bluuebunny/crossref_metadata_2025 huggingface dataset:
ELECTROMAGNETIC TRANSIENT RESPONSE OF A CONDUCTING SPHERE EMBEDDED IN A CONDUCTIVE MEDIUM
Authors: Singh Shri Krishna
Published: October 2002

This paper is concerned with the time‐domain electromagnetic prospecting of massive sulfide ore bodies which are surrounded by conductive host rocks. The electromagnetic transient response of a permeable and conducting sphere embedded in a finitely conducting infinite space is derived. The source is a magnetic dipole of arbitrary orientation which is located outside the sphere. The contributions from the displacement currents have been neglected. The solution thus obtained is compared with the known solution under “quasi‐static” approximation in which the displacement current in the sphere and both the conduction and the displacement currents in the outer medium are neglected. From the numerical results presented, it is clear that the validity of the quasi‐static approximation in the time domain, if the outer host rock is conductive, must be carefully investigated. If the finite outer conductivity is taken into account, magnetic modes are modified and electric modes become important. Five response functions, each a function of five parameters, are required to describe the secondary magnetic field.
ADDITIONAL COMMENTS ON THE ANALYTIC SIGNAL OF TWO‐DIMENSIONAL MAGNETIC BODIES WITH POLYGONAL CROSS‐SECTION
Authors: Nabighian Misac N.
Published: October 2002

In a previous paper (Nabighian, 1972), the concept of analytic signal of bodies of polygonal cross‐section was introduced and its applications to the interpretation of potential field data were discussed. The input data for the proposed treatment are the horizontal derivative T(x) of the field profile, whether horizontal, vertical, or total field component. As it is known, this derivative curve can be thought of as being due to thin magnetized sheets surrounding the causative bodies.
THE INVERSION AND INTERPRETATION OF GRAVITY ANOMALIES
Authors: Oldenburg Douglas W.
Published: October 2002

A rearrangement of the formula used for the rapid calculation of the gravitational anomaly caused by a two‐dimensional uneven layer of material (Parker, 1972) leads to an iterative procedure for calculating the shape of the perturbing body given the anomaly. The method readily handles large numbers of model points, and it is found empirically that convergence of the iteration can be assured by application of a low‐pass filter. The nonuniqueness of the inversion can be characterized by two free parameters: the assumed density contrast between the two media, and the level at which the inverted topography is calculated. Additional geophysical knowledge is required to reduce this ambiguity. The inversion of a gravity profile perpendicular to a continental margin to find the location of the Moho is offered as a practical example of this method.
THE TOKYO SURFACE SHIP GRAVITY METER: RECENT DEVELOPMENTS AND RESULTS OF COMPARISON MEASUREMENTS
Authors: Segawa Jiro , Bowin Carl
Published: October 2002

The Tokyo Surface Ship Gravity Meter (TSSG) employs a single vibrating string accelerometer which is inherently nonlinear. This leads to errors unless its frequency is essentially constant over the sampling intervals. A new processor incorporating pulse train logic and employing a rapid sampling rate of about 50/sec has been designed to replace the digital computer which used about 2/sec.
TWO PROBABLE LATE CRETACEOUS ASTROBLEMES IN WESTERN CANADA—EAGLE BUTTE, ALBERTA AND DUMAS, SASKATCHEWAN
Authors: Sawatzky H. B.
Published: October 2002

Seismic and borehole data at Dumas, Saskatchewan (T. 11, R.1 & 2, W2M) and surface geology and well control at Eagle Butte, Alberta (T. 8 & 9, R. 4 & 5, W4M) reveal structural features that suggest hyper‐velocity impact during late Cretaceous time. In both instances, the anomaly consists of a pronounced, highly disturbed central uplift, a rim syncline, and the suggestion of a positive outer lip. Although some deformation persists into Paleozoic strata, the majority of the relief involves Mesozoic rocks. Subsurface information appears to rule out any possibility of explaining these features by means of deep‐seated tectonic activity and/or solution collapse phenomena.
RADIATION FROM A FINITE CYLINDRICAL EXPLOSIVE SOURCE
Authors: Abo‐Zena Anas M.
Published: October 2002

For an elastic material with an infinite circular cylindrical hole, the exact solution due to a pressure on a finite length of the cylinder is obtained as a function of the Laplace transform parameter on time and Fourier transform parameter on the z-coordinate (the axis of the cylinder). The applied pressure is a function of the time and the position z. Numerical inversion of the Laplace and Fourier transforms are required to determine the field quantities in the time and space parameters. In the far field, the inverse Fourier transform can be obtained by an asymptotic expansion. It remains to obtain the inverse Laplace transform numerically. We have found that for cylinders whose radius is small compared with the smallest wavelength of interest, an analytical solution can be obtained. Graphical results for the cases of instantaneous explosion and progression of the detonation with constant velocity are given. In both cases an exponential decay of the explosion pressure is assumed.
FIELD RESULTS ON THE RELATIVE PERFORMANCE OF LATEROLOG 7 AND NORMAL DEVICES
Authors: Koithara Joseph , Chandra Dinesh
Published: October 2002

Laterolog 7, introduced to the petroleum industry nearly a quarter of a century ago, has been universally considered to be superior to the conventional normal and lateral devices in logging highly resistive formations. According to Doll (1951), Schlumberger (1958, 1969), and Pirson (1963), it provides (a) sharper discrimination between different beds and more accurate definition of their boundaries, especially for moderate to small bed thickness; and (b) closer approximation to true resistivities, particularly when the formations are thin and highly resistive and the mud is saline.
ACCURACY OF BOREHOLE GRAVITY DATA
Authors: Schmoker James W.
Published: October 2002

Repeated subsurface gravity measurements, obtained with the U.S. Geological Survey‐LaCoste and Romberg borehole gravity meter, were studied to determine the accuracy of the borehole gravity data, the dependence of accuracy upon elapsed time and vertical separation, and the precision of bulk densities calculated from borehole gravity measurements. The likelihood of poor interval gravity measurements increases sharply for vertical intervals greater than 150 ft, and increases approximately linearly with increasing time between readings. After a brief warmup period, data quality does not improve with the passage of time from the beginning of the survey. If the stations of a borehole gravity survey are separated by less than 70 ft, and the time between readings is less than 18 minutes, the gravity difference between two points in a borehole can be measured to ±10 μgals. For intervals greater than 20 ft, this is equivalent to a density error of [Formula: see text] or less.
SEISMIC STRIPPING HELPS UNRAVEL DEEP REFLECTIONS
Authors: Krey Theodor
Published: October 2002

Due to multiple reflections and low signal‐to‐noise ratio, very deep primary reflections often can be recognized only by using a high multiplicity of common‐reflection‐point (CRP) stacking, encompassing a large range of shot‐geophone distances. But in some areas, the structures of the near‐surface layers, say down to a depth of 1 km, may change substantially within the shot‐geophone distance range. In such cases it becomes necessary to include all of this upper geologic section in the time corrections normally used in CRP stacking. This is achieved by seismic stripping. In many cases, slant raypaths can be replaced by vertical raypaths and the inhomogeneities within the upper layers may be compensated for by normal surface consistent static time corrections. This method resulted in substantial improvements in definition of deep horizons in various field surveys. If the depths of the inhomogeneous layers become a large percentage of depths of the desired reflection horizons, say if they amount to 30 percent or more of the depth of interest, the corresponding stripping time corrections are no longer static in a strict sense, but may still be handled by simple approximate formulas, provided the deep reflectors of interest are nearly horizontal and formations in the overburden are moderate. In this case the stripping corrections are slightly varying with reflection time. Stripping corrections may also be included in the normal dynamic time corrections by dividing the total range of shot‐geophone distances into several subranges and determining the optimum stacking velocity for each subrange. Large stacking velocity variations occur in this case.
Broadband electromagnetic measurements over a massive sulfide prospect
Authors: Pridmore D. F. , Ward S. H. , Motter J. W.
Published: October 2002

This paper presents the results of measurements of the tilt angle and ellipticity of the polarization ellipse of the magnetic field, made at 14 frequencies in the range 10.5 Hz to 86 kHz, over a massive sulfide prospect in the foothills copper belt of California. As is typical of this class of deposit, the massive sulfides grade laterally into the disseminated sulfides of a tuff unit. The host rock resistivities are in the range 80 to 500 ο-m. The interpretation of the results is carried out using crude dike models in free space, although an attempt is made to account for the conductive host rock by examining the electric and magnetic fields generated by magnetic dipole sources over a homogeneous half‐space. The utility of broadband multifrequency electromagnetic (EM) measurements over a complex earth is shown clearly by the results over the prospect. The response of the massive sulfides, disseminated sulfides, and the host rock can all be distinguished when the tilt angle and ellipticity values are contoured in frequency‐distance space. A comparison is made of the results obtained using vertical‐loop, rotating vertical‐loop, and horizontal‐loop transmitter configurations. It is found at this mineral prospect that (1) the results from the vertical‐loop transmitter are easier to interpret, in terms of simple models, than those produced by the horizontal‐loop transmitter, (2) although the rotating vertical‐loop transmitter gives a larger response from the massive sulfides, the results show no more fine structure in the massive sulfides than that shown by the response from the vertical‐loop transmitter; and (3) moving the vertical‐loop transmitter does not give significantly more information about the geology.
A signal processing method for circular arrays
Authors: Henstridge John D.
Published: October 2002

The theory of spectral representations of stationary random processes can be a useful tool in signal processing. Using this theory, it is possible to derive simple methods of estimating the phase velocity of surface waves from observations made with a circular array. The methods are totally nondirectional, thus allowing the use of microseisms for exploration seismology. Furthermore, the methods can be extended to yield directional information about both correlated and uncorrelated signals.
A collocation formulation of wave equation migration
Authors: Pann K. , Shin Y. , Eisner E.
Published: October 2002

In solving the scalar wave equation in differential form for the purpose of seismic data migration, we apply the method of collocation to an upcoming wave equation which Claerbout introduced. In this method, a solution is written as a linear combination of a set of prescribed basis functions, and the upcoming wave equation is satisfied at a discrete set of space‐time points. We then demonstrate that, when certain multidimensional spline functions are used as the basis functions, the collocation method becomes algorithmically equivalent to a preferred Crank‐Nicolson finite‐difference formulation. Because of this equivalence, the mathematical procedures performed in the finite‐difference formulation can be reinterpreted from the point of view of the collocation method. The selection of parameters for the rational approximation of the second derivative in the preferred Crank‐Nicolson finite‐difference formulation has been based only on empirical judgment of the interpretability of the migrated seismic data, whereas in the collocation method, the selection corresponds to the choice of the simplest multidimensional splines as the basis functions. In addition, using the collocation method, the discrete finite‐difference solution can be naturally extended to the continuous space‐time domain by a method algorithmically consistent with the Crank‐Nicolson formulation.
Some aspects of regional‐residual separation of gravity anomalies in a Precambrian terrain
Authors: Gupta V. K. , Ramani N.
Published: October 2002

The Bouguer gravity field measured over two Archean greenstone belts of northwestern Ontario is analyzed using three different regional‐residual separation techniques. The purpose of the analysis is to obtain a residual map suitable for gravity modeling studies to help define the subsurface characteristics of the greenstone belts and associated granitic areas. The methods used to derive the regional and residual maps are spectral factorization, upward continuation, and graphical smoothing. The substantial differences in the three sets of maps emphasize the ambiguity and subjectivity of the separation process. Each method may yield nonunique results. For example, in the spectral factorization technique, the filter design is dictated by the clarity of the slope change between the short‐ and long‐wavelength features and, in the case of the upward continuation technique, by the choice of the continuation height. The graphical method is empirical clearly nonunique. The regional map obtained through graphical smoothing is the most satisfactory for the purpose stated since it bas been designed to have minimal contributions from the shallow and broad greenstone masses outcropping at the surface. These features are clearly visible in the spectrum‐based regional map and to a lesser extent in the upward‐continued regional map. All three types of residual maps follow the general outline of the geologic units and thus are probably equally useful for a qualitative study of the anomaly shapes. However, for quantitative modeling purposes, the graphically produced residual is most suitable, since it can be successfully fitted by models that are consistent with the known surface geology and measured density values. The location, spatial extent, and the amplitudes of the analytically produced residual anomalies, in many areas, show poor correlation with the surface measurements, rendering these maps less satisfactory.
Electromagnetic response of an embedded cylinder for line current excitation
Authors: Ogunade S. O.
Published: October 2002

Numerical results obtained from an extension of D’Yakonov’s (1959) exact solution for the case of a buried horizontal circular cylinder, excited by a horizontal line source of current above the surface of a uniform half‐space and parallel to the axis of the buried cylinder, are analyzed. Results show the field impedance [Formula: see text], the ratio of the vertical magnetic component to the horizontal magnetic component [Formula: see text] as well as the corresponding phase differences at the surface for a range of periods (T = 0.25 to 2 hours), varying cylinder conductivity [Formula: see text] and cylinder radii (a = 0.5 and 25 km). The results have possible application in the interpretation of long period magnetotelluric and geomagnetic measurements in auroral and equatorial electrojet regions.
A method for calculating synthetic seismograms which include the effects of absorption and dispersion
Authors: Ganley D. C.
Published: October 2002

A method is outlined for the calculation of synthetic seismograms which include the effects of absorption and dispersion. The absorption model used is the usual model of exponential decay of amplitude with distance given by [Formula: see text], where α is a linear function of frequency. This attenuation is accounted for mathematically by allowing the elastic modulus to be a complex function of frequency. This results in a complex velocity and wavenumber, and the reflection and transmission coefficients also become complex functions of frequency. The method is based upon the communication theory approach and is applicable to plane waves in a flat layered model. The source can be placed at an arbitrary depth. The equations are outlined in detail for a particular absorption‐dispersion pair taken from Futterman (1962). An example with a surface synthetic seismogram and synthetic traces at several depths is presented.
Obtaining three‐dimensional velocity information directly from reflection seismic data: An inverse scattering formalism
Authors: Weglein A. B. , Boyse W. E. , Anderson J. E.
Published: October 2002

We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.
International Geomagnetic Reference Field 1980 A Report by IAGA Division I, Working Group I
Authors: Peddie Norman W.
Published: October 2002

IGRF 1965, the first international geomagnetic reference field, was adopted by the International Association of Geomagnetism and Aeronomy (IAGA) in 1968 (IAGA Commission 2, Working Group 4, 1969). It consists of a model of the main field at 1965.0, along with a model of secular variation for use in extending the main field model in time, both backward (not earlier than 1955.0) and forward (not later than 1975.0). IGRF 1975, adopted later, consists of IGRF 1965 extended to 1975.0, along with a revised model of secular variation for use in extending the main field model up to 1980.0 (IAGA Division I Study Group, 1976).
Decomposition (DECOM) approach applied to wave field analysis with seismic reflection records
Authors: Ryu Jisoo V.
Published: October 2002

Seismic common‐depth‐point (CDP) gathered data contain waves of various reflection phases other than the primary events of interest. Such waves often form distinctive, separate peaks in the velocity spectrum derived from the CDP gather, and their propagation modes can often be identified. To exploit such separation and identification, a method is developed to decompose the CDP‐gathered data into several phases. The method combines normal moveout (NMO) removal, space‐time filtering, and NMO restoration. The space‐time operator central to this method is shown to have several useful properties. Its frequency response passes one quadrant pair in the frequency‐wavenumber domain and rejects the other. A set of marine reflection records is used to demonstrate the usefulness of the decomposition approach, particularly for separating primary from nonprimary waves, and waves of possible marine PSSP mode from all others. Both examples may bear some exploration significance.
An integral transform solution to the fundamental problem in resistivity logging
Authors: Gianzero Stanley , Anderson Barbara
Published: October 2002

This paper develops the analysis necessary for the computation of the response of a resistivity tool within a well bore as it traverses a thin‐invaded bed. The solution for the potential induced by a steady current source (point current electrode) is formulated in terms of both Fourier cosine and Fourier sine transforms with arbitrary coefficients. A suitable matching of the necessary boundary conditions results in a system of singular integral equations. An iterative solution (Neumann series) is obtained for these transform coefficients which, in turn, are used to determine the potential at an arbitrary point of measurement. The theory is applied to some typical focused resistivity tools, and the results are found to be in close agreement with similar results obtained via a resistor network (analog) solution.
Radiation impedance of torsionally vibrating seismic sources
Authors: Dorn Geoffrey A.
Published: October 2002

The thickness and shear‐wave velocity of a surface layer can theoretically be determined from seismic radiation impedance measurements using a torsional vibrator. These studies also provide physical insight into vibrator‐earth interaction. The radiation impedance of a circular disk vibrating torsionally on an anelastic half‐space has resonance peaks with a spacing that is a function of the ratio between baseplate radius and seismic wavelength. At low frequencies the shape of the impedance function is nearly independent of the baseplate flexure, although the magnitude is affected. At high frequencies the impedance depends strongly on the flexibility of the baseplate. The mass of the baseplate introduces an additional resonant effect, the frequency of which is a function of the baseplate mass. The presence of a surface layer produces an impedance curve which oscillates around the half‐space response. The amplitude of the oscillations is a function of the acoustic impedance contrast and depends upon the radiation pattern of the source. The oscillations are resonances caused by reflections within the surface layer, and both the period and amplitude of the oscillations are inversely proportional to the layer thickness. The amplitude of the layer resonance decreases rapidly as material damping increases. With impedance measurements over a sufficiently broad frequency range (up to about 500 Hz), it may be feasible to use half‐space oscillations and the layer resonances to determine the shear velocity and thickness of the layer of material beneath the baseplate.
The radio wave absorption technique in Mailaram copper mines, India
Authors: Rao V. Mohan , Rao I. B. Ramaprasada
Published: October 2002

Pritchett (1952) suggested that the possibility of using electromagnetic (EM) waves of 1.652 MHz frequency in drill holes to solve geologic problems is limited. Subsequently, Barret (1952) demonstrated that a portable radio‐frequency transmitter of limited power could be utilized for subsurface radio wave prospecting. He also concluded that the EM energy radiated from the transmitter in fact traveled through the rock mass but not along the paths of least attenuation such as mine shafts or tunnels. Electromagnetic fields in the range of 1 to 57 MHz frequencies were used for applications such as locating tunnels between boreholes (Lytle, 1979), determining bulk conductivity of granites (Lytle and Lager, 1976), and determining the skin depth for different zones between two boreholes using data inversion algorithms (Lager and Lytle, 1977). Petrovskii et al (1968) and Tarkhov et al (1973) reported the application of subsurface radio wave prospectings for solving various geologic problems.
Computing true amplitude reflections in a laterally inhomogeneous earth
Authors: Hubral Peter
Published: October 2002

Recently Bortfeld (1982) gave a cursory nonmathematical introduction to a procedure for computing the geometrical spreading factor of a primary zero‐offset reflection from the common datum point traveltime measurements of the event. To underline the significance and consequences of this method, a derivation and discussion of geometrical spreading factors is now given for two‐ and three‐dimensional earth models with curved reflecting boundaries. The spreading factors can be used easily to transform primary reflections in a zero‐offset seismic section to true amplitude reflections. These permit an estimation of interface reflection coefficients, either directly or in connection with a true amplitude migration. A seismic section with true amplitude reflections can be described by one physical experiment: the tuned reflector model. Hence the application of the wave equation (in connection with a migration after stack) is justified on such a seismic section. Also the geometrical spreading factors that are derived can be looked upon as a generalization of a well‐known formula (Newman, 1973), which is commonly used in true amplitude processing and trace inversion in the presence of a vertically inhomogeneous earth.
Two‐dimensional resistivity inversion
Authors: Tripp A. C. , Hohmann G. W. , Swift C. M.
Published: October 2002

Resistivity data on a profile often must be interpreted in terms of a complex two‐dimensional (2-D) model. However, trial‐and‐error modeling for such a case can be very difficult and frustrating. To make interpretation easier and more objective, we have developed a nonlinear inversion technique that estimates the resistivities of cells in a 2-D model of predetermined geometry, based on dipole‐dipole resistivity data. Our numerical solution for the forward problem is based on the transmission‐surface analogy. The partial derivatives of apparent resistivity with respect to model resistivities are equal to a simple function of the currents excited in the transmission surface by transmitters placed at receiver and transmitter sites. Thus, for the dipole‐dipole array the inversion requires only one forward problem per iteration. We use the Box‐Kanemasu method to stabilize the parameter step at each iteration. We have tested our inversion technique on synthetic and field data. In both cases, convergence is rapid and the method is practical if the number of parameters is not too large. The main limitations of the method are that the geometry of the model must be specified in advance, and that it is difficult to determine whether model misfit is due to 3-D effects or to underparameterization in the 2-D model. The technique should be used interactively, with models constrained by geologic information.
Mosource—A novel simple seismic source
Authors: Safar M. H.
Published: October 2002

One very popular method used for calibrating pressure detectors (hydrophones) in the seismic band is the comparison method. The comparison calibration method, which is widely used (Safar and Newman, 1981) in calibrating marine seismic streamers, can be briefly described as follows. A seismic source is placed at some distance from a standard hydrophone with known transfer function [Formula: see text] and sensitivity factor [Formula: see text]. The pressure detector under test is placed as near as possible to the standard hydrophone so that the Fourier transform of the incident pressure, [Formula: see text], generated by the seismic source at the pressure detector and the standard hydrophone, can be assumed to be the same. Thus the Fourier transform of the output voltages [Formula: see text] and [Formula: see text] of the standard hydrophone and the pressure detector are given as [Formula: see text], (1) and [Formula: see text], (2) where [Formula: see text] and [Formula: see text] are the transfer function and sensitivity factor of the pressure detector. Elimination of [Formula: see text] between equations (1) and (2) gives [Formula: see text]. (3)
Separation of S‐wave and P‐wave reflections offshore western Florida
Authors: Tatham Robert H. , Goolsbee Donald V.
Published: October 2002

Hard water‐bottom marine environments, such as offshore western Florida, have presented particular problems in the acquisition and processing of seismic reflection data. One problem has been the limited angle of incidence (less than critical) available to P‐wave penetration into the subsurface. Mode conversion from P‐wave to S‐waves (SV), however, is quite efficient over a broad range of angles of incidence. After the success of a previously reported physical model experiment, an experimental line was acquired offshore western Florida. The 19 mile line, located approximately 100 miles west of Key West, Florida, was shot and processed. Three key factors have contributed to the successful recording of mode‐converted S‐wave reflections: (1) recognition of the effect of the group length on attenuation of energy arriving at large angles of incidence; (2) tau‐p processing techniques that allow separation of energy by angle of incidence; and (3) velocity filtering over a range of hyperbolic normal‐moveout (NMO) velocities as part of the forward tau‐p transform. These three factors, two of them data processing techniques, have allowed separation of P‐ and S‐wave energy in the marine environment. Overall, S‐wave reflections have been unambiguously identified to a reflection time of 2 sec and may be interpreted to a reflection time of 2 sec. Integrating an S‐wave section with P‐wave interpretations of offshore Florida data allows an independent confirmation of structural events. This independent confirmation may be more significant than improvements in the P‐wave data quality alone. Lateraly stable [Formula: see text] values are computed in intervals 1500 to 5000 ft thick and to S‐wave reflection times as great as 3 sec. The opportunity of [Formula: see text], interpretations for lithologic identification, gas thickness estimates, and general stratigraphic trap exploration makes mode‐converted shear waves a new tool in this area.
The transient electromagnetic response of a magnetic or superparamagnetic ground
Authors: Lee T.
Published: October 2002

The effect of superparamagnetic minerals on the transient response of a uniform ground can be modeled by allowing the permeability of the ground μ to vary with frequency ω as [Formula: see text] Here [Formula: see text] and [Formula: see text] are the upper and lower time constants for the superparamagnetic minerals and [Formula: see text] is the direct current value of the susceptibility. For single‐loop data it is found that the voltage will decay as 1/t, provided that [Formula: see text] and [Formula: see text] Here, a is the radius of the wire loop and b is the radius of the wire, t represents time and [Formula: see text] is the permeability of free space. Even if a separate transmitter and receiver are used, the transient will still be anomalous. For this case the 1/t term in the equations is less important, and more prevalent now is the [Formula: see text] term. These results show that a uniform ground behaves in a similar way to a ground which only has a thin superparamagnetic layer. A difference is that whereas the amplitude of the 1/t term could be drastically reduced by using a separate receiver, this is not the case for a uniform ground. A magnetic ground for late times will decay as [Formula: see text]. However, if the conductivity of the ground is estimated from apparent conductivities it will be found that the value of the conductivity will be incorrect by a factor that is related to the susceptibility [Formula: see text] of the ground. For a weakly magnetic ground the estimated conductivity [Formula: see text] is related to the true value of the conductivity [Formula: see text].
Gravity and magnetic inversion with minimization of a specific functional
Authors: Guillen A. , Menichetti V.
Published: October 2002

The nonuniqueness of gravity or magnetic data inversion is well known. In order to remove ambiguity, some authors have sought solutions minimizing a functional describing geometrical or physical properties. Last and Kubik (1983), in particular, developed a method explaining the observed anomaly by structures of minimum volume. In this method the domain where anomalous sources are searched is divided into elementary prisms of a constant density or susceptibility contrast. Each elementary contrast is allowed to vary individually. Thus a contrast distribution is computed. The search for this kind of solution leads in general to geologically more appropriate bodies, but exceptions do occur. In this paper, the technique is broadened to include the search for solutions minimizing the moment of inertia with respect to the center of gravity or with respect to a given dip line passing through it. The resulting structures are both deeper and more compact, precisely as is required in specific cases. Theoretical and actual examples illustrate this flexible inversion technique.
Velocity anisotropy of shales and depth estimation in the North Sea basin
Authors: Banik N. C.
Published: October 2002

It is known that in the North Sea basin the depths to major reflectors as determined from surface seismic data are often larger than the well‐log depths. From a study of data sets which tie 21 wells, I found a strong correlation between the occurrence of the depth error and the presence of shales in the subsurface. Assuming that the error is caused by elliptical velocity anisotropy in shales, I measured the anisotropy from a comparison of the well‐log sonic data and the interval velocity profile obtained from the surface seismic data and also from a comparison of the seismic depth and the well‐log depth. It was found that the two methods of measurements agree with each other and also agree qualitatively with the previous laboratory measurements of anisotropy in shale samples. The results strongly suggest that the depth anomaly in the North Sea basin is caused by the velocity anisotropy of shales. A simple method to correct the seismic depth is given.
Numerical modeling of refraction arrivals in complex areas
Authors: Hill N. R. , Wuenschel P. C.
Published: October 2002

Use of refracted arrivals to delineate near‐surface complex structure can sometimes be difficult because of rapid lateral changes in the refraction event along the line of control. The interpreter must correlate over zones of interference and zones of weak signal. During correlation it is often difficult to stay on the correct cycle of the waveform. We present a method to model refracted arrivals numerically in an area where these problems occur. The computation combines plane‐wave field decomposition to calculate propagation in complex regions with a WKBJ method to calculate propagation in simple regions. To illustrate the method, we study a case where the near‐surface complex structure is caused by the presence of low‐velocity gaseous mud. The modeling produces synthetic seismograms showing the interference patterns and changes in intensity that are seen in real data. This modeling shows how correlations may be done over difficult areas, particularly where cycle skips can occur.
Recent advances in rock physics
Authors: Yale David P.
Published: October 2002

The need to extract more information about the subsurface from geophysical and petrophysical measurements has led to a great interest in the study of the effect of rock and fluid properties on geophysical and petrophysical measurements. Rock physics research in the last few years has been concerned with studying the effect of lithology, fluids, pore geometry, and fractures on velocity; the mechanisms of attenuation of seismic waves; the effect of anisotropy; and the electrical and dielectric properties of rocks. Understanding the interrelationships between rock properties and their expression in geophysical and petrophysical data is necessary to integrate geophysical, petrophysical, and engineering data for the enhanced exploration and characterization of petroleum reservoirs. The use of amplitude offsets, S‐wave seismic data, and full‐waveform sonic data will help in the discrimination of lithology. The effect of in situ temperatures and pressures must be taken into account, especially in fractured and unconsolidated reservoirs. Fluids have a strong effect on seismic velocities, through their compressibility, density, and chemical effects on grain and clay surfaces. S‐wave measurements should help in bright spot analysis for gas reservoirs, but theoretical considerations still show that a deep, consolidated reservoir will not have any appreciable impedance contrast due to gas. The attenuation of seismic waves has received a great deal of attention recently. The idea that Q is independent of frequency has been challenged by experimental and theoretical findings of large peaks in attenuation in the low kHz and hundreds of kHz regions. The attenuation is thought to be due to fluid‐flow mechanisms and theories suggest that there may be large attenuation due to small amounts of gas in the pore space even at seismic frequencies. Models of the effect of pores, cracks, and fractures on seismic velocity have also been studied. The thin‐crack velocity models appear to be better suited for representing fractures than pores. The anisotropy of seismic waves, especially the splitting of polarized S‐waves, may be diagnostic of sets of oriented fractures in the crust. The electrical properties of rocks are strongly dependent upon the frequency of the energy and logging is presently being done at various frequencies. The effects of frequency, fluid salinity, clays, and pore‐grain geometry on electrical properties have been studied. Models of porous media have been used extensively to study the electrical and elastic properties of rocks. There has been great interest in extracting geometrical parameters about the rock and pore space directly from microscopic observation. Other models have focused on modeling several different properties to find relationships between rock properties.
Entropy guided deconvolution
Authors: Wiggins Ralphe
Published: October 2002

The day‐to‐day application of minimum entropy deconvolution has rarely lived up to expectations based on a few of the first selected examples. This appears to be the result of (a) the multimaxima nature of the varimax function or other similar nonlinear norms, and (b) the excessive sensitivity of the estimated filter to the probability distribution of the underlying random series. As the distribution approaches Gaussian, the variance of the filter coefficients becomes unbounded. The alternative strategy proposed consists of solving for the inverse operator as a sequence of two‐term operators each having an independently determined lag. The amplitude and sign of the operator coefficient are estimated by least squares; the discrimination between minimum or maximum phase is determined by the varimax criterion.
Intermediate‐scale magnetic anomalies of the Earth
Authors: Arkani‐Hamed J. , Strangway D. W.
Published: October 2002

Four separate magnetic anomaly maps of the earth are derived from magnetometer satellite data acquired at dawn and at dusk using two different altitude ranges. The magnetic anomalies on the two dawn maps (or dusk maps) are well correlated for spherical harmonics of degree less than 51, suggesting that the time varying external magnetic field and leveling noise have negligible effects on these harmonics. Dawn and dusk maps have an appreciable asymmetric component for harmonics of degree n ⩽ 5 and n = 15 and 17, arising from the quasi‐stable external magnetic field. Dawn‐dusk covariant harmonics of degree [Formula: see text] with signal‐to‐noise ratios greater than 1.5 correlate well. Correlation coefficients are higher than 0.75, implying that these harmonics can be repeatably derived. A global scalar magnetic anomaly map is derived based on these harmonics. The map is then converted to a magnetic susceptibility anomaly map by an inversion technique. The susceptibility anomalies delineate the ocean‐continent differences as well as the boundaries of tectonic provinces, modern uplifts, crustal rifts, and sedimentary basins.
The Influence of pore pressure and confining pressure on dynamic elastic properties of Berea sandstone
Authors: Christensen N. I. , Wang H. F.
Published: October 2002

Compressional‐ and shear‐wave velocities of watersaturated Berea sandstone have been measured as functions of confining and pore pressures to 2 kbar. The velocities, measured by the pulse transmission technique, were obtained at selected pressures for the purpose of evaluating the relative importance of confining pressure and pore pressure on elastic wave velocities and derived dynamic elastic constants. Changes in Berea sandstone velocities resulting from changes in confining pressure are not exactly canceled by equivalent changes in pore pressure. For properties that involve significant bulk compression (compressional‐wave velocities and bulk modulus) an incremental change in pore pressure does not entirely cancel a similar change in confining pressure. On the other hand, it is shown that a pore pressure increment more than cancels an equivalent change in confining pressure for properties that depend significantly on rigidity (shear‐wave velocity and Poisson’s ratio). This behavior (as well as observed wave amplitudes) is related to the presence of high‐compressibility clay that lines grains and pores within the quartz framework of the Berea sandstone.
Method for depth estimation on aeromagnetic vertical gradient anomalies
Authors: Barongo J. O.
Published: October 2002

The straight‐slope technique introduced some years ago by Vacquier et al. (1951) is employed to develop simple empirical procedures that can be used to determine depth to the top/center of anomalous sources on measured aeromagnetic vertical gradient profiles. Five geologic bodies/structures in the form of their magnetic/geometric model equivalents, namely, point pole, point dipole, finite dipole, dipping dike, and dipping contact are considered. From analysis of the normalized theoretical curves due to those models it is observed that the horizontal projection of the straight part of the steepest sections of each curve is insensitive to changes in the inclination of the Earth’s magnetic field and also to the dip angle of dipping models. Further analysis of the curves using this observation leads to the conclusion that, when dealing with the interpretation of observed vertical gradient profiles, the length of the horizontal projection on a given profile must be doubled to obtain depth to the point‐pole, point‐dipole, or finite‐dipole source. For a geologic contact and a wide but shallow (i.e., the width more than twice the depth) dike, the length of the projection gives the depth for either source. However, a thin but deeply buried (i.e., the width less than twice the depth) dike, requires use of characteristic curves such as those developed in this study. Application of the procedures to observed vertical gradient results from the White Lake region of Ontario, Canada, has proven quite successful.
A study of methods for tomographic velocity estimation in the presence of low‐velocity zones
Authors: Ivansson Sven
Published: October 2002

This paper deals with the problem of seismic velocity estimation from first‐arrival traveltimes in a two‐dimensional (2-D) cross‐hole geometry where explosions are detonated in one borehole while recordings are made in another borehole and on the surface. Standard tomographic procedures are based on decomposition of the cross‐hole area into a number of cells and a simplifying assumption of straight raypaths. In the presence of significant low‐velocity zones, the resulting images may be contaminated. Different ways of performing tomographic inversion are tested on a number of synthetic examples. Images obtained by direct, unrestricted least‐squares inversion are often seriously distorted. However, methods using more cells and some kind of damping often give more satisfactory results. Because the risk of distorted images is always present in inversion procedures, comparison with synthetic data (forward modeling) is a valuable tool in the interpretation process. With a reasonably good initial solution, improvements can often be achieved by using iterative procedures to take account of ray‐bending affects as proposed in Bois et al.(1971). An alternative way of performing these calculations is described.
Obtaining multilayer reciprocal times through phantoming
Authors: Lankston Robert W. , Lankston Marian M.
Published: October 2002

A critical parameter in interpreting seismic refraction data with the generalized reciprocal method (GRM) is the reciprocal time, which must be available for each layer from which refracted rays return to the surface. The reciprocal time can be measured in the field, but this requires special equipment or procedures. Shooting to obtain the reciprocal time from each layer along a long seismic line may be operationally impractical. However, the method of phantoming arrivals overcame the problems. In phantoming, a reciprocal time is actually measured along any length of the seismic refraction line for any refractor and that value can be used as the reciprocal time in GRM processing if the first‐break arrival times are phantomed properly. Realizing that the reciprocal time may be extracted from overlapping normal forward and reverse shots and phantoming the data accordingly will save much field time and expense. An example shows the results of using a reciprocal time measured across one spread for simultaneously processing and interpreting collinear, overlapping spreads.
Isomorphic geodetic and electrical networks: An application to the analysis of airborne gravity gradiometer survey data
Authors: Eckhardt Donald H.
Published: October 2002

Early in 1987, the Bell Aerospace/Textron Gravity Gradiometer Survey System (GGSS) will be tested by the Air Force Geophysics Laboratory in an airborne survey of a 300 × 300 km region of Oklahoma and Texas. The survey pattern will be a grid with a 5 km separation between adjacent tracks, both north‐south and east‐west. One way to process the GGSS survey data is to analyze an electrical network that is isomorphic to the survey network. The integrated gradients between the nodes where the survey lines cross correspond to the applied voltages between the nodes of the electrical network; the gradient variances correspond to the internodal resistances; the elements of the adjusted gravity vector correspond to the nodal voltages; and the solution variances correspond to the resistances to ground. An error analysis is performed by calculating the resistance to ground of the electrical network; a technique for making the calculations in large networks is explored in detail. For sample survey scenarios with one ground‐truth control point near each corner of the survey square and with realistic values for the survey parameters, the standard deviation in the gravity disturbance is less than 1 mGal and the deflection of the vertical standard deviation is less than 0.25 arc-s at all nodes. With no ground truth, but with a gravimeter on the aircraft that can independently determine gravity to 10 mGal at all nodes, the adjusted standard deviation in gravity disturbance is less than 1 mGal.
k-t scattering formulation of the absorptive acoustic wave equation: Wraparound and edge‐effect elimination
Authors: Compani‐Tabrizi B.
Published: October 2002

The solution algorithm to the absorptive acoustic scalar wave equation with spatially varying velocity and absorptive fields is numerically examined in the context of the k-space time‐domain scattering formalism to construct an absorbing boundary potential which eliminates wraparound and edge effects. The absorptive potential is constructed by using the absorptive coefficient, i.e., the coefficient of the first temporal derivative in the differential equation. Numerical solutions, in two dimensions, show the stability of the algorithm and the elimination of wraparound and edge reflections through use of the constructed absorptive potential. The numbers of calculations and storage requirements per time step are on the order of [Formula: see text] and N, respectively, where N is the number of points into which the problem is discretized.