Formula: see text] to [Formula: see text]. When the medium is treated as homogeneous in the conversion from AVO to AVA, this velocity variation causes significant errors (about 10 percent) in both the gradient of AVA and in the normal incident reflection coefficient. Such errors produce errors of similar magnitude in the inversion of AVA data into the elastic parameters of velocity, Poisson’s ratio, and density. The errors depend on the velocity gradient, the offset range, the elastic parameter contrast across the interface, and the interface depth.
Partially coherent migration
Authors: Lee Delman , Jackson Geoffrey M. , Mason Iain M.
Published: October 2002

Partially coherent migration reduces the spurious details introduced by velocity macro‐model imperfections. In a partially coherent migration, instead of summing coherently over the full aperture to achieve maximum lateral resolution, (1) a coherent stack is performed over a limited window width, and then (2) the collection of coherent stacks for different windows along the full aperture are summed incoherently to produce an amplitude value for each output point. Amplitude accuracy of a migration is improved with some sacrifice in spatial (lateral) resolution. A parameter in partially coherent migration is the running coherent window width, which accounts for the spatial correlation of errors in the velocity model. The coherent window width controls the trade‐off between signal‐to‐noise ratio and lateral resolution. Assuming that timing errors introduced by imperfections of a velocity macro‐model are from a zero‐mean stationary Gaussian process, partially coherent migration is shown to raise the signal‐to‐noise ratio of the migrated image as compared to a conventional migration. The two competing aspects of signal‐to‐noise ratio and lateral resolution of the partially coherent migration in the presence of timing errors are analyzed in a stochastic framework. The intuitively attractive idea of limiting the coherent window width to the correlation length of the timing errors is confirmed numerically.
Modeling of streaming potential responses caused by oil well pumping
Authors: Wurmstich Burkhard , Morgan Frank Dale
Published: October 2002

The occurrence of streaming potentials is directly related to movement of fluids in the subsurface. To investigate whether streaming potential measurements in boreholes and at the surface can be used to monitor subsurface flow and detect subsurface flow patterns in oil reservoirs, we model streaming potential responses caused by oil well pumping in monitoring wells and at the earth's surface. Since the model parameters: permeabilities, cross‐coupling properties, and electric conductivities depend on a few basic rock‐physics parameters such as brine conductivity, amount of water saturation, and porosity, the model parameters are evaluated self‐consistently using rock‐physics models. Using a threedimensional, (3-D) finite‐difference algorithm, the governing differential equations that are drawn from nonequilibrium thermodynamics are solved numerically in three self‐consistent steps: solution of the hydraulic problem, computation of the streaming current sources based on the principle of conservation of charge, and solution of the resistivity problem. For simple models of oil reservoirs at shallow depth between 325 m and 500 m, we assume a total production rate of 500 bbl/day for all phases (gas/water or oil/water), a porosity of 0.2 in the reservoir, brine conductivities in the range of 0.3 S/m to 1.0 S/m, and water saturations in the range of 0.7 to 1.0. Maximum values of the computed streaming potential response are less than 0.6 mV at the surface and less than 9 mV in the monitoring wells. The streaming potential response depends on brine conductivity, conductivity structure, well casing, and reservoir dimensions and decreases rapidly with distance from the production well. The parameterization of the models establishes bounds for the expected streaming potential response that varies by approximately one order of magnitude. Because of the ac nature of pumping processes, signal stacking could perhaps be used to make the expected small signals discernible. Our models are mainly limited by poor knowledge of in‐situ, cross‐coupling properties.
The application of 3-D depth migration to the development of an Alaskan offshore oil field
Authors: Whitcombe David N. , Murray Eugene H. , St. Aubin Laurie A. , Carroll Randall J.
Published: October 2002

Inconsistencies in fault positioning between overlapping 3-D seismic surveys over the northwestern part of the Endicott Field highlighted lateral positioning errors of the order of 1000 ft (330 m) in the seismic images. This large uncertainty in fault positioning placed a high and often unacceptable risk on the placement of wells. To quantify and correct for the seismic positioning error, 3-D velocity models were developed for ray‐trace modeling. The lateral positioning error maps produced revealed significant variation in the mispositioning within the Endicott Field that were mainly caused by lateral variations in permafrost thickness. These maps have been used to correct the positions of mapped features and have enabled several wells to be successfully placed close to major faults. Prior to this analysis, these wells were considered too risky to place optimally. The seismic data were 3-D poststack depth migrated with the final velocity model, producing a repositioned image that was consistent with the ray‐trace predictions. Additionally, a general enhancement of data imaging improved the interpretability and enabled the remapping and subsequent successful development of the peripheral Sag Delta North accumulation.
Approximate polarization of plane waves in a medium having weak transverse isotropy
Authors: Rommel Björn E.
Published: October 2002

Many real rocks and sediments relevant to seismic exploration can be described by elastic, transversely isotropic media. The properties of plane waves propagating in a transversely isotropic medium can be given in an analytically exact form. Here the polarization is recast into a comprehensive form that includes Daley and Hron’s normalization and Helbig’s full range of elastic constants. But these formulas are rather lengthy and do not easily reveal the features caused by anisotropy. Hence Thomsen suggested an approximation scheme for weak transverse isotropy. His derivation of the approximate polarization, however, is based on a property that is not suitable to measure small differences between an isotropic and a weakly transversely isotropic medium. Therefore the approximation of the polarization is recast. The corrected approximation does show a dependence on weak transverse isotropy. This feature can be viewed as an additional rotation of the polarization with respect to the wavenormal. It depends on the anisotropy as well as the inverse velocity ratio. An approximate condition of pure polarization, which occurs in certain directions, is also obtained. The corrected approximation results in a better match of the approximate polarization with the exact one, providing the assumption of weak transverse isotropy is met. When comparing the additional rotation with the deviation of the (observable) ray direction from the wavenormal, the qSV‐wave indicates transverse isotropy most clearly.
Linearization of the eikonal equation
Authors: Aldridge David F.
Published: October 2002

Seismic traveltime tomography is a nonlinear inverse problem wherein an unknown slowness model is inferred from the observed arrival times of seismic waves. Nonlinearity arises because the raypath connecting a given source and receiver depends on the slowness. Specifically, if L(s) designates a raypath through the slowness model s between two fixed endpoints, then the path integral for traveltime [Formula: see text] is a nonlinear functional of s because it does not, in general, satisfy the superposition condition (i.e., [Formula: see text] where [Formula: see text] and [Formula: see text] are two different slowness models). The tomographic inverse problem can be solved after linearizing the traveltime expression about a known slowness model [Formula: see text]. This linearized expression is usually obtained by appealing to Fermat’s principle (e.g., Nolet, 1987). Alternately, the required relation can be rigorously derived via ray‐perturbation theory (Snieder and Sambridge, 1992). The purpose of this note is to present a straightforward derivation of the same result by linearizing the eikonal equation for traveltimes. Wenzel (1988) adopts this approach, but his method of proof cannot be generalized to heterogeneous 3-D media. A full 3-D treatment is given here. The proof is remarkably simple, and thus it is quite possible that others have discovered it previously.
Low‐ and high‐frequency radiation from seismic sources in cased boreholes
Authors: Gibson Richard L. , Peng Chengbin
Published: October 2002

An accurate characterization of borehole seismic sources is necessary to model and interpret waveforms observed in crosshole and reverse vertical seismic profiling (VSP) surveys, since the radiation pattern of a source will directly influence the amplitudes of elastic wave arrivals at receiver locations. Any attempt to study these data or perform inversions of amplitude data without incorporating the borehole effects will have serious limitations. Most previous studies of borehole seismic source radiation patterns have applied low‐frequency approximations to develop expressions for the radiation patterns of volume injection or stress sources (Heelan, 1953; White, 1960; White and Senghush, 1963; Lee and Balch, 1982; Lee, 1986; Kurkjian, 1986; Meredith, 1990; Winbow, 1991; Ben‐Menahem and Kostek, 1991). For example, Lee and Balch (1982) used this approach, along with a steepest descent solution, to derive closed‐form analytic expressions for the asymptotic far‐field radiation from sources located in uncased boreholes. Meredith (1990) applied the same methodology to study the radiation patterns of a variety of types of sources, though he also computed full waveform synthetic seismograms using the discrete wavenumber method. Likewise, Greenfield (1978) used full waveform numerical solutions to compute seismograms for force sources applied to the wall of a cylindrical cavity.
3-D resistivity inversion using the finite‐element method
Authors: Sasaki Yutaka
Published: October 2002

With the increased availability of faster computers, it is now practical to employ numerical modeling techniques to invert resistivity data for 3-D structure. Full and approximate 3-D inversion methods using the finite‐element solution for the forward problem have been developed. Both methods use reciprocity for efficient evaluations of the partial derivatives of apparent resistivity with respect to model resistivities. In the approximate method, the partial derivatives are approximated by those for a homogeneous half‐space, and thus the computation time and memory requirement are further reduced. The methods are applied to synthetic data sets from 3-D models to illustrate their effectiveness. They give a good approximation of the actual 3-D structure after several iterations in practical situations where the effects of model inadequacy and topography exist. Comparisons of numerical examples show that the full inversion method gives a better resolution, particularly for the near‐surface features, than does the approximate method. Since the full derivatives are more sensitive to local features of resistivity variations than are the approximate derivatives, the resolution of the full method may be further improved when the finite‐element solutions are performed more accurately and more efficiently.
Frequency‐wavenumber elastic inversion of marine seismic data
Authors: Zhao Huasheng , Ursin Bjørn , Amundsen Lasse
Published: October 2002

We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time‐space domain into the frequency‐wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least‐squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency‐wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer‐recursive formulas. The limited‐aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low‐frequency trends of the S‐wave velocity and density are found when the initial P‐wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.
The propagator matrix related to the Kirchhoff‐Helmholtz integral in inverse wavefield extrapolation
Authors: Amundsen Lasse
Published: October 2002

The Kirchhoff‐Helmholtz formula for the wavefield inside a closed surface surrounding a volume is most commonly given as a surface integral over the field and its normal derivative, given the Green’s function of the problem. In this case the source point of the Green’s function, or the observation point, is located inside the volume enclosed by the surface. However, when locating the observation point outside the closed surface, the Kirchhoff‐Helmholtz formula constitutes a functional relationship between the field and its normal derivative on the surface, and thereby defines an integral equation for the fields. By dividing the closed surface into two parts, one being identical to the (infinite) data measurement surface and the other identical to the (infinite) surface onto which we want to extrapolate the data, the solution of the Kirchhoff‐Helmholtz integral equation mathematically gives exact inverse extrapolation of the field when constructing a Green’s function that generates either a null pressure field or a null normal gradient of the pressure field on the latter surface. In the case when the surfaces are plane and horizontal and the medium parameters are constant between the surfaces, analysis in the wavenumber domain shows that the Kirchhoff‐Helmholtz integral equation is equivalent to the Thomson‐Haskell acoustic propagator matrix method. When the medium parameters have smooth vertical gradients, the Kirchhoff‐Helmholtz integral equation in the high‐frequency approximation is equivalent to the WKBJ propagator matrix method, which also is equivalent to the extrapolation method denoted by extrapolation by analytic continuation.
Electrode arrays for measuring groundwater flow direction and velocity
Authors: White P. A.
Published: October 2002

The movement of 2000 liters of salt water after injection into groundwater within gravels a few meters below the ground surface at three injection sites was traced by six different resistivity monitoring arrays; the resistivity rectangle, Schlumberger sounding, Wenner sounding, Wenner fixed‐spacing, mise‐à‐la‐asse and downhole electrode array. Five of the arrays indicated groundwater flow direction and seepage velocity. As evidence indicates, similar geological and hydrogeological conditions exist at the injection sites. Therefore, comparisons between the sensitivity of the five arrays can be made and are as follows: resistivity rectangle—maximum decrease of 60 percent in derived potential differences; Schlumberger sounding— maximum decrease of 28 percent in measured apparent resistivity; Wenner sounding—maximum decrease of 20 percent in measured apparent resistivity, Wenner fixedspacing—maximum decrease of 22 percent in apparent resistivity; downhole electrode—maximum decrease of 38 percent in measured resistance. Measured potentials and derived values of potential gradient measured by the mise‐à‐la‐masse array indicated groundwater flow direction but not seepage velocity. Estimates of seepage velocity given by the resistivity arrays for the three salt water injection sites are between 260 ± 40 m/day and 700 ±100 m/day. These estimates are in broad agreement with values of seepage velocity derived from the point‐dilution technique, from previous salt water injection experiments, and from groundwater conductivity measurements using downhole probes.
The application of TEM to Cyprus‐type massive sulfide exploration in Cyprus
Authors: Cooper Nick J. , Swift Roland
Published: October 2002

Cyprus‐type massive sulfide mineral deposits are difficult geophysical targets with small physical parameter contrasts between the silicically altered mineralization and the altered conductive pillow lavas in which they occur. During the period 1988–1991 two research projects studied the application of the transient electromagnetic (TEM) sounding method to exploration for such deposits. Initially, we tested the method over three mapped mineral deposits at Klirou, Philani, and Strongyli using SIROTEM MkI and IISE instruments. Surveys using both coincident‐ and central‐loop configurations failed to detect the mineralization at all three sites. Conductive anomalies seen beneath two of the deposits might be related to groundwater contamination by the mineral ions and may represent an exploration target. Based on this work, we implemented a new exploration strategy using TEM for structural mapping to identify possible mineral bearing structures. Initial results from the Mathiatis‐Sha Prospect resolved some interesting structures across the area.
Influence of steel casings on electromagnetic signals
Authors: Wu Xu , Habashy Tarek M.
Published: October 2002

Most wells in oil fields are cased with metal. The feasibility of measuring low‐frequency magnetic fields through such steel‐cased wells is of great interest for monitoring fluid movement during production. We report on experimental and modeling results regarding the effect of steel casing on electromagnetic signals transmitted through them. This effect includes the attenuation and phase shift of a signal diffusing through the casing wall. Sample casings are studied under low field strength in the linear regime where the casing's electrical properties are independent of the applied signals. Frequency spectra are measured for transverse‐electric and transverse‐magnetic polarizations from 0.1 Hz to 1 kHz. Numerical models, developed to simulate the casing response, match the experimental data very well. Finally, studies of the effects of the earth’s magnetic field and casing remanent magnetization show that these steady biases do not affect the ac signal detection.
Tests of Australian aerial radiometric data for use in petroleum reconnaissance
Authors: Saunders Donald F. , Branch J. F. , Thompson C. K.
Published: October 2002

Recon Exploration Pty. Ltd. has successfully completed initial testing of a new method for processing and interpretation of AGSO’s (Australian Geological Survey Organization, formerly Bureau of Mineral Resources) aerial gamma‐ray spectrometer data for petroleum exploration in the Canning Basin, Western Australia and the Otway Basin, Victoria. Count‐rate data for potassium and uranium were normalized to the thorium count rate for each sample to suppress unwanted effects of variations in surface lithology or soil type, soil moisture, vegetation cover, and counting geometry. The Canning Basin test area included five producing oil fields. All except one clearly exhibit significant and characteristic radiometric anomalies which include negative normalized potassium and more positive normalized uranium values. The Otway Basin test areas included PPL-1 commercial gas production which is associated with a group of significant radiometric anomalies similar to those in the Canning Basin. These results are similar to extensive ongoing tests in the U.S. and are explained in terms of well‐understood geological, geochemical, and geophysical models. Based on 69 wells in the three test areas, it is estimated that the chance of encountering hydrocarbons (economic production or shows) in wells within the radiometrically favorable zones is about 2.6 times greater than outside the favorable areas.
Depth‐imaging resolution of 3-D seismic recording patterns
Authors: von Seggern D.
Published: October 2002

The prestack imaging resolution capabilities of various 3-D seismic recording patterns are revealed when a Born‐approximate theory is applied to backscattered waves. The 3-D imaging resolution of such patterns is compactly studied using a constant‐velocity model with a point scatterer or a line scatterer at depth. By use of a well‐known acoustic imaging formula, it is shown that the resolution of a point scatterer in the X and Y directions is not significantly different for various realistic layouts of sources and receivers in land‐type recording, even though the recording patterns appear to be greatly dissimilar, provided the aperture remains constant. For marine‐type survey patterns, the image is almost as well‐resolved in the crossline direction as the inline direction. This is true whether the scattering object is a point or a line. In marine surveying, symmetric resolution of subsurface features can be achieved by conducting two orthogonal surveys at half the density of one unidirectional survey.