bluuebunny/crossref_metadata_2025 huggingface dataset:
Q estimation from vertical seismic profile data and anomalous variations in the central North Sea
Authors: Stainsby S. D. , Worthington M. H.
Published: October 2002

Four different methods of estimating Q from vertical seismic profile (VSP) data based on measurements of spectral ratios, pulse amplitude, pulse width, and zeroth lag autocorrelation of the attenuated impulse are described. The last procedure is referred to as the pulse‐power method. Practical problems concerning nonlinearity in the estimating procedures, uncertainties in the gain setting of the recording equipment, and the influence of structure are considered in detail. VSP data recorded in a well in the central North Sea were processed to obtain estimates of seismic attenuation. These data revealed a zone of high attenuation from approximately 4 900 ft to [Formula: see text] ft with a value of [Formula: see text] Results of the spectral‐ratio analysis show that the data conform to a linear constant Q model. In addition, since the pulse‐width measurement is dependent upon the dispersive model adopted, it is shown that a nondispersive model cannot possibly provide a match to the real data. No unambiguous evidence is presented that explains the cause of this low Q zone. However, it is tentatively concluded that the seismic attenuation may be associated with the degree of compaction of the sediments and the presence of deabsorbed gases.
Dielectric properties of reservoir rocks at ultra‐high frequencies
Authors: Shen L. C. , Savre W. C. , Price J. M. , Athavale K.
Published: October 2002

Conventional resistivity and induction tools measure the electrical conductivity of the formation. Interpretation of these logs is difficult in situations where the formation water resistivity is variable or unknown as a result, for example, of water, steam, or chemical flooding. Recent introduction of several dielectric tools offers a new technique in well logging. These sondes measure the relative dielectric permittivity of the formation at very‐high and ultra‐high radio frequencies. Because water has a much higher relative dielectric permittivity (about 80) than oil (about 2) or gas (about 1), the dielectric tool can distinguish hydrocarbon‐bearing zones from water‐bearing zones even when the formation fluid is nonconducting. However, in order to quantify the oil saturation in the formation, one needs an accurate formula that can relate the measured relative dielectric permittivity of the rock to the oil saturation in the rock. Present interpretation formulas have only a limited range of applicability. Therefore, our study was undertaken to answer the following question. Whereas Archie’s relationship relates the resistivity to oil saturation for resistivity logs, what is the corresponding saturation formula for dielectric logs? The approach we take is to measure core samples and obtain a broad data base from which we derive an interpretation formula. This paper describes how we developed a laboratory technique to measure reservoir core samples at ultra‐high frequencies, how the data are processed, and how an interpretation formula for water saturation is found. The data are obtained in the frequency range 800 to 1 200 megahertz (MHz), with the porosity of the rock ranging from 6 to 42 percent. The rocks are saturated with NaCl solution with salinity ranging from 0 to 182 000 ppm. Our study enabled us to develop a new and accurate interpretation technique for the dielectric tool called EPT (Electromagnetic Propagation Tool) manufactured by Schlumberger.
Inversion of vertical seismic profiles by iterative modeling
Authors: Grivelet Pierre A.
Published: October 2002

I present an application of iterative modeling to the inversion of vertical seismic profiles (VSPs). This method is derived from linear inversion which allows the extraction from VSP data of an impedance profile as a function of time and thus permits the prediction of impedance ahead of the drill bit. There are two steps in this process: first, detection of the major events on the seismogram which is achieved by a recursive detection algorithm; and second, an optimal estimate of the impedances carried out by a gradient algorithm. Seismic data are band‐limited, and consequently the solution of the inversion is nonunique. This nonuniqueness is handled by assuming a piecewise‐constant or blocked impedance model and by adding a priori constraints. Some synthetic examples are used to illustrate the method, and a field example shows a comparison between an impedance profile extracted from VSP data with this inversion method and an impedance profile from well logging data. In this example the accurate prediction of impedance values illustrates the usefulness of the method.
Surface heat flow measurements at the Puhimau hot spot
Authors: Dunn J. C. , Hardee H. C.
Published: October 2002

The Puhimau hot spot, on Kilauea Volcano, Hawaii, was thermally mapped using new high‐output thermopile heat flow sensors. This thermal geophysical technique allows rapid measurement of surficial heat flow, especially in regions of high heat flux where shallow burial depths can be used. Heat flow measurements ranged from 200 to [Formula: see text] over the central portion of the Puhimau hot spot. Analysis of the heat flow data combined with other geophysical measurements suggests that the Puhimau hot spot could be caused by a shallow and perhaps still molten body of magma beneath the local area. These geophysical measurements, along with a proposed shallow scientific drillhole, can provide valuable evaluation of geophysical techniques for locating magma bodies in the crust.
Nomogram for the complete interpretation of spontaneous potential profiles over sheet‐like and cylindrical two‐dimensional sources
Authors: Murty B. V. Satyanarayana , Haricharan P.
Published: October 2002

Interpretation of elongated SP anomalies is usually accomplished by assigning two‐dimensional (2-D) shapes such as inclined sheets and horizontal cylinders to the source. However, since the shapes of the profiles are similar, it is extremely difficult to distinguish the source as cylindrical or sheet‐like from a given field profile. By defining two characteristic ratios from anomalies between the two extrema on the profile, we present a nomogram which not only helps identify the shape of the 2-D anomaly source, but also facilitates estimating all the parameters. Using this nomogram a field profile can be interpreted in a very short time with ease and accuracy. The method is demonstrated on two examples. Error response of the parameters estimated due to errors in data was studied through imposing ±5 percent to ±25 percent errors in the two characteristic ratios in two synthetic profiles due to a cylinder and a sheet. While the results on the cylinder showed negligible errors, the percent errors for the sheet model, in general, are less than the percent errors imposed.
A gradient analysis‐based simplified inversion strategy for the magnetic anomaly of an inclined and infinite thick dike
Authors: Pal Poorna C.
Published: October 2002

The inclined thick dike extending infinitely in the direction of its dip, a common geometric approximation in geophysics, has been used in a variety of magnetic inversion techniques. However, in space techniques (Johnson, 1969, Won, 1981) and frequency techniques (Khurana et al., 1981) iterative computations are needed to obtain accurate estimates of the parameters of the source. Since rapid estimates are often needed, either nonograms (Gay, 1963) or analysis of symmetric and asymmetric components of the profile (Koulomzine et al., 1970) can be cost‐effective methods. A simplified inversion strategy employing the profile and its horizontal gradient is developed and described here as an effective alternative to these rapid methods of interpretation. Horizontal gradients have been used before (e.g., Stanley, 1977) for simplified interpretation of the magnetic profile over a geologic contact. As shown here, a similar strategy can be used in the case of an inclined thick dike of infinite depth extent.
The elastodynamic field of N interacting vibrators (two‐dimensional theory)
Authors: Tan T. H.
Published: October 2002

The elastodynamic field of N rigid strips, lying parallel on the surface of an elastic half‐space and harmonically excited in time by vertical forces, was calculated. It is assumed (1) the contact between the rigid strips and the surface of the half‐space is maintained during the motion of the strips, and (2) the horizontal component of the traction is zero on the surface of the half‐space. Calculation of the elastodynamic field is based on the integral representation of the particle displacement in the half‐space, together with the dynamic equations for the strip. From the integral representation and the dynamic equations, a set of coupled integral equations for the vertical component of the traction under the strips can be derived. This set of integral equations was solved numerically by the method of moments. The influence of the hold‐down mass and its spring system is also investigated. It is shown that its action can be accounted for by introducing a frequency‐dependent effective mass of the strips. At the resonance frequency of the hold‐down mass/spring system, the power radiated into the half‐space, is shown to be zero. Numerical results show that for a fixed strip width and fixed parameters of the elastic half‐space, the frequency at which the peak in the radiated power occurs decreases as the mass/unit length of the strip increases, whereas the ratio of the radiated P‐, S‐, and Rayleigh waves does not change at all. Since the frequency at which the peak in the radiated power occurs depends upon the mass/unit length of the strip, and since the influence of the hold‐down mass/spring is actually a frequency‐dependent effective mass of the strip, theoretically it is possible to optimize the radiated power of a vibrator for a frequency band of interest. Such a vibrator, if ever constructed, will most likely depend upon a feedback and control system. I show that the phase difference between the driving force and the velocity of the strip is a suitable feedback signal.
Shear‐wave vibrator signals in transversely isotropic shale
Authors: Peacock Sheila , Crampin Stuart
Published: October 2002

The experiments of Robertson and Corrigan (1983) on shale are among the first three‐component field observations of shear waves in transversely isotropic media to be published. Their data are reprocessed to highlight the effects of the shale’s anisotropy on shear waves. Two results emerge. First, shear‐wave splitting in a transversely isotropic substrate is most easily observed when the vibrator baseplate is oriented so that both SH‐ and SV‐waves reach the geophone. Second, the SV‐wave polarization deviates significantly from perpendicular to the raypath. Both results may significantly affect the interpretation. Both are found to agree with theoretical results and are modeled successfully by synthetic seismograms.
Use of autoconvolution to suppress first‐order, long‐period multiples
Authors: Tsai C. J.
Published: October 2002

A common problem in interpreting marine seismic data is the interference of water‐bottom multiples with primary reflections containing the structural or stratigraphic information. In deep ‐water areas, where considerable primary energy arrives before the first simple water‐bottom multiple, weak and deep crustal reflections are often obscured by the first‐order water‐bottom multiples. In order to obtain a more interpretable section, a technique involving a two‐step process was developed to suppress the first‐order water‐bottom multiples. First, the relation between the zero‐order, water‐bottom primary and its first‐order, simple water‐bottom multiple is used to derive statistically an inverse of the seismic wavelet in order to remove its effect, i.e., to wavelet‐shape the data. This wavelet processing provides a band‐limited estimate of the subsurface impulse response. The second step consists of using the autoconvolution of the wavelet‐shaped primary energy to estimate deterministically and subtract the actual first‐order, water‐bottom multiples, The method was applied to field data from the deep Gulf of Mexico. Different incidence angles for the input primaries and multiples, as well as dipping reflecting interfaces, introduce uncompensated traveltime errors. These errors reduce the ability to suppress multiples, thus restricting the validity of the method to low frequencies where common‐depth‐point stacking is less effective. On the other hand, curved interfaces may also cause amplitude prediction problems. In spite of this, the first‐order, water‐bottom multiple energy is significantly reduced (by up to 18 dB) on dip‐filtered, single‐channel data.
Plane‐wave Q deconvolution
Authors: Bickel S. H. , Natarajan R. R.
Published: October 2002

Often the information content of measured signals from distance sources is hidden, because the signal distorts, weakens, and loses resolution as it propagates. For seismic energy traveling in the earth, these propagation effects can be approximated by the constant (frequency‐independent) Q model for attenuation and dispersion. For a propagating plane wave, this model leads to a spatial attenuation factor that is an unbounded function of frequency. Consequently, the broadband inverse of the constant-Q filter does not exist. For a fixed distance between the source and receiver the effects of the propagation path can be deconvolved (removed) within the seismic band by reversing the propagation of the plane wave. This propagation reversal is done by a time reversal with Q replaced by —Q, thereby changing absorption to gain in the complex wavenumber. Normally, measured seismic traces contain returns from a variety of depths. The interference of waves with different amounts of attenuation complicates the inversion process. From a superposition of plane waves with reversed propagation, a general inverse to an attenuation earth filter is proposed. To account for the increased attenuation with depth, the plane‐wave inverse filter is now time‐varying. This time‐varying inverse filter has a simple Fourier integral representation where the wavenumber is complex, and the direction of propagation is chosen such that the wave is growing rather than attenuating with distance. To control the wavelet side lobes a frequency‐domain window function (Hanning window) is applied to the trace. This two‐step plane‐wave deconvolution scheme was demonstrated to be superior to conventional deconvolution procedures. Tests with field data indicate the method is effective in removing attenuation effects from both VSP (Vertical Seismic Profile) and surface measurements. Phase distortions are eliminated and interference between events is reduced within the seismic band. This inverse is nearly exact for events where the time‐bandwidth (propagation time‐signal bandwidth) product is less than the effective Q. For depths where the time‐bandwidth product is greater than [Formula: see text] large wavelet side lobes appear. The wavelet side lobes can be partially suppressed by tapering the edges of the spectrum. However, the large side lobes of wavelets from shallow reflectors limit the bandwidth that can be recovered from the deeper events to aproximately [Formula: see text], where t is the propagation time to the event. Advances in the inversion algorithm (e.g., a Wiener filter could be used in place of the Hanning window to control side lobes) could probably improve upon our results, but in most cases even a small amount of measurement noise limits the reflection sequences to time‐bandwidth products that are less than twice the effective Q.
Tracing of rays through heterogeneous media: An accurate and efficient procedure
Authors: Langan R. T. , Lerche I. , Cutler R. T.
Published: October 2002

We present an accurate and computationally efficient method for tracing rays through a medium of heterogeneous velocity. Efficiency is obtained through approximations, while accuracy is maintained by using higher‐order terms in the approximations when necessary. The method was developed as part of a general seismic inversion technique for traveltime information where the medium is discretized into rectangular cells, each of which is characterized by a velocity gradient. However, as a stand‐alone tool for forward modeling this method may be applied to other cell geometries and the velocity field need not be a linear function of position in each cell. We use path length as the independent variable rather than position or orientation. The position, orientation, and traveltime of the ray are algebraic expressions of path length, so that trigonometric functions are avoided. If either position or orientation is used as the independent variable, trigonometric expressions invariably arise in evaluating the dependent variables. Such transcendental functions are computationally inefficient in large problems.
Computation of residual statics using projectors
Authors: Čaklović Koraljka , Čaklović Lavoslav
Published: October 2002

The residual statics problem, as we know, is treated as the solution of one linear system of equations. If we assume that the static corrections are “surface consistent,” then we know that time shifts of each trace can be written as the sum of three terms [Formula: see text] where i = 1, …, [Formula: see text] is the shot position index with [Formula: see text] the number of shot positions, j = 1, …, [Formula: see text] is the receiver position index with [Formula: see text] the number of receiver positions, k = 1, …, [Formula: see text] is the common‐depth‐point (CDP) position index with [Formula: see text] the number of common depth points, [Formula: see text] = correction for ith shot position, [Formula: see text] = correction for jth receiver position, and [Formula: see text] = correction for each trace in the kth CDP gather. For every pair (i, j) we have one equation. We write system (1) in matrix form as [Formula: see text] where [Formula: see text] is the vector of unknown parameters; and [Formula: see text] is the vector which consists of the time shifts obtained by crosscorrelation of each trace in CDP gather with the corresponding reference trace.
Acoustic multipole sources in fluid‐filled boreholes
Authors: Kurkjian Andrew L. , Chang Shu‐Kong
Published: October 2002

Acoustic well logging methods historically have been based on the excitation and reception of axisymmetric wave phenomena in a fluid‐filled wellbore. We consider the reception of nonsymmetric wave phenomena excited by acoustic multipole sources. The first three orders of multipoles are the monopole, dipole, and quadrupole, and we examine these particular sources in detail. Existing sonic tools make use of a monopole source, while more recently, both dipole and quadrupole sources have been explored. An exact frequency‐wavenumber domain representation of the acoustic field in the borehole due to a multipole source is formulated and numerical methods are used to compute synthetic space‐time domain waveforms. We consider wideband monopole, dipole, and quadrupole excitations with center frequencies of 1, 4, and 12 kHz, and treat both slow and fast formation models. Finally, we derive low‐frequency, far‐field asymptotic expressions for the monopole, dipole, and quadrupole waveforms. At frequencies such that the shear wavelength is on the order of the borehole diameter or less, the difference between the monopole, dipole, and quadrupole waveforms is primarily in the nature of the surface wave mode which they excite: the monopole excites a Stoneley, or tube mode; the dipole excites a flexural mode; and the quadrupole excites a screw mode. By comparison, the compressional and shear head waves and the trapped waveguide modes do not change as much as the order of the multipole is changed. At low frequencies, where the shear wavelength is much longer than the diameter of the hole, the monopole excites a dominating tube mode, while the dipole and quadrupole excites dominating shear waves. Low‐frequency asymptotic expressions for the waveforms agree well with the numerically computed waveforms.
An objective real‐time data‐adaptive technique for efficient model resolution improvement in magnetotelluric studies
Authors: Jones Alan G. , Foster John H.
Published: October 2002

A scheme is described whereby the error associated with the least well‐resolved model eigenparameter in a magnetotelluric survey is reduced by focusing data collection on a specific range of frequencies. The scheme also gives a quantitative estimate of the statistical error associated with the least well‐resolved model parameter, and thus provides an objective criterion to the operator regarding when to cease data collection at that location. The scheme is based on a linearization of the relationship between variations in the model parameters and the changes thereby introduced to the computed response function. The matrix of partial derivatives describing this linearization is factored orthogonally by a singular value decomposition. The scheme is illustrated by applying it to a synthetic data set. Also, the algorithm has been coded in Basic on an HP9845 and employed in the field. An example is given of its field operation in a sedimentary basin environment.
Map displays from an interactive interpretation
Authors: Denham J. I. , Nelson H. Roice
Published: October 2002

Map displays built during interactive seismic interpretation provide information not obtainable with traditional mapping techniques. Several map displays derived from the 1983 interactive interpretation of a Gippsland Basin three‐dimensional (3-D) seismic survey are presented below. Similar map display results have since been obtained with the interactive interpretation of two‐dimensional (2-D) seismic surveys. These types of mapping results are among the most important contributions of interactive interpretation procedures.
Two‐dimensional topographic responses in magnetotellurics modeled using finite elements
Authors: Wannamaker Philip E. , Stodt John A. , Rijo Luis
Published: October 2002

We simulate the magnetotelluric response to two‐dimensional earth topography using finite elements. Linear interpolation of the secondary field parallel to strike over triangular elements allows accurate modeling of inclined resistivity boundaries, including topographic surfaces. To avoid discontinuities in field derivatives or resistivity, care must be taken that the nodal values of the field parallal to strike used to obtain the auxiliary secondary fields are kept within uniform earth media. The nodal locations may be shifted, but the derivatives still are evaluated at the field points of interest. Correct values may be returned at gentle breaks in slope as well as along straight surfaces. The finite‐element program is verified by comparison with the analytic transverse magnetic response of a hemicylindrical depression and with Rayleigh scattering and transmission surface results for transverse electric and transverse magnetic polarization. Agreement with the other methods generally is excellent, with the exception of some results of the transmission surface technique (especially the transverse magnetic mode). A result presented shows that placing the H-field sensors horizontally reduces topographic anomalies compared to locating sensors parallel to the slope. Moreover, if earth resistivity increases with elevation, the apparent resistivity is relatively nonanomalous near the base of the topography.
Reply by the author to T. R. LaFehr and K. C. Chan (Discussion on “The normal vertical gradient of gravity”GEOPHYSICS, 48, 1011–1031, July 1983; discussion GEOPHYSICS, 51, 1505–1508, July 1986).
Authors: Karl J. H.
Published: October 2002

Frequently, geophysical methods can be useful to those without detailed knowledge of physics: buried conducting objects can be found by a beachcomber using only a crude metal detector, conducting ore bodies can be located with an EM instrument, distinct basement units can be mapped on an aeromagnetic map as magnetic terrains, and salt domes are apparent on gravity maps of the Gulf Coast. In all of these cases, anomalous values of some measurement stand out distinctly against their background values. However, this is not the case with ground gravity surveys in areas of high topographic relief where elevation corrections can be far greater than the target anomalies.
Resolution of ambiguities of seismic refraction traveltime curves
Authors: Ackermann Hans D. , Pankratz Leroy W. , Dansereau Danny
Published: October 2002

Ambiguities are inherent in seismic refraction traveltime curves based on first arrivals recorded from a multi‐layered medium. Even for reversed profiles, inflections of traveltime curves caused by the onset of arrivals from successively deeper horizons frequently cannot be delineated from those caused by lateral geologic changes. In addition, the secondary arrivals which may represent essential portions of a traveltime curve are not available. Numerous inversions having different geologic implications are possible. Ambiguities may be resolved by using multiple shotpoints for each spread and combining their individual first‐arrival traveltime curves to yield a consistent set of curves for each refracting horizon. A set of rules applies for combining individual traveltime curves based on reversed, split, and offset profile configurations. The combined curves lend themselves to a unique inversion.
The special features of P-S arrivals
Authors: Nedlin G.
Published: October 2002

There is no reciprocity in the arrival times for P-S reflections, i.e., arrival times are different if the locations of the shot and geophone are exchanged. For P-S reflections in CMP panels, this results in terms in the arrival times [Formula: see text] which are linear in offsets [Formula: see text] The principle of reciprocity still holds if the medium is laterally homogeneous and the reflectors are horizontal. For a laterally homogeneous‐earth model, with a nonhorizontal reflector, the analysis of [Formula: see text] curves for P-S arrivals, particularly for terms linear in x, provides new opportunities for obtaining information about local (near the reflector) velocities and velocities which have been averaged over depth. If there is a dipping reflector (or if there is a lateral variation of earth parameters) the coincident shotgeophone P-S reflection does not correspond to the normal incident angle. Therefore, for coincident locations of the shot and geophone, there exists a converted S-wave of nonzero amplitude.
Stabilization of bottom‐hole temperature in the presence of formation fluid flows
Authors: Ribeiro F. B. , Hamza V. M.
Published: October 2002

Reliable estimates of bottom‐hole temperature (BHT) in oil wells are of considerable interest in reservoir engineering problems as well as in geothermal research. Because BHT measurements are usually made soon after drilling, true formation temperature can be obtained only by correcting for the effects of drilling disturbances. The magnitude of drilling disturbance depends upon duration of drilling, time elapsed after stoppage of drilling, well characteristics, thermal properties of drilling fluid, and the nature of heat exchange between the well and the formation.
Magnetic prospection on prehistoric sites in Western Canada
Authors: Gibson Terrance H.
Published: October 2002

Prehistoric sites in Western Canada present unusual conditions for magnetic prospection. Archaeological features are few and difficult to discern using standard prospection procedures. However, by addressing specific types of features, particularly fire hearths and fired rock and pottery, useful information about the cultural content of an archaeological site can be obtained. To secure comparative data, a number of replicative studies were conducted, with specific reference to determining a typical anomaly produced by the features. A small fire pit was kindled several times and repeatedly monitored with surveys using a single proton magnetometer. Fired rock received similar treatment. An in situ collection of local aboriginal pottery was also assayed. The experimental results indicated that fired rock will produce a detectable magnetic field after one firing, but a hearth must be rekindled at least three times to produce a significant anomaly. Pottery fragments also generate a small magnetic field which requires that the material be very close to the site surface to be discerned. The experiments also suggested that intepretation is enhanced by obtaining two magnetic readings per sensor station and using their difference to minimize ambient field fluctuations and natural magnetic variation caused by subsurface geology. The model data were used to interpret the results of a magnetic assessment of a large prehistoric campsite in Saskatchewan. Excavation results agreed well with the information provided by the predictive models. Two temporary dwelling remnants and two pottery vessels were exposed in areas determined to be magnetically significant. The magnetic assessment technique, when used to locate specific feature types, can be useful in prehistoric archaeological site assessment.
New prospects in shallow depth electrical surveying for archaeological and pedological applications
Authors: Hesse A. , Jolivet A. , Tabbagh A.
Published: October 2002

Three different improvements in the galvanic method of shallow‐depth electrical prospecting need to be made. (1) A better definition of the electrode array(s) is needed in order to reduce the “apparent anisotropy” effect and increase the depth of investigation; the square array is one solution. (2) A resistivity meter that can make measurements very rapidly needs to be built. The rapid decrease of the induced electric field for small electrode distances makes such measurements possible. We propose a resistivity meter with an 8 ms measurement time. (3) The electrode‐ground contact problem needs to be solved by using a resistivity meter that can endure high contact resistances. As an alternative solution, we also propose a new type of electrode: a liquid jet one. These improvements could make the resistivity method very attractive and competitive, and open large future developments for the method.
Layers and bright spots
Authors: Almoghrabi H. , Lange J.
Published: October 2002

Seismic amplitudes are affected by both geometric and lithologic features of reflecting layers. Observation of “bright spots” is a function of not only pore fluid saturations, but also of layer thickness and surrounding rock type. The numerical model developed uses a finite sum of reflected and mode‐converted waves to evaluate the application of wave analysis in determining pore fluid types. Amplitude analysis alone is not sufficient to define realistically pore fluid type, but when amplitude analysis is combined with phase and mode‐converted shear‐wave behavior, it is possible to differentiate between pore fluid types. Various configurations which lead to bright spots, including coal and limestone layers, are evaluated. An algorithm is developed, based on the numerical examples, which can differentiate gas zones from other bright spot data. Thickness of the plane layer is an important factor in defining the overall reflectivity due to interference of the reflected wave components. Gas saturation of a layer is not a sufficient condition for a bright spot, but can lead to “dull spots” for layers in the right thickness range (relative to the incident wavelength). The lithology of the boundary material determines the extremes in amplitude variation which result when thickness or wavelength is varied. If a priori knowledge of the lithology or thickness of the structure is available, the amplitude‐phase‐converted wave algorithm can be applied to other than bright spot data to characterize the structure. This indicates there are important applications of the amplitude‐phase‐converted wave algorithm to field development and to bright spot analysis for exploration.
Theory of induction sonde in dipping beds
Authors: Hardman R. H. , Shen L. C.
Published: October 2002

The analysis necessary for the computation of the response of an induction sonde in dipping beds is developed. The boundary‐value problem solved is for a bed of uniform thickness surrounded by two infinitely thick shoulder beds. The source is a magnetic dipole oriented in an arbitrary direction and located in any of the three media. The resulting electromagnetic fields in all three media are obtained. From these fields, induction logs are calculated for a focused induction sonde (6FF40) passing through a dipping bed. Under the assumptions of negligible borehole effect and no invasion, the analysis is also used to obtain correction charts for dipping beds.
Noise suppression by the radial amplitude‐slope rejection method
Authors: Neff D. B. , Wyatt S. B.
Published: October 2002

Raw geophysical data generally contain spurious noise values which, if not removed, can seriously degrade any results obtained when the data are processed. Such spurious values may be caused by “environmental” noise generated externally to the data‐gathering equipment; introduced by the data‐gathering equipment; or introduced during preliminary data‐handling (tape copying, etc.) processes. Data‐manipulation steps, such as the conversion of raw stacking velocities to interval velocities, can also generate noise components which must be removed before the results can be utilized reliably.
International Geomagnetic Reference Field Revision 1985
Authors:   IAGA, Division I, Working Group 1–1, Peddie Norman W.
Published: October 2002

IAGA Division I, Working Group 1 deals with the topic “Analysis of the Main Field and Secular Variations.” One of the more important functions of the working group is the periodic revision of the International Geomagnetic Reference Field (IGRF). The thirteen members of the working group have professional interests covering a broad spectrum of geomagnetic science, including the theory and practice of geomagnetic analysis and modeling, the theory of the origin of the magnetic fields of the Earth and other bodies, the theory of geomagnetic secular variation, the application of field models in magnetic survey data processing, and geomagnetic charting.
Inversion of P-SV seismic data
Authors: Carazzone James J.
Published: October 2002

In a layered elastic material, density, shear velocity, and compressional velocity can be found at any depth from broadband surface measurements at two distinct, nonzero, precritical values of plane‐wave incidence angle. Layer‐stripping inversion uses three‐component surface velocity measurements generated by a polarized surface source to determine subsurface properties incrementally. The surface velocity measurements initialize a first‐order, nonlinear, matrix Riccati equation (derived from the elastic wave equation) which takes advantage of an attractive fixed‐point condition in the complex frequency plane to extract subsurface mechanical impedances. Subsurface density and velocities are recovered from the inverted impedances at two or more plane‐wave incidence angles. General properties of the matrix Riccati equation in the complex frequency plane aid in incorporating bandwidth constraints. Inversion of synthetic plane wave data from a piece‐wise continuous model illustrates inversion effects when only a finite bandwidth is available and when different compressional and shear wavelength distance scales are present.
Transition zone reflections and permafrost analysis
Authors: Justice James H. , Zuba Chris
Published: October 2002

The usual study of seismic reflections is limited to those from sharply defined contrasts in acoustic impedance. For reflections resulting from transition zones in which acoustic impedance is continuously variable (such as the zones encountered in permafrost), the frequency‐selective nature of attenuation and phase distortion leads to a number of characteristics which may be used in the sense of pattern recognition to identify such reflections. An rms velocity‐analysis procedure can be used to estimate depths and velocity gradients associated with transition zones. Some simple approximations allow us to avoid solving a system of nonlinear equations in many cases of interest, and the result is a practical technique which can be applied to many transition zone reflections at reasonable computational cost.
Convergence of iterative gravity inversion
Authors: Granser Harald
Published: October 2002

Oldenburg (1974) presented an iterative inversion procedure based on (a rearrangement of) Parker’s (1973) formula for rapid calculation of the gravity anomaly caused by an uneven layer; the algorithm proved effective in practice (Sprenke and Kanasewich, 1982). Nevertheless, Oldenburg stated that straightforward application of the iterative procedure usually results in a divergent solution characterized by high‐frequency oscillations. Only in special cases (when the gravity anomaly can be accounted for by a layer with sufficiently small relief) is convergence obtained. However, Oldenburg did obtain convergence after suitable low‐pass filtering of the gravity anomaly. A criterion is derived to assure convergence of the iterative procedure. This criterion is concerned with the high‐frequency content of the layer’s topography and explains the results Oldenburg found empirically.
Fluid and solid motion in the neighborhood of a fluid‐filled borehole due to the passage of a low‐frequency elastic plane wave
Authors: Schoenberg Michael
Published: October 2002

The exact problem of the interaction of an arbitrary plane wave in a homogeneous elastic medium with a fluid‐filled circularly cylindrical borehole is formulated to analyze three‐axis, full‐waveform borehole seismic data. The plane elastic wave (which may be incident upon the borehole from any direction) is partially scattered around the hole and an acoustic field is induced in the borehole fluid. Since seismic wavelengths tend to be much larger than diameters of boreholes, the exact solution may be expanded in powers of Ω (a small number), the incident wavenumber times the borehole radius. In the limit as Ω→0, the scattered field in the elastic medium is of O(Ω); in this limit the borehole crosssection is undistorted and moves with the velocity of the incident wave as if no borehole were present. Neglecting terms proportional to [Formula: see text] or higher leaves three kinds of θ‐dependent terms, where θ is the azimuthal angle about the borehole axis measured with respect to the wavenumber vector of the incident wave. Terms independent of θ (n = 0) give radial motion for incident P- or SV-waves, or rotational motion for incident SH-waves, and fall off as inverse distance from the borehole axis, i.e., 1/r. Terms proportional to cos θ for incident P- or SV-waves or sin θ for incident SH-waves (n = 1) give axial motion that falls off as 1/r. Terms proportional to sin 2θ or cos 2θ (n = 2) give motion in the plane perpendicular to the borehole axis, part of which falls off as 1/r and part as [Formula: see text]. At the borehole wall, the n = 2 terms express the deformation of the borehole cross‐section into an ellipse whose major and minor axes interchange as the wave passes. In the limit as Ω→0, the fluid velocity is constant over the borehole cross‐section. In the plane perpendicular to the borehole axis the fluid is constrained to move with the solid. However, in the axial direction the fluid velocity differs from that of the borehole wall for incident P- or SV-waves (for incident SH-waves the axial fluid and solid velocities both vanish as Ω→0). The ratio of axial fluid velocity to axial solid velocity at the borehole wall, for given elastic medium and acoustic fluid properties, is a function of both the wave type and the angle between the incident wavenumber vector and the borehole axis. Further, for incident P-waves, the axial fluid and solid velocities are in‐phase while for incident SV-waves, they are 180 degrees out‐of‐phase. Thus, as a plane wave passes a given level in a fluidfilled borehole, the plane‐wave type and (for P- or SV-waves) its angle of propagation relative to the borehole axis are theoretically obtainable by measuring fluid and solid axial velocities at that level.
Design and applications of optimum multichannel linear moveout filters
Authors: Özdemir Hüseyin
Published: October 2002

Practical aspects of the optimum multichannel least‐squares (OMLS) linear moveout filter design parameters are investigated by examining them in the frequency‐wavenumber domain and applying them to simulated and field reflection seismograms. The results of these studies show that the so‐called “chatter parameter” should be omitted from the input design models of the OMLS moveout filters. Random noise relative weightings of about 0.3 to 0.5 are adequate for stabilizing the autocorrelation matrix of the normal equations. Linear moveout filters with weights higher than 0.5 act as high‐frequency filters and reduce the resolution of the data. A serious limitation of the OMLS linear moveout filters for seismic reflection applications is aliasing of the reject moveout window into the pass window which prevents weightings of the reject moveout window from being much higher than for pass‐moveout windows when higher weightings are required in practical applications such as grand‐roll reduction. Simulated data indicate that multichannel filtering is superior to stacking in improving the ratio of signal to correlated noise, especially when there are large static shifts in the input traces.
On: S. Hammer and M. J. Hall’s discussions on “Airborne gravity is here” by S. Hammer (GEOPHYSICS, 50, 170–171, January, 1985).
Authors: Davies F. Bryan
Published: October 2002

In response to Professor Hammer’s reply to his critics, surely the central discussion is the correct application of signal processing practice applied to the science of gravity prospecting.
On: “The normal vertical gradient of gravity” by J. H. Karl (GEOPHYSICS, 48, 1011–1013, July 1983).
Authors: LaFehr T. R. , Chan Kwok C.
Published: October 2002

In his reply to C. J. Swain’s (1984) discussion Karl states that no one has disagreed with his proposed (0.265 mGal/m) “average value” for the normal gravity gradient and that his global terrain model can be used to challenge the validity of the traditional approach to data reduction. Our investigations show that Karl is in error on both counts, and we hope that the following analyses will help toward a clearer understanding of this question.
Electrical conductivity of brine‐saturated fractured rock
Authors: Stesky R. M.
Published: October 2002

A theoretical analysis shows that electrical conductivity along fractures in a saturated porous rock is a function of many factors: fluid and rock conductivities, initial fracture aperture and contact area, fracture surface geometry (asperity height distribution and tip curvature), elastic moduli of the rock, and confining pressure or normal stress acting across the fracture. The conductivity in the fracture plane decreases approximately in proportion to log pressure, but the conductivity is influenced by the increased contact area, and hence flow‐path tortuosity, along the fracture surface at elevated pressures. Electrical conductivity in fractures is more affected by flow‐path tortuosity than is permeability. The dependence on pressure was tested using laboratory measurements of conductivity through split cores containing ground, saw‐cut surfaces in a variety of rocks under confining pressures to 200 MPa. The conductivity decreased approximately in proportion to log pressure (there was little effect of increased contact area, and hence tortuosity), which suggests that the contact area may not exceed a few percent of the total apparent area. Measurements of gas permeability through the same split cores showed that when the asperity deformation remained largely elastic, permeability and conductivity had a power of 3 relationship. When asperity collapse occurred, as in a dolomitic marble, the powerlaw relation no longer held; permeability decreased more rapidly under pressure than did conductivity. The different influences of porosity and flow aperture may account for the different behaviors of the two transport properties. The theory suggests a number of ways in which fracture parameters may be extracted from field data. Some of the methods rely on the scale dependence and pressure dependence of the fractured‐rock conductivity; other methods require correlating between different physical properties, such as seismic velocity, which are influenced by the presence of fractures.
Inversion of magnetotelluric data using localized conductivity constraints
Authors: Whittall Kenneth P.
Published: October 2002

I present an algorithm for the one‐dimensional magnetotelluric inverse problem of finding conductivity as a function of depth in the earth. The algorithm uses linear programming to solve an integral form of a nonlinear Riccati equation. This iterative scheme sacrifices the efficiency of direct inversion for the overwhelming advantages of incorporating localized conductivity constraints. I use localized conductivity constraints in two ways to combat the nonuniqueness of the nonlinear inverse problem. First, I impose physical constraints derived from external sources to restrict the nonuniqueness and construct conductivity models that are closer to reality. Second, I impose arbitrary constraints in an effort to assess the extent of nonuniqueness and explore the range of acceptable profiles. The first technique enhances the reliability of an interpretation, and the second measures the plausibility of particular conductivity features.
Alternative processing techniques and data improvement provided by single‐sweep recording
Authors: Belcher Steven W. , Pratt Thomas L. , Costain John K. , Çoruh Cahit
Published: October 2002

The conventional procedure used to acquire Vibroseis® seismic reflection data is to sum in the field the contributions from several vibrator sources distributed over the source array. An alternative method of recording the data which provides more flexibility in the processing is to record the output from each pad position in the source array rather than summing in the field. Prewhitening these data before summing can improve the signal‐to‐noise (S/N) ratio. If cancellation of surface waves by a source array is not a requirement, then processing each sweep as a separate source point can result in increased lateral resolution. These procedures were applied to seismic data over a buried rift basin in the southeastern United States. The results demonstrate improvement in the S/N ratio and spatial resolution that enable better interpretation of the complex, internal geometry of the basin.