bluuebunny/crossref_metadata_2025 huggingface dataset:
Geostatistical simulation for geophysical applications—Part II: Geophysical modeling
Authors: Shive P. N. , Lowry T. , Easley D. H. , Borgman L. E.
Published: October 2002

A companion paper (this issue) describes a method for producing three‐dimensional simulations of physical properties for different geologic situations. Here we create a simulation for a particular case, which is a near‐surface (<80 ft deep) description of a karst environment. We simulate seismic velocity, density, resistivity, and the dielectric constant for this situation. We then conduct (in the computer) hypothetical geophysical surveys at the surface of the model. These surveys are seismic refraction, microgravity, dc resistivity, and ground‐probing radar. Physical properties appropriate for cavities are then entered in the model. Repeating the geophysical surveys over the model with cavities provides a convenient method of evaluating their potential for cavity detection. Anomalies produced by normal variations in physical properties may simulate or obscure anomalies from target features. More data about the correlation of physical properties, particularly in the horizontal directions, will be required to evaluate this problem properly.
Apparent azimuthal shear anisotropy from normal‐moveout differentials
Authors: Iverson William P.
Published: October 2002

A simple normal‐moveout (NMO) correction can move common‐depth‐point (CDP) reflection times up or down a few milliseconds when the stacking velocity is varied a small fraction. Different stacking velocities on two orthogonal shear components are often required, such as in the cases of azimuthal anisotropic media (Thomsen, 1986) or transversely isotropic media (Levin, 1979). The difference between these two cases is that CDP reflection times are different on S1 and S2 in the case of azimuthal anisotropy, while CDP reflection times are equal for transverse isotropic media. The similarity is that both cases require different stacking velocities on the S1 and S2 components.
Radon transform migration below plane sloping layers
Authors: Bisset David A. , Durrani T. S.
Published: October 2002

A Radon transform mapping is developed which allows correct migration below plane sloping layers to be achieved. The mapping, which is the P-τ equivalent of a Fourier transform mapping, consists of p shifting and weighting. The effect of the mapping is to move the recording plane to a sloping interface. Migration then becomes conventional migration in a horizontally layered medium. Breaking the process into a sequence of steps gives a high level of insight into this particular wave‐field‐extrapolation problem. Applying the Radon transform mapping to a synthetic example of migration below a sloping layer produces excellent results. However, the method is accurate only for planar reflectors.
Modeling acoustic waves with paraxial extrapolators
Authors: Graves R. W. , Clayton R. W.
Published: October 2002

Modeling by paraxial extrapolators is applicable to wave‐propagation problems in which most of the energy is traveling within a restricted angular cone about a principal axis of the problem. Using this technique, frequency‐domain finite‐difference solutions accurate for propagation angles out to 60° are readily generated for both two‐dimensional (2-D) and three‐dimensional (3-D) models. Solutions for 3-D problems are computed by applying the 2-D paraxial operators twice, once along the x‐axis and once along the y‐axis, at each extrapolation step. The azimuthal anisotropy inherent to this splitting technique is essentially eliminated by adding a phase‐correction operator to the extrapolation system. For heterogeneous models, scattering effects are incorporated by determining transmission and reflection coefficients at structural boundaries within the media. The direct forward‐scattered waves are modeled with a single pass of the extrapolation operator in the paraxial direction for each frequency. The first‐order backscattered energy is then modeled by extrapolation (in the opposite direction) of the reflected field determined on the first pass. Higher order scattering can be included by sweeping through the model with more passes. The chief advantages of the paraxial approach are (1) active storage is reduced by one dimension compared to solutions which must track both forward‐scattered and backscattered waves simultaneously; thus, realistic 3-D problems can fit on today’s computers, (2) the decomposition in frequency allows the technique to be implemented on highly parallel machines, (3) attenuation can be modeled as an arbitrary function of frequency, and (4) only a small number of frequencies are needed to produce movie‐like time slices.
Seismic exploration on a floating ice sheet
Authors: Rendleman C. A. , Levin F. K.
Published: October 2002

Using a point‐source viscoelastic seismic wave modeling program, we simulated the seismograms that would be recorded for a system of an ice sheet floating on a water layer, the latter underlain by a solid containing a single isolated reflector. Ice and water layer thicknesses were 1.52–6.10 m. Sources were placed successively on the surface of the ice, in the water, and in the bottom; detectors (vertical geophones or hydrophones) were placed successively on the ice, in the water, and in the bottom. A source on the ice generated such strong antisymmetric modal energy that no reflections could be detected. A source buried 15–30 m below the bottom of the water resulted in clear reflections, whether the reflections were detected with surface geophones or buried hydrophones. Geophysicists have often observed data very similar to that which we modeled, but not universally. In practice, vibrators on floating ice produce usable reflections for a fixed but year‐to‐year variable water depth. To explain this observation, we are forced to assume that the floating annual ice of the Arctic is a strongly attenuative material.
Finite‐difference calculation of traveltimes in three dimensions
Authors: Vidale John E.
Published: October 2002

The traveltimes of first arriving seismic rays through most velocity structures can be computed rapidly on a three‐dimensional numerical grid by finite‐difference extrapolation. Head waves are properly treated and shadow zones are filled by the appropriate diffractions. Differences of less than 0.11 percent are found between the results of this technique and ray tracing for a complex but smooth model. This scheme has proven useful for earthquake location and shows promise as an inexpensive, well‐behaved substitute for ray tracing in forward‐modeling and Kirchhoff inversion applications.
Analysis of conventional and converted mode reflections at Putah sink, California using three‐component data
Authors: Frasier C. , Winterstein D.
Published: October 2002

In 1980 Chevron recorded a three‐component seismic line using vertical (V) and transverse (T) motion vibrators over the Putah sink gas field near Davis, California. The purpose was to record the total vector motion of the various reflection types excited by the two sources, with emphasis on converted P‐S reflections. Analysis of the conventional reflection data agreed with results from the Conoco Shear Wave Group Shoot of 1977–1978. For example, the P‐P wave section had gas‐sand bright spots which were absent in the S‐S wave section. Shot profiles from the V vibrators showed strong P‐S converted wave events on the horizontal radial component (R) as expected. To our surprise, shot records from the T vibrators showed S‐P converted wave events on the V component, with low amplitudes but high signal‐to‐noise (S/N) ratios. These S‐P events were likely products of split S‐waves generated in anisotropic subsurface media. Components of these downgoing waves in the plane of incidence were converted to P‐waves on reflection and arrived at receivers in a low‐noise time window ahead of the S‐S waves. The two types of converted waves (P‐S and S‐P) were first stacked by common midpoint (CMP). The unexpected S‐P section was lower in true amplitude but much higher in S/N ratio than the P‐S section. The Winters gas‐sand bright spot was missing on the converted wave sections, mimicking the S‐S reflectivity as expected. CRP gathers were formed by rebinning data by a simple ray‐tracing formula based on the asymmetry of raypaths. CRP stacking improved P‐S and S‐P event resolution relative to CMP stacking and laterally aligned structural features with their counterparts on P and S sections. Thus, the unexpected S‐P data provided us with an extra check for our converted wave data processing.
Traveltime inversion for dipping layers, large moveouts, and arbitrary source and receiver positions
Authors: Dodds D. J.
Published: October 2002

The seismic traveltime inversion algorithm presented here requires few limiting assumptions and is computationally efficient. The traveltime for a raypath in a layered earth (uniform or linearly varying sound speeds in each layer) can be written in closed form if the coordinates of the intersections between the raypath and the layer interfaces are known. The traveltime on an actual raypath is minimal with respect to neighboring paths. The raypath can thus be determined by equating the derivatives of the traveltimes with respect to the intersection coordinates to zero. This approach can be applied to the inverse problem, which seeks those layer parameter values which “best fit” the observed traveltimes from a CMP reflection gather. The result is a system of equations in which the intersection coordinates and layer parameters are independent variables, with the constraint that the traveltimes be minimal with respect to the coordinates. When this systemis linearized with a step‐size constraint, an efficient inversion algorithm results. The equations are solved without numerical differentiation or iterative solution of the forward problem at each step in the inversion. The number of operations required in each iteration is proportional to the number of moveouts and the third power of the number of interfaces. The algorithm has been applied to the estimation of sound speed in thin (e.g., 3–15 m) sea‐floor sediment layers from CMP reflection data obtained with a 3 kHz system bandwidth. Errors were reduced by fitting traveltime differences determined by crosscorrelation of events at different moveouts. In favorable conditions, the scatter in estimated sound speeds was 2 percent for a 15 m layer.
Borehole coupling at sonic frequencies
Authors: Lovell J. R. , Hornby B. E.
Published: October 2002

An elastic plane wave incident on a borehole couples through the borehole wall to produce a compressional wave inside the borehole, and the effect of this coupling varies with incident angle. Imaging experiments that include a downhole source and/or hydrophones must account for this effect to achieve optimal results. In configurations pertinent to VSP surveys and cross‐well surveys at seismic frequencies, a low‐frequency source can be assumed. Recently, however, both cross‐well and single‐well imaging experiments have been undertaken at sonic frequencies (above 2000 Hz) where low‐frequency approximations are no longer valid. We have developed new formulas which are valid over all frequencies and incident angles. For both shear and compressional incident waves, we present explicit formulas to describe this dependence. Contrary to what might be expected from low‐frequency approximations, we find that at certain angles and for high enough frequencies, marked resonances in the coupling terms for both shear and compressional incidence occur. Moreover, at all frequencies, the borehole coupling term depends significantly upon incident angle. For a given incident angle, and for high enough frequencies, the coupling term becomes periodic in frequency. We give analytic expressions for these high‐frequency resonances and present a simplified high‐frequency approximation that can be computed without using Bessel or Hankel functions. Results are presented for three different formation types; very hard, medium hard, and soft. For all formation types, significant variations in amplitude as well as strong shifts in phase are apparent, as functions of both frequency and incident angle. This distortion of the wave field should be taken into account for any imaging experiment that uses high‐frequency signals.
Long‐offset transient electromagnetic (LOTEM) depth soundings applied to crustal studies in the Black Forest and Swabian Alb, Federal Republic of Germany
Authors: Strack K. ‐M. , Lüschen E. , Kötz A. W.
Published: October 2002

The long‐offset transient electromagnetics (LOTEM) sounding method is a valuable complementary technique for deep seismic exploration as applied to earth crustal investigations. During 1986, two LOTEM surveys were conducted to augment completed seismic investigations for crustal studies in southern West Germany, east of the Rhine graben. Our studies were motivated by the geoscientific activities within the framework of the German Continental Deep Drilling (KTB) project. The survey objectives were (1) to determine the applicability of the LOTEM method to crustal geophysics, (2) to investigate the correlation of resistivity anomalies with velocity anomalies, and (3) to confirm the method and interpretation in an area of known geology with existing geophysical data. The Black Forest and the Urach geothermal area survey results exhibit conductive features in the upper 10 km of the crust which were not previously defined by other geophysical data. Importantly, the results demonstrate a very strong correlation of a low‐velocity zone with low electrical resistivity at 5 to 7 km depth within the crystalline basement at both locations.
Seismic stratigraphy of the mid‐Cretaceous unconformity (MCU) in the central Gulf of Mexico basin
Authors: Faust Michael J.
Published: October 2002

A widespread high‐amplitude reflection seen on seismic data throughout the Gulf of Mexico has been called the “Mid‐Cretaceous Unconformity” (MCU). This reflector seems to be a major stratigraphic boundary in the Gulf of Mexico basin. It is believed to correspond to Vail’s type 1 unconformity of mid‐Cenomanian age (94 Ma), which records an eustatic drop in sea level of approximately 60–100 m. The study area includes all of the Gulf of Mexico with the exception of areas of thick and highly deformed salt, where following the MCU with any degree of confidence becomes impossible. The MCU is easy to follow in multichannel seismic reflection profiles collected in the Gulf of Mexico by the Institute for Geophysics of the University of Texas at Austin. In the central, deeper part of the gulf, reflectors above and below the MCU are parallel. In the southern and eastern rims of the Gulf, along the Campeche and Florida escarpments, reflectors are truncated below the MCU and show onlap relationships above it. The MCU, therefore, may be interpreted as representing an unconformity along the southern and eastern rims of the Gulf of Mexico basin. The uncomformity appears to die out and grade into a conformable section toward the central part of the basin. Channeling is common in the MCU along the Campeche and Florida escarpments, which was probably initiated by subaerial exposure of the top of the escarpments during the mid‐Cretaceous lowstand. The downslope channels were cut in deep water.
Direct method for determining constant corrections to geophysical survey lines for reducing mis‐ties
Authors: Bandy W. L. , Gangi A. F. , Morgan F. D.
Published: October 2002

A least‐squares method of minimizing mis‐ties in geophysical surveys yields a simple, direct method for determining constant corrections along each crossing survey line. This “direct method” is a special case of the more general, orthogonal polynomial method of Foster et al. (1970). The constant corrections are determined directly from the observed data, eliminating the need to iterate or invert a matrix to determine the corrections as in previously published, constant‐correction algorithms. The magnitude of the constant correction to the field values along a particular line equals the difference between the mean mis‐tie value for that line and one‐half the mean mis‐tie for the entire survey. The method minimizes both the mis‐ties and the distortion of the original survey; namely, the mean squared mis‐tie for the entire survey and the mean squared corrections are both minimized. Application of the direct method to test cases in which known errors are added to known “true” field values along survey lines in an (x, y) plane indicates that (1) the mis‐ties are completely eliminated if their functional form contains only terms which are functions of either x or y, regardless of the functional form of the errors themselves, (2) the method preserves both the relative field values along the survey lines and the original mean error of the survey, (3) the corrections are independent of the true field, (4) errors common to both intersecting lines will remain in the final map, and (5) the resulting corrected field is not necessarily a more accurate representation of the “true” field even when the mis‐ties are completely eliminated.
Transient electromagnetic inversion: A remedy for magnetotelluric static shifts
Authors: Pellerin Louise , Hohmann Gerald W.
Published: October 2002

Surficial bodies can severely distort magnetotelluric (MT) apparent resistivity data to arbitrarily low frequencies. This distortion, known as the MT static shift, is due to an electric field generated from boundary charges on surficial inhomogeneities, and persists throughout the entire MT recording range. Static shifts are manifested in the data as vertical, parallel shifts of log‐log apparent resistivity sounding curves, the impedance phase being unaffected. Using a three‐dimensional (3-D) numerical modeling algorithm, simulated MT data with finite length electrode arrays are generated. Significant static shifts are produced in this simulation; however, for some geometries they are impossible to identify. Techniques such as spatial averaging and electromagnetic array profiling (EMAP) are effective in removing static shifts, but they are expensive, especially for correcting a previously collected MT data set. Parametric representation and use of a single invariant quantity, such as the impedance tensor determinant, are only useful in limited circumstances and can lead the MT interpreter astray. Transient electromagnetic (TEM) sounding data are relatively inexpensive to collect, do not involve electric field measurements, and are only affected at very early times by surficial bodies. Hence, using TEM data acquired at the same location provides a natural remedy for the MT static shift. We describe a correction scheme to shift distorted MT curves to their correct values based on 1-D inversion of a TEM sounding taken at the same location as the MT site. From this estimated 1-D resistivity structure an MT sounding is computed at frequencies on the order of 1 Hz and higher. The observed MT curves are then shifted to the position of the computed curve, thus eliminating static shifts. This scheme is accurate when the overlap region between the MT and TEM sounding is 1-D, but helpful information can be gleaned even in multidimensional environments. Other advantages of this scheme are that it is straightforward to ascertain if the correction scheme is being accurately applied and it is easy to implement on a personal computer.
An example of simultaneous recording where necessary signal separation is easily achieved
Authors: Pritchett William C.
Published: October 2002

The key to success in recording multiple data sets simultaneously from multiple sets of sources is being able to separate the multiple data sets satisfactorily. If at a given receiver position the energy level is greatly different from one source than from another source, then we may have difficulty in extracting the weaker trace from the stronger trace. We operated two sets of sources at two adjacent source positions, so that the energy levels from the two sets of sources at any receiver position were not greatly different and satisfactory separation of the traces was relatively easy. Reflections from adjacent source positions as recorded at any receiver position were also similar in that the rays were reflected from adjacent reflection points at depth. Actually, of course, our measurements responded not to rays but to waves which were reflected from rather large areas surrounding the reflection points. Reflections from adjacent reflection points were actually from areas which overlapped substantially; therefore, signals reflected from adjacent reflection points would not have been totally independent even with conventional recording from one set of sources. Slight, additional contamination of one trace by an adjacent trace because of less than perfect separation of simultaneously recorded data was of little consequence with our technique. We saved money by speeding up recording, and data quality was excellent. In our application of the technique the reflection targets were rather shallow, but the technique is not limited to shallow exploration. To best meet our exploration objectives, we used simultaneous recording to save field time and money. We used nonlinear sweeps in the field along with effective spectral flattening processing techniques to bring out higher frequencies and improve resolution. We used the stack‐array technique (Anstey, 1986) to suppress noise in the stacked data better. Some have objected that our technique cannot possibly work, and have shut their minds against discussion and favorable evidence. However, this technique is based upon nothing more controversial than a valid application of the theorem of superposition. Furthermore, the technique was validated by field results including the recording of 73 mi (117 km) of excellent data in 1984 and 1985 at relatively modest costs.
Empirical observations relating near‐surface magnetic anomalies to high‐frequency seismic data and Landsat data in eastern Sheridan County, Montana
Authors: Andrew John A. , Edwards Duncan M. , Graf Robert J. , Wold Richard J.
Published: October 2002

Our empirical synergistic correlations of aeromagnetic and seismic data and a Landsat lineament interpretation revealed lineations on the magnetic map that have expression on seismic sections. We observed a conjugate set of northwest‐southeast and northeast‐southwest trending magnetic lineaments (zones which offset and truncate near‐surface magnetic anomalies). We believe these OZs (offset zones) represent lateral faults in a wrench‐fault system. Lateral offsets appear to be 100s of meters to a few kilometers (fractions of a mile to a few miles). We observed a direct correlation between OZs and vertical faults in seismic data. Faults on seismic sections extend from near the surface to near the seismic basement. The faults are most pronounced in the Upper Cretaceous reflectors and seem to disappear with depth. Fault throws are inconsistent (reversing throw across faults). OZs trend northeast‐southwest in the north half of the study area and both northeast‐southwest and northwest‐southeast in the south half. The OZ direction of northeast‐southwest in the north half of the survey is confirmed with seismic data. The northwest‐southeast seismic line contains numerous faults and the northeast‐southwest seismic line contains few faults. Most northeast‐southwest faults do not appear to reach seismic basement and are not seen in an interpretation of the magnetic basement. In two cases, northwest‐southeast OZs and correlative Landsat lineaments coincide with mapped magnetic basement faults. These magnetic basement faults can be seen in seismic data too. Faults trending northwest‐southeast may represent Precambrian faults reactivated during the Laramide Orogeny. Movement along these faults possibly generated the northeast‐southwest faults. Most oil fields have an associated near‐surface magnetic anomaly. Other near‐surface magnetic anomalies occur over obvious, untested (in 1985), seismic character or amplitude anomalies in seismic events which correlate with producing intervals in the oil fields. This synergistic correlation is the most important single observation from our study. Different data types and interpretation techniques identified the same geologic trends and prospective geographical areas. This fundamentally important information is often lost in bickering over which filter or processing technique to use or in arguments over which data type is “more important” than others. Further, if the synergistic correlation of data types were not done, the importance of the anomalous features in each individual data type may not have been recognized.
Traveltime tomography: A comparison of popular methods
Authors: Phillips W. Scott , Fehler Michael C.
Published: October 2002

Noisy or inconsistent traveltime data yielded tomographic images that contain geologically unrealistic fluctuations. In addition to diverting attention away from structural patterns, these high‐wavenumber fluctuations can generate shadow zones and caustics that destabilize iterative solution schemes requiring ray tracing. We evaluated the performance of a number of popular methods that have been designed to reduce this effect, using synthetic crosswell data containing Gaussian noise. Quantitative comparisons between tomography methods were based on the misfit with the true model, solution stability under different sets of noise of the same level, and resolution‐covariance relationships. Other important factors included versatility and simplicity. Versatility is the ability to treat data with a wide range of noise levels as well as data generated by different structures. Simplicity is characterized by the number of adjustable inputs such as smoother shape, starting model, and damping or regularization parameters that may be required. Constraint parameters such as damping must be chosen before performing an inversion. The smallest‐misfits between solutions and true models were found for constraint parameters lying just below a “kink” or change in slope of the rms residual versus constraint parameter curve. The kink separates regions in which either data or smoothing constraints dominate the solution and provides a means for choosing the optimal constraint parameter. A first difference regularization method performed the best overall and proved both simple to use and versatile in terms of the range of noise levels for which it could be used effectively. Second difference schemes were not tested since the problem is singular in the limited coverage crosswell geometries that we used. Convolutional quelling proved the best of the damped least‐squares methods, but had resolution limited by the dimension and shape of the smoothing function. A simple averaging smoother worked reasonably well on data generated by a smooth model, while a median performed better on data generated by a model with large contrasts. An iterative [Formula: see text] norm method did not function well with Gaussian noise, but was effective in tests with long‐tailed noise distributions.
Multipole borehole acoustic waveforms: Synthetic logs with beds and borehole washouts
Authors: Randall C. J. , Scheibner D. J. , Wu P. T.
Published: October 2002

We give a two‐dimensional (2-D) velocity‐stress finite‐difference (vs-fd) formulation for the multipole borehole acoustic logging problem. Irregular boreholes, horizontal bedding, and axially varying alteration are encompassed by the model. Excellent agreement is obtained with transform techniques for constant radius boreholes and homogeneous formations. The method is used to generate waveforms for many positions of transmitter and receiver array relative to beds and washouts as in logging. First motion and semblance techniques are applied to the waveforms to extract formation slownesses, resulting in synthetic multipole logs which demonstrate the response of ideal multipole logging tools and signal processing to several environmental effects. For monopole, compressional, first‐motion logs, residual slowness errors remain at borehole washouts after borehole compensation. These errors increase as the effective measure point in the waveforms is moved back in time from true first motion, admitting greater interference from reflected and mode‐converted waves. Errors at bed boundaries are typically smaller than those at washouts. Stoneley slowness logs are obtained by narrow‐band filtering of low frequency monopole waveforms and application of the semblance slowness extraction algorithm STC. Similar processing applied to low frequency dipole waveforms yields flexural mode slowness logs. A small correction satisfactorily accounts for flexural mode dispersion properties, yielding formation shear slowness. Slowness errors for both Stoneley and dipole shear logs at washouts and bed boundaries are quite small, typically on the order of a few percent. Borehole compensation is of marginal benefit for both of these logs since they are based on modes of the borehole rather than head‐waves.
Naturally smooth inversions with a priori information from well logs
Authors: Pilkington M. , Todoeschuck J. P.
Published: October 2002

Regularization is usually necessary to guarantee a solution to a given inverse problem. When constructing a model that gives an adequate fit to the data, some suitable method of regularization which provides numerical stability can be used. When investigating the resolution and variance of the computed model parameters, the character of regularization should be specified by the a priori information available. This avoids arbitrary variation of the damping to suit the interpreter. For geophysical inverse problems we determine the appropriate level of regularization (in the form of parameter covariances) from power spectral analysis of well‐log measurements. For resistivity data, well logs indicate that the spatial variation with depth can be described adequately by a scaling noise model, that is, one in which the power spectral density is proportional to some power (α) of the frequency. We show that α, the scaling exponent, controls the smoothness of the final model. For α < 0, the model becomes smoother as α becomes more negative. As a specific example, this approach is applied to the magnetotelluric inverse problem. A synthetic example illustrates the smoothing effect of α on inversion. Comparison between the scaling noise approach and a previous Backus‐Gilbert type inversion on some field data shows that using the appropriate value of α (−1.8 for this example) results in a model which is structurally simple and contains only those features well resolved by the data.
Phase‐smoothed robust M-estimation of magnetotelluric impedance functions
Authors: Sutarno D. , Vozoff K.
Published: October 2002

Accurate estimation of impedance functions is essential for the correct interpretation of magnetotelluric (MT) measurements. Noise is inevitably encountered when MT observations are conducted and, consequently, impedance estimates are usually based on least‐squares (LS) regression. Least squares ultimately assumes simple Gaussian statistics. However, estimation procedures based on LS would not be statistically optimal, as outliers (abnormal data) are frequently superimposed on a normal ambient MT noise field which is approximately Gaussian. In this situation, the estimation can be seriously misleading. An alternative method for making unbiased robust estimates of MT impedance functions is based on regression M-estimation and the Hilbert Transform, operating on minimum‐phase MT impedance functions. In the resulting regression estimates, outlier contamination is removed and other departures from Gauss‐Markov optimality are not critical. Using MT data from the Columbia River Plateau and the EMSLAB Lincoln line, it is shown that the method can produce usable MT impedance functions even under conditions of severe noise contamination and in the absence of remote reference data.
Three‐dimensional multicomponent imaging of reservoir heterogeneity, Silo Field, Wyoming
Authors: Lewis Catherine , Davis Thomas L. , Vuillermoz Claude
Published: October 2002

The Reservoir Characterization Project at Colorado School of Mines acquired a three‐dimensional (3-D) multicomponent survey over Silo field in southeastern Wyoming with the objective of imaging reservoir heterogeneity. A 3-D shear‐wave survey resolved spatial variations in the fracture distribution of Niobrara chalks by detecting small percentages of anisotropy induced by fractures in chalks of the Niobrara reservoir. In addition, the compressional‐wave survey imaged structural drape over a zone of deeper salt dissolution, which fractured the brittle chalks. Rotation analysis of the shear‐wave survey took advantage of its 3-D nature to identify an azimuthal pattern of anisotropy associated with vertical fractures, known as extensive dilatancy anisotropy (EDA). The shear‐wave data were sorted by shot‐to‐geophone azimuth to search for the orthorhombic pattern of anisotropy that might be expected from the combined effects of sedimentary layering and vertical fractures, but it was not found at Silo Field. Although groundroll contaminated some of the “pie slices” of azimuth in the rotation analysis, the redundancy of ten “pie slices” enabled us to determine an overall fracture orientation of N 58° W. The 3-D shear‐wave survey yielded a picture of fracture variability that could not be determined from well control alone. Fracture‐identification logs and production records were used in interpreting the anisotropy determined from the shear waves. Large positive values of anisotropy in the Niobrara interval, up to 5 percent, coincided with good producers in the field, while smaller magnitudes of anisotropy were tied to poor producers. Combining the multicomponent seismic recording with 3-D survey techniques added lateral resolution to the reservoir description and rendered a more complete understanding of the pattern of anisotropy resulting from fractures in the reservoir.
Elastic wave propagation using cylindrical coordinates
Authors: Kessler David , Kosloff Dan
Published: October 2002

A pseudo‐spectral method for a solution of the equations of dynamic elasticity in cylindrical coordinates is based on the Chebychev expansion in the radial direction and the Fourier expansion in the angular direction and is suitable for simulating wave propagation in the vicinity of cylindrical objects. The numerical grid consists of a series of concentric rings, each one with a separate Chebychev‐Fourier mesh. One numerical grid is defined for the cylindrical cavity and another grid for the medium around the cavity. Combining these two numerical grids allows reduction of the number of grid points in the angular direction in the interior grid and thus increases the time step. This makes the use of polar coordinates much more economic. The numerical algorithm is applicable to any arbitrary heterogeneous medium.
A guide to the limits of resolution imposed by scattering in ray tomography
Authors: Williamson P. R.
Published: October 2002

Tomographic imaging is now in widespread use in geophysical inversion. Most early work in this field used the ray approximation to wave propagation, but more recently scattering effects have been addressed via the formalism of diffraction tomography. However, if the correct image cannot be adequately represented as a perturbation of a simple background, this may demand considerably more computational resources than ray tomography. Therefore it is of some interest to determine the scalelength of variation below which scattering cannot be neglected, so that ray tomography is no longer reliable. In the hypothetical case of monochromatic illumination of a region consisting of small perturbations to a homogeneous background, the way in which the two reconstruction algorithms map the data into the Fourier components of the object may be directly compared to reveal the effect of neglecting scattering. These mappings begin to differ significantly at a wave‐number corresponding to the first Fresnel zone radius; it seems reasonable to expect that a similar result should apply to cases with more general background velocities, and so to iterative (nonlinear) inversions. Therefore some kind of inverse scattering approach must be employed to ensure accurate imaging beyond this wavenumber to the limit of twice that of the illuminating radiation.
Combining wave‐equation imaging with traveltime tomography to form high‐resolution images from crosshole data
Authors: Pratt R. Gerhard , Goulty Neil R.
Published: October 2002

Traveltime tomography is an appropriate method for estimating seismic velocity structure from arrival times. However, tomography fails to resolve discontinuities in the velocities. Wave‐equation techniques provide images using the full wave field that complement the results of traveltime tomography. We use the velocity estimates from tomography as a reference model for a numerical propagation of the time reversed data. These “backpropagated” wave fields are used to provide images of the discontinuities in the velocity field. The combined use of traveltime tomography and wave‐equation imaging is particularly suitable for forming high‐resolution geologic images from multiple‐source/multiple‐receiver data acquired in borehole‐to‐borehole seismic surveying. In the context of crosshole imaging, an effective implementation of wave‐equation imaging is obtained by transforming the data and the algorithms into the frequency domain. This transformation allows the use of efficient frequency‐domain numerical propagation methods. Experiments with computer‐generated data demonstrate the quality of the images that can be obtained from only a single frequency component of the data. Images of both compressional [Formula: see text] and shear wave [Formula: see text] velocity anomalies can be obtained by applying acoustic wave‐equation imaging in two passes. An imaging technique derived from the full elastic wave‐equation method yields superior images of both anomalies in a single pass. To demonstrate the combined use of traveltime tomography and wave‐equation imaging, a scale model experiment was carried out to simulate a crosshole seismic survey in the presence of strong velocity contrasts. Following the application of traveltime tomography, wave‐equation methods were used to form images from single frequency components of the data. The images were further enhanced by summing the results from several frequency components. The elastic wave‐equation method provided slightly better images of the [Formula: see text] discontinuities than the acoustic wave‐equation method. Errors in picking shear‐wave arrivals and uncertainties in the source radiation pattern prevented us from obtaining satisfactory images of the [Formula: see text] discontinuities.
Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory
Authors: Zhu X. , McMechan G. A.
Published: October 2002

Biot theory proSvides a framework for computing the seismic response of fluid‐saturated reservoirs. Numerical implementation by 2-D finite‐differences allows investigation of the effects of spatial variations in porosity, permeability, and fluid viscosity, on seismic displacements of the solid frame and of the fluids (oil, gas, and/or water) in the reservoir. The porosity primarily influences wave velocities; the viscosity‐to‐permeability ratio primarily influences amplitudes and attenuation. Synthetic crosswell, VSP, and surface survey seismograms for representative reservoir models contain primary and converted reflections from fluid as well as lithologic contacts, and they illustrate the distribution of information available for describing a reservoir.
Two methods for computing the imaging condition for common‐shot prestack migration
Authors: Loewenthal D. , Hu Liang‐zie
Published: October 2002

This note addresses two methods of computing the imaging condition for prestack migration of common‐shot seismic data; our work is based on the ideas from reverse‐time migration for both poststack (Loewenthal and Mufti, 1983; McMechan, 1983) and prestack data (Chang and McMechan, 1986). In reverse‐time migration of poststack data, the whole stacked section is backward‐extrapolated in time, with half of the medium velocity to time zero. All exploding reflectors are imaged at once at time zero. The time zero is referred to as the imaging condition. In prestack migration, the imaging condition is more involved. Each spatial grid point (treated as a point diffractor) has a different excitation time, which is equal to the one‐way traveltime from the source to that grid point. Each point diffractor is imaged separately at its excitation (the “imaging time”).
Chemical and microbial processes causing anomalous magnetization in environments affected by hydrocarbon seepage
Authors: Machel H. G. , Burton E. A.
Published: October 2002

(Aero‐)magnetic anomalies have been reported from several commercial hydrocarbon accumulations. However, the processes responsible for such anomalies are relatively poorly understood. This paper conceptually discusses chemical and microbiological processes involved in generating anomalous magnetization related to hydrocarbon accumulations, including hydrocarbon seepage environments. Based on thermodynamic criteria and microbiologic activity, the formation and destruction of magnetic mineral assemblages can be predicted. Under the influence of hydrocarbons, magnetite and pyrrhotite are the most important magnetic minerals formed, and the most abundant magnetic mineral destroyed is hematite. Hence, the invasion of hydrocarbons may result in “positive,” “absent,” or “negative” magnetic contrasts relative to the total magnetization prior to hydrocarbon invasion, depending upon the amounts of authigenic magnetite and pyrrhotite formed relative to the amounts of hematite destroyed. Magnetism may be generated also by natural and anthropogenic processes that have no relationships to an underlying or adjacent hydrocarbon accumulation. Consequently, anomalous magnetization, even if associated with a hydrocarbon accumulation, may or may not be genetically related to it. Magnetic mineral assemblages and the resulting magnetic contrasts, such as those predicted in this paper, have been documented from some hydrocarbon seepage environments. Hence, anomalous magnetization can be used for hydrocarbon exploration in association with other surface exploration methods.
Velocity inversion by differential semblance optimization
Authors: Symes W. W. , Carazzone J. J.
Published: October 2002

Differential semblance optimization (DSO) is an approach to inversion of reflection seismograms which avoids the severe convergence difficulties associated with nonlinear least‐squares inversion. The method exploits both moveout and amplitude characteristics of reflections. We have implemented a version appropriate to plane‐wave (p‐tau) seismograms and layered constant‐density acoustic earth models. Theoretical and numerical analyses of this version of DSO indicate that stable and reasonably accurate estimates of both velocity trend and reflectivity can be derived. To test DSO further, we applied it to a marine data set from the Gulf of Mexico, where the method produced results which compare favorably to well‐log information. The method can be extended to incorporate laterally heterogeneous velocity models.
Spiking band‐limited traces with a relative‐entropy algorithm
Authors: Jacobs F. J. , van der Geest P. A. G.
Published: October 2002

A novel method for the inversion of band‐limited seismic traces to full bandwidth reflectivity traces, is based on a probabilistic spiky model of the reflectivity trace, in which position indicators and amplitudes of the spikes occur as random variables, and relies on relative entropy inference from information theory. First, an a priori model for general reflectivity traces in the prospect is derived from nearby wells. Second, the a priori distribution is updated into an a posteriori distribution for the specific trace being studied by the addition of the Fourier data of the seismic trace within a passband. Uncertainty about the Fourier coefficients can be accounted for by specification of a noise variance, which implicitly is infinite outside the passband. The update with relative entropy inference is justified because of its relationship with Bayesian inference. Application of maximum a posteriori (MAP) estimation to the a posteriori distribution results in the most likely spiky reflectivity trace of full bandwidth. A numerical algorithm for obtaining the MAP estimates of spike positions and spike amplitudes is derived from the concept of continuation and is described in detail. The algorithm avoids searching among all possible patterns of spike positions.
Instantaneous frequency and amplitude at the envelope peak of a constant‐phase wavelet
Authors: Barnes A. E.
Published: October 2002

Robertson and Nogami (1984) have shown that the instantaneous frequency at the peak of a zero‐phase Ricker wavelet is exactly equal to that wavelet’s average Fourier spectral frequency weighted by its amplitude spectrum. Bodine (1986) gave an example which shows this is also true for constant‐phase bandpass wavelets. Here I prove that this holds for any constant‐phase wavelet. I then develop an equation expressing this quantity as a function of propagation time through an attenuating medium. A corresponding equation is derived for the amplitude of the envelope peak. Taken together, these may aid in the analysis of seismic data as suggested by Robertson and Nogami (1984), Bodine (1986), and Robertson and Fisher (1988).
Approximate inversion of high‐frequency electromagnetic soundings using complex image theory
Authors: Anderson Walter L.
Published: October 2002

Electromagnetic (EM) soundings in an intermediate range between quasi‐static and radar frequencies (e.g., 30 kHz – 300 MHz) were studied with an approximate inversion method for shallow‐layered earth models using complex image theory. The half‐space image theory formulas for calculating forward soundings for any dipole source are easily extended to accommodate a multilayered earth, and only involve elementary complex functions. Approximate inversion using the modified image formulas is compared with more exact numerical integration inversion for horizontal‐layered models to yield the conductivity, thickness, and dielectric permittivity of each layer. A nonlinear least‐squares algorithm was used to obtain parameter and linear parameter error estimates. The results, using known exact forward models and one field data case, indicate that approximate image inversion is more than an order‐of‐magnitude faster than numerical integration inversion. However, approximate inversion could not always resolve deeper layer parameters as well as with exact inversion. Accuracy of both methods, however, depends on the frequency range used. Nevertheless, approximate inversion can be a useful quick reconnaissance tool, and could easily be written for on‐site personal computers.
Inversion of pole‐pole data for 3-D resistivity structure beneath arrays of electrodes
Authors: Park S. K. , Van G. P.
Published: October 2002

We have developed a practical algorithm for inverting gridded resistivity data for three‐dimensional structure and applied it to data from an experiment designed to detect leaks from ponds. This method yields relatively accurate reconstructions of structure when applied to synthetic data, but lateral contrasts in resistivity are mapped much more accurately than are vertical contrasts. The best results are obtained when transmitting electrodes are located directly above the suspected leak. Application to real data yields results which are consistent with well data and an adjacent Schlumberger sounding.