bluuebunny/crossref_metadata_2025 huggingface dataset:
A simple method for the analysis of magnetic anomalies over dike‐like bodies
Authors: Babu H. V. Ram , Vijayakumar V. , Rao D. Atchuta
Published: October 2002

Magnetic anomalies may be simply analyzed using a dike model. In this model, the depth to the source is approximately 1.25 S, where S is the straight‐slope distance measured on the steepest flank. The dip of the body may be evaluated from θ, the combined magnetic angle found from the ratio of the maximum amplitude to the minimum amplitude. In the presence of remanence, the body dip δ may be found from θ only when the direction of resultant magnetization is either known or assumed, and magnetization direction may be found only if the dip is known. The minimum susceptibility contrast k of the source may be calculated from the total amplitude A and intensity T of the inducing field using the relationship k = 0.3 A/T. A large number of aeromagnetic anomalies have been interpreted using this method. A few such anomalies are presented here to illustrate the applicability of the method.
Multicomponent seismic studies using complex trace analysis
Authors: René R. M. , Fitter J. L., , Forsyth P.M. , Kim K. Y. , Murray D. J. , Walters J. K. , Westerman J. D.
Published: October 2002

The methods of complex signal analysis are applicable to multicomponent trace is defined by real orthogonal components derived by applying the Hilbert transform to the real components. Polarization attributes, including the instantaneous phase difference, signed reciprocal ellipiticity, tilt angle, and rise angle, can be displayed in trace format or in radial time-attribute plots. Polarization attributes are readily interpreted despite the non‐stationary character of seismic signals. Average attributes are defined by weighting with the geometric mean of instantaneous amplitudes. Multicomponent walkaway data have been obtained by detonating explosives in air and using triaxial in‐clined (Gal[Formula: see text]erin) geophones on a mud flat in the Great Salt Lake Desert, Utah. Polarization attributes of these data define some of the principal characteristics of both ambient noise and source‐generated waves. The direct, critical refraction, and reflection events show linear polarization with a slight forward tilt of the particle motion. Polarization of the air wave and the initial por‐tion of the air‐coupled wave is consistent across all traces in the walkaway data. The air wave begins with prograde particle motion; after approximately 2 1/2 cycles, particle motion changes to a retrogade elliptic phase. In the data considered, most of the air‐coupledwave is due to higher modes of the Rayleigh wave ( [Formula: see text], [Formula: see text],…). The [Formula: see text] and [Formula: see text] modes generated in the immediate vicinity of the explosive source exhibit opposite polarities of phase difference, corresponding to retrograde and prograde elliptic particle motions, respectively. By zeroing all data with average signed reciprocal ellipticity outside the range between −0.125 and −1, the [Formula: see text] waves are automatically selected for subsequent display with little contamination by other waves. Such procedures facilitate identification of waves according to their polarization characteristics. A desert mud flat may provide an excellent environment for study of Rayleigh waves, including air‐coupled waves, due to its flat terrain, sparse vegetation, and lateral uniformity of sediments.
Limitations of determining density or magnetic boundaries from the horizontal gradient of gravity or pseudogravity data
Authors: Grauch V. J. S. , Cordell Lindrith
Published: October 2002

The horizontal‐gradient method has been used since 1982 to locate density or magnetic boundaries from gravity data (Cordell, 1979) or pseudogravity data (Cordell and Grauch, 1985). The method is based on the principle that a near‐vertical, fault‐like boundary produces a gravity anomaly whose horizontal gradient is largest directly over the top edge of the boundary. Magnetic data can be transformed to pseudogravity data using Fourier techniques (e.g., Hildenbrand, 1983) so that they behave like gravity data; thus the horizontal gradient of pseudogravity also has maximum magnitude directly over the boundary. The method normally is applied to gridded data rather than to profiles. The horizontal‐gradient magnitude is contoured and lines are drawn or calculated (Blakely and Simpson, 1986) along the contour ridges. These lines presumably mark the top edges of magnetic or density boundaries. However, horizontal‐gradient magnitude maxima (gradient maxima) can be offset from a position directly over the boundary for several reasons. Offsets occur when boundaries are not near‐vertical, or when several boundaries are close together. This note predicts these offsets. Many other factors also cause offsets, but they are less straightforward and usually are only significant in local studies; we discuss these factors only briefly.
Practical aspects of reflectivity modeling
Authors: Mallick Subhashis , Frazer L. Neil
Published: October 2002

This paper is intended to help those not familiar with the “lore” of layered earth modeling to avoid some common problems. In the computation of the reflectivity function, an easily incorporated phase‐integral approximation is used away from turning points when the velocity gradient is smaller than the frequency. Hanning windows, or segments thereof, work well for both the slowness integral and the frequency integral. For the quadrature of the slowness integral the Filon method of Frazer is easily coded and vectorizes well; Levin’s Filon method and the Clenshaw‐Curtis‐Filon method of Xu and Mal are more difficult to vectorize, but more powerful because they require fewer evaluations of the reflectivity function. A modification of Strick’s power law is a convenient way to calculate complex frequency‐dependent seismic velocities. The complex frequency technique for avoiding time aliasing is explained by use of the Poisson sum formula. In writing code for vector computers, such as the CRAY, if frequency‐independent velocities are used, the frequency loop should be deepest, whereas if frequency‐dependent velocities are used, then the p‐loops should be deepest.
On: “Effects of porosity and clay content on wave velocities in sandstones” by D. Han, A. Nur, and D. Morgan (GEOPHYSICS, 51, 2093–2107, November 1986”.
Authors: Nobes David C. , Schneider George , Hodgson Stephen
Published: October 2002

At the outset, we must declare our philosophical bias: we believe that, if at all possible, equations relating one physical property to another should be based on some physical model. If there are two equations that can be said to relate one property to another equally well, within statistical bounds, then the equation that is based on physical principles is preferable. We acknowledge that the relationships among in this case, porosity, clay content, and seismic velocity are not always clear or easily tested, and we appreciate the efforts of Han et al. However, we have a comment and a related question regarding the statistical significance of their results.
Gravity anomaly resolution at the Garber field
Authors: Ferris Craig
Published: October 2002

A gravity survey was conducted over the Garber field in 1939 to ascertain if a gravity anomaly was associated with the Garber structure. Gravity station spacing was 805 m (2640 ft) on a 1609 m (1 mile) grid. I was party chief of the gravity survey which was terminated, prior to completion, because a gravity anomaly was not recognized by the client company. I was not satisfied with this decision and returned to the Garber field in 1950, to conduct an experiment to determine if closer station spacing would disclose a gravity anomaly over the Garber structure. I used gravity station spacing of 201 m (660 ft) on a 402 m (1320 ft) grid. This gravity station spacing was considered a microgravity survey in 1950.
Hybrid calculations of the three‐dimensional electromagnetic response of buried conductors
Authors: Gupta P. K. , Bennett L. A. , Raiche A. P.
Published: October 2002

The hybrid method for computing the electromagnetic response of a three‐dimensional conductor in a layered, conducting half‐space consists of solving a finite‐element problem in a localized region containing the conductor, and using integral‐equation methods to obtain the fields outside that region. The original scheme obtains the boundary values by iterating between the integral‐equation solution and the finite‐element solution, after making an initial guess based on primary values from the field. A two‐dimensional interpolation scheme is then used to speed the evaluation of the [Formula: see text] to [Formula: see text] Green’s function convolution integrals required by most problems. The two algorithms presented are modifications of the original scheme. Both contain a search routine to identify a set of unique points where the convolution integral evaluations are required. By replacing the two‐dimensional interpolation with a one‐dimensional interpolation and reading the convolution integrals from a reference table, computation time was reduced by up to 70 percent and accuracy was improved. The first algorithm retains the iterative technique for enforcing consistency between the integral‐equation and finite‐element solutions on the boundary of the region. The second algorithm solves the coupled integral‐equation/finite‐element system directly. For some models, the direct method has reduced the computation time to 10 percent of that required by the original scheme. In practice the direct scheme is also more stable.
The pseudospectral method: Comparisons with finite differences for the elastic wave equation
Authors: Fornberg Bengt
Published: October 2002

The pseudospectral (or Fourier) method has been used recently by several investigators for forward seismic modeling. The method is introduced here in two different ways: as a limit of finite differences of increasing orders, and by trigonometric interpolation. An argument based on spectral analysis of a model equation shows that the pseudospectral method (for the accuracies and integration times typical of forward elastic seismic modeling) may require, in each space dimension, as little as a quarter the number of grid points compared to a fourth‐order finite‐difference scheme and one‐sixteenth the number of points as a second‐order finite‐difference scheme. For the total number of points in two dimensions, these factors become 1/16 and 1/256, respectively; in three dimensions, they become 1/64 and 1/4 096, respectively. In a series of test calculations on the two‐dimensional elastic wave equation, only minor degradations are found in cases with variable coefficients and discontinuous interfaces.
On: “Alternative processing techniques and data improvement provided by single‐sweep recording,” by S. W. Belcher, T. L. Pratt, J. K. Costain, and C. Çoruh (GEOPHYSICS, 51, 1736–1742, September, 1986)
Authors: Maliphant Peter
Published: October 2002

The subject of single‐sweep Vibroseis recording has been a source of discussion among U.K. acquisition personnel for some time.
The critical reflection theorem
Authors: Fokkema Jacob T. , Ziolkowski Anton
Published: October 2002

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.
Accurate depth migration by a generalized phase‐shift method
Authors: Kosloff Dan , Kessler David
Published: October 2002

A new depth migration method derived in the space‐frequency domain is based on a generalized phase‐shift method for the downward continuation of surface data. For a laterally variable velocity structure, the Fourier spatial components are no longer eigenvectors of the wave equation, and therefore a rigorous application of the phase‐shift method would seem to require finding the eigenvectors by a matrix diagonalization at every depth step. However, a recently derived expansion technique enables phase‐shift accuracy to be obtained without resorting to a costly matrix diagonalization. The new technique is applied to the migration of zero‐offset time sections. As with the laterally uniform velocity case, the evanescent components of the solution need to be isolated and eliminated, in this case by the application of a spatially variant high‐cut filter. Tests performed on the new method show that it is more accurate and efficient than standard integration techniques such as the Runge‐Kutta method or the Taylor method.
A case for upward continuation as a standard separation filter for potential‐field maps
Authors: Jacobsen Bo Holm
Published: October 2002

Separation filtering is incomplete even under the ideal synthetic condition of known power spectra of the regional and residual fields. I have designed some Wiener filters, which minimize the inevitable separation error, from previous statistical source models of Naidu, and Spector and Grant. This formulation includes the classic separation filters of Strakhov and of Elkins as Wiener filters. A proposed generalization of Wiener filters, denoted as uniformly suboptimum filters, quantitatively supports the statement that a wide span of separation problems may be solved adequately using some convenient, small standard filter family. A uniform random‐source model without assumed vertical correlations invokes upward continuation filters. In addition to this role as a Wiener filter, the upward continuation operator is given by elementary functions in both space and wavenumber domains, is numerically stable, and is also physically comprehensible when applied to real, nonrandom anomalies. In view of these distinguishing features, I propose to use the upward continuation operator to build a convenient, standard family of separation filters.
Gravity ideal bodies
Authors: Ander Mark E. , Huestis Stephen P.
Published: October 2002

The interpretation of gravity anomaly data suffers from a fundamental nonuniqueness, even when the solution set is bounded by physical or geologic constraints. Therefore, constructing a single solution that fits or approximately fits the data is of limited value. Consequently, much effort has been applied in recent years to developing inverse techniques for rigorous deduction of properties common to all possible solutions. To this end, Parker developed the theory of an ideal body, which characterizes the extremal solution with the smallest possible maximum density. Gravity ideal‐body analysis is an excellent reconaissance exploration tool because it is especially well suited for handling sparse data contaminated with noise, for finding useful, rigorous bounds on the infinite solution set, and for predicting accurately what data need to be collected in order to tighten those bounds. We present a practical three‐ dimensional gravity ideal‐body computer code, IDB, that can optimize a mesh with over [Formula: see text] cells when used on a CRAY computer. Using actual gravity data, we use IDB to produce ideal‐body tradeoff curves that bound the solution set and show how to restrict the bound on the solution further by applying geologic and geophysical data to the tradeoff curves. As an example, we compare two‐dimensional and three‐dimensional ideal‐body results from a study of a positive anomaly associated with the Lucero uplift located on the western flank of the Rio Grande rift in New Mexico.
Full‐waveform inversion of plane‐wave seismograms in stratified acoustic media: Theory and feasibility
Authors: Pan G. S. , Phinney R. A. , Odom R. I.
Published: October 2002

We have implemented an inversion procedure for obtaining velocity and density profiles from multioffset data in a layered acoustic medium. Using an iterative modeling technique and the p-τ representation, the procedure is derived from the nonlinear least‐squares formalism of Tarantola and Valette. The feasibility of this method depends upon obtaining Fréchet derivatives during the modeling process and on vectorizing the Thompson‐Haskell reflectivity algorithm. Test data sets for this study are gathers of two to four plane‐wave synthetic seismograms which may contain both precritical and postcritical arrivals generated by a seismic wavelet. These examples demonstrate convergence to the correct velocity and density profiles with reasonable accuracy.
Linearized inversion of multioffset seismic reflection data in the ω-k domain: Depth‐dependent reference medium
Authors: Ikelle L. T. , Diet J. P. , Tarantola A.
Published: October 2002

The computation of synthetic seismograms can be linearized with respect to a reference medium that issno close to the actual medium. Using a least‐squares formulation, the inverse problem can then be set up as a problem of quadratic optimization. The inverse problem is greatly simplified if the reference medium is symmetric. For a homogeneous reference medium, a rigorous and economic solution can be obtained by Fourier transforming all spatial variables. In particular, the solution can be obtained through an explicit formula that does not require the resolution of any linear system (as is the case when not working in the Fourier domain). However, the assumption of a homogeneous reference medium is generally not realistic. In some situations, the reference medium can be depth‐dependent. It can then be shown that by Fourier transforming time and all spatial variables except depth, the inverse problem also has an elegant and economic solution. If [Formula: see text] is the (unknown) difference between the reference medium and the true (2-D) medium, the Fourier‐transformed solution [Formula: see text] can be obtained by solving, for each value of the horizontal wavenumber [Formula: see text] a linear system whose dimension equals the number of depth samples.
Reflection seismology over azimuthally anisotropic media
Authors: Thomsen Leon
Published: October 2002

Recent surveys have shown that azimuthal anisotropy (due most plausibly to aligned fractures) has an important effect on seismic shear waves. Previous work had discussed these effects on VSP data; the same effects are seen in surface recording of reflections at small to moderate angles of incidence. The anisotropic effects on different polarization components of vertically traveling shear waves permit the recognition and estimation of very small degrees of azimuthal anisotropy (of order ⩾1 percent), as in an interferometer. Anisotropic effects on traveltime yield estimates of anisotropy which are averages over large depth intervals. Often, raw field data must be corrected for these effects before the reflectors may be imaged; two variations of a rotational algorithm to determine the “principal time series” are derived. Anisotropic effects on moveout lead to abnormal moveout unless the survey line is parallel to the fractures. Anisotropic effects on reflection amplitude permit the recognition and estimation of anisotropy (hence fracture intensity) differences at the reflecting horizon, i.e., with high vertical resolution.
Simplified frequency‐domain expressions for potential fields of arbitrary three‐dimensional bodies
Authors: Hansen R. O. , Wang Xiaomu
Published: October 2002

Models based on homogeneous polyhedral bodies offer great flexibility in representing the potential fields of complex geologic sources. However, existing expressions for the gravity and magnetic fields of such bodies suffer from two disadvantages. First, the surface of the body must be specified as a set of triangular facets, which makes input to a modeling program rather awkward. Second, each facet of the body must be rotated into a special position, which generates substantial computational overhead and makes the analytic expressions difficult to interpret. In this paper, Pedersen’s Fourier transform expressions for the potential fields due to homogeneous polyhedral bodies are recast in a simpler, coordinate‐invariant form. The resulting expressions are then rewritten as a sum of contributions from each vertex of the body. This greatly simplified form is used as the basis for a modeling program that is substantially faster and more straightforward than existing programs. Furthermore, the analytic expressions promise to be useful for further investigation of an inverse method based on polyhedral‐body models.
Improved inversion of geopotential field anomalies for lithospheric investigations
Authors: von Frese R. R. B. , Ravat D. N. , Hinze W. J. , McGue C. A.
Published: October 2002

Instabilities and the large matrices which are common to inversions of regional magnetic and gravity anomalies often complicate the use of efficient least‐squares matrix procedures. Inversion stability profoundly affects anomaly analysis, and hence it must be considered in any application. Wildly varying or unstable solutions are the products of errors in the anomaly observations and the integrated effects of observation spacing, source spacing, elevation differences between sources and observations, geographic coordinate attributes, geomagnetic field attitudes, and other factors which influence the conditioning of inversion. Solution instabilities caused by ill‐posed parameters can be efficiently minimized by ridge regression with a damping factor large enough to stabilize the inversion, but small enough to produce an analytically useful solution. An effective choice for the damping factor is facilitated by plotting damping factors against residuals between observed and modeled anomalies and by then comparing this curve to curves of damping factors plotted against solution variance or the residuals between predicted anomaly maps representing the processing objective (e.g., downward continuation, differential reduction to the radial pole, etc.). To obtain accurate and efficient large‐scale inversions of anomaly data, a procedure based on the superposition principle of potential fields may be used. This method involves successive inversions of residuals between the observations and various stable model fields which can be readily accommodated by available computer memory. Integration of the model fields yields a well‐resolved representation of the observed anomalies corresponding to an integrated model which normally could not be obtained by direct inversion because the memory requirements would be excessive. MAGSAT magnetic anomaly inversions over India demonstrate the utility of these procedures for improving the geologic analysis of potential field anomalies.
Cellular‐automaton fluids: A model for flow in porous media
Authors: Rothman Daniel H.
Published: October 2002

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method solves the Navier‐Stokes equations numerically using the cellular‐automaton fluid model introduced by Frisch, Hasslacher, and Pomeau. The cellular‐ automaton fluid is extraordinarily simple—particles of unit mass traveling with unit velocity reside on a triangular lattice and obey elementary collision rules—but is capable of modeling much of the rich complexity of real fluid flow. Cellular‐automaton fluids are applicable to the study of porous media. In particular, numerical methods can be used to apply the appropriate boundary conditions, create a pressure gradient, and measure the permeability. Scale of the cellular‐automaton lattice is an important issue; the linear dimension of a void region must be approximately twice the mean free path of a lattice gas particle. Finally, an example of flow in a 2-D porous medium demonstrates not only the numerical solution of the Navier‐Stokes equations in a highly irregular geometry, but also numerical estimation of permeability and a verification of Darcy’s law.
Calculation of the magnetic gradient tensor from total field gradient measurements and its application to geophysical interpretation
Authors: Nelson J. Bradley
Published: October 2002

The very low inherent noise levels of superconducting quantum interference device (SQUID) sensors have led to proposals for the use of airborne SQUID magnetic gradiometers as geophysical interpretation tools. The quantity measured by such systems will be the gradient tensor, the spatial rate of change of the vector components of the magnetic field. By contrast, existing airborne gradiometers measure the spatial rate of change of the magnitude of the total field. This work describes a technique whereby the gradient tensor can be calculated from measurements of either the vertical or horizontal total field gradients throughout a plane. The signal‐to‐noise ratio of the calculated tensor components is essentially the signal‐to‐noise ratio of the original total field gradient measurements. The resulting tensor components may be upward or downward continued with standard techniques. Two advantages of using the tensor gradients instead of the total field gradients have been determined. Because the tensor components are not a function of the direction of the Earth’s field, contour plots do not suffer the skewing problems that total field or vertical gradient plots do. Thus, tensor gradient contour plots may be easier to interpret or may enhance the information obtained from total field or vertical gradient maps. In addition, the dipole‐tracking algorithm developed by Wynn et al. (1975) has been shown to be quite successful in determining the depth and horizontal location of block‐shaped bodies. The error in depth estimation is a strong inverse function of the ratio of the closest point of approach to largest dimension of the body. However, if the smallest separation is more than twice the largest dimension of the body, errors in depth estimation are less than 10 percent. Because the tensor components are calculated on a horizontal plane, they can be upward continued to meet this condition.
Comparison of gradient analysis techniques for linear two‐dimensional magnetic sources
Authors: Nelson J. Bradley
Published: October 2002

Six techniques are presented for analyzing magnetic gradient [Formula: see text] and most require the computation of the total gradient [Formula: see text] Four of the methods are mathematically rigorous: one is based on the crossing points of the [Formula: see text] and [Formula: see text] profiles; a second, reported by Atchuta Rao et al., uses G and [Formula: see text]; and two more are based on the total gradient line‐shape. Two other methods, based on the half‐slope points of [Formula: see text] and G, are rule‐of‐thumb techniques similar to the familiar half‐slope method for total field anomalies. These methods have been used to obtain depth estimates from simulated profiles over thick and narrow dikes contaminated by dc offsets, linear trends, and random noise. The methods vary in their sensitivities to small dc offsets, local trends, and random noise. The crossing‐point method is found to be very sensitive to all three types of noise, while the complex gradient is quite sensitive to offsets and trends, but only slightly affected by random noise. Depth estimates based on these methods, using real data, may contain errors of 5–10 percent. The two line‐shape analysis methods are only slightly sensitive to trends and offsets and, depending upon the relative values of the maxima and minima, may or may not be sensitive to random noise. However, they are only applicable to wide dikes. Depth estimates from these techniques (for wide dikes) are considered to be the most accurate of the four mathematically rigorous methods investigated (errors < 5 percent). The half‐slope methods are not sensitive to trends or offsets but are sensitive to random noise ( ∼ 5 percent). However, uncertainty in the source geometry may produce small errors in the depth estimates for thick dikes (2–4 percent) and sizable errors in the depth estimates for narrow dikes ( > 10 percent). While these uncertainties are much less than those found when the half‐slope method is applied to the total field profile, they are significant compared to the errors caused by the various noise sources considered. Thus, the accuracy of these methods is quite dependent upon the source geometry.
Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone
Authors: Eberhart‐Phillips D. , Han D-H. , Zoback M. D.
Published: October 2002

We use a multivariate analysis to investigate the influence of effective pressure [Formula: see text], porosity ϕ, and clay content C on the compressional velocity [Formula: see text] and shear velocity [Formula: see text] of sandstones. Laboratory measurements on water‐saturated samples of 64 different sandstones provide a large data set that was analyzed statistically. For each sample, relationships between effective pressure and [Formula: see text] and [Formula: see text] have been determined. All samples were well fit by relationships that have an exponential increase in velocity at low [Formula: see text], tapering to a linear increase with [Formula: see text] for [Formula: see text] greater than 0.2 kbar. There are differences in the pressure dependences of velocity for different rocks, particularly at very low pressures; however, the differences cannot be attributed to ϕ or C. For the combined set of measurements from all samples, the best fitting formulations are [Formula: see text] and [Formula: see text]. While this is admittedly a very simplified parameterization, it is remarkable how well the velocity of the rocks considered here can be predicted based on only the three parameters, ϕ, C, and [Formula: see text]. The model accounts for 95 percent of the variance and has rms error of 0.1 km/s. An increased value of [Formula: see text] can indicate a decrease in [Formula: see text], a decrease in porosity, or an increase in clay content or some combination thereof.
Statistical analysis of airborne gamma‐ray data for geologic mapping purposes: Crixas‐Itapaci area, Goias, Brazil
Authors: Pires A. C. B. , Harthill N.
Published: October 2002

Q‐mode factor analysis, K‐means clustering, and G‐mode clustering were used on digitized gamma‐ray spectrometer data from an aerial survey of the Crixas‐Itapaci area, Goias, Brazil. The data points including seven variables—eU, eTh, K, total count, U/Th, U/K, and Th/K—were digitized for a 2 km square grid. For the northwest corner of the area the data were gridded at 1 km. The Q‐mode classification method supplied results that do not show a good correspondence with the known geology. The K‐means clustering procedure barely identified the main lithologic features of the area. The G‐mode technique produced results that correlate well with the known geology and identified the greenstone belts present in the area by discriminating their ultramafic and mafic components from adjacent felsic rocks. Statistical analysis of aerial gamma‐ray spectrometer data can be very helpful in mapping geologic units in poorly known areas. It can also be used for mineral exploration purposes if mineralization is known to be associated with lithologies that can be identified by the techniques used in this study.
Field examples of negative coincident‐loop transient electromagnetic responses modeled with polarizable half‐planes
Authors: Smith Richard S. , West G. F.
Published: October 2002

The negative transients observed in coincident‐loop measurements are believed to be caused by polarizable conductive structures (i.e., structures whose in‐phase conductivity increases with frequency). For most structures, it is not possible to predict negative transients as large as some of those observed in the field unless the polarizability is exceptionally large. Previous work shows that modest polarizabilities can be used to predict negative transients of the correct magnitudes when the conducting structures are such that the following qualitative conditions apply: (1) the transmitter is positioned proximal to the conducting structure in a manner which ensures a large early‐time fundamental inductive current is induced in the structure; (2) the polarization current is proximal to the receiver and results in a measurable negative polarization response; and (3) the positive response associated with the fundamental inductive current decays away sufficiently rapidly that the total response can change sign. These conditions are termed the “favorable coupling conditions.” A polarizable half‐plane model is a structure which satisfies these conditions. The positions near the edge of the half‐plane, where the favorable coupling conditions are best satisfied, are those which are most conducive to observing negative transients. Field examples of negative transients associated with either an overburden which comes to an edge or a dipping sheet‐like structure can be modeled with a weakly polarizable half‐plane. We believe that most of the negative transients observed in the field are likely to be associated with structures which satisfy the favorable coupling conditions.
The seismic refraction method: A viable tool for mapping shallow targets into the 1990s
Authors: Lankston Robert W.
Published: October 2002

Geometrical considerations show that first arrivals can be recorded from below hidden layers. A certain minimum amount of data must be collected in order to resolve lateral versus vertical subsurface changes and thereby to determine the interpretation method. Field procedures, therefore, are independent of the interpretation method. The optimum XY parameter in the generalized reciprocal method (GRM) of processing refraction seismic data is significant as a quality control factor in refraction data interpretation. By comparison of the optimum XY value that is recovered through velocity analysis and time‐depth function analysis with a value for optimum XY that is calculated from the migrated depth section, the hidden‐layer condition can be recognized. In addition to identifying the hidden‐layer condition on the basis of first arrivals alone, the GRM allows the hidden layers to be accommodated; and depth precisions of less than 5% are possible.
On: “Induced‐polarization effects in time‐domain electromagnetic measurements” by M. F. Flis, G. A. Newman, and G. W. Hohmann (GEOPHYSICS, 54, 514–523, April 1989).
Authors: Smith Richard
Published: October 2002

Flis et al. provide useful insight into the time‐domain response of three‐dimensional polarizable bodies; however, their inference that negative transients are caused by a polarization current which reverses direction disagrees with the previously published theoretical results of Smith et al. (1988) and Smith and West (1988), who found that the polarization current is always negative (provided that the chargeability m and charging current are positive).
Geothermal signatures and uranium ore deposits on the Stuart Shelf of South Australia
Authors: Houseman G. A. , Cull J. P. , Muir P. M. , Paterson H. L.
Published: October 2002

An analysis of temperature data from drill holes on the Stuart Shelf of South Australia demonstrates a major thermal anomaly associated with the Olympic Dam copper‐uranium‐gold deposit. The average heat flow on the Stuart Shelf (seven locations, excluding Olympic Dam) is [Formula: see text], but an additional heat flow of approximately [Formula: see text] is present in the sediments overlying the orebody. Although some of the anomalous heat flow appears to be generated in the mid‐Proterozoic basement at depths greater than 1 km, uranium assays indicate that approximately [Formula: see text] can be attributed to concentrations defining the orebody. Major anomalies in heat flow can be readily detected in the flat‐lying cover of Cambrian and late Proterozoic sediments. The Tregolana shale within this sequence is a widespread homogeneous unit, typically 100–200 m thick. It is easily identified on temperature logs by its high thermal gradient relative to other sections in the hole. The heat flow anomaly at Olympic Dam is clearly distinguished by measuring thermal gradients within the Tregolana shale; gradients in the Tregolana shale at Olympic Dam are close to 83 °C/km, with a standard deviation (SD) of 6 °C/km, compared to 51 °C/km (SD = 7 °C/km) elsewhere on the Stuart Shelf.
Experimental evidence for the Biot‐Gardner theory
Authors: Mörig R. , Burkhardt H.
Published: October 2002

Seismic wave attenuation has been a subject of interest during the last 40 years because it may be of use in interpreting seismic data. From this attenuation parameter, more detailed information about the lithology of the subsurface may be deduced if we understand the absorption mechanisms by which dissipation of seismic energy is governed. We are, therefore, studying in the laboratory the effects of different parameters such as porosity, permeability, pore fluid, and saturation state on the absorption of seismic waves in porous rocks over a wide spectrum ranging from seismic to ultrasonic frequencies (Burkhardt et al., 1986).
Convolutional quelling in seismic tomography
Authors: Meyerholtz Keith A. , Pavlis Gary L. , Szpakowski Sally A.
Published: October 2002

This paper introduces convolutional quelling as a technique to improve imaging of seismic tomography data. We show the result amounts to a special type of damped, weighted, least‐squares solution. This insight allows us to implement the technique in a practical manner using a sparse matrix, conjugate gradient equation solver. We applied the algorithm to synthetic data using an eight nearest‐neighbor smoothing filter for the quelling. The results were found to be superior to a simple, least‐squares solution because convolutional quelling suppresses side bands in the resolving function that lead to imaging artifacts.
Palmietfontein kimberlite pipe, South Africa—A case history
Authors: da Costa Alberto J. M.
Published: October 2002

The Palmietfontein kimberlite pipe is located 150 km northwest of Johannesburg, South Africa. It was emplaced at the contact between mafic rocks of the Bushveld complex and syenites of the Pilanesberg complex, and coincides with the intersection of two major faults. Palmietfontein is one of the larger known kimberlite pipes in South Africa; it has a surface area of 12 ha and is diamondiferous. The present geophysical study was designed to assist in planning an extensive program of trenching and drilling. Unweathered kimberlite has geophysical responses very similar to the country rock at Palmietfontein. Weathering and alteration of the upper 50 m of the pipe, however, have resulted in various physical changes, which has made the target amenable to investigation by various geophysical techniques. The surveys used in this study are gravity, electrical, seismic refraction, and airborne and ground magnetics and electromagnetics (EM). The boundary of the pipe was accurately defined, and the dip of the wallrock contact was determined by using various models and combinations of techniques. A small satellite body of kimberlite was also discovered during the course of this investigation. The most suitable techniques for kimberlite prospecting, particularly when the top portion of the kimberlite is weathered, are airborne EM and magnetics, combined with the Slingram ground-EM system. For more quantitative results, gravity and seismic surveys should be used.
Polarity reversals in reflections from layered media
Authors: Keys Robert G.
Published: October 2002

A polarity reversal is a 180-degree change in the phase of a seismic reflection as a function of offset. Polarity reversals occur when the P-wave reflection coefficient passes through zero when plotted as a function of the angle of incidence.
Offset‐dependent mis‐tie analysis at seismic line intersections
Authors: Huston Daniel C. , Backus Milo M.
Published: October 2002

Offset‐dependent line‐intersection displays can be of significant direct interpretive value. On our data set from a proprietary location, use of these displays permits a refined structural interpretation and improves the usefulness of amplitude and amplitude‐versus‐offset displays for direct hydrocarbon detection. The degree of data reproducibility at each intersection may be exposed as a function of offset through the use of prestack and partial‐range stack splice and difference displays. At a set of marine line intersections, after only cursory processing, the range of residual amplitudes found by subtracting strike traces from dip traces is from −20 dB to +6 dB relative to the input. The average is about −8 dB. The poorest line intersection ties occur below the edges of deep bright spots, where velocity anomalies leading to time mis‐ties greater than 10 ms can occur. Shallow near‐surface velocity anomalies, out‐of‐plane arrivals including fault plane reflections, and, occasionally, water reverberation variations contribute locally to the data mis‐ties. Location errors are ubiquitous but of secondary importance, and random noise is more than 20 dB down. A simple and inexpensive routine splice display of line intersection data can be of significant value for quality control, for processing evaluation, and for interpretation. Issues of data reliability, such as screening of amplitude‐versus‐offset (AVO) anomalies by shallow gas and transmission‐path problems for large CMP offsets, as well as other problems in operational and research geophysics, may be addressed by analysis of line intersections in the offset domain.
A boundary integral equation‐discrete wavenumber representation method to study wave propagation in multilayered media having irregular interfaces
Authors: Bouchon Michel , Campillo Michel , Gaffet Stephane
Published: October 2002

We present a method which combines boundary‐integral equation techniques with the discrete wavenumber Green’s function representation to study wave propagation in multilayered media having irregular interfaces. The approach is based on the representation of the interfaces by distributions of body forces, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green’s functions are evaluated by the discrete wavenumber method. Propagator matrices are introduced to relate force distributions on neighboring interfaces. The solution then requires the inversion of a matrix at each interface. The dimensions of the linear system are independent of the number of layers considered, and the computation time varies linearly with the number of interfaces. We apply the method to calculate surface and vertical seismic profiles in the presence of synclinal or anticlinal structures.
Stability of wide‐angle absorbing boundary conditions for the wave equation
Authors: Renaut R. A. , Petersen J.
Published: October 2002

Numerical solution of the two‐dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approximations to the one‐way wave equation and is commonly called an absorbing boundary. Here we investigate order 2 absorbing boundary conditions which include the standard paraxial approximation. Absorption properties are compared analytically and numerically. Our numerical results confirm that the [Formula: see text] or Chebychev‐Padé approximations are best for wide‐angle absorption and that the Chebychev or least‐squares approximations are best for uniform absorption over a wide range of incident angles. Our results also demonstrate, however, that the boundary conditions are stable for varying ranges of Courant number (ratio of time step to grid size). We prove that there is a stability barrier on the Courant number specified by the coefficients of the boundary conditions. Thus, proving stability of the interior scheme is not sufficient. Furthermore, waves may radiate spontaneously from the boundary, causing instability, even if the stability bound on the Courant number is satisfied. Consequently, the Chebychev and least‐squares conditions may be preferred for wide‐angle absorption also.
Magnetic interpretation in three dimensions using Euler deconvolution
Authors: Reid A. B. , Allsop J. M. , Granser H. , Millett A. J. , Somerton I. W.
Published: October 2002

Magnetic‐survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using Euler’s homogeneity relation. The method employs gradients, either measured or calculated. Data need not be pole‐reduced, so that remanence is not an interfering factor. Geologic constraints are imposed by use of a structural index. Model studies show that the method can locate or outline confined sources, vertical pipes, dikes, and contacts with remarkable accuracy. A field example using data from an intensively studied area of onshore Britain shows that the method works well on real data from structurally complex areas and provides a series of depth‐labeled Euler trends which mark magnetic edges, notably faults, with good precision.