bluuebunny/crossref_metadata_2025 huggingface dataset:
Relations between potential fields and some equivalent sources
Authors: Pedersen L. B.
Published: October 2002

The concept of equivalent sources is described from first principles. Two types of sources that produce the same magnetic field are studied in detail: thin sheets and uniaxially magnetized half‐spaces. Simple analytic solutions show that their magnetization variations are essentially given by the pseudogravity field and the magnetic field, respectively. While the former varies slowly to account for the slow variation in the vertically integrated magnetization, the latter varies rapidly to account for the spatial variation in rock magnetization close to the observation points. An extension of these simple distributions is the sandwich distribution. Using statistical arguments, we construct sandwich distributions. The depths and mean magnetizations of each layer are found from the decay of the azimuthally averaged power spectrum. The equivalent layer magnetizations closely resemble the magnetic field anomaly when upward‐continued to a height equal to the mean depth of the layer.
A robust integral equation solution for electromagnetic scattering by a thin plate in conductive media
Authors: Walker P. W. , West G. F.
Published: October 2002

An integral equation solution for electromagnetic (EM) scattering by a thin plate robustly models scattering in either perfectly resistive, very resistive, or conducting host media. Because the solution is not restricted to modeling certain ranges of host conductivity, it can be used to model scattering over the large ranges in conductivity encountered in geophysics. The solution is developed around a pair of coupled integral equations for the scattering distributions on the plate. In one equation, the scattering distribution is the scalar potential set up by the scattered charge distribution. In the other, it is the component of the scattered magnetic field perpendicular to the plate. The equations are solved numerically using the Galerkin method with simple polynomial basis functions. To find the fields scattered by the conductor, the scattered current density is first calculated from the scalar potential and the magnetic field. The scattered fields can then be found by integrating over the scattered current density. To test the solution, we model horizontal loop EM responses with our solution and compare the results with those from two established integral equation solutions. One of these solutions models pure induction and is used to test our solution when the host is perfectly resistive. Agreement with this solution is very good. Comparisons with the other solution, an electric field integral equation, tests our solution when the host medium is conductive. Agreement with the latter solution is good where induction is not too strong: i.e., where the electric‐field solution is known to work well. Our solution therefore can accurately model EM scattering by a plate in a host medium with any conductivity.
A brief comparison of some Kirchhoff integral formulas for migration and inversion
Authors: Docherty Paul
Published: October 2002

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.
Standardization in gravity reduction
Authors: LaFehr T. R.
Published: October 2002

Gravity reduction standards are needed to improve anomaly quality for interpretation and to facilitate the joining together of different data sets. To the extent possible, data reduction should be quantitative, objective, and comprehensive, leaving ambiguity only to the interpretation process that involves qualitative, subjective, and geological decisions. The term (Bouguer anomaly) describes a field intended to be free of all nongeologic effects—not modified by a partial geologic interpretation. Measured vertical gradients of gravity demonstrate considerable variation but do not suggest, as often reported, that the normal free‐air gradient is in error or needs to be locally adjusted. Such gradients are strongly influenced by terrain and, to a lesser extent, by the same geologic sources which produce Bouguer anomalies. A substantial body of existing literature facilitates the comprehensive treatment of terrain effects, which may be rigorously implemented with current computer technology. Although variations in topographic rock density are a major source of Bouguer anomalies, a constant density appropriate to the area under investigation is normally adopted as a data reduction standard, leaving a treatment of the density variations to the interpretation. A field example from British Columbia illustrates both the variations in vertical gravity gradients which can be encountered and the conclusion that the classical approach to data reduction is practically always suitable to account for the observed effects. Standard data reduction procedures do not (and should not) include reduction‐to‐datum. The interpreter must be aware, however, that otherwise “smooth” regional Bouguer anomalies caused by regional sources do contain high‐frequency components in areas of rugged topography.
Consistent modeling of the electrical and elastic properties of sedimentary rocks
Authors: Sheng Ping
Published: October 2002

An effective medium theory is formulated which reproduces many of the observed electrical and elastic characteristics of sedimentary rocks within a unified framework. The effective medium consists of fluid, solid, and cement components, with the component material properties related to those of the composite through a differential effective medium (DEM) scheme. The resulting microstructure of the composite both conducts electricity through the fluid phase and supports shear. Besides deriving Archie’s law, the theory gives an excellent account of the shear‐wave and compressional‐wave velocity correlations, and predicts corrections to the Wyllie equation that are consistent with observed deviations. The three‐component DEM also accommodates clay conductivity and finite‐frequency dielectric behavior.
Monitoring leaks from storage ponds using resistivity methods
Authors: Van Gregory P. , Park Stephen K. , Hamilton Patrick
Published: October 2002

Two common methods for detecting leaks from storage ponds are detection of contaminants in monitoring wells and use of two asphaltic liners with a seep collection system between them. However, significant quantities of the impounded fluid may have leaked by the time contaminants are detected in the wells. Double liners have the advantage that leaks are detected before the fluid escapes into the environment, but they are expensive. An alternative approach is to use electrical resistivity methods to detect leaks. Several studies have mapped conductive zones with electrical methods and have inferred the presence of contaminated groundwater (e.g., Greenhouse and Harris, 1983). A fundamental ambiguity in any such survey is that the subsurface may contain conductive sediments (such as clay or silt) that may be mistaken for contaminated water, however. Parra (1988) proposed an alternative method that detects holes in a liner by mapping the electrical response due to a short circuit across an insulating liner which results from conductive fluid in a hole. An important result is that the electrical response of the leak is detectable only within a few meters with this method.
Tuning effect and interference reflections from thin beds and coal seams
Authors: Gochioco Lawrence M.
Published: October 2002

The Ricker and Widess criteria of resolving thin beds are established and widely accepted axioms. Analysis of tuning effects from an isolated thinning bed is commonly used in estimating the thickness of a thin bed. However, frequency and amplitude tuning effects may also result from a sequence of thin beds. Depending on the thicknesses, acoustic properties, and the relative location of thin beds in space, tuning effects from interference reflections can sometimes deform the seismic wavelet and cause complex waveforms. Coal seams as thin as 1/20 of the predominant wavelength can produce reflections, and these reflections may be a composite of primary and multiple reflections. Interference reflections from two closely spaced coal seams were recorded and used to interpret a seam anomaly (roll) that may create adverse conditions for longwall mining. The seismic data and computer model results correlated with findings of several boreholes.
Premine study of shallow coal seams using high‐resolution seismic reflection methods
Authors: Henson Harvey , Sexton John L.
Published: October 2002

Geological investigations in the Illinois Basin coalfields have shown that significant differences in safe and economical exploitation of coal depends directly on accurate mapping of the roof rock overlying the seam, as well as on geological structures in the coal measures. In roof rock transition zones above the Herrin (No. 6) coal where the nonmarine Energy shale changes to the Anna shale, a change often occurs from low to high sulfur coal and from low to high stability roof rocks. In many instances, use of borehole data alone is inadequate to locate these features in advance of mining. High‐resolution seismic reflection data collected near Harco, Illinois were used as part of premine planning to help predict roof instability, areas of low sulfur coal, and geologic disturbances. Several faults, channels, and facies changes affecting the Herrin (No. 6) and the Springfield (No. 5) coal seams at depths of 137 m and 167 m, respectively, were interpreted and modeled. One‐ and two‐dimensional synthetic seismograms calculated from geological data from drill holes along the seismic line were used to aid in the interpretion of the seismic reflection data. Results obtained from the high‐resolution reflection survey combined with drill hole information clearly show that use of borehole data alone is inadequate to locate geological features that might affect coal mine operations, even if the boreholes were spaced 25 m apart. Thus, high‐resolution reflection surveying should be employed whenever feasible for the safe and economical exploitation of coal deposits.
Reservoir sonics: A North Sea case study
Authors: Hornby Brian E. , Murphy William F. , Liu Hsui‐Lin , Hsu Kai
Published: October 2002

Full waveform sonic data, acquired in a borehole penetrating a North Sea reservoir, were used to explore new techniques for analysis and interpretation of sonic data. Analysis of direct sonic arrivals included correlations with core‐derived permeability, inversion for compressional and shear velocities, and interpretation of compressional and shear velocities in terms of formation parameters. The velocities are found to be sensitive indicators of lithology and water saturation. In addition to the standard processing for compressional and shear velocities, inversion of sonic traveltimes resulted in a compressional wave‐velocity log with a 0.15 m vertical resolution. Using a process similar to prestack seismic migration, reflected sonic arrivals were used to form images of bedding features to a distance of 12 m from the borehole. The well intersects a region of strong normal faulting. Locations of high angle features and strong dip changes on the sonic‐derived images were consistent with the locations of faults indicated on the dipmeter‐derived structural cross‐sections.
Variations of the VLF-EM primary field: Analysis of airborne survey data, New Brunswick, Canada
Authors: Vallée Marc A. , Chouteau Michel , Palacky G. J.
Published: October 2002

Variations in intensity of the primary VLF-EM field have a significant effect on the quality of airborne and ground surveys in which the total field is measured. An analysis of the results of a recent VLF-EM survey and base station records in New Brunswick, Canada, revealed major variations in the primary VLF-EM field due to changes in the transmitting power and to solar flares. To study the effect of systematic primary field variations over the survey area, VLF-EM field intensity was calculated using radio propagation model based on uniform conductive earth and anisotropic‐layered ionosphere. The model correctly predicted a decrease in the primary field generated by the NAA transmitter by about 40 percent in a direction perpendicular to a survey line. Such a change is sufficiently important to require repeated calibrations of the receiver between the survey lines. The model also indicated that the phase difference between contributions of the ground and sky waves should vary over the survey area. Such variations explain opposite polarities of sudden amplitude variations due to solar flares that were observed during the survey.
Estimating a shear modulus of a transversely isotropic formation
Authors: Ellefsen K. J. , Toksöz M. N. , Tubman K. M. , Cheng C. H.
Published: October 2002

We have developed a method that estimates a shear modulus [Formula: see text] of a transversely isotropic formation using the tube wave generated during acoustic logging. (The symmetry axis of the anisotropy is assumed to parallel the borehole.) The inversion, which is implemented in the frequency‐wavenumber domain, is based upon a cost function that has three terms: a measure of the misfit between the observed and predicted wavenumbers of the tube wave, a measure of the misfit between the current estimate for [Formula: see text] and the most‐likely value for [Formula: see text], and penalty functions that constrain the estimate to physically acceptable values. The largest contribution to the value of the cost function ordinarily comes from the first term, indicating that the estimate for [Formula: see text] depends mostly on the data. Because the cost function only has one minimum, it can be found using standard optimization methods. The minimum is well defined indicating that the estimate for [Formula: see text] is well resolved. Estimates for [Formula: see text] from synthetic data are almost always within 1 percent of their correct value. Estimates for [Formula: see text] from field data that were collected in a formation with a high clay content are typical of transversely isotropic rocks.
Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications
Authors: Lefeuvre Frédéric , Nicoletis Laurence , Ansel Valérie , Cliet Christian
Published: October 2002

An original method is presented that allows us to measure the local shear‐wave birefringence properties over any depth interval. It requires the acquisition of two shear‐wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths [Formula: see text] and [Formula: see text], the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least‐squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polarizations at a depth [Formula: see text] for two linear and mutually perpendicular polarizations at depth [Formula: see text]. This allows for the measurement of the birefringence properties in all azimuthal directions to determine the directions for which a linearly polarized shear‐wave propagates. In addition, the method can be applied to perform the deconvolution of the upgoing wavefield by the downgoing wavefield to obtain a reflection matrix. Then the matrix can be interpreted in terms of anisotropy below the receiver depths (particularly below the well bottom) and in terms of anisotropy of the reflector itself. The proposed method is validated on synthetic data and is applied to real data from the Paris basin. For this particular data set, the birefringence is located in two layers; the first layer consists of unproductive sands and clays while the second one corresponds to a carbonate oil reservoir from the Dogger formation. The natural directions in both layers are very close to the main directions known for the regional stress field. The presence of fractures in the reservoir layer can explain the strong birefringence ratio (>6 percent).
Linearized tomographic inversion of first‐arrival times
Authors: Simmons James L. , Backus Milo M.
Published: October 2002

A linearized tomographic‐inversion algorithm estimates the near‐surface slowness anomalies present in a conventional, shallow‐marine seismic reflection data set. First‐arrival time residuals are the data to be inverted. The anomalies are treated as perturbations relative to a known, laterally‐invariant reference velocity model. Below the sea floor the reference model varies smoothly with depth; consequently the first arrivals are considered to be diving waves. In the offset‐midpoint domain the geometric patterns of traveltime perturbations produced by the anomalies resemble hyperbolas. Based on simple ray theory, these geometric patterns are predictable and can be used to relate the unknown model to the data. The assumption of a laterally‐invariant reference model permits an efficient solution in the offset‐wavenumber domain which is obtained in a single step using conventional least squares. The tomographic image shows the vertical‐traveltime perturbations associated with the anomalies as a function of midpoint at a number of depths. As implemented, the inverse problem is inherently stable. The first arrivals sample the subsurface to a maximum depth of roughly 500 m (≈ one‐fifth of the spread length). The model is parameterized to consist of fifteen 20-m thick layers spanning a depth range of 80–380 m. One‐way vertical‐traveltime delays as large as 10 ms are estimated. Assuming that these time delays are distributed over the entire 20-m thick layers, velocities much slower than water velocity are implied for the anomalies. Maps of the tomographic images show the spatial location and orientation of the anomalies throughout the prospect for the upper 400 m. Each line is processed independently, and the results are corroborated to a high degree at the line intersections.
Electromagnetic modeling of 3-D structures by the method of system iteration using integral equations
Authors: Xiong Zonghou
Published: October 2002

A new approach for electromagnetic modeling of three‐dimensional (3-D) earth conductivity structures using integral equations is introduced. A conductivity structure is divided into many substructures and the integral equation governing the scattering currents within a substructure is solved by a direct matrix inversion. The influence of all other substructures are treated as external excitations and the solution for the whole structure is then found iteratively. This is mathematically equivalent to partitioning the scattering matrix into many block submatrices and solving the whole system by a block iterative method. This method reduces computer memory requirements since only one submatrix at a time needs to be stored. The diagonal submatrices that require direct inversion are defined by local scatterers only and thus are generally better conditioned than the matrix for the whole structure. The block iterative solution requires much less computation time than direct matrix inversion or conventional point iterative methods as the convergence depends on the number of the submatrices, not on the total number of unknowns in the solution. As the submatrices are independent of each other, this method is suitable for parallel processing.
A spectral scheme for wave propagation simulation in 3-D elastic‐anisotropic media
Authors: Carcione José M. , Kosloff Dan , Behle Alfred , Seriani Geza
Published: October 2002

This work presents a new scheme for wave propagation simulation in three‐dimensional (3-D) elastic-anisotropic media. The algorithm is based on the rapid expansion method (REM) as a time integration algorithm, and the Fourier pseudospectral method for computation of the spatial derivatives. The REM expands the evolution operator of the second‐order wave equation in terms of Chebychev polynomials, constituting an optimal series expansion with exponential convergence. The modeling allows arbitrary elastic coefficients and density in lateral and vertical directions. Numerical methods which are based on finite‐difference techniques (in time and space) are not efficient when applied to realistic 3-D models, since they require considerable computer memory and time to obtain accurate results. On the other hand, the Fourier method permits a significant reduction of the working space, and the REM algorithm gives machine accuracy with half the computational effort as the usual second-order temporal differencing scheme. The new algorithm provides spectral accuracy for band limited wave propagation with no temporal or spatial dispersion. Hence, the combination REM/Fourier method could be considered at present the fastest and the most accurate of all the algorithms based on spectral methods in terms of efficiency of computer time. The technique is successfully tested with the analytical solution in the symmetry axis of a 3-D homogeneous transversely isotropic solid. Computed radiation patterns in clay shale and sandstone show the characteristics predicted by the theory. A final example computes synthetic seismograms showing the effects of shear‐wave splitting of a model where an azimuthally anisotropic cracked shale layer is inside a transversely isotropic sandstone.
An integrated approach to lithologic inversion—Part I: Theory
Authors: Lörtzer G. J. M. , Berkhout A. J.
Published: October 2002

For the complex problem of lithologic inversion a new formalism is proposed, using a spatial distribution of seismic velocities ([Formula: see text]) and densities (ρ) as input. At each subsurface grid point, the inversion result consists of the most likely lithotype (gas, sand, shale, etc.) together with its related litho parameters (frame strength, porosity, etc.). The inversion method is based on the Bayesian theory of parameter estimation, allowing specification of inaccuracies in the input and the incorporation of geological knowledge. An important advantage of the proposed inversion method is that for each practical situation the necessary accuracy of [Formula: see text], [Formula: see text] and ρ can be predetermined to distinguish between specific lithotypes or to estimate a specific litho parameter with a prespecified accuracy. For instance, inversion results show that water saturation can only be estimated for an unrealistic accurate input. On the other hand, for the estimation of porosities it is generally sufficient to have compressional velocities available with a realistic accuracy.
Air‐gun signatures and the minimum‐phase assumption
Authors: Hargreaves Neil D.
Published: October 2002

The air‐gun array signature is close to minimum‐phase as a function of continuous time, in the sense that for processing purposes its phase spectrum can be derived from the Hilbert transform of the logarithm of its amplitude spectrum. This phase spectrum is different, however, from the minimum‐phase spectrum that is estimated by spiking deconvolution for a sampled and time‐windowed version of the signature. As a consequence, there can be large phase errors when spiking deconvolution is applied to an air‐gun signature or to a recording instrument response. The errors can be shown to consist primarily of a time shift and, at least visually over a limited bandwidth, a phase rotation of the output wavelet. The time shift is introduced by time sampling, while the phase rotation is caused by the spectral smoothing generated by time windowing. If the seismic wavelet as a whole, and not just the air‐gun signature, is minimum‐phase, then the total residual phase error after spiking deconvolution, including also the error due to data noise, can also be shown to be close to a time shift and a phase rotation. This may be physical justification for the phase rotation schemes that are often successful in matching seismic data and well‐log synthetics. The minimum‐phase assumption can be used for statistical air‐gun array signature deconvolution, providing that a limited amount of deterministic information (the instrument slopes and the source and receiver depths in the approach used here) is available to guide the process in those areas of the spectrum that are critical to the phase computation. Date examples show that, with care, almost identical results can then be obtained from either purely statistical deconvolution or deterministic deconvolution plus statistical deconvolution of multiples and ghosting.
Airborne gamma‐ray spectrometric background estimation using full spectrum analysis
Authors: Minty B. R. S.
Published: October 2002

We have developed a new technique for estimating airborne gamma‐ray spectrometric backgrounds. The background comes from three sources, namely aircraft, cosmic and atmospheric (radon) radiation. The aircraft and cosmic components are independently estimated by suitable calibration and the monitoring of a 3–6 MeV “cosmic” channel. Multichannel observations of the spectra are used to estimate the atmospheric background directly based on the observation that for gamma‐ray counts above the Compton continuum, the low energy [Formula: see text] photopeak at 0.609 MeV for atmospheric radiation suffers far less attenuation relative to the [Formula: see text] peak at 1.76 MeV than is the case for radiation from uranium in the ground. Since thorium and potassium sources do not contribute appreciably to these peak countrates, they can be used to calculate the contributions of radon and uranium to the observed spectrum. The technique appears to be less susceptible to errors due to the effects of variations in the vertical distribution of airborne radon and its daughters than upward‐looking detector techniques.
The effects of statics on tomographic velocity reconstructions
Authors: Squires Livia J. , Blakeslee Samuel N. , Stoffa Paul L.
Published: October 2002

Seismic first arrival times from crosshole, VSP, and reversed VSP (RVSP) experiments are collectively inverted by least‐squares for the velocity distribution between two boreholes. The tomographic reconstruction exhibits a large lateral velocity contrast that is not supported by the surface reflection data from the same location. After examining the traveltime residuals from the three tomographic datasets separately, we conclude that the velocity contrast is due primarily to static delays in the RVSP first arrival times. When a first‐order correction is made for the statics, tomographic inversion results in a velocity reconstruction that is more consistent with the surface reflection data. To isolate the velocity errors produced by the RVSP statics, we compute a residual tomogram by subtracting the statics adjusted tomogram from the original. The residual tomogram shows that the statics introduce errors not only in the region sampled by the RVSP rays, but they indirectly contaminate other regions of the tomogram as well. We reproduce this velocity error distribution as part of a model study designed to simulate the effects of statics on tomographic velocity reconstructions. Results indicate that traveltime errors on the order of 2 percent can result in tomographic velocity errors of up to 7 percent.
A generalized Maxwell‐Wagner theory for membrane polarization in shaly sands
Authors: de Lima Olivar A. L. , Sharma Mukul M.
Published: October 2002

The effects of charged clay platelets on the frequency dependent electrical properties of shaly materials are analyzed using simplified models for the membrane polarization around charged spheres immersed in electrolytic solutions, under a thin double layer approximation. The polarization is defined through two possible mechanisms: (1) a surface conductivity related with a modified Stern double layer model (S‐model) according to Schurr‐Schwarz theory; (2) a coupled electro‐diffusional mechanism occurring in a Guoy‐Chapman double layer using Fixman’s approach (D‐model). By comparing the electric potential in such microscopic models with the external potentials derived for the equivalent homogeneous sphere using a Maxwell‐Wagner approach, we obtain the total current conductivity functions for these two models. The theory, therefore, provides explicit expressions relating the total conductivity functions to the model parameters. The behavior of the S‐model is described by a complex conductivity exhibiting a simple Debye characteristic. In the D‐model, both the conductivity and the dielectric permittivity are given as complex properties, showing similar but much wider dispersion than that of a Debye substance. Our representation of the grains and their associated ionic double layers by an equivalent sphere with effective properties allows us to extend our results to simulate rocks containing clays. This is accomplished using generalized mixture equations written in terms of the total conductivity functions. The frequency behavior of both models are compared and their fit to experimental data on clay‐water systems and shaly materials suggest that the D‐model is more appropriate for representing the dielectric behavior of clay bearing rocks. The theory can be adapted to estimate the clay parameters of a shaly sandstone using electromagnetic borehole measurements.
Electromagnetic borehole fields in a layered, dipping‐bed environment with invasion
Authors: Howard A. Q. , Chew W. C.
Published: October 2002

Electromagnetic modeling of an induction sonde (1–100 kHz) in a dipping‐bed environment is a 3-D problem. The capability for such an analysis is necessary for interpretation of oil‐well logs in offshore environments where most holes are deviated. 3-D geometrical effects require vector field analysis. The method accounts for transverse magnetic mode (TM) coupling arising from surface charges deposited by eddy currents passing through bed boundaries. If borehole and invasion effects are included, the only available rigorous analytical methods are finite elements or finite‐difference techniques. These approaches require large‐scale computing. In contrast, our method is approximate and is an extension of the geometrical‐factor theory and Born approximation. The variational method does not require matrices and is numerically simpler than the more rigorous finite element method. The method uses a new electric field vector integral equation developed by Chew. The formulation accounts for low‐frequency behavior at bed boundaries where current channeling and surface charge phenomena dominate the interactions. The receiver voltage has two parts, a volumetric term [Formula: see text] and a surface term [Formula: see text]. The term [Formula: see text] reduces to the Born result when the dip angle goes to zero; [Formula: see text] accounts for the surface charge effect and is only significant when the receivers are in close proximity to a bed boundary. The local nature of the charge interaction results from double scattering events, which are necessary to produce this effect. The charge term is second order as explained intuitively in terms of polarization. The bed boundary interaction is proportional to the factor [Formula: see text], where [Formula: see text] is the dip angle, and [Formula: see text] and [Formula: see text] are the conductivities of the adjacent beds. Since the charge interaction is strongly nonlinear in conductivity, common induction log interpretation, which assumes linearity, is expected to fail near bed boundaries. Results for dip angles up to 60 degrees for variational results and eigenfunction solutions for the case of no borehole or invasion show good agreement. A few 3-D results are computed with simultaneous layering, dip, and invasion.
Formation resistivity variation due to steam flooding: A log study
Authors: Ranganayaki R. P. , Akturk S. E. , Fryer S. M.
Published: October 2002

An investigation of the pre‐ and poststeam resistivity logs, in a production pattern in a heavy‐oil field in Southern California, shows that the formation resistivity in steamed formations decreases by a factor of two to three. Shales as well as sands are affected by the steam flood. The observed drop in the resistivity of the reservoir correlates well with the increase in temperature. The study shows the potential of using resistivity variations to map and monitor thermal enhanced oil recovery process.
Acquisition and processing of wide‐aperture ground‐penetrating radar data
Authors: Fisher Elizabeth , McMechan George A. , Annan A. Peter
Published: October 2002

A 40-channel wide‐aperture ground penetrating radar (GPR) data set was recorded in a complicated fluvial/aeolian environment in eastern Canada. The data were collected in the multichannel format usually associated with seismic reflection surveys and were input directly into a standard seismic processing sequence (filtering, static corrections, common‐midpoint gathering, velocity analysis, normal‐ and dip‐moveout corrections, stacking and depth migration). The results show significant improvements, over single‐channel recordings, in noise reduction and depth of penetration (by stacking), and in spatial positioning and reduction of diffraction artifacts (by migration). These characteristics increase the potential for reliable interpretation of structural and stratigraphic details. Thus, without having to develop any new software, GPR data processing technology is brought to the same level of capability, flexibility, and accessibility that is current in seismic exploration.
Incomplete AVO near salt structures
Authors: Ross Christopher P.
Published: October 2002

Amplitude versus offset (AVO) measurements for deep hydrocarbon‐bearing sands can be compromised when made in close proximity to a shallow salt piercement structure. Anomalous responses are observed, particularly on low acoustic impedance bright spots. CMP data from key seismic profiles traversing the bright spots do not show the expected Class 3 offset responses. On these CMPs, significant decrease of far trace energy is observed. CMP data from other seismic profiles off‐structure do exhibit the Class 3 offset responses, implying that structural complications may be interfering with the offset response. A synthetic AVO gather was generated using well log data, which supports the off‐structure Class 3 responses, further reinforcing the concept of structurally‐biased AVO responses. Acoustic, pseudo‐spectral modeling of the structure substantiates the misleading AVO response. Pseudo‐spectral modeling results suggest that signal degradation observed on the far offsets is caused by wavefield refraction—a shadow zone, where the known hydrocarbon‐bearing sands are not completely illuminated. Such shadow zones obscure the correct AVO response, which may have bearing on exploration and development.
Examples of reverse‐time migration of single‐channel, ground‐penetrating radar profiles
Authors: Fisher Elizabeth , McMechan George A. , Annan A. Peter , Cosway Steve W.
Published: October 2002

A single‐channel, ground‐penetrating radar (GPR) profile portrays a distorted, unfocused image of subsurface structure due to apparent position shifts associated with dipping reflectors and to diffractions from corners and edges. A focused image may be produced from such data by using any of the migration algorithms previously developed for seismic data; we use reverse‐time migration based on the scalar wave equation. Field work was performed over a simple stratigraphic soil sequence and a complicated fluvial environment. In the migrated images, reflector continuity is enhanced and the level of detail available for high‐resolution interpretation is significantly increased.
The gravity anomaly of two‐dimensional sources with continuous density distribution and bounded by continuous surfaces
Authors: Ruotoistenmäki Tapio
Published: October 2002

The gravity anomaly of a complicated two‐dimensional (2-D) source having arbitrary surfaces and density varying in either horizontal or vertical direction is calculated using a combination of closed form solutions and numerical integration. The surfaces and density can be defined by continuous or piecewise continuous two‐dimensional functions in the integration interval. For example, the anomalies for intrusions or folded sedimentary units, having an arbitrary density in the horizontal direction and a polynomial density distribution in the vertical direction, can be calculated using surfaces represented by functions of the horizontal dimension. When modeling dipping layered intrusions or sedimentary beds the surfaces are represented by functions of the vertical dimension in which case the density can be an arbitrary function of depth and a polynome function of horizontal coordinate. The accuracy of the method is defined by the user. The method gives simple and general equations to calculate anomalies of complicated sources which have no closed form solution, thus reducing the number of algorithms needed in interpretation programs.
Parametric estimators for current excitation on a thin plate
Authors: Walker Peter W. , West Gordon F.
Published: October 2002

Parametric analysis is used to predict whether induction or current channeling dominates the current excitation in a conductive body in the earth. Knowing that one mode dominates the current response permits the use of relatively simple models that account for only a single mode of excitation in place of more complicated general ones that account for both modes of the current response. This is useful both in forward modeling and in inversion. In interpretation, predicting the current excitation is useful for verifying that the assumed mode of excitation is consistent with the interpreted body. Prediction is done with a set of “current excitation ratios” that we demonstrate for a thin conductive plate in a conductive half‐space. To derive the excitation ratios, parametric theory is used to estimate the strength of the inductive and galvanic modes of the current response of the plate. The ratios then follow by dividing the inductive estimate into the galvanic one. When this ratio is less than one, induction will dominate the current response. When it is greater than one, current channeling will dominate. Current excitation ratios are simple to calculate, and consist of two components. One component is a product of model parameters such as conductivity, dimension, and permeability, and can be calculated by hand. The second component consists of what we term the “local impedance” of the source field at the conductor. This component can be calculated with a simple half‐space or layered earth electromagnetic modeling algorithm and then contoured for later reference. The predictive capability of the current excitation ratios is tested by calculating the current response on a vertical plate in a half‐space with a full electromagnetic scattering solution. We find the correspondence between the two to be very good, and that it is possible to successfully predict the dominant mode of the current response through parametric theory where assumptions used in the parametric analysis are valid.
Estimation of polarization and slowness in mixed wavefields
Authors: Cho Woon Hyun , Spencer Terry W.
Published: October 2002

A new algorithm is developed for estimating the moveout velocities and polarization states in mixed wavefields recorded on multicomponent array data in the presence of random noise. The algorithm is applicable to a spatial and temporal data window in which more than two events are present. Three fundamental attributes of the waves are determined: polarization angle, apparent slowness, and the change in amplitude between adjacent detectors. In implementing the method, it is assumed that data is recorded at equispaced geophones located in a spatial window in which the three parameters are constant. Robustness is achieved by averaging the transfer matrix over all combinations of the subarrays that have the same transfer matrix. Application of a least‐squares criterion reduces the mathematics to an eigenvalue problem. The eigenvalues are complex, and their magnitude determines the amplitude change factor. The phase is a linear function of frequency with slope that determines the vertical slowness. The eigenvectors are the polarizations. The input data consists of the cross‐power spectra between subarrays that contain the same number of elements and are shifted by zero or one geophone separation. Examples illustrate the application of the algorithm to synthetic data. Numerical test results show that the performance of the method is not sensitive either to the time overlap between events or to the degree of similarity between waveforms.
A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars
Authors: Tang Xiao Ming
Published: October 2002

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.
The effect of oil under in‐situ conditions on the seismic properties of rocks
Authors: Clark Virginia A.
Published: October 2002

Direct hydrocarbon indicators (DHIs) on seismic sections are commonly thought to be diagnostic only of gas. However, oil sands can also generate DHIs such as bright spots and flat events since oils under in‐situ conditions can contain large amounts of solution gas. This dissolved gas substantially decreases the velocity of sound and the density of the oils as compared to measurements of these properties at surface conditions. Hydrocarbon indicators caused by oil sands are investigated by first measuring the elastic properties of an oil as a function of gas‐oil ratio, next, calculating the elastic properties of additional oil compositions under in‐situ conditions using standard pressure‐volume‐temperature (PVT) measurements, and then calculating the compressional velocity in oil‐saturated rocks for several typical oils using Gaasmann’s equation. The potential for seismic anomalies caused by oil‐saturated rocks is higher than thought because the properties of oil under reservoir conditions can differ significantly from those of surface oils. Specifically: 1) The properties of oil depend on its composition: the higher the API gravity and the gas‐to‐oil ratio (GOR), the lower the density and velocity of sound (adiabatic bulk modulus) and the lower the velocity of a rock saturated with the oil. 2) Calculations of oil‐sand velocities using the in situ properties of oils show that areas having light oils and/or poorly consolidated rocks are the most likely areas in which to encounter oil DHIs. Since overpressured areas can have both poorly consolidated rocks and high GOR oils, they are especially prone to large oil responses.
Removing vibrator‐induced correlation artifacts by filtering in frequency‐uncorrelated time space
Authors: Okaya David A. , Karageorgi Eleni , McEvilly Thomas V. , Malin Peter E.
Published: October 2002

Vibrator‐to‐ground coupling can produce resonance‐induced energy that propagates with the primary sweep and produces serious artifacts in the correlated seismogram due to the frequency structure of this offending energy. For sweeps linearly increasing in frequency, the resulting artifact is observed (uncorrelated) to increase in frequency at a linear rate differing from the original sweep. Upon crosscorrelation with the pilot sweep, the artifact‐producing energy becomes distributed over an extended range of time while the normal reflected sweep is compressed, by design, into a narrow correlation wavelet. The resulting traces thus exhibit strong amplitudes that increase monotonically in dominant frequency. Display of individual uncorrelated seismograms using a Fourier frequency‐uncorrelated time (F-T) transformation reveals the relationship between the primary sweep and the induced artifact. “Surgical” filtering in this new F-T space provides for a first‐order removal of both the artifact and the energy in sweep harmonics as induced by the stong first arrivals. Two‐dimensional (2-D) spectral filtering of the modulus of the (complex) 2-D transform of the F-T data provides better rejection of the unwanted energy. Application of this trace‐by‐trace filtering process to a badly contaminated crustal-scale multichannel CDP profile in the southern San Joaquin Valley, California, reveals significant reflections from the middle and lower crust that were obscured in the unfiltered profile.
Singular value decomposition of the velocity‐reflector depth tradeoff, Part 1: Introduction using a two‐parameter model
Authors: Stork Christof
Published: October 2002

A singular value decomposition (SVD) of a two‐parameter model serves to introduce several characteristics of a raypath inversion of the standard reflection seismology recording geometry. Two important families of eigenvectors consist of constructive interference and destructive interference of velocity and reflector depth. The eigenvalue that corresponds to the velocity‐reflector depth destructive interference is very sensitive to the maximum ray angle in the data. For a cable length equal to twice the reflector depth, the theoretical linear resolution is quite high. The relative weighting between velocity and reflector depth is not critical so long as the weight is near 1.0.