bluuebunny/crossref_metadata_2025 huggingface dataset:
Rock lithology and porosity determination from shear and compressional wave velocity
Authors: Domenico S. N.
Published: October 2002

Data examined in this study are previously published laboratory shear (S) and compressional (P) wave velocity measurements on water‐saturated sandstone, calcareous sandstone, dolomite, and limestone cores, as well as laboratory porosity measurements on the sandstone and limestone cores. Sandstone and limestone porosities range from .092 to .299 and from .006 to .229, respectively. Differential pressure was varied from 500 to 6000 psi, corresponding to approximate burial depths from 290 to 3460 m, respectively. Sandstone, limestone, and dolomite are effectively separated by Poisson’s ratio σ or, equivalently, by the ratio of P- to S-wave velocity. Separation of sandstone and limestone appears to result from the difference in σ of the matrix material, namely, quartz (.056) and calcite (.316), respectively. An empirical function, [Formula: see text], was fit by regression analysis to sandstone and limestone velocity ([Formula: see text] and [Formula: see text]) versus porosity (ϕ) values at each differential pressure. In this equation A and B are constants at each pressure, A being approximately equal to the reciprocal matrix velocity. Decreasing standard deviation indicates that the equation becomes an appreciably more accurate representation of the measured data as pressure increases. Average values of A are near reciprocal velocities of quartz (sandstone averages) and calcite (limestone averages). The constant B, rate of change of reciprocal velocity with porosity, is a critical measure of the sensitivity of velocity to porosity, hence the usefulness of velocity in estimation of porosity. Sandstone S-wave B values are from 2 to 5 times greater than all other values, indicating that sandstone S-wave velocity is by far the most sensitive to porosity variation. Least sensitive is limestone P-wave velocity.
Automated interpretation of airborne electromagnetic data
Authors: DeMoully G. T. , Becker A.
Published: October 2002

Recent improvements in equipment quality make it possible to increase the usefulness of airborne electromagnetic (EM) systems in areas of moderate electrical conductivity for the purpose of constructing simple electrical property maps which can be related to surficial geology. This application of airborne electromagnetics may be demonstrated and evaluated using Barringer/Questor Mark VI Input® survey results in places where independent verifications of the airborne data interpretation are available. For this purpose we have developed a set of computer algorithms which read digitally recorded Input data and interpret them automatically in terms of a simple electrical section that is defined by a single conductive layer whose thickness, conductivity, and subsurface depth are determined from the data. Because this technique is formally based on a one‐dimensional, three‐layer, three‐parameter, horizontally stratified earth model, it is only applicable in regions where the surficial formations are mildly dipping and the conductive layer is covered by, and rests on, highly resistive materials. The interpretation method is illustrated by three field examples. At the first field survey site, in Alberta, Canada, airborne EM survey data are used to map the depth of the interface between coarse and clayey sands. Data from a second survey site, this time in the Western USA, are interpreted to yield the section of a subsurface valley filled with conductive clay. The final example, taken from British Columbia, Canada, involves the mapping of all the three parameters for a weathered volcanic unit.
Corrections to Millett’s table of electromagnetic coupling phase angles
Authors: Brown R. J.
Published: October 2002

Millett (1967) published tables of values of the mutual impedance due to inductive coupling between two collinear dipoles on a uniform, nonpolarizable half‐space. In the course of a recent study (Brown, 1984) I have noticed significant errors, of two different kinds, in the phase angles (ϕ) given by Millett (1967). One kind of error is evidently typographical in nature and occurs only twice, in the M = 3 table, for θ = .01 and .02. The tabled values apparently had their decimal points shifted one place. The second and more serious kind of error is an apparently random error within the range ±0.003 degrees. This is not significant for larger |ϕ|, say |ϕ| > 1 degree, but the values of |ϕ| in Millett’s tables go down to 0.006 degrees (down to 0.0045 degrees after correction) where such errors are clearly significant, particlarly if one is working with logarithmic quantities as is common.
AN EXPERIMENTAL DEVICE FOR COMPUTING MAGNETIC AND GRAVITATIONAL ANOMALIES
Authors: Fisher J. W.
Published: October 2002

Based upon the fact that gravitational and magnetic anomalies are functions of the solid angle subtended at the point of measurement by the contours of the anomalous body, an electro‐magnetic model is described which permits direct measurement of the desired quantities in terms of mutual inductance. A model of the subsurface “structure” is made in the form of a coil in which the vertical spacing of the turns is kept constant and the shape of the helix conforms to the contours of the structure. A small search coil is then located at the point corresponding to that at which a gravimetric or magnetometric observation is desired. The mutual inductance between the search coil and the main coil is then measured and may be expressed in terms of the magnetic or gravity anomaly arising from the simulated structure. For magnetic anomalies the search coil is made as compact as possible whereas in the case of gravity anomalies the search coil is in the form of a long solenoid of small diameter, evenly wound along its length, in order to affect the integration necessary to measure the magnetic potential analogous to the desired gravitational quantity.
RELATIVE GRAVITY MEASUREMENTS USING PRECISION PENDULUM EQUIPMENT
Authors: Gay Malcolm W.
Published: October 2002

The precision with which relative‐gravity values may be obtained by the use of suitable pendulum equipment is illustrated by actual data obtained in establishing calibration stations used to facilitate the calibration of gravimeters. A résumé of the operating technique, together with the salient features of the Gulf pendulum equipment is given in connection with a tabulated summary of the various factors which must be considered in designing and operating pendulums in order to attain the desired precision of [Formula: see text] g.
FORMULAS AND CURVES FOR THE INTERPRETATION OF CERTAIN TWO‐DIMENSIONAL MAGNETIC AND GRAVITATIONAL ANOMALIES
Authors: Pentz Harold H.
Published: October 2002

Curves and formulas for the interpretation of the two‐dimensional “dike” and “step” are given because they offer an easy, rapid method of solving all cases to which they apply. Horizontal and vertical polarization of the bodies are considered. This method applies to torsion balance surveys, and to magnetic surveys where the horizontal and vertical components of the earth’s magnetic field are measured. Two curves for the interpretation of an anomaly in terms of a point pole (or a point mass) are given. The depth to the two‐dimensional structures is considered, with formulas and curves.
THE RELIABILITY OF GEOPHYSICAL ANOMALIES ON THE BASIS OF PROBABILITY CONSIDERATIONS
Authors: Elkins Thomas A.
Published: October 2002

When data are used which contain random errors, there is always some question as to whether a supposed anomaly may not be real but due only to errors in the data. This paper describes a method of testing this point, which is worked out in detail assuming the Gaussian error law for the case of independent values. Possible applications of the method to the problems of contouring data, and evaluating and ranking anomalies are suggested. Examples of the use of the method on gravity and soil gas analysis data are also given.
THE MECHANICS OF THE UPSIDE DOWN CORE
Authors: Lynton Edward D.
Published: October 2002

Very frequently cores taken from trays and oriented by the Herrick‐Lynton method of magnetic core orientation have been wrongly marked as to top and bottom. If the bottom of the core is run as top, the resulting orientation is not 180° off unless the points of the compass are marked similarly to a Brunton Compass, namely, transposition of east and west.
On: “Interpretation of magnetic bodies using Hilbert transforms” by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri Rao (GEOPHYSICS, 47, 376–387, March, 1982).
Authors: Pauls Rob
Published: October 2002

The Fourier and Hilbert transform techniques have played extremely important roles in geophysical data processing. We were naturally very interested to find the paper by Mohan et al. which described a possible application of the Hilbert transform approach in magnetic interpretation. However, we found some very serious problems in the paper.
Evaluation of direct hydrocarbon indicators through comparison of compressional‐ and shear‐wave seismic data: a case study of the Myrnam gas field, Alberta
Authors: Ensley Ross Alan
Published: October 2002

Shear waves differ from compressional waves in that their velocity is not significantly affected by changes in the fluid content of a rock. Because of this relationship, a gas‐related compressional‐wave “bright spot” or direct hydrocarbon indicator will have no comparable shear‐wave anomaly. In contrast, a lithology‐related compressional‐wave anomaly will have a corresponding shear‐wave anomaly. Thus, it is possible to use shear‐wave seismic data to evaluate compressional‐wave direct hydrocarbon indicators. This case study presents data from Myrnam, Alberta which exhibit the relationship between compressional‐ and shear‐wave seismic data over a gas reservoir and a low‐velocity coal.
Prestack inversion with plane‐layer point source modeling
Authors: McAulay Alastair D.
Published: October 2002

Prestack inversion with point‐source plane‐layer modeling has many advantages over poststack or normal incidence inversion. For example, it permits the determination of absolute compressional and shear velocities, density variations, and the accurate accounting of interbed and surface multiples. I neglect shear effects in this paper by assuming that they are adequately suppressed by velocity filtering. In the forward modeling step, a spherical wave expansion into plane waves is used to account for the point source. The plane‐wave reflection response for a set of plane layers is extended to the nonnormal incidence case. I use a Hankel transform to account for cylindrical symmetry. Generalized linear inversion is used because the fast recursive approaches available for normal incidence inversion are no longer applicable. I provide the derivation for the required derivative matrix, and I take into account the band‐limited nature of the data in frequency, time, and space. I demonstrate that moveout of events on realistic simulated prestack data enables the determination of absolute compressional velocity in the velocity‐depth profile, even though the data are band‐limited in frequency. I assume that preprocessing has adequately removed the shear and surface effects and that density is constant. Low frequencies in the velocity profile may be obtained more accurately than with velocity analysis used for stacking, because interbed multiples and other modeling phenomena are accounted for in the computation. Autoregressive modeling procedures that predict into the low frequencies of the velocity profile are also less accurate and cannot generate absolute velocity. I suggest future research leading to cost‐effective inversion of real data.
A new solution method for the wave equation in inhomogeneous media
Authors: Pai D. M.
Published: October 2002

A fundamental mathematical algorithm is presented for solving the wave equation in inhomogeneous media. This method completely generalizes the Haskell matrix method, which is the standard method for solving the wave equation in laterally homogeneous media. The Haskell matrix method has been the mathematical basis for many seismic techniques in exploration geophysics. In the method presented the medium is divided into layers and vertically averaged within each layer. The wave equation, within a layer, is then decoupled into an eigenvalue equation of the horizontal coordinate and a wave equation of the vertical coordinate. The eigen‐value equation is solved numerically. The vertical equation is solved analytically, once the eigenvalues are found. The solution throughout the medium is constructed by matching layer solutions at layer interfaces. The solution process of this method is “modular,” in the sense that each layer corresponds to an independent module and all the modules together form the final, total solution. Such a modular solution process has the following advantages. First, in a 2-D problem, for example, each module is a 1-D problem, which is a much simpler problem numerically than the original full 2-D problem. Second, the module solutions can be used repeatedly to form the solution corresponding to different problems. For example, in modeling. only those layers which differ between two models require recalculation. The solution to plane‐wave diffraction by a cylinder is obtained using this method, and it agrees well with the analytical solution.
A ray inversion method for refraction analysis
Authors: Jones Glyn M. , Jovanovich D. B.
Published: October 2002

A new technique is presented for the inversion of head‐wave traveltimes to infer near‐surface structure. Traveltimes computed along intersecting pairs of refracted rays are used to reconstruct the shape of the first refracting horizon beneath the surface and variations in refractor velocity along this boundary. The information derived can be used as the basis for further processing, such as the calculation of near‐surface static delays. One advantage of the method is that the shape of the refractor is determined independently of the refractor velocity. With multifold coverage, rapid lateral changes in refractor geometry or velocity can be mapped. Two examples of the inversion technique are presented: one uses a synthetic data set; the other is drawn from field data shot over a deep graben filled with sediment. The results obtained using the synthetic data validate the method and support the conclusions of an error analysis, in which errors in the refractor velocity determined using receivers to the left and right of the shots are of opposite sign. The true refractor velocity therefore falls between the two sets of estimates. The refraction image obtained by inversion of the set of field data is in good agreement with a constant‐velocity reflection stack and illustrates that the ray inversion method can handle large lateral changes in refractor velocity or relief.
Splines in geophysics
Authors: Gonzalez‐Casanova Pedro , Alvarez Roman
Published: October 2002

Modeling and contouring of geophysical data often require distributions of regularly spaced values. Splines have been shown to be the most accurate methods to obtain such distributions. We emphasize the general problem of interpolating random distributions of data on a given surface. Splines are classified into unidimensional, quasi‐bidimensional, and strictly bidimensional; based on this classification, a systematic derivation of the corresponding interpolating techniques is conducted. Two approaches are presented to obtain unidimensional splines: one based on the continuity of the first and second derivatives of the polynomials involved, and the other based on a variational approach. Quasi‐bidimensional splines are constructed based on the unidimensional approach, while strictly bidimensional splines are generated by minimizing the bidimensional curvature. Quasi‐bidimensional splines can be used for processing data distributions along nearly parallel lines; linear projections and parameterization are the techniques used in interpolating this type of distribution. Strictly bidimensional splines minimize curvature through the analytic solution of the Euler‐Lagrange equation or by a finite‐difference algorithm. The maximum error, mean error, and standard deviation between interpolated data and exact field values produced by various prisms show that quasi‐bidimensional splines are 2.7 percent more accurate in the maximum error than strictly bidimensional splines when both techniques are applied to regularly spaced data. However, for irregularly spaced data, three examples containing 300, 600, and 900 random data points show the superiority of the thin‐plate approach over the quasi‐bidimensional splines. A comparison between various interpolation densities on regular grids, starting from a set of 327 randomly distributed magnetic stations, illustrates some differences between geophysically meaningful interpolations and interpolations carried out only for contouring purposes.
Efficient microcomputer‐based finite‐difference resistivity modeling via Polozhii decomposition
Authors: James Bryan A.
Published: October 2002

Finite‐difference modeling for direct current resistivity problems can be cast in a form allowing rapid and efficient solution on a microcomputer. Almost a million nodes can be accommodated on a microcomputer with only 256 kilobytes of memory. The Polozhii decomposition procedure (Polozhii, 1965) allows a three‐dimensional (3-D) problem with no more than a one‐dimensional (1-D) property variation to be transformed into a series of decoupled and independent one‐dimensional problems. The decomposition utilizes matrix transforms analogous to analytic spatial Fourier and Hankel transforms. These matrix transforms, along with recursive formulas for the solution of the 1-D problems, yield a process which can be thought of as a continuation operator when compared with current popular methods of potential field continuation using the Fourier transform. The result is that only a single plane of node potentials needs to be determined fully. By setting up more complicated models as separate regions with differing 1-D models the above procedures can be used to create a problem where the unknown potentials along the boundary planes between the regions are cast in terms of known outer boundary potentials and known applied source terms. Once all interior boundary potentials have been calculated, the solution on any arbitrary plane of nodes in any region can be quickly calculated using the standard Polozhii decomposition procedure. Execution times for a variety of grid sizes composed of two such regions show much slower growth with increasing numbers of nodes than conventional finite‐difference solution schemes. Test cases for comparison with analytic calculations yield errors of 5 percent or less for problems composed of 756 000 nodes. The choice of boundary condition, however, has a significant influence on the accuracy obtained.
On the least‐squares residual anomaly determination
Authors: Abdelrahman E. M. , Riad S. , Refai E. , Amin Y.
Published: October 2002

This paper discusses an approach to determine the least‐squares optimum order of the regional surface which, when subtracted from the Bouguer gravity anomaly data, minimizes distortion of the residual component of the field. The least‐squares method was applied to theoretical composite gravity fields each consisting of a constant residual component (sphere or vertical cylinder) and a regional component of different order using successively increasing orders of polynomial regionals for residual determination. The overall similarity between each two successive residual maps was determined by computing the correlation factor between the mapped variables. Similarity between residual maps of the lowest orders, verified by good correlation, may generally be considered a criterion for determining the optimum order of the regional surface and consequently the least distorted residual component. The residual map of the lower order in this well‐correlated doublet is considered the most plausible one and may be used for gravity interpretation. This approach was successfully applied to the Bouguer gravity of Abu Roash dome, located west of Cairo in the Western Desert of Egypt.
Use of integrated energy spectra for thin‐layer recognition
Authors: Marangakis Andrew , Costain John K. , Coruh Cahit
Published: October 2002

The detection and resolution of thin beds are important problems in reflection seismology. A thin bed is defined as one for which the two‐way traveltime thickness is less than the tuning thickness for the incident wavelet. Reservoir thickness and shape are of critical importance in estimating hydrocarbon reserves. Previous studies of thin‐bed resolution have focused attention on the time domain, i.e., on the properties of the seismic trace and wavelet Widess (1973) defined a thin bed as one whose thickness is less than λ/8, where λ is the dominant wavelength of the seismic wavelet in the thin bed. He based this criterion on the observation that for thin beds of thickness less than or equal to λ/8, the reflected wavelet is essentially the shape of the derivative of the incident wavelet.
Numerical modeling of the electromagnetic response of three‐dimensional conductors in a layered earth
Authors: Best M. E. , Duncan P. , Jacobs F. J. , Scheen W. L.
Published: October 2002

This paper describes a numerical modeling program which was developed for computing the electromagnetic response of a three‐dimensional conductor in a layered earth. The algorithm is a hybrid one, in the sense that a finite‐element method is combined with an integral equation approach for the complete solution of the problem. In this approach, two relatively small matrices are inverted to obtain the secondary magnetic fields at the interior nodes of the subdivided volume. The finite‐element method requires special attention at low frequencies, i.e., when the body dimensions are small compared with the skin depth. The method was tested with various models involving spheres and rectangular dikes, and comparisons have been made with analytical, numerical, and scale‐modeling data. These comparisons generally show good agreement between our numerical model and the other models tested. Examples are given which show the flexibility and usefulness of this modeling algorithm when applied to a ground or airborne prospecting system with a coil separation of 10 m.
Inversion of potential field data in Fourier transform domain
Authors: Mareschal J. C.
Published: October 2002

A relationship is derived between the Fourier transform of a potential field at the Earth’s surface and the transform of the inducing source distribution. The Fourier transform of the field is the Laplace transform of the source distribution spectrum when the Laplace transform variable p is equal to the wavenumber. This relationship can be used to determine all possible source distributions compatible with the data. The solution is the superposition of a particular solution to an inhomogeneous problem and of the general solution to the homogeneous problem (i.e., for which the field vanishes at the surface). Source distribution can be expanded into a set of known functions; coefficients of the expansion are determined by solving a system of linear equations. Physical constraints can be introduced to restrict the variation range of the coefficients of expansion. Two examples are presented to illustrate the method: a synthetic gravity profile and a heat flow profile are inverted to determine density or heat source distributions compatible with the data.
Integral equation solution for the transient electromagnetic response of a three‐dimensional body in a conductive half‐space
Authors: SanFilipo William A. , Hohmann Gerald W.
Published: October 2002

The time‐domain integral equation for the three‐dimensional vector electric field is formulated as a convolution of the scattering current with the tensor Green’s function. The convolution integral is divided into a sum of integrals over successive time steps, so that a numerical scheme can be formulated with a time stepping approximation of the convolution of past values of the solution with the system impulse response. This, together with spatial discretization, leads to a matrix equation in which previous solution vectors are multiplied by a series of matrices and fed back into the system by adding to the primary field source vector. The spatial discretization, based on a modification of the usual pulse basis formulation in the frequency domain, includes an additional subset of divergence‐free basis functions generated by integrating the Green’s function around concentric closed rectangular paths. The inductive response of the body is more accurately modeled with these additional basis functions, and a meaningful solution can be obtained for a body in free space. The resulting algorithm produces good results even for large conductivity contrasts. Internal checks, including convergence with respect to spatial and temporal discretization, and reciprocity, demonstrate self‐consistency of the numerical scheme. Independent checks include (a) comparison with results computed for a prism in free space, (b) comparison with results computed for a thin plate, (c) comparison of our conductive half‐space algorithm with an asymptotic solution for a sphere, and (d) comparison with results from inverse Fourier transformation of values computed using a frequency‐domain integral equation algorithm. Qualitative features of the results show that the relative importance of current channeling and confined eddy currents induced in the body depends upon both conductivity contrast and geometry. If the free‐space time constant is less than the time window during which currents in the host have not yet propagated well beyond the body, current channeling dominates the response. In such cases, simple superposition of free‐space results and the background is a poor approximation. In cases where the host currents diffuse beyond the body in a time less than the free‐space time constant of the body, the total response is approximately the sum of the free‐space and background (half‐space) responses.
The midpoint method: Magnetic interpretation of dikes and faults
Authors: Murthy I. V. Radhakrishna
Published: October 2002

A method of magnetic interpretation of arbitrarily magnetized dikes and faults is developed, based on the properties of a new characteristic point called the “midpoint.” Anomaly profiles at two levels are considered, the maximum and minimum anomalies on them are located, and their midpoints are plotted. The rate of shift of the midpoint with elevation is a measure of the direction of magnetization. The distances between the points of maximum and minimum anomalies and the ratio of horizontal to vertical gradients in the case of faults are used to calculate the other parameters. I also suggest application of the method to anomalies of sheet‐like bodies.
A microprocessor‐based controller and data acquisition system for LaCoste and Romberg air‐sea gravity meters
Authors: Valliant H. D. , Halpenny J. , Cooper R. V.
Published: October 2002

A microprocessor‐based controller and data acquisition system for LaCoste and Romberg dynamic gravity meters has been designed, tested, and is now operationally functional. The system controls the motion about the three axes of the stable platform and the gravity meter, as well as acquiring gravity data and storing it on magnetic tape. Output format is compatible with LaCoste and Romberg format. Extensive testing has assured that the digital system functions correctly. Recent deep‐ocean surveys using the new straight‐line meter (SL-1) in conjunction with the new electronics, have resulted in unadjusted cross‐over differences of 1.35 mGal.
Downward continuation of heat flow data: Method and examples from the western United States
Authors: Mareschal Jean‐Claude , Cunningham James P. , Lowell Robert P.
Published: October 2002

We outline a method to determine, directly from the data, a subsurface temperature distribution which is compatible with the surface heat flow and takes into consideration the effect of the shallow heat sources. The analysis assumes that (1) the crust is in conductive equilibrium, (2) the lateral changes in thermal conductivity can be neglected, and (3) the depth of the heat sources is proportional to the wavelength of the variations in surface heat flow. We apply the technique to determine the crustal temperatures in two tectonically active regions of the western United States. In the Rio Grande rift, temperatures higher than 1 100°C are predicted at a depth of 20 km. In the transition region between the Colorado Plateau and the Basin and Range, the variability in surface heat flow is partially accounted for by shallow heat sources; however, the increase in heat flow toward the Basin and Range seems associated with deep seated (i.e., lower crust or upper mantle) variations in the thermal regime.
Acoustic reflections from complex strata
Authors: Stephens Richard B. , Sheng Ping
Published: October 2002

Rock strata may contain fine‐scale structures which are too small to be identified directly, but which can give rise to anomalous seismic reflection amplitudes. The variance caused by such anomalies severely hampers the use of reflection amplitudes for layer identification, and techniques are required which can identify or correct for the effects of such fine structure. We have done calculations which explore the consequences of two general structure types: wavy interfaces and very thin layers. In each case, a formalism is set up which enables us to identify systematically all of their effects. Computer modeling of realistic formations verified our calculations. We suggest that the strongly wavelength‐dependent response of such layers and their characteristic response waveforms may provide convenient tools for identifying fine‐scale features in strata.
Analysis and prediction of geophone performance parameters
Authors: Huan S. L. , Pater A. R.
Published: October 2002

In the past, designers relied greatly on simplified geophone models to describe the physical quantities of a geophone. Several iterations of fine tuning the geophone variables were required to achieve a desired geophone characteristic. Although many geophone prototypes were built before a geophone design was finalized, it was still impossible to assure an optimum geophone design. An easier, faster, and more accurate method of predicting geophone parameters is described and the method of computer‐aided geophone design is outlined. A description of a nonlinear geophone model is presented and a numerical method to compute the nonlinear magnetic flux density distribution is outlined. An integration algorithm is used to compute the geophone sensitivity and open‐circuit damping. The measurement of geophone distortion is described, and the harmonic distortion due to nonlinearity of sensitivity and damping is computed. The data of a geophone spring constant were obtained through a recent experiment, and the harmonic distortions caused by the nonlinearity of the spring are computed. Finally, the total harmonic distortion of a geophone is obtained. Programs developed to predict geophone sensitivity, damping, and distortion are described. It is shown that the method used to compute the nonlinear flux density distribution converges properly and the results obtained are meaningful. Three different types of geophones are analyzed and a comparison between the simulated and measured data is made. In all three cases, good correlation exists between the parameters predicted and the parameters actually measured. Information obtained by geophone parameter prediction can be very useful in the geophone design process, in optimizing geophones, and in achieving higher performance levels.
Crone pulse electromagnetic response of a conducting thin horizontal sheet—Theory and field application
Authors: Rai S. S.
Published: October 2002

The horizontal, conducting thin‐sheet model represents a special interest in interpretation of electromagnetic field data since it is a suitable interpretation model for the surficial conductive layer, a common occurrence in many terrains. For small thicknesses of overburden layers [Formula: see text]separation) the resolution of layer thickness and conductivity is not possible and interpretation needs to be carried out in terms of the layer conductance. An attractive feature of the thin‐sheet model is the simplicity with which the time‐domain response [Formula: see text] can be calculated. The step response of an infinitely thin layer was derived by Maxwell (1891). In this paper I derive the Crone pulse electromagnetic (PEM) response of a conducting infinitely thin horizontal layer. Applicability of the study is demonstrated by means of a field example.
Interpretation of Crone pulse electromagnetic data
Authors: Bartel David C. , Hohmann Gerald W.
Published: October 2002

Time‐domain electromagnetic (TEM) prospecting systems, including the Crone pulse electromagnetic (PEM) system, are becoming more widely used in the search for massive sulfides. We have developed interpretation aids for the moving‐source configuration of the Crone PEM system using the PLATE and SPHERE programs developed by the University of Toronto. PLATE models a thin rectangular sheet in free space and SPHERE models a two‐layer sphere in free space. The effects of varying the model parameters, particularly the dip, depth, and conductance for large plates, are shown. As the dip of a plate goes from 0 to 90 degrees, the negative side lobe over the conductor becomes less pronounced. The depth can be estimated from the amplitude of the positive peak over the edge of a conductor. The depth of exploration for the Crone PEM system is approximately twice the coil separation for shallow dipping plates, and one coil separation for steeply dipping plates when there is not a significant half‐space or overburden response. The ratio of the on‐conductor and off‐conductor side‐lobe areas gives an estimate of the dip if the depth of the target has been determined. The resolution of dip for plates dipping more than 60 degrees is poor. The conductance of a plate can be determined from either channel‐ratios or the estimated time constant. Channel‐ratios sometimes provide better estimates, because they have less dependence on the size of the conductor at earlier times. At early times, the target response can be obscured by conductive overburden. Only at late times would interpretation aids be useful in evaluating the target parameters. A dip‐depth nomogram and channel‐ratios gave good first estimates of the target parameters of three field examples interpreted by computer modeling.
Depth estimates from ratios of gravity, geoid, and gravity gradient anomalies
Authors: Bowin Carl , Scheer Edward , Smith Woollcott
Published: October 2002

The utility of combining geoid, gravity, and vertical gravity gradient measurements for delineation of causative mass anomalies is explained and compared with spatial and spectral methods for depth estimation. Depth rules for various source geometries are reviewed and new rules developed for geoid, gravity, and vertical gravity‐gradient data. Both spatial and frequency‐domain methods are discussed. Simple ratios of single observations of different data types (e.g., geoid, gravity, or vertical gravity gradient) are shown to provide information comparable to the traditional spatial and frequency analyses of one data type alone.
Velocity analysis for feathered marine data
Authors: Kalra Ashok K.
Published: October 2002

It is impossible to ensure that the marine streamer shall strictly follow the line of profile (containing the shotpoints) in marine data acquisition surveys. In fact it rarely does so. Deviations of the streamer from the line of profile are termed “feathering” which can vary from a few degrees to 30 degrees or more, depending on sea conditions. Feathered marine data are not quite suitable for conventional velocity analysis for stacking purposes. Errors introduced in the use of conventional analysis are addressed and an accurate velocity analysis approach is suggested.
A new shipboard three‐component magnetometer
Authors: Isezaki Nobuhiro
Published: October 2002

The three components of the geomagnetic field were measured at sea by STCM (Shipboard Three Component Magnetometer) with a relative accuracy of 50 ± 25 nT. The STCM was controlled by a microcomputer, and the three geomagnetic components were calculated by reducing the magnetic field due to the ship’s remanent and induced magnetic moments, the only assumption being that the magnetic field is linearly related to the magnetic moments. Although STCM has no particular magnetic compensation device, it can be set at any place on board of any kind of ship. In the KH82-5 cruise, the three component measurements were conducted along latitude 42 °N north of the Mendocino fracture zone where there are well‐defined magnetic anomaly lineations trending north and south. STCM measured the north component anomalies with very small amplitudes compared to the east and downward component anomalies, which shows that lineations trend north and south. The three measured component anomalies are almost identical to the anomalies calculated from the well‐established time scale; thus, STCM measures the three components correctly. The vector geomagnetic measurements are more useful for analysis of marine geomagnetic anomalies than are the total‐intensity measurements. The DELPWAKASHIO 84/1 cruises provide good examples for examination of the linearity of magnetic anomalies on a single track by using the Fourier transform of the horizontal and vertical component anomalies.
A least‐squares smooth fitting for irregularly spaced data: Finite‐element approach using the cubic B-spline basis
Authors: Inoue Hiroshi
Published: October 2002

A new method of multivariate smooth fitting of scattered, noisy data using cubic B-splines was developed. An optimum smoothing function was defined to minimize the [Formula: see text] norm composed of the data residuals and the first and the second derivatives, which represent the total misfit, fluctuation, and roughness of the function, respectively. The function is approximated by a cubic B‐spline expansion with equispaced knots. The solution can be interpreted in three ways. From the stochastic viewpoint, it is the maximum‐likelihood estimate among the admissible functions under the a priori information that the first and second derivatives are zero everywhere due to random errors, i.e., white noise. From the physical viewpoint, it is the finite‐element approximation for a lateral displacement of a bar or a plate under tension which is pulled to the data points by springs. From a technical viewpoint, it is an improved spline‐fitting algorithm. The additional condition of minimizing the derivative norms stabilizes the linear equation system for the expansion coefficients.
A recursive method for the separation of upgoing and downgoing waves of vertical seismic profiling data
Authors: Aminzadeh F.
Published: October 2002

An important part of the processing of vertical seismic profiling (VSP) data is the separation of upgoing and downgoing waves. I introduce a new method for separation based on a time‐domain recursive linear filter. The separation method uses an approximation to an optimal, frequency‐domain, nonlinear filter solution as the starting point. The time‐domain recursive linear (approximate) filter converges to the optimal (exact) solution. Since the computation is in the time domain and since this filter is linear, some of the temporal aliasing and other problems resulting from the forward and inverse Fourier transforms are avoided. Specifically, instability for some frequencies (spectral singularities) is not experienced here. This method uses a priori information of the opposite stepouts of the upgoing and downgoing waves. Equal spacing between borehole measurement points is not required. Further, the computational time may be controlled according to the desired accuracy. An important feature of this method is that it locates the reflecting boundaries of the subsurface. Having located the homogeneous layers, it allows variable‐length windows of traces for separation, which eliminates the undesirable effects of smearing and extending wave fields beyond their origins. Also, knowledge of acoustic impedances for accurate implementation of the optimum filter is no longer required.
A stable free‐surface boundary condition for two‐dimensional elastic finite‐difference wave simulation
Authors: Vidale John E. , Clayton Robert W.
Published: October 2002

Two of the persistent problems in finite‐difference solutions of the elastic wave equation are the limited stability range of the free‐surface boundary condition and the boundary condition’s treatment of lateral variations in velocity and density. The centered‐difference approximation presented by Alterman and Karal (1968), for example, remains stable only for β/α greater than 0.30, where β and α are the shear [Formula: see text] and compressional [Formula: see text] wave velocities. The one‐sided approximation (Alterman and Rotenberg, 1969) and composed approximation (Ilan et al., 1975) have similar restrictions. The revised‐composed approximation of Ilan and Loewenthal (1976) overcomes this restriction, but cannot handle laterally varying media properly.
High‐resolution common‐depth‐point seismic reflection profiling: Instrumentation
Authors: Knapp Ralph W. , Steeples Don W.
Published: October 2002

Seismic recording hardware must be a deliberately designed system to extract and record high‐resolution information faithfully. The single most critical element of this system is the detector. The detector chosen must be capable of faithfully generating the passband expected and furthermore, must be carefully coupled to the ground. Another important factor is to shape the energy passband so that it is as flat and broad as possible. This involves low‐cut filtering of the data before A/D conversion so the magnitude of the low‐frequency signal does not swamp the high‐frequency signal. The objective is to permit boosting the magnitude of the high‐frequency signals to fill a significant number of bits of the digital word. Judicious use of a low‐cut filter is the main element of this step, although detector selection is also a factor because detectors have a −6 dB/octave velocity response at frequencies less than the resonant frequency of the detector. Finally, recording instrument quality must be good. Amplifiers should have low system noise, large dynamic range, and precision of 12 or more bits.
Biot‐Gardner theory of extensional waves in porous rods
Authors: White J. E.
Published: October 2002

Many measurements have been made on fluid‐saturated porous rods executing extensional, flexural, and torsional motion. Measurements for extensional and flexural motion yield a loss parameter for Young's modulus waves [Formula: see text], and the measurement for torsional motion yields [Formula: see text] for shear waves. [Formula: see text] has then been calculated for compressional waves in bulk rock, on the assumption that the fluid‐saturated rock is an isotropic solid. I point out the fallacy of computing [Formula: see text] from these measurements and also urge workers to recognize the losses due to simple fluid viscosity in interpreting their data on extensional waves in rods. By application of published theory, I show that peaks in attenuation of extensional waves are to be expected at frequencies of several hertz to several kilohertz, depending upon rod radius. Computed curves are compared with published measurements on Navajo sandstone saturated with water, ethanol, and n‐decane. In each case, computed peak frequency agrees with published measurements. Shift of the peak frequency with temperature from 4 °C to 25 °C is due to change of viscosity of the saturating fluid (water).
Geothermics of the Williston basin in Canada in relation to hydrodynamics and hydrocarbon occurrences
Authors: Majorowicz J. A. , Jones F. W. , Jessop A.M.
Published: October 2002

Over 8 400 bottom‐hole temperature (BHT) values from the Canadian part of the Williston Basin were analyzed and a temperature high was discovered in the Weyburn area of southeastern Saskatchewan. Geothermal gradients, thermal conductivities, and heat flow have been investigated for most of the Mesozoic‐Cenozoic clastic unit as well as the Upper Paleozoic carbonate‐evaporite unit. Regional heat flow variations with depth occur which are closely related to the hydrodynamics governed by the topography and geology. The blanketing effect of low‐conductivity shaly formations may cause a temperature anomaly in the south where the thickest Phanerozoic cover exists. However, the Weyburn high can be explained only partially in this way. Hydrodynamics has also contributed to formation of the temperature anomaly there. The process of forming the anomaly by the blanketing effect and hydrodynamics also contributed to oil deposition. There is a correlation between Mississippian oil occurrences in the southeastern part of the basin and the location of the Weyburn temperature high.
Application of the pole‐dipole resistivity technique to the detection of solution cavities beneath highways
Authors: Smith Douglas L.
Published: October 2002

Using a multiconductor electrode cable and a 30‐post switching system, pole‐dipole electrical resistivity measurements with a linear electrode array demonstrated a strong correlation between resistivity anomalies and subsurface voids at four sites in Florida. Solution cavities below the water table are filled with a groundwater‐solute mixture which is characterized by a lower electrical resistivity than the enclosing country rock (Eocene and younger limestone). Air‐filled cavities above the water table exhibit markedly high‐resistivity anomalies. Confirmation drilling of postulated cavities and other anomalies suggests the method can be used with confidence for identification and location of highway‐threatening solution cavities with diameters as small as 3 to 5 m to a depth of 25 to 30 m.
An alternate derivation of the three‐dimensional Hilbert transform relations from first principles
Authors: Nelson J. Bradley
Published: October 2002

Several techniques for determining the location, geometry, and strength of a source are based on a knowledge of the magnetic gradients generated by that source. Hood (1965), Bhattacharyya (1966), and Rao et al. (1981) detailed three of these gradient methods. For many years, geophysicists have used the two‐dimensional (2-D) Hilbert transform to approximate the vertical gradient from measurements of the horizontal gradient in the magnetic‐field intensity (Nabighian, 1972; Stanley and Green, 1976; Stanley, 1977; Mohan et al., 1982). This technique is of limited applicability because of the implicit assumption that the source is a linear, 2-D body oriented at right angles to the profile direction.
On: “Radio‐frequency geotomography for remotely probing the interiors of operating mini‐ and commercial sized oil‐shale retorts” by S. F. Somerstein, M. Berg, D. Chang, N. Chung, H. Johnson, B. Richardson, J. Pizzicara, and W. W. Salisbury (GEOPHYSICS, 49, 1288–1300, August, 1984).
Authors: Christensen N. I. , Wang H. F.
Published: October 2002

The original concept of biomedical X‐ray tomography has been used for exploration of overburden and oil‐shale properties in the radio‐frequency range and is known as geotomography. The potential and practical application of this emerging tool in probing oil‐shale was recently reported by Somerstein et al. (1984).