bluuebunny/crossref_metadata_2025 huggingface dataset:
Radiation from seismic sources in cased and cemented boreholes
Authors: Gibson Richard L.
Published: October 2002

Far‐field, stationary phase approximations are often used to study the radiation of P‐ and S‐waves from seismic sources located in boreholes, usually with an assumption of low frequency and in application to uncased boreholes. These two assumptions allow explicit analytical results for the radiation patterns to be derived, as boundary condition equations can be solved analytically in fairly simple forms. Applying the same methodology to cased and cemented boreholes, however, is much more difficult because of the increased number of simultaneous boundary condition equations. I circumvent this difficulty by solving the boundary condition equations numerically using propagator matrices, as is generally done in the calculation of synthetic full‐waveform acoustic logs. In this way, the assumption of low frequency is also avoided, and a generalized stationary‐phase solution for sources in general, concentrically layered borehole models is easily obtained. Computation of the radiation patterns for cased and uncased boreholes in various formations shows that the amplitude reduction, because of the introduction of casing, is a function of both source type and of formation velocities. Axial stress sources are less affected by the casing than either radial stress or volume‐injection sources, and as formation velocity decreases, the effect of the casing becomes more significant as the impedance contrast between steel and the formation becomes larger. The new generalized stationary‐phase solution also shows that as frequency approaches 1000 Hz, the results obtained by low‐frequency approximations for stress sources can be inaccurate and that the energy radiated from the source becomes more highly directed in the horizontal directions. The radiation pattern begins to change relatively rapidly as a function of frequency, so that the resulting observations from broad‐band sources will show changes in waveforms that mimic the effects of attenuation. These changes occur because the length of the source becomes important as wavelength decreases, demonstrating the need to consider the influence of frequency, as well as casing and cement, on source radiation.
Dip‐moveout processing for depth‐variable velocity
Authors: Artley Craig , Hale Dave
Published: October 2002

In dip‐moveout (DMO) processing, the seismic velocity is often assumed to be constant. While several approximate techniques for handling vertical velocity variation have recently become available, here we propose a method for computing the kinematically exact DMO correction when velocity is an arbitrary function of the depth. While not known in advance, the raypath from source to receiver and the corresponding zero‐offset raypath satisfy several relationships, which are used to form a system of nonlinear equations. By simultaneously solving the equations via Newton‐Raphson iteration, we determine the mapping that transforms nonzero‐offset data to zero‐offset. Unlike previous schemes that approximately handle vertical velocity variation, this method makes no assumptions about the offset, dip, velocity function, or hyperbolic moveout. Tests using both synthetic and recorded seismic data demonstrate the effectiveness of this variablevelocity DMO. These tests show this method accurately handles vertical velocity variation, while use of constant‐velocity DMO can lead to significant errors. Comparing this technique to a formulation that approximately handles velocity variation, however, suggests that the improved accuracy of the exact technique may not be justified because of uncertainty in the velocity model and increased cost. While improved accuracy alone may not justify the use of this method in 2-D, its flexibility may in other cases. Changes could be made to handle 3-D DMO, DMO for mode‐converted waves, DMO in anisotropic media, or prestack divergence correction.
Diffraction tomography for crosswell imaging of nearly layered media
Authors: Dickens Thomas A.
Published: October 2002

Diffraction tomography is a high‐resolution imaging technique applicable to the mapping of formation velocities away from the borehole, achieving a spatial resolution of better than one acoustic wavelength when used to image synthetic model data. However, traditional filtered back‐propagation diffraction tomography algorithms are based on weak‐scattering and constant‐background velocity assumptions, which limits their applicability to models of realistic structural complexity. Results are obtained using a new, computationally efficient single‐mode (P‐wave) diffraction tomography algorithm that is applicable to models, including geologically realistic ones, whose strongest variations can be approximated as a set of horizontal layers. The algorithm starts with a layered model of the subsurface velocity structure, which may be constructed from well logs or by using traveltime tomography. Application of layered diffraction tomography updates this model to reveal 2-D structures such as faults, pinch‐outs, and dips. An overview of the layered diffraction tomography algorithm and information on its computational implementation are presented. Layered diffraction tomography can, given an accurate initial model, successfully image complex structures for which filtered back‐propagation fails, with a spatial resolution on the order of one‐third wavelength. Synthetic crosswell data are used to construct images of models ranging from an isolated simple target to geologically realistic structures containing faults, erosional surfaces, and dipping beds. The initial layered model must represent the actual subsurface structure with as much fidelity as possible; it is important to use all available a priori information in the construction of this model. The enhanced spatial resolution provided by diffraction tomography does not require the use of high‐angle reflections; in the presence of noise, image quality and resolution can be largely maintained by using only a short time window of (the high S/N) data immediately following the first break that is employed for traveltime imaging.
Reconnaissance geologic mapping of a portion of the rain‐forest‐covered Guiana Shield, Northwestern Brazil, using SIR-B and digital aeromagnetic data
Authors: de Miranda Fernando Pellon , McCafferty Anne E. , Taranik James V.
Published: October 2002

This paper documents the result of an integrated analysis of spaceborne radar (SIR-B) and digital aeromagnetic data carried out in the heavily forested Guiana Shield. The objective of the research is to interpret the geophysical data base to its limit to produce a reconnaissance geologic map as an aid to ground work planning in a worst‐case setting. Linear geomorphic features were identified based on the interpretation of the SIR-B image. Digital manipulation of aeromagnetic data allowed the development of a color‐shaded relief map of reduced‐to‐pole magnetic anomalies, a terrace‐magnetization map, and a map showing the location of maximum values of the horizontal component of the pseudogravity gradient (magnetization boundary lines). The resultant end product was a reconnaissance geologic map where broad terrane categories were delineated and geologic faults with both topographic and magnetic expression were defined. The availability of global spaceborne radar coverage in the 1990s and the large number of existing digital aeromagnetic surveys in northwestern Brazil indicate that this approach can be potentially useful for reconnaissance geologic mapping elsewhere in the Guiana Shield.
Prestack depth migration by means of controlled illumination
Authors: Rietveld W. E. A. , Berkhout A. J.
Published: October 2002

The prestack depth migration process involves a huge amount of computations required for the extrapolation process of the prestack data. Especially for 3-D surveys, full prestack migration takes too much computation time to be economic yet. We propose an efficient as well as an accurate procedure that enables us to migrate prestack data in a target‐oriented way using the method of controlled illumination. Use of controlled illumination combined with depth migration is a special case of the more general concept of “areal” shot‐record migration. The method differs from conventional plane‐wave stacking methods in the sense that in the approach of controlled illumination the control of the source wavefield is put at the target, and by the fact that it is always followed by depth migration. It is shown that controlling the complexity of the incident wavefield at the target level leads to a high‐quality image in an efficient way.
On: “The straight‐slope method for basement depth determination revisited,” by J. R. Skilbrei (April 1993 GEOPHYSICS, 58, p. 593–595).
Authors: Steenland Nelson C.
Published: October 2002

After interpreting aeromagnetic data on a worldwide basis for more than 20 years without recourse to any ancillary data, subsequent basement drilling showed an accuracy of ±7.5 percent for the contoured maps, not individual depth values, of the bottom of new sedimentary basins. The fields were resolved into intrabasement, suprabasement, and intrasedimentary anomalies, and depths were computed to their sources of thick prisms and thin plates with two universally applied coefficients. More than once, intrasedimentary volcanics were handled routinely. The author’s statement in paragraph three of his Introduction is not correct.
Electrical efficiency—A pore geometric theory for interpreting the electrical properties of reservoir rocks
Authors: Herrick David C. , Kennedy W. David
Published: October 2002

Knowledge of the way pore geometry affects the conductivity of rocks is important for the evaluation of sedimentary rocks for hydrocarbon potential. Virtually all formation evaluation from logs, however, uses the empirical Archie equation that has never been given a satisfactory physical basis. As an alternative, we have formulated a new model based on the efficiency with which water‐bearing rocks conduct electric currents as determined by the conducting phase geometry. Electric current densities are not uniform throughout the conducting phase in the pore system of a rock. Numerical model studies show high current density in pore throats and low current density in nearly stagnant volumes in isolated parts of the pore system. The electrical efficiency of a rock is the ratio of the average power developed in all water‐bearing parts of the pore system to the power developed in a straight tube with the same length and water volume as the rock. It is inherently independent of the bulk volume of water in the rock and determined only by the nonuniform current distribution caused by pore geometry and hydrocarbons in the pore system. Electrical efficiency can be calculated a priori given the geometrical distribution of the conducting phase. Empirical relationships between electrical efficiency and water content can be used to calculate hydrocarbon saturations from log data.
A theory of normal moveout
Authors: Castle Richard J.
Published: October 2002

Three geophysical principles are shown to be sufficient to determine the most general, practical normal moveout (NMO) equation. The principles are reciprocity in a common midpoint (CMP) gather, finite slowness, and exact constant velocity limit. The resulting equation is the shifted hyperbola NMO equation that has three parameters. Comparisons at both near and far offsets between the shifted hyperbola NMO equation and the results for layered media assign geophysical meaning to the parameters. Two of the parameters, zero offset time and NMO velocity, are constants and control the very near offset behavior. The third parameter is dimensionless and controls the far offset behavior of the NMO curve, but it may be a function of offset so as to exactly fit any traveltime curve. The parameters may be found by a linear least‐squares fit to data. The theory applies to all offsets for nonturning wave reflections in an isotropic earth for both P‐waves and converted (P - SV) waves.
Migration using the shortest‐path method
Authors: Moser T. J.
Published: October 2002

The shortest‐path method for the calculation of seismic rays and traveltimes in complicated media is compared with two methods for traveltime calculation that are based on a finite‐difference solution of the eikonal equation, namely the algorithm of Vidale and a modification by Gray of the algorithm of van Trier and Symes. This comparison consists of two parts: first, the performance of the three algorithms in forward modeling is tested, and second, their application in Kirchhoff migration is demonstrated. The comparison of the forward modeling shows a very close resemblance between the shortest‐path method and the eikonal equation solver of Vidale, but quite large differences with Gray’s version, which was developed exclusively for application to migration and therefore favors speed at the cost of a possible loss of accuracy. Surprisingly, application of the three methods to the migration of the Marmousi data set shows differences only in small details. The flexibility of the shortest path method allows for application in exploding reflector migration; each reflector can be reconstructed from zero‐offset traveltime data by only one forward calculation. Investigation of the effect of smoothing of the slowness model shows that a moderate amount of smoothing delays the traveltimes by about 1 to 2 percent but has no visible effect on the migration results.
Ground‐penetrating radar monitoring of a controlled DNAPL release: 200 MHz radar
Authors: Brewster Michael L. , Annan A. Peter
Published: October 2002

A controlled release of tetrachloroethylene was performed in a saturated, natural sandy aquifer to evaluate the effectiveness of various geophysical techniques for detecting and monitoring dense nonaqueous phase liquids (DNAPLs) in the subsurface. Tetrachloroethylene, typical of most DNAPLs, has a low relative dielectric permittivity (2.3), which contrasts with the high relative permittivity (80) of the pore water it displaces, making it a potential target for detection by ground‐penetrating radar (GPR). GPR data were acquired using 200 MHz antennas. Radar sections collected at different times over the same spatial location clearly show the changes induced by the movement of DNAPL in the subsurface. Temporal changes can be examined through the evolution of a radar data trace collected at a single spatial location. Normal moveout analysis of common‐midpoint (CMP) data demonstrates induced changes in electromagnetic (EM) wave velocities of up to 30 percent caused by the presence of DNAPL. The distribution of DNAPL can be mapped in three dimensions at different times using a network of 16 radar lines. The 200 MHz GPR proved to be an effective technique for monitoring the movement of DNAPL in the subsurface. Direct detection of DNAPLs by radar is also feasible in this simple environment.
Detection of gas in sandstone reservoirs using AVO analysis: A 3-D seismic case history using the Geostack technique
Authors: Fatti Jan L. , Smith George C. , Vail Peter J. , Strauss Peter J. , Levitt Philip R.
Published: October 2002

The Geostack technique is a method of analyzing seismic amplitude variation with offset (AVO) information. One of the outputs of the analysis is a set of direct hydrocarbon indicator traces called “fluid factor” traces. The fluid factor trace is designed to be low amplitude for all reflectors in a clastic sedimentary sequence except for rocks that lie off the (mudrock line.) The mudrock line is the line on a crossplot of P‐wave velocity against S‐wave velocity on which water‐saturated sandstones, shales, and siltstones lie. Some of the rock types that lie off the mudrock line are gas‐saturated sandstones, carbonates, and igneous rocks. In the absence of carbonates and igneous rocks, high amplitude reflections on fluid factor traces would be expected to represent gas‐saturated sandstones. Of course, this relationship does not apply exactly in nature, and the extent to which the mudrock line model applies varies from area to area. However, it is a useful model in many basins of the world, including the one studied here. Geostack processing has been done on a 3-D seismic data set over the Mossel Bay gas field on the southern continental shelf of South Africa. We found that anomalously high amplitude fluid factor reflections occurred at the top and base of the gas‐reservoir sandstone. Maps were made of the amplitude of these fluid factor reflections, and it was found that the high amplitude values were restricted mainly to the gas field area as determined by drilling. The highest amplitudes were found to be located roughly in the areas of best reservoir quality (i.e., highest porosity) in areas where the reservoir is relatively thick.
THE CALCULATION OF GRAVITY ANOMALIES DUE TO BODIES OF FINITE EXTENT
Authors: Levine S.
Published: October 2002

A new method for calculating the gravity anomalies due to mass distributions of finite extent and simple geometrical form has been developed. The principle of the method is the construction, in a plane, of curves which represent the boundaries of the body, such that the gravity effect is directly proportional to the area enclosed by such curves. The advantage of this method for bodies of considerable extent is emphasized. This approach is more rapid than that of the sector or graticule diagrams commonly employed.
A NOTE ON THE DETERMINATION OF THE VISCOSITY OF SHALE FROM THE MEASUREMENT OF WAVELET BREADTH
Authors: Ricker Norman
Published: October 2002

From the breadth of a wavelet for a given travel time, it is possible to calculate the viscosity of the formation through which the seismic disturbance has passed. This calculation has been carried out for the Cretaceous Shale of Eastern Colorado, and the value thus found ranges from [Formula: see text] to [Formula: see text], with a mean value of [Formula: see text] grams per cm. per second.
Modeling of a constant Q: Methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique
Authors: Blanch Joakim O. , Robertsson Johan O. A. , Symes William W.
Published: October 2002

Linear anelastic phenomena in wave propagation problems can be well modeled through a viscoelastic mechanical model consisting of standard linear solids. In this paper we present a method for modeling of constant Q as a function of frequency based on an explicit closed formula for calculation of the parameter fields. Several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant Q approximation. The proposed method enables substantial savings in computations and memory requirements. Experiments show that the new method also yields higher accuracy in the modeling of Q than, e.g., the Padé approximant method.
A procedure for optimally removing localized coherent noise
Authors: Linville A. Frank , Meek Robert A.
Published: October 2002

Primary reflections in seismic records are often obscured by coherent noise making processing and interpretation difficult. Trapped water modes, surface waves, scattered waves, air waves, and tube waves to name a few, must be removed early in the processing sequence to optimize subsequent processing and imaging. We have developed a noise canceling algorithm that effectively removes many of the commonly encountered noise trains in seismic data. All currently available techniques for coherent noise attenuation suffer from limitations that introduce unacceptable signal distortions and artifacts. Also, most of those techniques impose the dual stringent requirements of equal and fine spatial sampling in the field acquisition of seismic data. Our technique takes advantage of characteristics usually found in coherent noise such as being localized in time, highly aliased, nondispersive (or only mildly so), and exhibit a variety of moveout patterns across the seismic records. When coherent noise is localized in time, a window much like a surgical mute is drawn around the noise. The algorithm derives an estimate of the noise in the window, automatically correcting for amplitude and phase differences, and adaptively subtracts this noise from the window of data. This signal estimate is then placed back in the record. In a model and a land data example, the algorithm removes noise more effectively with less signal distortion than does f-k filtering or velocity notch filtering. Downgoing energy in a vertical seismic profile (VSP) with irregular receiver spacing is also removed.
Robust AVO analysis
Authors: Ursin Bjørn , Ekren Bjørn Olav
Published: October 2002

Amplitude variation with offset (AVO) analysis is sensitive to errors in the moveout correction. To reduce moveout errors, AVO‐effects are estimated using time windows. For each time window, block‐NMO is used to avoid NMO‐stretch, and correction for residual NMO is performed by an iterative cross‐correlation technique. The data in a moveout‐corrected time window are modeled as a constant pulse multiplied by an amplitude function that is approximated by a polynomial in the offset coordinate. Conversion of data from offset to angle, or slowness, is therefore avoided. The seismic pulse and the polynomial coefficients are found by the least‐squares method. This is a separable least‐squares problem and the polynomial coefficients and the pulse can be estimated separately. The reduced nonlinear optimization problem for the coefficients is expressed as a Rayleigh quotient, providing the solution in one step. Once the coefficients have been found, the estimate of the pulse is computed by an explicit formula. This gives an efficient computational scheme. The method is demonstrated on a shallow seismic anomaly in the Barents Sea, offshore northern Norway.
Wave propagation in heterogeneous, porous media: A velocity‐stress, finite‐difference method
Authors: Dai N. , Vafidis A. , Kanasewich E. R.
Published: October 2002

A particle velocity‐stress, finite‐difference method is developed for the simulation of wave propagation in 2-D heterogeneous poroelastic media. Instead of the prevailing second‐order differential equations, we consider a first‐order hyperbolic system that is equivalent to Biot’s equations. The vector of unknowns in this system consists of the solid and fluid particle velocity components, the solid stress components, and the fluid pressure. A MacCormack finite‐difference scheme that is fourth‐order accurate in space and second‐order accurate in time forms the basis of the numerical solutions for Biot’s hyperbolic system. An original analytic solution for a P‐wave line source in a uniform poroelastic medium is derived for the purposes of source implementation and algorithm testing. In simulations with a two‐layer model, additional “slow” compressional incident, transmitted, and reflected phases are recorded when the damping coefficient is small. This “slow” compressional wave is highly attenuated in porous media saturated by a viscous fluid. From the simulation we also verified that the attenuation mechanism introduced in Biot’s theory is of secondary importance for “fast” compressional and rotational waves. The existence of seismically observable differences caused by the presence of pores has been examined through synthetic experiments that indicate that amplitude variation with offset may be observed on receivers and could be diagnostic of the matrix and fluid parameters. This method was applied in simulating seismic wave propagation over an expanded steam‐heated zone in Cold Lake, Alberta in an area of enhanced oil recovery (EOR) processing. The results indicate that a seismic surface survey can be used to monitor thermal fronts.
The footprint/altitude ratio for helicopter electromagnetic sounding of sea‐ice thickness: Comparison of theoretical and field estimates
Authors: Kovacs Austin , Holladay J. Scott , Bergeron Clyde J.
Published: October 2002

Helicopter‐towed electromagnetic (HEM) induction sounding systems are typically used for geologic surveys. More recently, HEM systems have been used for the remote measurement of sea‐ice thickness and shallow sea bathymetry. An important aspect of this remote sensing technology is the area, or footprint, in which the secondary field is predominantly generated by induced currents. A knowledge of the size of the footprint is important to understanding the accuracy of HEM sounding results over lateral variations in relief or conductivity. Conventional wisdom among workers in the field held that the footprint diameter is a few times the HEM antenna altitude. We confirm this view using airborne measurements over sea ice to calculate the footprint size/antenna altitude ratio. These findings are compared to various theoretical estimates and are found to be in reasonable agreement. For a vertical coaxial coil antenna arrangement, the apparent footprint diameter was found to be about 1.3 times the antenna height above the sea‐ice/water interface, and for a horizontal coplanar coil figuration the ratio is about 3.8 times the antenna height.
Interpolation of potential‐field data by equivalent layer and minimum curvature: A comparative analysis
Authors: Mendonça Carlos A. , Silva João B. C.
Published: October 2002

Interpolation using only the observations at discrete points is an ill‐posed problem because it admits infinite solutions. Usually, to reduce ambiguity, a priori information about the sample function is introduced. Current interpolation methods in mineral exploration introduce only the constraints of continuity and smoothness of the interpolating function. In interpolating potential‐field anomalies, the constraint that the sampled function is harmonic may be introduced by the equivalent‐layer method (ELM). We compare the performance of the ELM and the minimum curvature method (MCM) in interpolating potential‐field anomalies by applying these methods to synthetic magnetic data simulating an aeromagnetic survey. In the case the anomaly flanks and peak are undersampled, the ELM performs better than the MCM in recovering the anomaly gradients and peak. In the case of elongated linear anomalies, the ELM recovers the exact linear pattern, but the MCM introduces spurious oscillations in the linear pattern. Also, the ELM is able to reduce the data from a survey flown at different heights to a common level. In contrast, the MCM, being a 2-D interpolation method, cannot account for variations in the vertical coordinates of the observation points.
Vertical resolution of a seismic survey in stratigraphic sequences less than 100 m deep in southeastern Kansas
Authors: Miller Richard D. , Anderson Neil L. , Feldman Howard R. , Franseen Evan K.
Published: October 2002

A 400-m long, 12‐fold high‐resolution common depth point (CDP) reflection seismic profile was acquired across shallow converging Pennsylvanian strata in the Independence area of southeastern Kansas. One of the principal objectives was to determine practical vertical resolution limits in an excellent shallow seismic‐data area with borehole control. The dominant frequency of the CDP stacked data is in excess of 150 Hz based on peak‐to‐peak measurements. Interference phenomena observed on stacked seismic data incorporated with models derived from log and drill‐hole information suggest a practical vertical resolution limit of about 7 m, or one‐third of the dominant wavelength. This practical resolution is slightly less than the predicted (theoretical) resolution limit of 5 m based on the generally accepted one‐quarter wavelength axiom. These data suggest conventional rules of thumb describing resolution potential are not accurate when reflectors on shallow, narrow bandwidth data converge rapidly across horizontal distances less than the Fresnel Zone.
Prediction of elastic‐wave velocities in sandstones using structural models
Authors: Bryant Steven , Raikes Sue
Published: October 2002

Elastic‐wave propagation in fluid‐saturated sandstones depends upon two sets of rock features: (1) the volume fractions and elastic constants of the rock constituents (quartz, clay, water, etc.) and (2) microstructural geometry (grain contacts, pore aspect ratios). While the former data are usually obtainable, the latter are relatively inaccessible. We present a new method for determining microstructural data using idealized but physically representative models of sandstone. The key to the method is the simulation of certain depositional and diagenetic processes in a manner that completely specifies the geometry of the resulting models. Hence, the geometric features of the grain space and void space required for various theories of elastic propagation can be calculated directly from the models. We find good agreement between predictions and measurements of compressional‐ and shear‐wave velocities in both clean and clay‐bearing saturated sandstones. In contrast with previous efforts at predicting velocities, we use no adjustable parameters and require no additional measurements on samples, such as dry velocities or analysis of thin‐section images. The results suggest that it is feasible to predict elastic velocities directly from geological models in the absence of rock samples.
Simultaneous determination of time delays and stacking weights in seismic array beamforming
Authors: Mao Weijian , Gubbins David
Published: October 2002

An algorithm for the estimation of time delays and weights in an arbitrary‐single or three‐component seismic array is developed by the use of a linearized waveform inversion technique. This algorithm differs from conventional crosscorrelation methods in its ability to simultaneously obtain time delays and weights by minimizing residuals of all possible waveform fittings, and by its robustness in the presence of high random noise levels and local geological scattering. There are N stations in an array, and for each station, a beam is formed by a weighted linear combination of the remaining (N − 1) seismic traces. The time delays and weights are model parameters to be found by minimizing the sum of N objective functions. Two optimization algorithms for solving the least‐squares problem, singular‐value decomposition and conjugate gradient, are compared, and the conjugate gradient method is found to be satisfactory and faster for large arrays. The algorithm was tested using synthetic array data with high noise, real data from shots in a borehole to a linear array on land, and Ms 6.7 earthquake data recorded with a broadband three‐component array. The success with synthetic and real data shows the algorithm to be useful for seismic data stacking, residual static corrections, and phase picking when the data quality is poor.
Elimination of harmonic distortion in vibroseis data
Authors: Li Xiao‐Ping , Söllner Walter , Hubral Peter
Published: October 2002

We present a new approach to eliminate the harmonic distortion in vibroseis data. This technique is based on the definition of the sweep for the case where the instantaneous frequency varies linearly with time. The method requires no more than the computation of a purely deterministic phase‐shift filter that has the phase spectrum of a hypothetical “kth harmonic distortion.” With this particular phase‐shift filter, all harmonic distortions in the base‐plate signal and those caused by the first strong arrival in the vibroseis trace (which leads to the “correlation ghost sweeps”) are removed. The process consists of (1) applying the deterministic pure phase‐shift filter to the vibroseis trace and the base‐plate signal; (2) setting time values equal to zero for negative times in both the filtered base‐plate signal and the filtered vibroseis trace; and (3) applying the inverse pure phase‐shift filter to both base‐plate signal and vibroseis trace prior to performing the usual crosscorrelation. The correlated trace thus obtained will be freed substantially of correlation noise; i.e., the correlation‐ghost sweeps (produced by severe harmonic distortion both at negative and positive correlation times) are eliminated without degrading the seismic information content of the trace. The new method of elimination has been successfully applied to synthetic and real harmonically distorted vibroseis data and is compared with the standard correlation technique that uses the pilot sweep as the correlator.
The generalized SH‐wave equation
Authors: Carcione José M. , Cavallini Fabio
Published: October 2002

We present a generalization of the SH‐wave equation for anisotropic and dissipative media. The most general case in which SH‐waves are decoupled from P‐ and SV‐waves at all propagation angles is that of propagation in the plane of symmetry of a monoclinic medium. In the isotropic case, the SH constitutive equation involves only one elastic coefficient (the rigidity); here, three elastic coefficients are needed. Moreover, dissipation is introduced by using Boltzmann’s law based on several relaxation mechanisms. Anisotropic attenuation and velocity dispersion are guaranteed by choosing different relaxation functions for the principal axes. The wave equation, in the displacement and velocity‐stress formulations, is solved by using time‐domain spectral modeling techniques. The snapshots and seismograms of the computed displacement field show attenuation and anisotropy effects on traveltime (mainly because of anisotropy) and amplitude (because of combined anisotropy and dissipation), in agreement with the theoretical patterns of energy velocity and attenuation curves.
Shell Processing Support Format for Land 3-D Surveys
Authors:   SEG Technical Standards Committee on Ancilliary Data Formats
Published: October 2002

The Shell SPS ancillary data format provides a means of encoding field ancillary data on magnetic media in both human readable and machine readable form. The format was defined by groups within Shell Internationale Petroleum Maatschappij in conjunction with comments from other users within the geophysical community. Since the format has gained wide acceptance, the SEG Technical Standards Committee requested that the format be made available publicly by endorsing it as an SEG standard. Shell very graciously agreed to provide this format to the geophysical industry.
Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part I—2.5-D modeling method
Authors: Song Zhong‐Min , Williamson Paul R.
Published: October 2002

Crosshole experiments usually have sources and receivers confined to a plane, and it is assumed that there is negligible variation in the properties of the medium normal to this plane. Therefore, the problem appears two‐dimensional, except for the sources which are 3-D points rather than lines. This configuration is denoted as two‐and‐one‐half‐dimensional. We present a frequency‐domain approach to modeling acoustic wave propagation in such situations which allows correct treatment of point sources but takes advantage of the assumed 2-D nature of the medium to avoid full 3-D simulations. The approach uses a Fourier transform with respect to the out‐of‐plane coordinate to reduce the problem of modeling in 3-D to repeatedly solving a 2-D equation, which we accomplish using finite differences. The discrete inverse Fourier transform from the out‐of‐plane wavenumber implies the existence of an infinite number of spurious “ghost sources” spaced periodically in the out‐of‐plane direction. These sources generate significant artifacts on the time‐domain traces, even when their spatial period is much greater than the (in‐plane) dimensions of the survey area, because of time‐wrapping in the transform from the frequency domain. We describe two methods for reducing these artefacts, the more effective of which entails exponential damping by adding a positive imaginary part to the frequency, compensated by ramping of the wrapped time domain records. We check the modeling scheme by analysis of direct and scattered arrivals from simple models. The observed seismograms agree well with those calculated using Born theory, and so confirm the potential of this modeling method for use in inversion.
Crosswell electromagnetic inversion using integral and differential equations
Authors: Newman Gregory
Published: October 2002

The crosswell electromagnetic (EM) inverse problem is solved with an integral‐equation (IE) formulation using successive Born approximations in the frequency domain. Because the inverse problem is nonlinear, the predicted fields and Green’s functions are continually updated. Updating the fields and Green’s functions relates small changes in the predicted data to small changes in the model parameters through Fréchet kernels. These fields and Green functions are calculated with an efficient 3-D finite‐difference solver. Since the resistivity is invariant along strike, the 3-D fields are integrated along strike so the 2-D kernels can be assembled. At the early stages of the inversion, smoothing of the electrical conductivity stabilizes the inverse solution when it is far from convergence. As the solution converges, this smoothing is relaxed and more effort is made to reduce the data misfit. Bounds on the conductivity are included in the solution to eliminate unrealistic estimates. The robustness of the inversion scheme has been demonstrated with synthetic and field data that are underdetermined from the standpoint of the smooth models being sought. Two synthetic examples with added Gaussian noise were considered, including data arising from an IE solver. This IE solver is different from the one embedded in the inversion algorithm and has provided a stronger check on the scheme. The synthetic examples show it is more difficult to reconstruct a target’s conductivity than its geometry at a single frequency. The inversion scheme has been successfully tested using data collected at the Richmond‐field site near Berkeley, California, where it has imaged a salt water plume injected into the interwell region. The data in this experiment consisted of two sets of measurements, taken before and after the injection of 50 000 gallons of 1 Ωm salt water. Findings show that underdetermined inversion using small amounts of field data can be sufficient to produce useful, but smoothed, maps of the conductivity. The data in this instance need be only single frequency and single component.
3-D seismic tracking with probabilistic data association
Authors: Woodham Catherine A. , Sandham William A. , Durrani Tariq S.
Published: October 2002

In this paper, a new approach to the problem of tracking a seismic event through a 3-D data set is presented. The method under consideration was originally developed for tracking targets in a cluttered environment and uses Probabilistic Data Association (PDA) to assess the probability of each return being the correct return. This theory has been modified for use in seismic event tracking, which unlike target tracking, is a static problem, and this new approach has been tested on both real and synthetic 3-D data sets. The tracker successfully picks out the chosen horizon in both the synthetic and real 3-D data sets. The accuracy of the 3-D tracker may be improved by tracking through the data set in two perpendicular directions and correlating the results. Results show that it is also possible to include a diagonal track in the correlation.
Geometrical‐spreading and ray‐caustic decomposition of elementary seismic waves
Authors: Hubral Peter , Tygel Martin , Schleicher Jörg
Published: October 2002

The computation of the geometrical‐spreading factor and the number of caustics is often considered to be the most fundamental step in computing zero‐order ray solutions for elementary‐wave Green’s functions along a ray that originates at a point source and passes through a 3-D laterally inhomogeneous isotropic medium. Here, a new factorization method is described that establishes both quantities recursively along the ray segments into which the total ray can be subdivided. As a consequence of the proposed method, the point‐source geometrical‐spreading factor and the number of ray caustics along the total ray can be decomposed into (1) point‐source spreading factors of the ray segments and (2) certain Fresnel zone contributions at the ray‐segment connection points. In a so‐called “3-D simple medium,” by which any 3-D laterally inhomogeneous medium can be approximated, the new factorization approach permits a simple computation of both quantities. It thus simplifies and provides new insights into the computation of ray‐theoretical Green’s functions.
Scale‐dependent seismic velocity in heterogeneous media
Authors: Mukerji Tapan , Mavko Gary , Mujica Daniel , Lucet Nathalie
Published: October 2002

The measurable traveltimes of seismic events propagating in heterogeneous media depend on the geologic scale, the seismic wavelength, and the propagation distance. In general, the velocity inferred from arrival times is slower when the wavelength is longer than the scale of heterogeneity and faster when the wavelength is shorter. For normal incidence propagation in stratified media, this is the difference between averaging seismic slownesses in the short wavelength limit, and averaging elastic compliances in the long wavelength limit. In two and three dimensions there is also the path effect. Shorter wavelengths tend to find faster paths, thus biasing the traveltimes to lower values. In the short wavelength limit, the slowness inferred from the average traveltime is smaller than the mean slowness of the medium. When the propagation distance is much larger than the scale of the heterogeneity, the path effect causes the velocity increase from long to short wavelengths to be much larger in two dimensions than in one dimension, and even larger in three dimensions. The amount of velocity dispersion can be understood theoretically, but there is some discrepancy between theory and experiment as to what ratio of wavelength to heterogeneity scale separates the long and short wavelength limits. The scale‐dependent traveltime implies that a measured velocity depends not just on rock properties, but also on the scale of the measurement relative to the scale of the geology. When comparing measurements made at different scales, for example logs and surface seismic, it is not always correct to simply apply the Backus average; the correct procedure will vary from case to case with the scale of the geology. Scale effects must be included with other viscoelastic mechanisms of dispersion when comparing measurements made at different frequencies. The amount of observed scale‐dependent dispersion also depends on the spatial resolution of the receiver array. For example, the first‐break time of the average trace from a stack, a large group array, or a large laboratory transducer may be earlier than the average of first‐break times measured with individual small‐scale receivers.
Anisotropic parameters of layered media in terms of composite elastic properties
Authors: Brittan John , Warner Mike , Pratt Gerhard
Published: October 2002

In elastic earth models, at a wide variety of scales, the subsurface is a layered sequence of different constituent media. It is therefore important to understand the elastic properties of such a sequence, in particular to determine the response of the layering to an investigating seismic wave. It can be shown that if the individual layer thicknesses are much less than the wavelength of a seismic wave passing through the stack, the wave will propagate as though it were traversing a homogenous, anisotropic medium (Postma, 1955). This property has been subjected to rigorous testing both experimentally (Melia and Carlson, 1984) and numerically (Carcione et al., 1991). The elastic properties of this “equivalent medium” can be derived algebraically from the elastic properties of the materials that compose the layers (Backus, 1962). The homogenous equivalent medium will be transversely isotropic (hereafter referred to as TI), the axis of symmetry lying perpendicular to the layering.
Q‐factor approximation of electromagnetic fields for high‐frequency sounding in the 300 kHz to 30 MHz range over layered media
Authors: Anderson Walter L.
Published: October 2002

A new method for rapid approximation of electromagnetic (EM) fields for high‐frequency sounding (HFS) over a layered earth is presented in this paper. The essence of this method uses a Q‐factor correction for extending a closed‐form, half‐space analytic solution to a layered earth model. Use of the Q‐factor in this context was first studied by Wait (1953, 1962). Kraichman (1976) also discusses the problem of when the Q‐factor method can be used to provide a good approximation to an exact layered earth solution.
Studying the TEM response of a 3-D conductor at a geological contact using the FDTD method
Authors: Wang Tsili , Tripp Alan C. , Hohmann Gerald W.
Published: October 2002

Many mineral targets are located near contact zones. Since the change of resistivity across the contact can distort or obscure the transient electromagnetic (TEM) response of the target, it is important to understand the possible effects.
On: “Migration by Fourier transform,” by R.H. Stolt (January 1978 GEOPHYSICS, 43, p. 23–48).
Authors: Dutta Somaditya
Published: October 2002

In this paper the migrated section is given by two equations. However, I find a factor (c/2) is missing in either equation (51) or (52). The necessary derivation follows.
Sonic logging of compressional‐wave velocities in a very slow formation
Authors: Tichelaar Bart W. , van Luik Klaas W.
Published: October 2002

Borehole sonic waveforms are commonly acquired to produce logs of subsurface compressional and shear wave velocities. To this purpose, modern borehole sonic tools are usually equipped with various types of acoustic sources, i.e., monopole and dipole sources. While the dipole source has been specifically developed for measuring shear wave velocities, we found that the dipole source has an advantage over the monopole source when determining compressional wave velocities in a very slow formation consisting of unconsolidated sands with a porosity of about 35% and a shear wave velocity of about 465 m/s. In this formation, the recorded compressional refracted waves suffer from interference with another wavefield component identified as a leaky P‐wave, which hampers the determination of compressional wave velocities in the sands. For the dipole source, separation of the compressional refracted wave from the recorded waveforms is accomplished through bandpass filtering since the wavefield components appear as two distinctly separate contributions to the frequency spectrum: a compressional refracted wave centered at a frequency of 6.5 kHz and a leaky P‐wave centered at 1.3 kHz. For the monopole source, the frequency spectra of the various waveform components have considerable overlap. It is therefore not obvious what passband to choose to separate the compressional refracted wave from the monopole waveforms. The compressional wave velocity obtained for the sands from the dipole compressional refracted wave is about 2150 m/s. Phase velocities obtained for the dispersive leaky P‐wave excited by the dipole source range from 1800 m/s at 1.0 kHz to 1630 m/s at 1.6 kHz. It appears that the dipole source has an advantage over the monopole source for the data recorded in this very slow formation when separating the compressional refracted wave from the recorded waveforms to determine formation compressional wave velocities.
Attenuation and anisotropy: The effect of extra fine layering
Authors: Sams Mark S.
Published: October 2002

Layering that is finer than that typically resolved by sonic logging will contribute to apparent attenuation and anisotropy in the sonic‐to‐seismic frequency range. The significance of this contribution can be discerned through resolution enhancement of sonic and density logs. In this study a borehole compensated sonic and density log recorded in a cyclical sedimentary sequence have been enhanced by response matching with a high‐resolution microresistivity log. The additional resolved layering increases the layer‐induced dispersion by 50%, with the additional attenuation showing a peak with a Q of 135 at 1.2 kHz. The increase in average anisotropy is frequency dependent with a minimum increase of 50% at zero frequency. In the absence of high‐resolution data, the effects of layering can be severely underestimated, resulting in poor estimates of the intrinsic properties of rocks and their pore fluids.