bluuebunny/crossref_metadata_2025 huggingface dataset:
STEADY STATE POLAR SENSITIVITY CURVES
Authors: Johnson C. H.
Published: October 2002

The resultant amplitude, “A,” of the combined outputs of a group of geophones is derived as a function of the difference in time of arrival, ΔT, at extreme geophones in the group—the number of geophones and the period of the waves being parameters. “A” plotted as a function of ΔT is shown to have principal and secondary maxima whose amplitudes, separation, and sharpness are discussed. The relative response of the geophone group to waves from every direction is considered and illustrated by polar sensitivity curves. The changes in the polar sensitivity curves effected by changes in the number of geophones, the geophone spread, or the wave length, are considered. The effect of introducing artificially controlled time differences between geophone outputs, so as to vary the direction of maximum response (so‐called variable compounding) as is done in the Rieber Sonograph, is considered. By this means the resultant response of the group of geophones can be focused, so as to emphasize waves arriving from any specific direction. While the results are strictly applicable only to the case of steady state, sinusoidal waves, they may apply qualitatively to all the waves encountered in seismic exploration. The versatility of variable compounding is pointed out.
TERRAIN CORRECTIONS FOR GRAVIMETER STATIONS
Authors: Hammer Sigmund
Published: October 2002

In this paper the correction for the gravitational attraction of the topography on a gravity station is considered as consisting of two parts; (1) the restricted but conventional “Bouguer correction” which postulates as a convenient approximation that the topography consists of an infinite horizontal plain, and (2) the “Terrain correction” which is a supplementary correction taking into account the gravitational effect of the undulations of the terrain about the plane through the gravity station. The paper illustrates the necessity of making terrain corrections if precise gravity surveys are desired in hilly country and presents terrain correction tables with which this quantity may be determined to a relative accuracy of one‐tenth milligal. This accuracy is required to fully utilize the high instrumental precision of modern gravimeters.
THREE‐DIMENSIONAL INDUCED POLARIZATION AND ELECTROMAGNETIC MODELING
Authors: Hohmann Gerald W.
Published: October 2002

The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response varies significantly with conductivity contrast; the peak response occurs at higher contrasts for two‐dimensional bodies than for bodies of limited length. Very conductive bodies can produce negative IP response due to EM induction. An electrically polarizable body produces a small magnetic field, so that it is possible to measure IP with a sensitive magnetometer. Calculations show that horizontal loop EM response is enhanced when the background resistivity in the earth is reduced, thus confirming scale model results.
REMANENT MAGNETIZATION FROM COMPARISON OF GRAVITY AND MAGNETIC ANOMALIES
Authors: Shurbet D. H. , Keller G. R. , Friess J. P.
Published: October 2002

Gravity and magnetic anomalies caused by deeply buried rock bodies in northwest Texas are compared. Interpretation of the gravity anomalies by modeling is used to locate and define the geometry of the body in a way analogous to the use of bathymetry in studies concerned with magnetization of seamounts. The direction of magnetization is then determined from the spatial relationship between the gravity and magnetic anomalies. This procedure amounts to an in‐situ determination of direction of magnetization of the body. In one example direction of magnetization indicates the time of intrusion and in another it indicates regional heating since intrusion.
THE SEISMIC WAVE SYSTEM FROM A SURFACE IMPACT
Authors: Mooney Harold M.
Published: October 2002

A theory presented in an earlier paper (Mooney, 1974) has been used to compute seismic waveforms produced by a surface impact. Surface detectors are assumed which measure displacement, velocity, acceleration, or strain in either vertical or horizontal components. A physically plausible source waveform is considered which is unidirectional, symmetrical about a peak, and with zero slopes at beginning and end. Theoretical waveforms are presented for models simulating projectile, hammer, and weight‐drop impacts onto granite, concrete, and soil. The waveforms show small but clear P arrivals, large Rayleigh pulses, and no recognizable S waves. P waves are larger on the horizontal sensors, Rayleigh on the vertical. The waveforms differ markedly from one detector type to another and show little resemblance to the source waveform. Distinctive pulse length and amplitude pulse paramaters are selected. Pulse lenths are shown to be relatively insensitive to detector distance, hence conversion factors can be obtained from which to infer source pulse length. These factors were applied to accelerometer waveforms obtained experimentally from steel pellet impacts onto granite, yielding a source pulse length of 30 μsec. This value was used to compute theoretical waveforms which show satisfactory agreement with the experimental waveforms. The measured amplitude parameters are shown to depend upon detector distance r and source pulse length T and amplitude H as [Formula: see text]where n = 1, 1/2 for P and Rayleigh waves, respectively; p = 0, 1/2 for P and Rayleigh waves; and m = 0,1,2,1 for detectors which measure displacement, particle velocity, acceleration, and horizontal strain. An increase in Poisson’s ratio v for the medium produces increased time separation between P and Rayleigh arrivals, and increase in P pulse length and amplitude, no changes in Rayleigh pulse length, and a decrease in Rayleigh amplitude as [Formula: see text].
GRAVITY VERTICAL GRADIENT MEASUREMENTS FOR THE DETECTION OF SMALL GEOLOGIC AND ANTHROPOGENIC FORMS
Authors: Fajklewicz Zbigniew J.
Published: October 2002

The gravity tower vertical gradient has been applied to the solution of a number of important geologic, mining, and engineering problems, particularly to the search for and investigation of geologic structures and the detection of caverns and old mine workings. The effective application of the method depends upon recognizing the difference between the theoretical gravity vertical gradient [Formula: see text] and the gradient [Formula: see text] measured by means of a tower and gravimeter. The former is a derivative of the function g, the latter its differential quotient. Consequently, the differences between [Formula: see text] and [Formula: see text] in the same point may attain high values. Thus, e.g., for a sphere with a radius of 1 m, a density of 2.0 gm/cc and the depth of occurrence of its center equaling 1.2 m, the difference of the theoretical absolute amplitudes [Formula: see text] Eötvös units. Application of the method of the gravity tower vertical gradient on an industrial scale was possible due to the introduction of (1) a new design of the measuring tower, (2) detailed analysis of errors, and (3) a new method of calculating the topographic correction of the gravity vertical gradient. The paper sums up the results of five years of research work and industrial applications. During that period several thousand measurements of the gravity vertical gradient were made.
STRUCTURE INDEPENDENT VELOCITY ESTIMATION
Authors: Doherty Stephen M. , Claerbout Jon F.
Published: October 2002

Many commonly used velocity estimation procedures assume that the reflectors are horizontal. Because of this, their performance tends to degrade as the reflectors become curved or discontinuous. Much of this degradation can be traced to the fact that data recorded over nonhorizontal reflectors need not resemble in detail the subsurface in the area where they were recorded. Diffraction and scattering are the major complicating factors. Beginning with the scalar wave equation and using a small dip assumption, approximate wave equations which quite accurately model both near‐ and wide‐angle reflections generated by one or more sources can be found. Finite difference formulations of these equations can be used to demonstrate that surface recorded seismic reflections which have been downward continued to the depth of their source reflectors must resemble those reflectors in detail. This property of downward continuation can be exploited to improve velocity estimates by using downward continuation as a preprocessor for velocity estimation techniques. Both synthetic and field data examples show that estimates based on downward continued data do not exhibit diffraction effects and are not dependent upon reflector dip. Synthetic data examples also illustrate that the use of downward continuation allows accurate velocity estimates to be made from no record data recorded over an earth in which the reflectors are random functions of the horizontal and vertical coordinates. For reasonable data parameters, theoretical considerations indicate that the coherence of properly downward continued random reflector data measured along the true velocity hyperbolic should be greater than a similar measure on the corresponding surface data. This coherence increase should make velocity estimates based on downward continued random reflector data less susceptible to noise than estimates based on surface recorded data.
THREE‐DIMENSIONAL RESISTIVITY AND INDUCED‐POLARIZATION MODELING USING BURIED ELECTRODES
Authors: Daniels Jeffrey J.
Published: October 2002

The three‐dimensional induced‐polarization and resistivity‐modeling problem for buried source and receiver electrodes is solved by using a modified form of Barnett’s surface‐integral technique originally developed for surface‐electrode configurations. Six different buried electrode configurations are considered in this study: three types of hole‐to‐hole configurations, hole‐to‐surface and surface‐to‐hole configurations, and the single hole (bipole‐bipole) configuration. Results show there is no “best” method for all situations encountered in the field. The choice of method depends upon depth of the body, spacing of drill holes, and electrical properties of the body. In hole‐to‐hole measurements, the geometric factor (necessary for the computation of the apparent resistivity) becomes infinitely large or infinitely small whenever the receiving bipole is placed at a depth so that it lies on a zero equipotential surface. This leads to the formation of apparent resistivity anomalies that are extremely sensitive to the presence of the body but that are also complicated and not easily correlated with the position of the body. It is shown that diagnostic and easily interpretable anomalies are obtained by selecting the proper source‐receiver configurations.
MIGRATION BY FOURIER TRANSFORM
Authors: Stolt R. H.
Published: October 2002

Wave equation migration is known to be simpler in principle when the horizontal coordinate or coordinates are replaced by their Fourier conjugates. Two practical migration schemes utilizing this concept are developed in this paper. One scheme extends the Claerbout finite difference method, greatly reducing dispersion problems usually associated with this method at higher dips and frequencies. The second scheme effects a Fourier transform in both space and time; by using the full scalar wave equation in the conjugate space, the method eliminates (up to the aliasing frequency) dispersion altogether. The second method in particular appears adaptable to three‐dimensional migration and migration before stack.
DIRECT INVERSION OF TRANSMISSION SYNTHETIC SEISMOGRAMS
Authors: Loewenthal D. , Gutowski P. R. , Treitel S.
Published: October 2002

Seismograms are routinely used to extract information about the internal structure of the subsurface. The basic philosophy is to idealize the earth with a simple model characterized by resolvable parameters. Further, we assume that the seismograms obey simple mathematical relations, such as the wave equation, and that these seismograms are uniquely determined by the given parameters. The computation of seismograms for a given model whose parameters are specified gives rise to the “forward problem”. The determination of the parameters of the model from the seismogram generally constitutes the “inverse problem”. While the forward problem is often relatively simple, the inverse problem tends to be much more involved. One of the few cases for which the inverse problem has a simple direct solution is given for a model consisting of a homogeneous one‐dimensional layered medium. The layers overlie a homogeneous half‐space, and are excited by a normally incident plane wave. Such direct solutions to the inverse problem are in contrast to the iterative inversion techniques of the Gilbert‐Backus type. We have chosen to treat the inverse problem for the seismogram escaping into the homogeneous substratum, i.e., the transmission seismogram. We do so because this time series is a simple autoregressive, or all‐pole process. The problem is studied both with and without white noise. The Wiener‐Levinson algorithm has been found to be well suited for the direct inversion of the noise‐free case, while the “maximum entropy” algorithm is generally more appropriate for noisy data. Numerical examples serve to clarify and illustrate these points.
Investigation of a VLF airborne resistivity survey conducted in northern Maine
Authors: Arcone Steven A.
Published: October 2002

Airborne wavetilt resistivity surveys and profiles at VLF have been analyzed for the effects of topography, altitude, and wavetilt phase and amplitude. Topographic relief is known to affect at least one electric field component, flight altitude often varies over relief, and phase, upon which the airborne measurement depends and which cannot be separated from amplitude by an airborne antenna system, depends on the earth’s resistivity stratification and the relative strength of displacement to conduction current. A mountainous area in northern Maine of predominantly slate, but containing an igneous stock, was surveyed at 150 m mean flight altitude. The 150-m survey was repeated at 300 m, and two of the 150-m flight lines were repeated at a total of three other altitudes. A comparison of the 150-m survey with the topography and with the 300-m survey revealed that although most of the resistivity information of the 150-m survey was retained at 300 m, serious differences arose due to topographic influences. Profiles of the individual electric field components at the various altitudes then revealed that topography was distorting resistivity values through its effect upon only the vertical component of the electric field. The separate influences of phase and amplitude were analyzed using the results of a ground survey of the total, complex surface impedance. The phase of the tilt proved to be important in the airborne differentiation of the rock types. The entire 150-m survey was reevaluated with topographic effects removed from the vertical electric field. The resolution of the igneous geology improved and several of these improvements were verified by the ground measurements. In addition, it is concluded from a comparison of the 300-m survey with both the topographically corrected and uncorrected 150-m surveys that wavetilt is not preserved with altitude over ground resistivity anomalies.
An electrochemical model of the induced‐polarization phenomenon in disseminated sulfide ores
Authors: Wong J.
Published: October 2002

A disseminated sulfide ore is idealized by a system of electronically conducting metallic spheres randomly dispersed in an electrolytically conducting host medium. When an external electric field is applied, the transport of cations and anions in the interphase region near the metal‐electrolyte interface will involve both drift and diffusion flux densities. The flow of ions to or from the metal‐electrolyte interface causes an excess or deficit of inactive ions to accumulate there, since the metal is neither a source nor sink for these ions. These inactive ions are loosely held to the metallic particles by image forces, and concentration gradients build up which oppose the migration of these ions due to electric fields. In addition to the inactive anions and cations, a minor concentration of active cations is assumed to exist in the electrolytic medium, and the electric fields at the electrolyte‐metal interface cause these to engage in electrochemical reactions making possible charge transfer across the interface. Under these conditions, coupled partial differential equations describing the temporal and spatial variations in the concentrations of active and inactive ions can be derived by considering the net flux of cations and anions into a small test volume of the host medium. The variations are expressed as perturbations on the background concentrations and are found when the partial differential equations are solved using the Laplace transformation and separation of variables in spherical coordinates. The perturbation concentrations are Gouy‐Chapman types of diffuse distributions localized near the metal‐electrolyte interface with thickness on the order of the Debye screening length. The cloud of loosely held ions surrounding each metallic particle and the diffusion‐controlled charge transfer reaction at the interface are responsible for inducing a time‐ or frequency‐dependent electric dipole moment on each particle. With the assumption that no mutual interactions exist between these dipoles, the effective conductivity (in frequency domain) of an assemblage of metallic spheres residing in an electrolytic host medium can be found by using Maxwell’s formula. The resulting frequency dispersion in the effective conductivity is the basis of the induced‐polarization (IP) effect. Conductivity and resistivity spectra calculated from this electrochemical model are compared to laboratory measurements on synthetic metalliferous ores, and good fits with the experimental data are obtained by using physically reasonable values for the various parameters in the model.
A technique for the continuous representation of dispersion in seismic data
Authors: Robinson John C.
Published: October 2002

The dispersion relation derived by Futterman (1962) for an absorption model which is linear with frequency has been analyzed. For the case of an impulsive source, it has been found that the relation can be viewed as a frequency‐dependent time rescaling, which transforms into a simple frequency‐dependent inverse frequency rescaling. This frequency rescaling is conveniently referenced to a so‐called base frequency of the user’s choice. This eliminates any need for specifying Futterman’s low cutoff frequency and, furthermore, allows the user to preserve the overall time scaling of seismic data while bringing the seismic events into better “focus” with dispersion removal or correction. Examples of applications of the technique to both introduction of dispersion into synthetic seismic data and removal of dispersion from seismic data are shown. The synthetic data show that the linear absorption model is causal only when accompanied by dispersion.
The new gravity system—changes in international gravity base values and anomaly values
Authors: Woollard George P.
Published: October 2002

An assessment is made of (1) the reliability of the changes in the absolute gravity datum and standard incorporated in the IGSN 71 values of Morelli et al (1974), and (2) the effect of these changes and those incorporated in the new international gravity formula (Geodetic Reference System 1967) defining theoretical gravity values at sea level on gravity anomaly values. Pendulum‐interval comparisons with modern absolute gravity intervals between Washington, D.C.; Teddington, England; Paris, France; and Potsdam, East Germany indicate that the correction of 14 mgal to the Potsdam datum is correct to within .03 ± .016 mgal. Although there appear to be occasional discrepancies in the IGSN 71 values of the order of 0.1 mgal, in general their reliability appears to approximate ±0.05 mgal. A discrepancy of approximately −0.03 mgal per 1000 mgal of absolute gravity is indicated, however, in the gravity standard defined by the IGSN 71 values over the range of modern absolute gravity determinations between Fairbanks, Alaska and Bogotá, Colombia. An evaluation of the earlier attempt to standardize gravity on a global scale (Woollard and Rose, 1963) indicates a mean datum difference of 14.7 mgal (standard deviation 0.2 mgal) relative to IGSN 71 values at 776 sites having a worldwide distribution. No discernible difference in gravity standard from that of the IGSN 71 values is indicated except in South America, where the Woollard and Rose values are found to incorporate a difference in standard of O.2 mgal per 1000 mgal. It is shown that anomaly conversions from the old to the new gravity system can be effected directly using the old anomaly values. Two correction terms are required, specifically, (1) a constant representing the difference in base value used relative to the IGSN 71 value for the base, and (2) a latitude‐dependent term representing the difference in theoretical sea level gravity using the old International Gravity Formula (IGF) and the new GRS 67 formula. Test conversions of anomaly values on the old gravity system for regional areas involving data from several sources indicate that, in general, anomaly conversion to the new gravity system can be obtained with a reliability of about 0.3 to 0.5 mgal. The limiting factor is the unknown variation in gravimeter calibration standards represented.
Gravity anomalies of two‐dimensional bodies of irregular cross‐section with density contrast varying with depth
Authors: Murthy I. V. Radhakrishna , Rao D. Bhaskara
Published: October 2002

The line‐integral method of Hubbert (1948) is extended to obtain the gravity anomalies of two‐dimensional bodies of arbitrary cross‐sections with density contrast varying linearly with depth. The cross‐section is replaced by an N‐sided polygon. The coordinates of two vertices of any given side are used to determine the associated contribution to the gravity anomaly. The gravity contribution of each side is then summed to yield the total gravity effect. The case where density contrast varies exponentially with depth is also considered. This technique is used to obtain the structure of the San Jacinto Graben, California, where sediments filling the graben have an exponential increase in density with depth.
Seismic array noise studies at Roosevelt Hot Springs, Utah geothermal area
Authors: Douze E. J. , Laster S. J.
Published: October 2002

As part of a study of a geothermal steam field at Roosevelt Hot Springs in Utah, the background seismic noise was investigated using seismometer arrays. Roosevelt Hot Springs is located on the Wasatch front in southern Utah, an area characterized by Tertiary intrusions. Arrays of vertical seismometers with spacings of 50 to 100 m were installed at selected locations. The data from three arrays were studied in detail; one was located directly above the geothermal reservoir, one was in the valley to the west, and one was in the Mineral Mountains to the east of the reservoir. The principle analysis technique consisted of computing frequency‐wavenumber spectra of the noise in the frequency range from 0.5 to 10 Hz. For frequencies less than 1.0 Hz, the arrays were too small for adequate resolution, and at frequencies higher than 10.0 Hz, the noise showed no spatial organization. The theoretical response of seismometer arrays to waves arriving from numerous directions, such as would be the case directly above a geothermal reservoir, is developed to allow comparison with the experimental results. During times of cultural activity (mainly road traffic and trains in the valley), the noise was highly variable in amplitude and consisted almost exclusively of Rayleigh waves from the cultural sources. At quiet times, the noise field was more complex. For the arrays at the reservoir and in the valley, the results of frequency‐wavenumber computations indicate that the noise consists of isotropic Rayleigh waves. No waves were detected that could be related to the geothermal reservoir. The array in the Mineral Mountains, farther away from the cultural noise sources, showed a completely different noise field. The noise consisted of high‐velocity P‐waves from a source to the east of the known geothermal area.
Connection between formation factor for electrical resistivity and fluid‐solid coupling factor in Biot’s equations for acoustic waves in fluid‐filled porous media
Authors: Brown Robert J. S.
Published: October 2002

The coefficient of inertial coupling between fluid and solid for elastic waves in fluid‐filled porous media is shown to be equal to or greater than the porosity times the low‐frequency electrical‐resistivity formation factor, being equal to this product when effects of fluid viscosity are minimal, as they may be for high‐frequency measurements on porous materials of high permeability and porosity. At sufficiently low frequencies, the coupling is due primarily to viscous forces. At intermediate frequencies, viscous forces increase inertial coupling, and inertial forces increase viscous coupling. Thus, porosity and formation factor measurements provide lower limits to coupling coefficients that can be used in the interpretation of acoustic data.
Coincident loop transient electromagnetic master curves for interpretation of two‐layer earths
Authors: Raiche A. P. , Spies B. R.
Published: October 2002

A set of apparent conductivity master curves has been calculated for the coincident loop transient electromagnetic (TEM) method used over a two‐layer earth. Conductivity contrasts range from 0.001 to 1000. Loop radius/layer depth ratios range from 0.01 to 100. The time range is sufficient to see the entire shape of the curves from the early to the late time asymptotes. These curves allow the determination of the parameters of a two‐layer earth for accurate data over a sufficient time range. Examples using the curves to interpret multilayered earths are given. The curves are also used to show the limitations placed on interpretation by existing TEM equipment.
An Introduction to the generalized reciprocal method of seismic refraction interpretation
Authors: Palmer Derecke
Published: October 2002

The generalized reciprocal method (GRM) is a technique for delineating undulating refractors at any depth from in‐line seismic refraction data consisting of forward and reverse traveltimes. The traveltimes at two geophones, separated by a variable distance XY, are used in refractor velocity analysis and time‐depth calculations. At the optimum XY spacing, the upward traveling segments of the rays to each geophone emerge from near the same point on the refractor. This results in the refractor velocity analysis being the simplest and the time‐depths showing the most detail. In contrast, the conventional reciprocal method which has XY equal to zero is especially prone to produce numerous fictitious refractor velocity changes, as well as producing gross smoothing of irregular refractor topography. The depth conversion factor is relatively insensitive to dip angles up to about 20 degrees, because both forward and reverse data are used. As a result, depth calculations to an undulating refractor are particularly convenient even when the overlying strata have velocity gradients. The GRM provides a means of recognizing and accommodating undetected layers, provided an optimum XY value can be recovered from the traveltime data, the refractor velocity analysis, and/or the time‐depths. The presence of undetected layers can be inferred when the observed optimum XY value differs from the XY value calculated from the computed depth section. The undetected layers can be accommodated by using an average velocity based on the optimum XY value. This average velocity permits accurate depth calculations with commonly encountered velocity contrasts.
Fundamentals of frequency domain migration
Authors: Chun Joong H. , Jacewitz Chester A.
Published: October 2002

Frequency domain migration is founded upon the wave equation, and so includes diffractions and other effects. This paper seeks to motivate and illuminate frequency domain migration using straightforward geometric techniques and simple frequency domain observations.
Computation of the time‐domain response of a polarizable ground
Authors: Guptasarma D.
Published: October 2002

Computation of the theoretical time‐domain response of a polarizable ground on the basis of a frequency‐domain model of relaxation, e.g., a Cole‐Cole or any other model that involves a fractional power of the complex frequency variable, runs into difficulties either because the Laplace transform can only be written as a very slowly converging summation or because it cannot be written in closed computable form. A clear way around this is to use a digital linear filter. A filter is presented in this paper that has been designed specifically to work well with complex impedance functions that tend asymptotically to real values at both extremes of the frequency variable, the magnitude descending monotonically from the low‐frequency asymptote to the high frequency asymptote. This filter produces the step response from the real part of the impedance‐versus‐frequency function with reasonable accuracy for all impedance functions that one may like to represent by models of electrical relaxation for a polarizable ground, but it does not work for functions containing sharp resonances or discontinuities.
Reconciliation of the discrete and integral Fourier transforms
Authors: Cordell Lindrith , Grauch V. J. S.
Published: October 2002

In the application of harmonic analysis to potential‐field geophysical studies, relationships derived in terms of the continuous Fourier integral transform are evaluated in terms of the discrete Fourier transform. The discrete transform, obtained by transforming a finite number of equispaced samples of the actual aperiodic continuous function, is too low at the dc level and increasingly too high in the high frequencies, compared with the theoretical integral transform. As a consequence, overly restrictive limitations must be placed on high‐frequency‐amplifying operators such as differentiation and downward continuation. Also, a spurious and troublesome azimuthal distortion occurs in the discrete Fourier analysis of three‐dimensional (3-D) (map) data represented as grids. The discrete transform can be made essentially equivalent to the integral transform if, before sampling, the continuous aperiodic input function is made periodic by shifting the function by integer multiples of the data interval and summing. Doing so requires extrapolation of the data function beyond the limits of the data interval. An equivalent‐source technique illustrates the principle. For practical application to large data sets, a high‐frequency band‐limited filter determined by the low‐frequency spectra accomplishes an analogous extrapolation in the frequency domain.
Theoretical seismic wave radiation from a fluid‐filled borehole
Authors: Lee Myung W. , Balch A. H.
Published: October 2002

This paper concerns far‐field radiation of compressional P and shear S waves into the surrounding medium from a fluid‐filled borehole in an infinite medium and tube waves propagating along a borehole, using a low‐frequency approximation. Two kinds of sources are considered: (1) a volume displacement point source acting on the axis of a borehole, and (2) a uniform radial stress source acting on the wall of a borehole. When the tube‐wave velocity is close to the shear‐wave velocity, the effect of the borehole fluid on the P‐wave radiation pattern and on the S‐wave radiation pattern is substantial.
Iterative deconvolution
Authors: Ioup George E. , Ioup Juliette W.
Published: October 2002

In a recent article, LaCoste (1982) proposed a method of deconvolution by successive approximations and several significant modifications to the method. In this note we give some background on this approach and comment on certain details of its implementation.
The influence of salt domes on paleotemperature distributions
Authors: O’Brien J. J. , Lerche I.
Published: October 2002

A characteristic of salt domes is that an enhanced heat flux is associated with them, due to the contrast in thermal conductivity between rock salt and typical sedimentary formations. We present a simple analytical model of heat flow in the vicinity of an isolated salt dome, with numerical evaluations for some sample cases. In addition to an enhanced surface heat flow, these models show that on the upper flanks of a salt dome a temperature higher than the regional trend is predicted, thus enhancing hydrocarbon maturation at these depths. On the lower flanks a temperature lower than the regional trend is predicted, thus inhibiting overmaturation. The magnitude of this temperature anomaly depends upon the position of the measurement point, both vertical and radial, relative to the salt dome; roughly speaking it is confined to within one salt dome radius of the salt‐sediment interface. The magnitude of the anomaly can be quite large for typical salt domes. These basic ideas are corroborated by observing downhole measurements from a salt dome in the Gulf of Mexico. The good agreement allows us to bracket the height of that particular dome at between 9 000 and 15 000 m, and also permits us to determine that the total sediment thickness overlying the basal salt is between 13 200 and 19 200 m at the location of the salt dome. These results indicate that the presence of a salt dome can have a significant impact on the subsurface temperature distribution and, hence, on the thermochemical maturation of any source rocks or hydrocarbon accumulations in close proximity to the salt dome. In addition to providing trapping structures, a salt dome also provides an enhanced environment for hydrocarbon maturation on its upper flanks and for inhibiting over‐maturation on its lower flanks. Such effects should be included when evaluating the hydrocarbon potential of a salt dome province.
Heat flow in the Uinta Basin determined from bottom hole temperature (BHT) data
Authors: Chapman David S. , Keho T. H. , Bauer Michael S. , Picard M. Dane
Published: October 2002

The thermal resistance (or Bullard) method is used to judge the utility of petroleum well bottom‐hole temperature data in determining surface heat flow and subsurface temperature patterns in a sedimentary basin. Thermal resistance, defined as the quotient of a depth parameter Δz and thermal conductivity k, governs subsurface temperatures as follows: [Formula: see text] where [Formula: see text] is the temperature at depth z=B, [Formula: see text] is the surface temperature, [Formula: see text] is surface heat flow, and the thermal resistance (Δz/k) is summed for all rock units between the surface and depth B. In practice, bottom‐hole and surface temperatures are combined with a measured or estimated thermal conductivity profile to determine the surface heat flow [Formula: see text] which, in turn, is used for all consequent subsurface temperature computations. The method has been applied to the Tertiary Uinta Basin, northeastern Utah, a basin of intermediate geologic complexity—simple structure but complex facies relationships—where considerable well data are available. Bottom‐hole temperatures were obtained for 97 selected wells where multiple well logs permitted correction of temperatures for drilling effects. Thermal conductivity values, determined for 852 samples from 5 representative wells varying in depth from 670 to 5180 m, together with available geologic data were used to produce conductivity maps for each formation. These maps show intraformational variations across the basin that are associated with lateral facies changes. Formation thicknesses needed for the thermal resistance summation were obtained by utilizing approximately 2000 wells in the WEXPRO Petroleum Information file. Computations were facilitated by describing all formation contacts as fourth‐order polynomial surfaces. Average geothermal gradient and heat flow for the Uinta Basin are [Formula: see text] and [Formula: see text], respectively. Heat flow appears to decrease systematically from 65 to [Formula: see text] from the Duchesne River northward toward the south flank of the Uinta Mountains. This decrease may be the result of refraction of heat into the highly conductive quartzose Precambrian Uinta Mountain Group. More likely, however, it is related to groundwater recharge in late Paleozoic and Mesozoic sandstone and limestone beds that flank the south side of the Uintas. Heat flow values determined for the southeast portion of the basin show some scatter about a mean value of [Formula: see text] but no systematic variation.
Microgravimetric and gravity gradient techniques for detection of subsurface cavities
Authors: Butler Dwain K.
Published: October 2002

Microgravimetric and gravity gradient surveying techniques are applicable to the detection and delineation of shallow subsurface cavities and tunnels. Two case histories of the use of these techniques to site investigations in karst regions are presented. In the first case history, the delineation of a shallow (∼10 m deep), air‐filled cavity system by a microgravimetric survey is demonstrated. Also, application of familiar ring and center point techniques produces derivative maps which demonstrate (1) the use of second derivative techniques to produce a “residual” gravity map, and (2) the ability of first derivative techniques to resolve closely spaced or complex subsurface features. In the second case history, a deeper (∼ 30 m deep), water‐filled cavity system is adequately detected by a microgravity survey. Results of an interval (tower) vertical gradient survey along a profile line are presented in the second case history; this vertical gradient survey successfully detected shallow (<6 m) anomalous features such as limestone pinnacles and clay pockets, but the data are too “noisy” to permit detection of the vertical gradient anomaly caused by the cavity system. Interval horizontal gradients were determined along the same profile line at the second site, and a vertical gradient profile is determined from the horizontal gradient profile by a Hilbert transform technique. The measured horizontal gradient profile and the computed vertical gradient profile compare quite well with corresponding profiles calculated for a two‐dimensional model of the cavity system.
The application of high‐order differencing to the scalar wave equation
Authors: Dablain M. A.
Published: October 2002

The second‐order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high‐order approximations for these derivatives. A one‐dimensional model is used to illustrate the relative accuracy of [Formula: see text] central‐difference schemes. For comparison, [Formula: see text] pseudospectral schemes are used as an additional measure of performance. The results indicate that [Formula: see text] differencing can achieve similar accuracy as the [Formula: see text] spectral scheme. For practical illustration, a two‐dimensional form of the [Formula: see text] algorithm is used to compute the exploding reflector response of a salt‐dome model and compared with a fine‐grid [Formula: see text] result. Transmissive sponge‐like boundary conditions are also examined and shown to be effective.
Experience with the generalized reciprocal method of seismic refraction interpretation for shallow engineering site investigation
Authors: Hatherly P. J. , Neville M. J.
Published: October 2002

The shallow seismic refraction method has been used routinely during the initial investigation at many dam sites in New South Wales. By using computer processing techniques and advanced interpretational features of the generalized reciprocal method, it has been possible to derive a picture of the subsurface layering from the refraction results even in geologically complex environments. Close cooperation between the geophysicist and geologist is necessary to ensure proper use of the seismic results. The results may be used to guide subsequent drilling programs and to aid design and construction. This approach to engineering site investigations is demonstrated with results from two recent investigations.
The effects of cathodically protected pipelines on aeromagnetic surveys
Authors: Gay S. Parker
Published: October 2002

Many types of cultural noise are found in present‐day high‐resolution aeromagnetic data, and such noise must be removed if surveys flown in areas of existing cultural features are to be interpreted properly—particularly areas of oil and gas production. One of the worst causes of cultural noise in such areas is the dc electrical current passed through pipelines to prevent corrosion. This practice is called “cathodic protection,” and it is in common use worldwide; however, there is little or no discussion of the resulting magnetic anomalies in the geophysical literature. Cathodically protected pipeline (CPP) anomalies are particularly troublesome at the level of airborne surveys because they fall off slowly as the first power of the distance, rather than as the square or cube of the distance as in most sources of random cultural noise. However, the curve shapes of CPP anomalies are readily calculable: they depend upon the strike directions of the pipeline and the aeromagnetic profile, and on the inclination and declination of the Earth’s magnetic field. The amplitude of CPP anomalies depends upon the height of the magnetometer above the pipeline and the strength of the current in the line. Standard curves were plotted for several CPP anomalies due to long, straight, horizontal pipelines, worldwide, and were used to verify the existence of CPP anomalies in production survey lines and tie lines for an aeromagnetic survey at the magnetic latitude of Oklahoma, USA.
Analysis of electrical conduction in the grain consolidation model
Authors: Schwartz Lawrence M. , Kimminau Stephen
Published: October 2002

In the grain consolidation model the diagenetic processes of compaction and cementation are represented in terms of the growth of an array of originally spherical grains. Grain growth toward the nodes of the pore space leads to an electrical formation factor F(ϕ) that increases slowly as the porosity ϕ decreases. By contrast, grain growth toward the throats of the pore space leads to a rapidly increasing F(ϕ). In all the cases we have examined, the value of the percolation threshold, [Formula: see text] is less than 0.055. Network simulation techniques have been developed to calculate the electrical conductivity of the ordered versions of the grain consolidation model. We find that the minimum‐area approximation employed in our earlier work is generally quite satisfactory. The network techniques can also be used to model the effects of mixed pore‐space fluid saturation, with results that are physically reasonable although not necessarily in agreement with empirical rules regarding saturation.
The effects of transverse isotropy on reflection amplitude versus offset
Authors: Wright J.
Published: October 2002

Studies have shown that elastic properties of materials such as shale and chalk are anisotropic. With the increasing emphasis on extraction of lithology and fluid content from changes in reflection amplitude with shot‐to‐group offset, one needs to know the effects of anisotropy on reflectivity. Since anisotropy means that velocity depends upon the direction of propagation, this angular dependence of velocity is expected to influence reflectivity changes with offset. These effects might be particularly evident in deltaic sand‐shale sequences since measurements have shown that the P-wave velocity of shales in the horizontal direction can be 20 percent higher than the vertical P-wave velocity. To investigate this behavior, a computer program was written to find the P- and S-wave reflectivities at an interface between two transversely isotropic media with the axis of symmetry perpendicular to the interface. Models for shale‐chalk and shale‐sand P-wave reflectivities were analyzed.
A new slant on seismic imaging: Migration and integral geometry
Authors: Miller D. , Oristaglio M. , Beylkin G.
Published: October 2002

A new approach to seismic migration formalizes the classical diffraction (or common‐tangent) stack by relating it to linearized seismic inversion and the generalized Radon transform. This approach recasts migration as the problem of reconstructing the earth’s acoustic scattering potential from its integrals over isochron surfaces. The theory rests on a solution of the wave equation with the geometrical‐optics Green function and an approximate inversion formula for the generalized Radon transform. The method can handle both complex velocity models and (nearly) arbitrary configurations of sources and receivers. In this general case, the method can be implemented as a weighted diffraction stack, with the weights determined by tracing rays from image points to the experiment’s sources and receivers. When tested on a finite‐difference simulation of a deviated‐well vertical seismic profile (a hybrid experiment which is difficult to treat with conventional wave‐equation methods), the algorithm accurately reconstructed faulted‐earth models. Analytical reconstruction formulas are derived from the general formula for zero‐offset and fixed‐offset surface experiments in which the background velocity is constant. The zero‐offset inversion formula resembles standard Kirchhoff migration. Our analysis provides a direct connection between the experimental setup (source and receiver positions, source wavelet, background velocity) and the spatial resolution of the reconstruction. Synthetic examples illustrate that the lateral resolution in seismic images is described well by the theory and is improved greatly by combining surface data and borehole data. The best resolution is obtained from a zero‐offset experiment that surrounds the region to be imaged.
Onshore high‐resolution seismic profiling applied to sedimentology
Authors: Jongerius P. , Helbig K.
Published: October 2002

High‐resolution seismic profiling is a valuable method for the exploration of the shallow subsurface. Currently, a resolution of 0.5 m can be attained. This resolution is sufficient to recognize small sedimentary features (channels, dunes, linear ridges, etc.) and to reconstruct the environment of deposition, The surveys described in this paper were carried out under favorable conditions on intertidal flats and beaches.