bluuebunny/crossref_metadata_2025 huggingface dataset:
The asymptotic response of three‐dimensional basin offsets to magnetotelluric fields at long periods: The effects of current channeling
Authors: Hermance John F.
Published: October 2002

A simple, inexpensive numerical algorithm is used to analyze the asymptotic long‐period behavior of magnetotelluric (MT) fields in the vicinity of lateral offsets in sedimentary basins. The model is based on the distortion or channeling of telluric currents in a horizontal thin sheet. Although a gross oversimplification of nature, the model represents a class of structures which, because of excessive computer costs, have been relatively unstudied previously. Within, and closely adjacent to, the region of the three‐dimensional (3-D) offset, significant distortion of the MT parameters occurs. Skewness coefficients vary from negligible values to over 0.7. Principal resistivities vary by an order of magnitude. On the other hand, there is not a clear correlation between the degree of distortion of the parameters usually evaluated during MT surveys and the magnitude of conventional 3-D indicators (e.g., the skewness coefficient). Calculations have simulated the technique of averaging resistivity parameters from a large number of field sites in order to arrive at a regionally representative one‐dimensional (1-D) model. The results indicate that unless care is taken in adapting the nature of the averaging algorithm to the class of distortions encountered, significant bias of the averaged parameters may result. Our results also suggest that for this class of structures grave problems may be associated with using the principal resistivity perpendicular to geologic strike, the so‐called transverse magnetic (TM) mode, to infer an equivalent two‐dimensional (2-D) model for the region. A 2-D model would likely show significant modulations in the physical character of the basement which are, in fact, an artifact of telluric distortion caused by current channeling in the surficial heterogeneity.
Diffusion of electromagnetic fields into the earth from a line source of current
Authors: Oristaglio M. L.
Published: October 2002

The popularity of time‐domain electromagnetic (EM) systems in geophysical exploration has stimulated much interest in transient solutions of Maxwell’s equations. Although the fields at the surface of the earth are of the most practical value, the patterns of current flow in the ground can also be very enlightening, as demonstrated by Nabighian (1979) who showed the development and diffusion of the now famous “smoke ring” of current in the earth after shut‐off of a steady current in a loop at the surface. Nabighian’s result, which is based on Weaver’s (1970) general theory of EM induction in a half‐space, is an approximate image solution involving a single current filament; however, calculation of the full solution by numerical integration of the appropriate Hankel transforms showed that the real currents in the earth follow a similar smoke‐ring pattern (Nabighian, 1979; Lewis and Lee, 1978). Since the two‐dimensional (2-D) approximation is often used in solving EM scattering problems, it is interesting to consider the currents generated by a line source at the surface of a half‐space.
COCORP: Minnesota and Arkansas Areas
Authors: Kaufman S.
Published: October 2002

The Consortium for Continental Reflection Profiling (COCORP) announces the availability of data packages and tapes for the Minnesota and Arkansas areas for the cost of reproduction and shipping. These data were produced by COCORP whose operation is part of the U.S. Geodynamics Project sponsored by the National Academy of Sciences and funded by the National Science Foundation. The executive group of the consortium consists of members from Cornell University, Dartmouth College, Princeton University, Rice University and the University of Wisconsin. Cornell University is the operating institution.
Bottom‐hole temperature stabilization with continued circulation of drilling mud
Authors: Middleton M. F.
Published: October 2002

Determination of true formation temperature from measured bottom‐hole temperature (BHT) is important for well log interpretation and geothermal studies, especially with the current realization of the role of temperature in hydrocarbon maturation. A “bulk” thermal diffusivity of the borehole‐rock system of approximately [Formula: see text], initially suggested by Leblanc et al (1982), is confirmed by comparison with a two‐media borehole model. In general, time‐consecutive BHT measurements exhibit slower stabilization than those predicted by thermal conduction models. A simple model of thermal stabilization of a borehole with continued circulation after cessation of drilling is proposed. By modeling the thermal sink due to continued circulation of drilling mud as an exponentially decaying sink, thermal stabilization curves more consistent with observation are obtained. A good estimate of true formation temperature can be obtained by a curve‐matching technique where the observed BHT data are well behaved and the physical conditions in the borehole closely match the assumed model. However, it is virtually impossible in some cases to obtain a precise estimate of true formation temperature with BHT measurements from well log runs with current BHT stabilization models.
On: “Inversion of gamma‐ray data for elemental abundances,” by D. J. Crossley and A. B. Reid (GEOPHYSICS, January, 1982, p. 117–126).
Authors: Grasty R. L. , Carson J. M.
Published: October 2002

The paper by Crossley and Reid (1982) deals with the analysis of multichannel airborne gamma‐ray spectra. In their final summary, they state that the background gamma‐ray spectrum generated by cosmic radiation can apparently fluctuate within short (∼ seconds) time intervals. They remark that this conclusion leads to doubts as to the validity of measuring background radioactivity over lakes for airborne surveys. This procedure is standard practice in Canada where lakes are abundant (Richardson et al, 1975).
Geophysics Is Alive and Well
Authors: Barry Kevin M.
Published: October 2002

The fact that geophysics is alive and well today is quite obvious and this fact has generated a high level of optimism within all of us. The exploration geophysicist must, by nature, be an optimist when he probes the unknown subsurface with various sensing devices and techniques to locate the earth’s hidden resources. The pessimist is not inclined to take the risk of predicting anything he cannot put his finger on. There is an oft‐quoted rhyme that fits the situation well: Between the optimist and the pessimist, The difference is droll: The optimist sees the doughnut, But the pessimist sees the hole. In reviewing present activities and technology in exploration, we can appreciate why the geophysicist is not concerned with the hole — dry, empty, or otherwise — but is more optimistic than ever. In the last several years, our industry and SEG have seen an explosive growth in practically all areas of exploration geophysics, and in many respects 1981 is unique in the history of milestones in our profession.
Some aspects of attenuation and dispersion of electromagnetic waves in fluid‐saturated porous rocks and applications to dielectric constant well logging
Authors: Pascal H. , Pascal F. , Rankin D.
Published: October 2002

The properties of attenuation and dispersion of electromagnetic (EM) waves in fluid‐filled porous rocks are analyzed. A mathematical model of a two‐phase system for such rocks is developed. From this model the coupled equations which describe the propagation are formulated and an equation of dispersion is obtained in terms of frequency and the electrical properties of the medium constituents. Several numerical examples of both coupled and noncoupled models of propagation are used to illustrate the importance of these models for the interpretation of dielectric constant well logging.
A comparative study of the relation figures of magnetic anomalies due to two‐dimensional dike and vertical step models
Authors: Ram Babu H. V. , Subrahmanyam A. S. , Atchuta Rao D.
Published: October 2002

Magnetic anomalies in vertical and horizontal components, when plotted one against the other in polar form, result in a curve called the relation figure (Werner, 1953). In this paper, a comparative study of the relation figures of magnetic anomalies due to two‐dimensional (2-D) dike and vertical step models is made. The relation figures for these two models are found to be ellipses with different properties. The tangent at the origin to the ellipse is parallel to the major axis of the ellipse for the dike model, whereas it is perpendicular to the major axis for the vertical step. This property may be used to distinguish whether the source is a dike or a vertical step. For both of the models, the angle made by the axis of symmetry of the ellipse with the coordinate axis is equal to θ, the combined magnetic angle. The ratio between the lengths of the major and minor axes of the ellipse is directly related to the width‐to‐depth ratio of the dike or the bottom‐to‐top depth ratio of the vertical step. A few characteristic points defined on the ellipse are used to evaluate the body parameters. The major portion of the ellipse is obtained in the close vicinity of the source. Because of symmetry, the ellipse may be extrapolated easily outside the data length, and hence the effect of noise caused by adjacent objects is kept at a minimum.
Transient fields of a current loop source above a layered earth
Authors: Hoversten G. M. , Morrison H. F.
Published: October 2002

The electric field induced within four layered models by a repetitive current wave form in a circular loop transmitter is presented along with the resulting magnetic fields observed on the surface. The behavior of the induced electric field as a function of time explains the observed sign reversal of the vertical magnetic field on the surface. In addition, the differences between magnetic field responses for different models are explained by the behavior of the induced electric fields. The pattern of the induced electric field is shown to be that of a single “smoke ring,” as described by Nabighian (1979), which is distorted by layering but which remains a single ring system rather than forming separate smoke rings in each layer.
Investigation of multiple reflections and wave conversion by means of a vertical wave test (vertical seismic profiling) in southern Mississippi
Authors: Lash C. C.
Published: October 2002

A vertical wave test employing the vertical seismic profiling (VSP) technique in southern Mississippi confirmed suspicions that apparent multiple reflections might include converted waves as well as multiply reflected compressional waves. Both compressional (P) and shear (S) waves generated near the source were observed to travel to great depths, and P‐to‐S conversions were apparent in deep zones as well as shallow. P‐wave reflections were observed in agreement with predictions from synthetic records based on the sonic log. Up‐traveling P‐waves were reflected a short distance below the surface, at the base of the low‐velocity layer, and were followed as down‐traveling P‐waves to 200 ft depth by means of a vertical spread. Below 2000 ft and following the first P wave train, the predominate energy appeared to be down‐traveling P‐waves which could not be traced back to the reflection of up‐traveling P‐waves. The continuity of wavelets indicated instead that the strong down‐traveling S‐waves generated near the source produced P‐waves by S‐to‐P conversion somewhere in the zone between 800 and 1400 ft. The interference on the recordings made with an individual seismometer, or a small group of seismometers, using dynamite shots as the source was generally of a low‐frequency nature, so that the signal‐to‐noise (S/N) ratio was improved by the use of a high passband filter. The interference was greatly reduced without the need for a filter on recordings in which the source was a distributed charge of 100 ft length. The distributed charge produced much less shear‐wave energy in the P reflection band, demonstrating that the interference encountered when using a concentrated charge source was the consequence of the generation of S‐waves near the source. The distributed charges were previously chosen as a means for effectively eliminating secondary (ghost) reflections, an unwanted form of multiple reflections.
The effects of noise on minimum‐phase Vibroseis deconvolution
Authors: Bickel Samuel H.
Published: October 2002

Ristow and Jurczyk (1975) proposed a mixed‐phase Vibroseis® inverse filter which is the usual minimum phase spiking deconvolution filter convolved with a Weiner‐Levinson minimum phase wavelet having the same amplitude spectrum as the Vibroseis wavelet. A problem exists since (for large time‐bandwidth products) the Vibroseis signal approximates a band‐limited signal and noise may have to be added to ensure convergence of the Wiener‐Levinson algorithm. This processing noise level can alter the resulting minimum phase wavelet. Since the deconvolution filter is influenced by the ambient or environmental noise as well as by the processing noise, the proposed correction to spiking deconvolution may not always yield meaningful results. It is shown that although the Vibroseis wavelet may span several octaves, it is not only band‐limited but can be approximated by a narrow‐band signal representation. In this formulation, the center frequency for the wavelet is considered to be the average of the high and low frequencies. The phase associated with this center frequency is independent of time but depends upon both the signal bandwidth and the deconvolution noise platform. Finally, this paper examines distortions in the deconvolved wavelet arising from both processing and environmental noise‐induced variations in the phase and envelope delay. The reflection sequence is assumed to be white, and a minimum phase, nearly constant Q, earth model is assumed. Curves are presented which show the residual phase error as a function of attenuation, processing noise, and the environmental signal‐to‐noise (S/N) ratio. It was found that although both types of noise will cause some residual phase error, phase compensation can correct for many of the phase distortions and polarity reversals that may be present in the deconvolved data only if the environmental noise is smaller than the processing noise.
A technique to determine the three‐dimensional attitude and true velocity of a refractor
Authors: Russell D. R. , Keller G. R. , Braile L. W.
Published: October 2002

Three‐dimensional (3-D) seismic reflection surveys have been the subject of much recent interest. However, use of the seismic refraction technique (Musgrave, 1967) in 3-D analyses should also be of considerable utility even though homogeneous layers separated by planar interfaces (not necessarily parallel or horizontal) must be assumed in most applications. A particular advantage of the refraction method is the straightforward determination of velocities.
An electronic gravimeter to measure g(r)
Authors: Nieto Michael Martin , Goldman T. , Gutschick Vincent P.
Published: October 2002

We point out that a battery may be designed so that in a gravitational field it will have a gravitationally induced emf in addition to an electrochemical one. The gravitationally induced emf of a battery with a small “effective” electrochemical potential and a long “effective” length can readily be measured to very high precision by means of any precise voltmeter, and in particular by a Josephson junction. Such a device may be employed to measure any component of the gravitational acceleration vector. It can be constructed compactly enough to be placed down a borehole. Thus, in principle it is an extremely precise and adaptable tool for geophysical exploration.
Homomorphic deconvolution: Application to gravitational and magnetic field waveforms
Authors: Papazis Pandelis K. P. , Jensen Oliver G.
Published: October 2002

The gravitational and magnetic field waveforms which represent potential fields of geologic structures can be expressed as the sum of overlapping, delayed replicas of a certain basic waveform. Such field waveforms, therefore, can be thought of as the outcome of a convolutional process. One way of separating signals which have been combined through convolution or multiplication is by using a set of systems called homomorphic systems. A particular feature of the process called homomorphic deconvolution is that no previous assumption of the character or nature of the basic waveform need be made. It is this feature of homomorphic deconvolution which makes it attractive for applications to gravitational and magnetic field waveforms.
On: “Inversion of normal incidence seismograms” by A. Bamberger, G. Chavent, Ch. Hemon, and P. Lailly (GEOPHYSICS, May 1982, p. 757–770)
Authors: Mendel J. M.
Published: October 2002

In an early section of their paper, Bamberger et al present analyses which lead them to conclude (p. 759) “This is why we replace Kunetz’s sequential…determination of [Formula: see text] by an iterative but simultaneous determination of all the impedance values [Formula: see text], k = 2, …, 300.” Unfortunately, their analysis leading to this conclusion is, as we demonstrate below, incorrect. In fact, the correct analyses can lead to a rather surprising conclusion, due in part to an interesting experiment performed by the authors that is summarized in their Figure 2.
Exact seismograms for a point force using generalized ray theory
Authors: Kanasewich E. R. , Kelamis P. G. , Abramovici F.
Published: October 2002

Exact synthetic seismograms are obtained for a simple layered elastic half‐space due to a buried point force and a point torque. Two models, similar to those encountered in seismic exploration of sedimentary basins, are examined in detail. The seismograms are complete to any specified time and make use of a Cagniard‐Pekeris method and a decomposition into generalized rays. The weathered layer is modeled as a thin low‐velocity layer over a half‐space. For a horizontal force in an arbitrary direction, the transverse component, in the near‐field, shows detectable first arrivals traveling with a compressional wave velocity. The radial and vertical components, at all distances, show a surface head wave (sP*) which is not generated when the source is compressive. A buried vertical force produces the same surface head wave prominently on the radial component. An example is given for a simple “Alberta” model as an aid to the interpretation of wide angle seismic reflections and head waves.
Ghosting and marine signature deconvolution: A prerequisite for detailed seismic interpretation
Authors: Jovanovich Dushan B. , Sumner Roger D. , Akins‐Easterlin Sharon L.
Published: October 2002

Detailed lithologic interpretation of seismic sections and/or pseudo‐sonic logs generated from seismic data requires that the seismic trace can be modeled as a reflection series convolved with a zero‐phase broadband wavelet. Ghosting and marine signature deconvolution processing is a prerequisite for assuring that the seismic wavelet on a marine CDP section will be zero phase. A deterministic approach to deconvolution is centered around the concept of abandoning the purely statistical method of wavelet estimation and actually measuring the seismic wavelet. A proper signature recording for marine data is, therefore, a crucial component of deterministic deconvolution. Another important element in the deterministic deconvolution sequence is the application of a deghosting filter to remove near‐surface reflections. Proper application of a deghosting filter significantly improves the correlation between log synthetics and the seismic trace. It has been found that statistical deconvolution schemes, because of the number of statistical hypotheses required to produce a deconvolution filter, produce residual wavelets that are highly variable in character and whose average phases cover the entire phase spectrum, modulo 2π. Examples of a Gulf Coast marine line which was shot with Aquapulse™, air gun, and Maxipulse™ sources by the RV Hollis Hedberg are presented to demonstrate the differences between statistical and deterministic deconvolution processing sequences. It will be shown, using sonic logs from wells adjacent to the seismic line, that the deterministic deconvolution sections for all three sources are close to zero phase while the statistical deconvolution sections have residual average phase errors between 180 and 270 degrees. The deterministic deconvolution sections have a high degree of correlation among themselves and to the wells adjacent to the line, while the statistical deconvolution sections correlate poorly to each other and to the wells. Synthetic seismograms and their impedance logs, and the seismic sections and their corresponding pseudo‐sonic logs, are used to demonstrate how deconvolution influences lithologic interpretation. ™Western Geophysics Co.
Statistical determination of geophysical well log response functions
Authors: Nosal Eugene A.
Published: October 2002

The vertical response function of induction logging tools is shown to be derivable from a power spectrum analysis of the measurement. The vertical response function is the one‐dimensional sequence of weights that characterizes how the tool combines the rock conductivities along the borehole to form an output called the apparent conductivity; it is the system impulse response. The value of knowing this function lies in the possible use of filter theory to aid in data processing and interpretation. Two general notions establish the framework for the analysis. The first is that logging is a linear, convolutional operation. Second, the earth’s conductivity profile forms a stochastic process. The probabilistic component is fleshed out by reasonably based assumptions about the occurrence of bed boundaries and nature of conductivity changes across them. Brought together, these tenets create a characterization of the conductivity sequence that is not a stationary process, but rather is intrinsic, as defined in the discipline of geostatistics. Such a process is described by a variogram, and it is increments of the process that are stationary. The connection between the power spectrum of the measurement and the system response function is made when the convolutional model is merged with the conductivity process. Some examples of induction log functions are shown using these ideas. The analysis is presented in general terms for possibly wider application.
Quantitative interpretation of self‐potential anomalies due to two‐dimensional sheet‐like bodies
Authors: Rao D. Atchuta , Babu H. V. Ram
Published: October 2002

A method for quantitative interpretation of self‐potential anomalies due to a two‐dimensional sheet of finite depth extent is proposed. In the case of an inclined sheet, positions and amplitudes of the maximum, minimum, and zero‐anomaly points are picked and then the origin is located on the horizontal gradient curve using the template of Rao et al (1965). The parameters of the sheet may be evaluated either geometrically or by using some analytical relations among the characteristic distances. When the sheet is vertical, the parameters may be evaluated using the positions of half and three‐quarter peak amplitudes.
International geomagnetic reference field—Its evolution and the difference in total field intensity between new and old models for 1965–1980
Authors: Peddie Norman W.
Published: October 2002

The total magnetic field near the surface of the Earth is a sum of several constituent fields. Part of the total field consists of fields that are transient or rapidly varying. These fields are caused, either directly or indirectly, by electric currents in the upper atmosphere and beyond. The part of the total field that is more permanent arises from sources that are located inside the Earth. Evidence suggests that this part has two principal constituents: the main field and the crustal field.
Airborne gravity is here!
Authors: Hammer Sigmund
Published: October 2002

The achievement of practical and useful airborne gravity exploration for petroleum is a major culmination of more than twenty years of research and development. Commercial surveys have now been conducted for three years. The precision and anomaly resolution attainable are twice as good as that of current shipborne gravity data. This paper presents data to demonstrate the precision of airborne gravity and discusses its usefulness (with simultaneous magnetics and topography). Industrial acceptance of the method portends a new era in geophysical exploration for oil and gas which gives promise to double the effectiveness of explorations on land in both time and cost.
A note on airborne gravity terrain corrections
Authors: Hammer Sigmund
Published: October 2002

Terrain corrections for airborne gravity surveying have been a cause of some concern in the exploration industry (Hammer, 1974). Some skepticism still persists that the problem may be troublesome. As a matter of fact, an essential feature of the present field procedure in airborne gravity surveying is to make observations in a more or less square array of intersecting lines, along which narrow beam radar recordings of the terrain clearance provide topographic information to calculate the terrain corrections (Navazio and Gumert, 1981). In addition, this yields a topographic contour map of the area which is very useful for many other purposes. What has not been generally appreciated is that taking observations in the air, at some distance above the topography, actually is a major advantage with respect to the terrain corrections. The magnitude and general behavior of the terrain correction problem in airborne gravity is demonstrated herein by very simple simulated calculations.
The possibility of remote sounding of the earth’s resistivity profile
Authors: El‐Raey M.
Published: October 2002

A variety of methods have been developed to solve the general problem of determining underground resistivity from surface measurements using two current electrodes and two collinear potential electrodes (Ghosh, 1971; Parker, 1971; Inman et al, 1973; Inman, 1975; Koefoed, 1979). Nevertheless, problems associated with measurement errors, nonlinearities, and nonuniqueness have not been completely resolved. Recently, a method of interpretation of direct current resistivity measurements, using a linearized Backus and Gilbert technique was advanced by Oldenburg (1978). In this method, the resistivity is assumed to be a continuous function of depth, and an iterative technique is used to construct a resistivity model whose calculated responses agree with observations within a prescribed error. The nonuniqueness of the problem was resolved by determining only averages of resistivity at depth. However, even in this method the nonlinearity of the problem prohibits definitive statements about advantages and disadvantages of any particular electrode configuration until a large variety of resistivity structures have been considered. The main problems are (1) a nonlinear resistivity profile, (2) a nonlinear current penetration, (3) a nonlinear dependence of measurable potential on resistivity, and (4) a nonlinear depth investigation characteristic.
Seismic shear‐wave observations in a physical model experiment
Authors: Tatham Robert H. , Goolsbee Donald V. , Massell Wulf F. , Nelson H. Roice
Published: October 2002

The observation and common‐depth‐point (CDP) processing of mode‐converted shear waves is demonstrated for real data collected in a physical model experiment. The model, submerged in water, represented water depth scaled to 250 ft, the first subsea reflector at 4000 ft, and the last reflector at 7000 ft below the sea floor with a structural wedge at the center. Very efficient mode conversion, from P to SV and back to P, is anticipated for angles of incidence at the liquid‐solid interface (sea floor) between 35 and 80 degrees. The model, constructed of Plexiglas and 3180 resin, will support elastic shear‐wave propagation. One anticipated problem, internal reflections from the sides of the model, was solved by tapering the sides of the model to 45 degrees off vertical. The P wave reflection coefficient at an interface between Plexiglas and water is 35 percent for vertical incidence, but it diminishes to very nearly zero between 43 and 75 degrees. Thus, by tapering the sides of the model, any undesired internal P wave reflections had to undergo at least two reflections at angles of incidence in the low reflection coefficient range for P waves. Data were collected in both an end‐on CDP mode, with offsets from 1000 ft to 20,000 ft, and a variety of walkaway experiments with scaled ranges from 1000 ft to 31,000 ft. Processing and analysis of the data confirm the existence of mode‐converted shear‐wave reflections in a modeled marine environment. In particular, the S wave reflections from all interfaces are identified on both the 100 percent gathered records and the final stacked records. These SV wave reflections were isolated for stacking by considering those portions of the gathered records, both offset and arrival time, that correspond to optimum angles of incidence. In addition, τ-p processing isolated particular angles of incidence, further confirming the incidence angle‐range criterion. Thus, the desired events are unambiguously identified as mode‐converted shear waves.
The normal vertical gradient of gravity
Authors: Karl John H.
Published: October 2002

Most gravity surveys are conducted to estimate subsurface density contrasts for one application or another. From large‐scale crustal studies to relatively small exploration surveys, it is necessary to determine in some way what the normal gravity field should be in order to identify anomalous features. The anomalies then represent deviations to be interpreted in light of the original model. It is a central limitation of potential field methods that this model, sometimes representing a so‐called “regional” field, is not unique. In the case of gravity, this model has traditionally involved geometrical approximations. It is generally assumed that variations in station elevations are small compared with the radius of the earth—an obviously excellent approximation, but one needs to be mathematically consistent.
On: “The deconvolution of phase‐shifted wavelets” by S. Levy and D. W. Oldenburg (GEOPHYSICS, v. 47, p. 1285–1294)
Authors: Bickel Samuel H.
Published: October 2002

The recent paper by Levy and Oldenburg describes the deconvolution problem when a wavelet is phase‐shifted upon reflection from a boundary. In order to resolve the ambiguities in the reflectivity function associated with these phase shifts, the authors suggest the use of complex deconvolution. However, as we will show here, there is a question whether this more involved procedure yields any different results from those that would be obtained by deconvolving the real part of the trace and then taking the Hilbert transform for amplitude and phase analysis.
Resolution performance of Wiener filters
Authors: Bickel S. H. , Martinez D. R.
Published: October 2002

To improve the resolution of seismic events, one often designs a Wiener inverse filter that optimally (in the least‐squares sense) transforms a measured source signature into a spike. When this filter is applied to seismic data, the bandwidth of any noise which is present increases along with the bandwidth of the signal. Thus the signal‐to‐noise ratio is degraded. To reduce signal ambiguity it is common practice to prewhiten the Wiener filter. Prewhitening the filter improves the output signal‐to‐ambient noise ratio, but at the same time it reduces resolution. The ability to resolve the temporal separation between events is determined by the resolution time constant which we define as the ratio of signal energy to peak signal power from the filter. For unfiltered wavelets the resolution time constant becomes the reciprocal of resolving power recently described by Widess (1982). For matched filter signals the resolution time constant can be regarded as the inverse of the frequency span of the signal. Although it is satisfying that the resolution time constant definition agrees with other measures of resolution, this more general definition has two major advantages. First, it incorporates the effect of filtering; second, it is easily generalized to incorporate the effects of noise by assuming that the filter is a Wiener filter. For a given amount of noise the Wiener filter is a generalization of the matched filter. Marine seismic wavelets demonstrate how reducing the noise level improves the resolution of a Wiener filter relative to a matched filter. For these wavelets a point of diminishing return is reached, such that, to realize a further small increase in resolution, a large increase in input signal‐to‐noise ratio is required to maintain interpretable information at the output.
The rotating current dipole
Authors: Hall S. H.
Published: October 2002

The rotating horizontal electric dipole ring source of this frequency‐domain EM method possesses the property that its E and H fields will couple strongly with steeply dipping conductive targets regardless of their strike direction. The extent to which this coupling is optimized depends upon the polarization of the source field and upon varying source‐target proximity. The state of polarization in E and H is determined by applying infinitesimal dipole moment theory to a rotating HED source on the surface of a conducting half‐space. It is shown that the source is equivalent to a 2-HED ring source of orthogonal dipoles with a phase difference of π/2 between them. Anomaly optimization is examined by analog modeling observations of the vertical magnetic field response of a vertically dipping graphitic target immersed in an NaCl electrolyte and oriented 0, 45, 90, and 135 degrees with respect to the source‐target center line. It is found that the extent of optimization for this model configuration is 60–85 percent for near‐surface targets. Since the method maximizes both conductive and inductive secondary response, modeling surveys are repeated with graphitic targets insulated from and in electrical contact with the modeled host electrolyte. By discriminating in this way between inductive and conductive response, it is found that, at the inductive limit of the response, current gathering provides the major portion of the anomaly and the individual conductive and inductive optimizations combine in such a manner as to improve the net optimizing ability.
Does draping aeromagnetic data reduce terrain‐induced effects?
Authors: Grauch V. J. S. , Campbell David L.
Published: October 2002

Contrary to intuition, draped aeromagnetic surveys (when compared to typical level surveys) amplify, rather than reduce, the problem of magnetic‐terrain anomalies. Calculations of the total magnetic field of various simple magnetic topographies on level and draped surfaces support this conclusion. In cases where draped surfaces are lower than level surfaces, the draped profiles exhibit steeper gradients and deeper polarity lows over topography than do the level profiles. On the other hand, where draped surfaces are higher than level surfaces, all anomalies are attenuated, so that magnetic‐terrain effects might be reduced relative to subsurface sources (depending upon the magnetization of each). The difference in magnetic behavior between level and draped data can be explained by a contribution of a vertical derivative component in the draped case that is absent in the level case. The contribution is most significant near topographic features because both the observation surface and the topographic surface are changing vertically.
Response of a current loop antenna in an invaded borehole
Authors: Chew W. C.
Published: October 2002

The problem of the radiation of a current loop antenna in a multicylindrical medium is formulated exactly in terms of an integral. The integrand is calculated using an iterative scheme making the integral more tenable to approximation. This closely approximates the response of a dielectric logging tool such as the deep propagation tool (DPT) or an induction tool in invaded boreholes. To gain more physical insight into the waves, an asymptotic approximation of the integral is derived. The large parameter for the validity of this approximation is the ratio of the transmitter‐receiver separation to the diameter of the invasion around the borehole. An iterative scheme is devised to compute systematically the approximation for an arbitrary number of cylindrical layers. The multicylindrical layer model is a good model of the invasion zone, borehole, and tool housing. The final approximation to the azimuthal electric field contains three terms. The first term resembles the response of a current loop in a homogeneous medium with electrical properties of the outermost medium or the formation. The higher order terms are improvements. The approximation is better at lower frequencies, implying that it is also good for the induction logging tool.
Electrical modeling of the inhomogeneous invaded zone
Authors: Drahos D.
Published: October 2002

The ideal rock model in electrical well logging for prospecting hydrocarbon consists of three cylindrical layers characterized by homogeneous resistivities. The second layer of the model respresents the zone of invasion, where under real circumstances the resistivity is not constant but changes with the distance from the borehole. This condition could be taken into consideration, but the solution of the electrical direct problem for such case is very complicated. Any kind of invasion resistivity profile can be approximated by many cylindrical layers of homogeneous resistivities. A recursive formula is derived by which the many‐layer problem can be solved simply. Numerical calculations were made to study the effect of the inhomogeneity of the invaded zone. Apparent resistivities of different Laterolog and normal arrangements were calculated for several models having linearly increasing resistivity profile in the invaded zone. These apparent resistivity values were evaluated by least‐squares fitting to determine the equivalent electrical parameters of the usual model of three homogeneous layers. The results show that there is practically no error in determination of the true resistivity, but the depth of invasion may be significantly smaller than that of the linear resistivity profile.
The relationship between acoustic properties and the petrographic character of carbonate rocks
Authors: Rafavich F. , Kendall C. H. St. C. , Todd T. P.
Published: October 2002

Laboratory studies of the detailed relationships between acoustic properties and the petrographic character of brine‐ and air‐saturated carbonate rocks with a wide range of facies, porosities, lithologies, and rock fabrics indicate that porosity is the major factor influencing both P- and S-wave impedance and velocity. Primary lithology and secondary mineralogy have only a small influence on impedance and velocity. Combined use of P- and S-wave velocity data discriminates porosity changes from lithologic changes. All other variables, including pore‐fluid type and petrographic fabric, have no significant influence on velocities. Laboratory measurements of P‐wave velocity under simulated in‐situ conditions reproduce well‐log velocity values reliably. Laboratory porosity‐velocity trends agree with the time‐average equation when the correct matrix velocities are used. Rock property results were used to interpret porosity/lithology variations for an inverted seismic section from the Williston basin. Where well control was available, the porosity/lithology interpretation was found to be in agreement with the subsurface control.
Seismic approaches for structural studies of the Sudbury basin
Authors: Messfin Derbew , Moon Wooil
Published: October 2002

This study investigates the feasibility of applying seismic techniques in the search for ore deposits, with particular emphasis given to locating orebodies at great depths. The basic procedure followed was essentially an understanding of the forward problem, whereby the effects of the subsurface structure in a typical mining district were thoroughly studied. The initial stage of the study was devoted to determining the elastic parameters by laboratory measurement of seismic velocities and densities of core samples obtained from the Sudbury basin, Canada. By virtue of its ability to handle lateral as well as vertical inhomogeneities, fast computing time and flexibility, the asymptotic ray theory was judged to be more suitable for studying the effect of geologic structures typically found in the Sudbury basin. Both large‐scale and small‐scale models, representing actual geologic conditions in Sudbury, were constructed. The computed seismic response of the large‐scale models shows that the micropegmatite/oxide‐rich quartz gabbro and the mafic norite/granite gneiss contacts are characterized by substantially strong reflections, indicating that these two interfaces can serve as marker horizons in future seismic surveys. In the small‐scale models of mineralized structures, the sulfide body was outlined by a distinctly high amplitude of reflection. Both the traveltime and the dynamic characteristics of these models have features that are indicative of the presence of mineralized structures.
Underground oil‐shale retort monitoring using geotomography
Authors: Daily William
Published: October 2002

Geophysical tomographs (geotomographs) were made of two underground oil‐shale retorts: (1) the Occidental Oil Shale Inc. miniretort constructed for ignition tests at the demonstration mine at Logan Wash, Colorado; and (2) the Geokinetics Oil Shale Inc. Retort 25 near Vernal, Utah. These experiments demonstrate that geotomography may be a valuable diagnostic tool for underground oil‐shale retorting processes. At the Geokinetics in‐situ retort, the technique delineated the zones of high permeability in a cross‐section of the retort. At the Occidental modified in‐situ miniretort, the technique imaged the high temperature zone of the retort with a spatial resolution of about 2 m, and showed its temporal development over a period of eleven days.
An interpretive analysis of magnetotelluric data
Authors: Ranganayaki R. P.
Published: October 2002

A simple analysis to determine the dimensionality of magnetotelluric resistivity variations, to separate the near‐surface resistivity variation from the variations at depth, and to find the relative resistivity variations with depth is described. Parameters derived from the magnetotelluric impedance tensor are mapped in pseudosection and planar view for two‐dimensional (2-D) model data and for survey data from Montana. These data illustrate procedures that can qualitatively map complex resistivity structures in the lateral distance‐frequency domain or, equivalently, the lateral distance‐scaled vertical distance domain. Phase‐dependent parameters have better vertical resolution than parameters related to scalar apparent resistivity, but the latter allow estimates of the resistivities encountered. Phase parameters for the Montana data provide a semiquantitatively accurate cross‐section of a geologically known anticlinal structure. This suggests a means of subsurface structural mapping with magnetotelluric data. The use of these parameters with sufficiently dense and accurate data provides a first‐order indication of structure for subsequent quantitative modeling.
Computation of Green’s tensor integrals for three‐dimensional electromagnetic problems using fast Hankel transforms
Authors: Anderson Walter L.
Published: October 2002

A new method is presented that rapidly evaluates the many Green’s tensor integrals encountered in three‐dimensional electromagnetic modeling using an integral equation. Application of a fast Hankel transform (FHT) algorithm (Anderson, 1982) is the basis for the new solution, where efficient and accurate computation of Hankel transforms are obtained by related and lagged convolutions (linear digital filtering). The FHT algorithm is briefly reviewed and compared to earlier convolution algorithms written by the author. The homogeneous and layered half‐space cases for the Green’s tensor integrals are presented in a form so that the FHT can be easily applied in practice. Computer timing runs comparing the FHT to conventional direct convolution methods are discussed, where the FHT’s performance was about 6 times faster for a homogeneous half‐space, and about 108 times faster for a five‐layer half‐space. Subsequent interpolation after the FHT is called is required to compute specific values of the tensor integrals at selected transform arguments; however, due to the relatively small lagged convolution interval used (same as the digital filter’s), a simple and fast interpolation is sufficient (e.g., by cubic splines).
On: “Numerical integration of related Hankel transforms by quadrature and continued fraction expansion” by A. D. Chave (GEOPHYSICS, 48, p. 1671–1686, December, 1983).
Authors: Anderson Walter L.
Published: October 2002

Chave presents an excellent algorithm and computer subprogram that evaluate Hankel transforms by quadrature and continued fraction summation. This subprogram would be a valuable addition to any mathematical computer library. Chave refers to digital filter (convolution) methods as “the standard numerical approach to the computation of Hankel transforms,” and makes numerous references to my published work (Anderson, 1979, 1982). However, some readers may misinterpret some of his statements regarding convolution methods, which I hope to clarify by this discussion.
Multidimensional linearized inversion and seismic migration
Authors: Berkhout A. J.
Published: October 2002

This paper discusses the close relationship between seismic migration and multidimensional inversion according to the linearized inverse scattering theory. The linearized inverse scattering approach represents a mixed modeling‐inversion procedure. Unlike seismic migration, the actual inversion process is carried out on the difference between a modeled reference response and the actually measured data. The output is generally presented in terms of the elastic parameters of the medium. Seismic migration represents a direct inversion method: the downward extrapolation process is carried out directly on the measured data. Output is presented in terms of reflectivity. If the reference medium has been chosen in such a way that (1) the total wave field in the reference medium can be split into a downward traveling source wave field and an upward traveling response (the propagation of both wave fields being defined by the one‐way wave equation) and that, (2) the upward traveling response in the reference medium can be neglected with respect to the upward traveling response in the actual medium, then seismic migration and linearized inversion define identical inversion processes. Typically, the above conditions are fulfilled in a homogeneous reference medium. In iteractive multidimensional inversion, the full inverse scattering problem is approached by a number of linearized inversion steps. I show that each linear step consists of a prestack migration process and a prestack modeling process, the modeling output being used to remove the contribution of multiple scattering. Finally, I argue that for a proper inversion process, information on the elastic parameters outside the seismic frequency bandwidth (temporally and spatially) should be accounted for in the reference medium.