bluuebunny/crossref_metadata_2025 huggingface dataset:
Attenuation and anisotropy of channel waves in coal seams
Authors: Buchanan D. J. , Jackson P. J. , Davis R.
Published: October 2002

In recent years channel‐wave seismology has shown itself to be a useful aid to coal mining. Small geologic faults which interrupt a coal seam can seriously disrupt mining by modern longwall methods. Such features have been accurately predicted at distances of several hundred meters by underground seismic surveys. The useful range of the method in a particular seam depends critically on the rate at which channel waves in the frequency range of interest (50 to 500 Hz) are attenuated during passage through the coal; when no faulting is located by a given survey, it is always important to know at what range a fault would have been detected had it been present. To this end, the attenuation characteristics must be studied. Frequently, coal seams are highly anisotropic wave‐guides. Perpendicular to the bedding plane one or two “cleat” or cleavage planes exist, along which the coal is extensively cracked and jointed. Recent work by Crampin (1978, 1981) and by Hudson (1981) has shown that such systems of parallel cracks in crustal rocks lead to anisotropic propagation of body waves, with both velocity and attenuation varying considerably as a function of angle of travel through the cracked medium. The polarization of seismic energy propagating through such media can no longer be defined as simple shear or compression. It is reasonable to expect that guided channel waves in coal seams will exhibit similar properties. A number of transmission surveys have been carried out to investigate both attenuation and anisotropy. The principal requirement for such surveys is that in‐seam shot and geophone arrays be designed to provide a large range of both source‐detector distance and angle of travel through the coal. Given this condition, anisotropy of group velocity can be detected by adapting Dziewonski’s multiple filter analysis of single traces to transmission stacking over selected raypath angles (Dziewonski et al, 1969); attenuation similarly can be investigated by a least‐squares regression of the logarithm of the amplitude spectrum of a particular mode onto the path length. The methods and results of these investigations are reported here, the significance of anisotropy for the collection and processing of in‐seam data is discussed, and consideration is given to the type and size of errors introduced into the position of fault predictions made on the basis of an isotropic model. The equivalence of Fermat’s principle and Snell’s law for anisotropic raypaths results in a computationally efficient modification to enable our previously reported dynamic trace gathering (DTG) stacking procedure to be used for such data.
Seismic reflections from a gas‐water contact
Authors: Dutta N. C. , Odé H.
Published: October 2002

Using the Biot theory, we have performed calculations to show that viscous fluid flow affects seismic wave amplitudes and reflection coefficients at a gas‐water boundary in a porous sand reservoir. Our formulation of the boundary value problem for fluid‐filled porous rocks is applicable at all angles and follows parallel to the classical reflection and transmission problem solved by Knott, Zöeppritz, and others for two elastic media in perfect contact. It is pointed out that there are two major differences between the two: (1) in the present case, we deal with the propagation of inhomogeneous waves, and (2) there are interference fluxes of energy between various types of waves. The latter exists only at an oblique incidence. In our model, loss of seismic energy is mainly due to mode converted type II waves of Biot at the gas‐water contact which propagate away from the boundary in the manner of a diffusion process at low frequencies. Both seismic energy loss and reflection coefficients are studied over a wide range of frequencies and angles of incidence. We find that for a porous unconsolidated sandstone [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] the energy loss associated with a single gas‐water boundary is approximately 2.5 percent at 100 Hz for P‐waves incident at 30 degrees and that the loss increases with frequency as [Formula: see text]. Further, at a given frequency, the loss of energy is minimal at normal incidence (∼1.2 percent at 100 Hz) and maximal (∼6 percent at 100 Hz) in the neighborhood of the critical angle (∼42 degrees). We find that the inelastic losses are significantly higher at the frequencies at which seismic logging tools operate (50 percent at 10 kHz near the critical angle). As far as the amplitude reflection coefficients are concerned, we find that the effect of the fluid flow across a single gas‐water boundary is to reduce the reflection coefficient with increasing frequency (when the wave is incident from the gas saturated rock) at all angles of incidence. In the exploration frequency band, the reduction is about 1.5–3 percent, whereas the reduction is approximately 40–50 percent in the logging frequency band. For high frequencies (10 kHz and higher) classical interpretation breaks down, and hence it appears that for frequencies at which the seismic logging tool operates corrections should be made to the classical theory.
Resistivity/depth mapping with airborne electromagnetic survey data
Authors: Sengpiel Klaus‐Peter
Published: October 2002

Using the homogeneous half‐space as a universal interpretation model, all of the secondary field data obtained with a single‐frequency airborne electromagnetic (EM) system that satisfies the superposed dipole condition can be converted to the model parameters [Formula: see text] (apparent resistivity) and [Formula: see text] (apparent depth). These parameters have been investigated for their behavior above various conductivity models and at various flight altitudes, first for theoretical examples and then for several applications in the field. The values of [Formula: see text] and [Formula: see text] are good approximations of the true resistivity and true depth of an extended, buried conductor only where the shielding effect of the cover is small. Moreover, a depth value has a meaning only within the lateral limits of a target conductor. A method is described to locate these lateral limits and to select acceptable depth and resistivity values by means of the “area of [Formula: see text],” which is derived from the horizontal gradient of log [Formula: see text] and the maxima of [Formula: see text]. The results of the resistivity/depth mapping method are presented in the form of two contour maps. Examples of the practical application of the method, over known sulfide ore bodies and over a salt water intrusion, show that reliable data can be obtained on the depth, dip, and extent of these kinds of conductors, as well as on the approximate resistivity of the conductors and the host rock.
Werner deconvolution of profile potential field data
Authors: Kilty Kevin T.
Published: October 2002

Werner (1953), in analyzing the magnetic fields of dipping, magnetized dikes, proposed a method of separating the field contributed by a particular dike under study from the interference of neighboring dikes. In addition to being a means of effecting a regional‐residual separation, Werner’s method of analysis also had the advantage of being easily programmed on a digital computer. This made it a convenient method for analyzing the large amounts of data from reconnaissance aeromagnetic surveys, and it became the basis of the automatic interpretation schemes of Hartmann et al (1971) and Jain (1976). The purpose of this note is to discuss some limitations of the Werner method of deconvolution and also to point out some possible extensions of the method to the general interpretation of potential field data.
Lattice filtering applications to deconvolution of seismic data
Authors: Robinson John C.
Published: October 2002

Lattice digital filtering techniques have only recently been exposed to any significant extent through the technical literature, primarily in articles not directly related to reflection seismology. The most basic “all‐zero” lattice filter dates back only around a decade. This paper first reviews current technology in adaptive lattice filtering from the standpoint of seismic deconvolution. An “all‐pole” deconvolution technique is developed next; then a new “pole‐zero” lattice is adapted to seismic deconvolution, and operational methodologies for its effective implementation and stabilization are developed. Some advantages of deconvolution by lattice filtering and other potential applications of lattice filters to seismic data processing are suggested. The adaptive abilities and effectiveness of seismic deconvolution by the three lattice types are tested and compared with stationary Wiener deconvolution. The test data, are realistically nonstationary, thus allowing all three of the adaptive lattice filters to perform favorably in comparison to the nonadaptive or stationary Wiener filter.
A least‐squares approach to depth determination from gravity data
Authors: Gupta O. P.
Published: October 2002

The present paper deals with a numerical approach to determine the depth of a buried structure from the residual anomaly. The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of the form [Formula: see text]. Formulas have been derived for a sphere, vertical and horizontal cylinders, and for a vertical fault (thin plate approximation). The procedure is applied to synthetic data with and without random errors. Finally, a field example is presented in which the depth to a fault is estimated at 3.8 km and verified from drilling results.
Analysis of aeromagnetic measurements from the Cascade Range in central Oregon
Authors: Connard G. , Couch R. , Gemperle M.
Published: October 2002

Shallow Curie‐point isotherm depths, indicated by the analysis of magnetic anomalies, young silicic volcanism, hot springs, and high heat flow mark the Cascade Range of central Oregon as a potentially important geothermal resource area. Aeromagnetic measurements in the central Cascades between 43°00′ and 44°15′N latitude and 121°00′ and 122°30′W longitude exhibit predominant northwest‐southeast lineations and less prominent north‐northeast by south‐southeast lineations. Longer wavelength components of the magnetic anomalies (greater than 25 km), possibly related to deeper sources, trend approximately north‐south parallel to the Cascade Range. Magnetic anomalies show a right‐lateral offset of the High Cascades Volcanism at 43°30′N latitude, which is consistent with the tectonic structures of the Basin and Range province southeast of the area. Magnetic source depth calculations show that the High Cascades occupy a structural depression or graben on the eastern side of the Western Cascades. Spectral analysis of the magnetic anomalies suggests that the High Cascades are underlain by Curie‐point isotherm depths as shallow as 9 km. These shallow Curie‐point isotherm depths imply thermal gradients greater than 50°C/km and surface heat flow greater than [Formula: see text].
Predictive deconvolution in shot‐receiver space
Authors: Morley Larry , Claerbout Jon
Published: October 2002

Standard predictive multiple suppression techniques in marine reflection seismology usually resort to one‐dimensional assumptions about the underlying earth model. The methods presented here use a multiple model which assumes vertical incidence propagation in the water layer, yet relaxes common assumptions of zero offset and zero dip. In particular, different reflectivities and water depths are assumed at source and receiver locations. One of these methods, seafloor‐consistent multiple suppression, models each seismic trace as a convolution of an average frequency response with anomalous shot, geophone, midpoint, and offset responses. In the log‐frequency domain, this becomes a separable, additive model which can be solved by linear least‐squares techniques. The anomalous amplitude responses are solved for each frequency in “shot‐receiver” space with frequency as the outer loop of the algorithm. Once the seismic data set has been resolved into average and anomalous amplitude responses, the multiple reverberation response is identified with the product of the anomalous shot and geophone responses. Since one can argue on physical grounds that the reverberation response for any particular trace must be minimum phase, it suffices to solve only for amplitude responses and ignore phase contributions. The methods are applied to a deep water marine seismic line from the Flemish Cap area of the Labrador Sea with extremely encouraging results.
A comparison of adjustment procedures for leveling aeromagnetic survey data
Authors: Green A. A.
Published: October 2002

Two techniques for leveling aeromagnetic survey data are compared. The first estimates a set of values for the magnetic intensity at each flight‐line/tie‐line intersection point. These are obtained after an intersection‐moving procedure to reduce loop closures and are subject to the constraint that the datums calculated from the differences between the raw data and the corrected data have minimum along‐line variation. The procedure (a least‐squares method) is equivalent to the older manual loop closure methods used for magnetic, gravimetric, and geodetic surveying. The second method involves the fitting of polynomials to the observed flight‐line/tie‐line intersection errors along each line in the survey. These are then subtracted from the raw data and intersection locations are adjusted to give minimum intersection errors. In the analysis of two surveys the least‐squares method was found to be superior as a leveling procedure. It produced datums which were similar in amplitude and had a high correlation with the base station magnetometer recordings. The polynomial method produced datums which had greater amplitudes and showed a tendency to fluctuate at the ends of lines.
Numerical study of Love wave propagation
Authors: Kelly K. R.
Published: October 2002

Love wave propagation is studied by investigating numerical modeling results for several examples of geologic interest. The modal characteristics of the results are clarified by the use of narrow band‐pass filters and two‐dimensional Fourier transforms in range and time. Such processing makes it possible to study changes in phase and group velocity for the various modes and to locate points of reflection. This permits one to gain insight into changes in the physical properties of the surface channel supporting the waves.
Finite‐difference calculations of the transient field of an axially symmetric earth for vertical magnetic dipole excitation
Authors: Goldman M. M. , Stoyer C. H.
Published: October 2002

A finite‐difference formulation of the coaxial‐loop or wire‐loop transient electromagnetic (EM) prospecting systems is used to model the fields from a buried cylindrical conductor whose axis is coincident with that of the field system. Solutions are obtained directly in the time domain. The formulation is implicit and two‐dimensional (2-D) in space. The variable‐directions method reduces each advance of one step in time from one 2-D problem to a large number of one‐dimensional (1-D) problems. The result is a reduction in computational effort. In order to avoid including the air in the finite‐difference grid, an integral equation approach is used to formulate the surface boundary condition. Thus, two sets of 1-D finite‐difference solutions and one Fredholm integral equation solution are required for each step forward in time. Comparison with analytical solutions shows excellent agreement in the case of a four‐layer earth. All computations were carried out for a perfectly conducting basement, but the method can be used for finitely conducting basement as well. If the basement is an insulator, an additional integral equation solution is required on the lower boundary. Results for a buried cylindrical conductor show that there is a high degree of sensitivity to conductor size. Inversion of transients to a stratified model can be useful if the effect of finite conductor size is taken into account. For cylindrical conductors with lateral extent comparable to or larger than the source‐receiver separation, the inversion results are valid. For conductors with lateral extent small compared with source‐receiver separation, the inversion will yield a stratified model which shows better agreement between actual and inverted thicknesses than resistivities. The involved resistivities are somewhat higher than those actually present in this case.
Structural inversion of salt dome flanks
Authors: May B. T. , Covey J. D.
Published: October 2002

Accurate location of the salt‐sediment interface is one of the first problems to be solved during exploration around salt domes. However, determination of salt boundaries from seismic data has been notoriously missing even though forward modeling has shown that the salt flank reflection can be one of the highest amplitudes on a seismic record. The sources of difficulty are that conventional data acquisition and processing are usually designed to attenuate any signal that arrives at high incidence angles, including reflections originating from steeply dipping structures such as salt flanks. For example, if regional stacking velocities are used during processing, the salt flank reflection can be so attenuated as to be unobservable. Inverse modeling by ray methods is known to be a suitable technique for reconstruction of steeply dipping structures, provided key marker reflections are identified. Salt flank reflections have been recovered in two field‐recorded examples through application of unusually high stacking velocities; the reflections characteristically have very large migration distances and cross other reflections at high angles. The inverse model computed for one example produced a salt flank with dip rates up to 70 degrees, and the computed structure compared to drilling data is accurate to within 1 percent. Results from the second example are also consistent with known geology but are more striking: dip rates of 90 degrees are achieved and the model shows a slight overhang of salt. These results show there is nothing in principle to prevent inversion of steeply dipping structures from surface‐recorded seismic data, including such extreme cases as overhanging salt domes.
The linear quadripole‐dipole array in geoelectrical investigations
Authors: Yadav G. S. , Singh C. L.
Published: October 2002

The use of a linear quadripole as an energizing source in geoelectrical prospecting stemmed from an idea of Corson and Lorrain (1962). It was applied as a square array in the experimental studies of resistivity modeling by Doicin (1976). In the present paper a similar energizing source is used and is designated a “linear quadripole source.”
Near‐surface faulting effects on seismic reflection times
Authors: Honeyman W.
Published: October 2002

The depth conversion of seismic reflection records has been the subject of many papers, particularly where faults or other geologic features are present. The common‐depth‐point (CDP) stacked seismic sections with large spread lengths of the order of 2 km have resulted in different interpretation problems. Al‐Chalabi (1979) considered the effect on stacking velocities of subsurface inhomogeneities where different rays in the CDP gather do not penetrate the same type of earth column. He showed that small time delays of 10 msec produce steps in the hyperbolic offset distance‐time curve of the CDP gather and produce stacking velocity variations of the order of ten percent. Levin (1973) considered a time delay in only one ray of the CDP gather and its effect on both stacking velocity and the zero‐offset time [Formula: see text]. This paper models the effect of near‐surface faults on the zero‐offset time [Formula: see text] of deeper layers as determined by the CDP method. This is particularly important since the zero‐offset time is plotted on the processed final record.
Computer simulation of low‐frequency electromagnetic data acquisition
Authors: San Filipo William A. , Hohmann Gerald W.
Published: October 2002

Computer simulation of low‐frequency electromagnetic (EM) digital data acquisition in the presence of natural field noise demonstrates several important limitations and considerations. Without a remote reference noise removal scheme, it is difficult to obtain an adequate ratio of signal to noise below 0.1 Hz for frequency‐domain processing and below 0.3 Hz base frequency for time‐domain processing for a typical source‐receiver configuration. A digital high‐pass filter substantially facilitates rejection of natural field noise above these frequencies; however, at lower frequencies where much longer stacking times are required, it becomes ineffective. Use of a remote reference to subtract natural field noise extends these low‐frequency limits by one decade, but the remote reference technique is limited by the resolution and dynamic range of the instrumentation. Gathering data in short segments so that natural field drift can be offset for each segment allows a higher gain setting to minimize dynamic range problems. The analysis is also applicable to the induced polarization technique in which similar problems arise at low frequencies in the presence of telluric noise.
Applications of bidimensional spline functions to geophysics
Authors: Enriquez José Oscar Campos , Thomann Jean , Goupillot Michel
Published: October 2002

Two bidimensional spline functions are applied to the interpolation and automatic contouring of data from a ground magnetic survey of the Rhinegraben, between Karlsruhe and Strasbourg. These bidimensional spline functions can be applied in the general case, i.e., where a set of nonequispaced data is given. These splines define a surface passing through the original points. The most promising spline functions are the thin plate (“plaque mince”) and the pseudocubic spline, studied by Atteia (1966), Thomann (1970), and Duchon (1975, 1976). A contouring method based on them has been implemented.
Accommodating lateral velocity changes in Kirchhoff migration by means of Fermat’s principle
Authors: Carter Jerry A. , Frazer L. Neil
Published: October 2002

When velocity varies laterally as well as with depth, an exact Kirchhoff depth migration requires that rays be traced from each depth point in the section to each source/receiver location. Because such a procedure is prohibitively expensive, Kirchhoff migration is usually carried out by using a velocity function that depends only on depth. This paper introduces a new method, based on Fermat’s principle, which is a compromise between these two extremes. The slowness (reciprocal velocity) function is written as the sum of two functions, the first of which is large and depends only on depth, while the other is small and varies both with depth and position along the line. Raypaths are traced for the first slowness function and are used to calculate migration curves. For each depth point these same raypaths are used to calculate traveltime perturbations due to the laterally varying part of the slowness. The traveltime perturbations are added to the migration curve to obtain an approximation to the exact migration curve. More precisely, suppose that the slowness function can be written in the form [Formula: see text] where [Formula: see text] Using a(z), we generate a table giving two‐way traveltime T as a function of scatterer depth z and surface offset Δ, and a raypath table which gives the ray offset ξ as a function of scatterer depth, surface offset, and ray depth [Formula: see text] For fixed z, T(Δ, z) is a migration curve and conventional Kirchhoff migration of zero‐offset reflection data ψ(x, t) is performed by summation along such curves: [Formula: see text] by [Formula: see text] where W is a weighting factor. The raypath table is used to calculate the traveltime perturbation [Formula: see text] where the integral is taken over the unperturbed raypath. For fixed x and z the new migration curve is [Formula: see text] and migration is per formed by [Formula: see text] This new migration scheme is much less expensive than the exact Kirchhoff scheme because only one set of rays need be traced. Numerical tests have shown that this scheme works surprisingly well even when the lateral variation of velocity is large.
On: “Analysis of error due to presence of gaps in the measurement of rock samples in a coaxial line” by Frank S. C. Huang and Liang C. Shen (GEOPHYSICS, February, 1983, p. 206–212).
Authors: Singh Ramesh P.
Published: October 2002

Huang and Shen presented an interesting paper pointing out a correction due to the presence of unavoidable gaps between the sample and sample holder (coaxial line) on the measurement of dielectric constant and conductivity of core rock samples. Huang and Shen’s following statement on p. 206 is misleading: “Thus low‐frequency tools for measuring the electric properties of a formation can measure the conductivity accurately but not the dielectric constant.” At low frequency below 10 MHz, displacement current is almost negligible for most of the Earth’s materials. Therefore, the question of the dielectric constant with the low‐frequency tools does not arise.
Solution of the fundamental problem in resistivity logging with a hybrid method
Authors: Tsang Leung , Chan Andrew K. , Gianzero Stanley
Published: October 2002

The fundamental resistivity logging problem of a resistivity tool in the presence of both vertical and horizontal boundaries is solved with a hybrid method. The hybrid method combines the mode concept in waveguide theory together with the finite‐element method. In the mathematical formulation, the horizontal boundaries are used to separate the geometry of the problem into different regions. In each region, the waveguide modes are obtained through the solution of an equivalent variational problem. The solutions are calculated by a one‐dimensional finite‐element method. The vertical boundaries are taken into account in these calculations. The orthonormality of modes in each region allows a series representation of the potential in the regions. Boundary conditions at horizontal bed boundaries then couple the modes between different regions and enable the solutions for the potential to be expressed in terms of reflection and transmission matrices of modes. The source excitation determines the amplitudes of the modes. The results of the hybrid method are in excellent agreement with those of the integral transform solution. Numerical results of the apparent resistivity are illustrated as a function of formation properties. The effects of an invaded zone are also examined by considering radial inhomogeneous profiles in the formation. The results of the hybrid method are numerically efficient because it reduces the two‐dimensional finite‐element problem into a one‐dimensional one. It also provides a physical interpretation of the solution in terms of modes.
Root‐mean‐square velocities and recovery of the acoustic impedance
Authors: Oldenburg D. W. , Levy S. , Stinson K.
Published: October 2002

The loss of low‐frequency information in reflection seismograms causes serious difficulties when attempting to generate a full‐band impedance profile. Information about the low‐frequency velocity structure is available from rms (stacking velocities). We show how rms velocities can be inverted with additional point velocity constraints (if they are available) to construct either smooth or blocky velocity structures. Backus‐Gilbert averages of the constructed velocity are then autoregressive solutions for recovering a full band reflectivity from band‐limited seismograms. Our final result is therefore a full‐band acoustic impedance which is consistent with the seismic data section, stacking velocities, and available point constraints.
Field observations of electromagnetic pulse propagation in dielectric slabs
Authors: Arcone Steven A.
Published: October 2002

The propagation of electromagnetic pulses in naturally occurring dielectric surface layers has been examined. Pulse duration used in field experiments reported here has been on the order of nanoseconds with pulse bandwidths in the high VHF to low UHF band. The layers were sheets of fresh water ice and granite at thicknesses ranging between .4 and 4 m. Both transverse electric (TE) and transverse magnetic (TM) modes were attempted but only the TE propagation could be interpreted. Analog recordings of wide‐angle reflection and refraction (WARR) profiles were taken and recorded in a continuous graphic display. The displays allowed easy identification of phase fronts thereby facilitating study of of the dispersion of the pulses. The phase and group velocities of the wave‐group packets agree well with the velocities predicted from dispersion curves derived from the modal waveguide equation. In one case the Airy phase of wave‐packet propagation occurred. The best measure of the dielectric constant of the layer was the frequency of the air wave.
An attempt to formulate well‐posed questions in gravity: Application of linear inverse techniques to mining exploration
Authors: Richard Vincent , Bayer Roger , Cuer Michel
Published: October 2002

The aim of this paper is to use linear inverse theory to interpret gravity surveys in mining exploration by incorporating a priori information on the densities and data in terms of Gaussian or uniform probability laws. The Bayesian approach and linear programming techniques lead to the solution of well‐posed questions resulting from the exploration process. In particular, we develop a method of measuring the possible heterogeneity within a given domain by using linear programming. These techniques are applied to gravity data taken over the massive sulfide deposit of Neves Corvo (Portugal). We show how crude constraints on the densities lead to a first estimation of the location of sources, while further geologic constraints allow us to estimate the heterogeneity and to put definite bounds on the ore masses.
Array estimators and the use of microseisms for reconnaissance of sedimentary basins
Authors: Asten M. W. , Henstridge J. D.
Published: October 2002

A “natural field” seismic technique is possible to attain by observing microseisms with a suitably designed array and by digitally processing the data to obtain estimates of the phase velocities of Rayleigh waves. Wavelengths of interest in detecting depth to the basement of sedimentary basins are in the range 2 to 20 km, and correspond to wave periods from 1 to 7 s. An array of five or seven seismometers deployed as an expanding cross configuration simplifies field procedures and is adequate for phase velocity measurements of Rayleigh waves in the required wavelength range, provided high‐resolution frequency‐wavenumber spectral analysis is used. This analysis can be implemented on a minicomputer in the field. Results obtained from observation in a sedimentary basin of known structure show predominantly fundamental‐mode Rayleigh wave propagation. The scatter of velocity estimates is small enough to allow inversion by curve matching, and depth to the basement can be computed to an accuracy of ±30 percent without requiring restrictive assumptions of a seismic velocity structure.
Stable plane‐wave decomposition and spherical‐wave reconstruction: Applications to converted S-mode separation and trace interpolation
Authors: Cabrera J. Julian , Levy Shlomo
Published: October 2002

Plane‐wave decomposition of the vertical displacement component of a spherical‐wave field corresponding to a compressional point source is solved as a set of inverse problems. The solution method utilizes the power and stability of Backus and Gilbert (smallest and flattest) model‐construction techniques, and achieves computational efficiency through the use of analytical solutions to the involved integrals. The theory and algorithms developed in this work allow stable and efficient reconstruction of spherical‐wave fields from a relatively sparse set of their plane‐wave components. Comparison of the algorithms with discrete integration of the Hankel transform shows very little or no advantage for the transformation from the time‐distance (t-x) domain to the intercept time‐angle of emergence (τ-γ) domain if the seismograms are equisampled spatially. However, when the observed seismograms are not equally spaced or the transformation τ-γ to t-x is performed, the proposed schemes are superior to the discrete integration of the Hankel transform. Applicability of the algorithms to reflection seismology is demonstrated by means of the solution of the problem of trace interpolation, and also that of the separation of converted S modes from other modes presented in common‐source gathers. In both cases the application of the algorithms to a set of synthetic reflection seismograms yields satisfactory results.
Extremal bias coupling in magnetotellurics
Authors: Pedersen L. B. , Svennekjaer M.
Published: October 2002

Bias effects due to uncorrelated noise on electrical and magnetic channels are cast into a quantitative framework which allows for an immediate conservative judgment of impedance tensor quality from a single station set up. The horizontal magnetic field is regarded as input to a linear system with the horizontal electrical field and the vertical magnetic field as outputs. The coherence between inputs, the predicted coherence between outputs and inputs, and the polarization characteristics of the inputs, determine the extremal bias effects. Exact expressions for impedance tensor elements and tipper elements are given. Moreover, rotation angle of principal impedance direction, skew, and ellipticity are calculated. Finally, we study some practical examples that show some of the characteristics predicted by our model.
Comparison of the ℓ1 and ℓ2 norms applied to one‐at‐a‐time spike extraction from seismic traces
Authors: Barrodale I. , Zala C. A. , Chapman N. R.
Published: October 2002

We present an algorithm for deconvolving a seismic trace by extracting spikes one at a time, thereby obtaining a sparsely populated spike train. Three versions of this algorithm are then compared empirically, by applying them to several examples of synthetic and real seismic data. The first two versions correspond to the use of the [Formula: see text] (least‐absolute‐values) and [Formula: see text] (least‐squares) norms, while the third is a faster and more compact version of the [Formula: see text], algorithm. The [Formula: see text] procedures are shown to exhibit different characteristics which are often desirable, and the results are generally superior to those of the [Formula: see text] procedure for one‐at‐a‐time spike extraction. The use of the fast [Formula: see text] algorithm is advocated in practice for efficient and effective deconvolution.
Efficient calculation of the electromagnetic fields of an extended source
Authors: Boerner D. E. , West G. F.
Published: October 2002

Many electromagnetic geophysical systems employ a spatially extended source (i.e., a large rectangular horizontal loop or a long grounded wire) to generate the electromagnetic (EM) field. In forward or inverse modeling, the theory and computational algorithms are usually derived for infinitesimal electric or magnetic dipole sources, or infinite line currents. However, it is often not sufficiently accurate to approximate an extended source in such a manner. Also, in many instances topographic and access problems can force the use of a source which has a complicated shape. Conceptually, there is no difficulty in expressing the actual source as an integral (line or surface) of the appropriate elementary source. However, if the integration is carried out numerically, the algorithm for calculating the field of the elementary source may have to be evaluated many times, and the calculation may become impractically long.
Wave‐equation datuming before stack
Authors: Berryhill John R.
Published: October 2002

This note describes the extension to unstacked seismic data of a computationally efficient form of the Kirchhoff integral published several years ago. In the previous paper (Berryhill, 1979), a wave‐equation procedure was developed to change the datum of a collection of zero‐offset seismic traces from one surface of arbitrary shape to another, even when the velocity for wave propagation is not constant. This procedure was designated “wave‐equation datuming,” and its applications to zero‐offset data were shown to include velocity‐replacement datum corrections and multilayer forward modeling. Extending this procedure to unstacked data requires no change in the mathematical algorithm. It is necessary only to recognize that operating on a common‐source group of seismic traces has the effect of extrapolating the receivers from one datum to another, and that, because of reciprocity, operating on a common‐receiver group changes the datum of the sources. Two passes through the data, common‐source computations, then common‐receiver computations, are required to change the datum of an entire seismic line before stack from one surface to another. Common‐source and common‐receiver trace groups must take the form of symmetric split spreads if both directions of dip are to be treated equally; reciprocity allows split spreads to be constructed artificially if the data were not actually recorded in the required form.
On: “Does draping aeromagnetic data reduce terrain‐induced effect?” by V. J. S. Grauch and David L. Campbell (GEOPHYSICS, v. 49, p. 75–80, January, 1984).
Authors: Hansen Richard O.
Published: October 2002

Grauch and Campbell have raised an important question about the uses of draped flying. However, certain common geologic situations which draped flying is intended to address are not discussed in their paper. One example is the case in which shallow, high‐susceptibility material overlies magnetic structures of interest at considerable depth. The shallow material may be a relatively thin, surficial or near‐surficial volcanic flow. An appropriate model for this situation would be a uniformly magnetized dipole sheet located at the surface of the topography, with prismatic bodies buried at depth.
A critique of seismic deconvolution methods
Authors: Jurkevics Andrejs , Wiggins Ralphe
Published: October 2002

Different seismic pulse compression methods are evaluated. These include several algorithms for computing prediction error filters: Wiener filtering, Burg’s method, the [Formula: see text] norm criterion, Kalman filtering, and two time‐adaptive methods. Algorithms which do not assume a minimum‐phase condition for the seismic wavelet include minimum entropy, homomorphic, and zero‐phase deconvolution. The sensitivity of these algorithms is examined for various earth reflectivity functions, source waveforms, and signal distortions. The results indicate that standard Wiener predictive deconvolution is robust under a wide variety of input conditions. However, a substantial improvement in pulse compression can be obtained by the Burg algorithm under conditions of short data segments and by minimum entropy deconvolution for seismograms consisting of mixed‐phase wavelets combined with sparse reflectivity series.
Scale‐model response of a thin vertical conductor below a conductive, inductive, or laterally inhomogeneous overburden layer
Authors: Joshi M. S. , Gupta O. P. , Negi J. G.
Published: October 2002

The electromagnetic conductors of interest are often overlain by a partially conducting overburden layer which may be uniform or varying in conductance (conductivity‐thickness product) and which may or may not be in galvanic contact with the target conductor below. Laboratory scale‐model experiments for the Slingram configuration are conducted to simulate such realistic conditions. Results generally indicate the following. (1) The overburden with uniform conductance and inductive coupling with the massive sulfide vein‐type orebody attenuates the response of the target and causes a clockwise rotation of the anomaly index diagram (AID) related to its conductance. The better the conductor, the more serious would be the error in estimating its conductance. The depth index curves in the AID shift toward greater depth‐to‐the‐top of the conductor. (2) A conductively coupled overburden distinctly improves the response of the target as expected according to the concept of negative electromagnetic screening. There is a counterclockwise rotation of the AID accompanied by higher sensitivity in in‐phase as well as out‐of‐phase components simultaneously. (3) A laterally inhomogeneous overburden layer produces diagnostic response profiles.
On: “Reflection and transmission of plane compressional waves by R. D. Tooley, T. W. Spencer, and H. F. Sagori, (GEOPHYSICS, 30, 552, April, 1965).
Authors: Denham L. R. , Palmeira R. A. R.
Published: October 2002

One of the most widely reproduced figures for the partition of energy of a seismic wave at an interface between two media is from Tooley et al.’s 1965 paper. Recently we referred to this paper and noticed some anomalies in the curves shown there in Figure 11. We looked at the values of the curves at zero angle of incidence and noted that while the values of a P-wave velocity ratio of 2, 3, and 4 agree with the values given by the simplified formula {(V2−V1)/(V2+V1)}**2, the values shown for the P-wave velocity ratios less than 1 do not agree. For a ratio of 0.25, the coefficient at zero angle should be 0.36; it is shown as about 0.72. A ratio of 0.5 should give a coefficient of 0.11; 0.52 is shown. There are similar discrepancies for all the other ratios less than 1.
On: Short note “Higher order autospectra by maximun entropy method”, by R. O. Plaisted and H. G. Peña (GEOPHYSICS, 48, 1409–1410, October, 1983).
Authors: Matsuoka Toshifumi , Ulrych Tad J.
Published: October 2002

Recently Rosenblatt (1980) and Lii and Rosenblatt (1982) developed a phase estimation method for nonminimum phase MA processes by using the bispectrum which contains the required phase information of the wavelet. The computation of the bispectrum is, consequently, of importance in geophysical signal processing, particularly in the difficult problem of wavelet estimation.
Refinements to the linear velocity inversion theory
Authors: Hagin Frank G. , Cohen Jack K.
Published: October 2002

The linear inversion method presented by Cohen and Bleistein in 1979 gives seriously degraded results when large reflectors are encountered. Obviously there is an irrecoverable loss of information when such a linear algorithm is applied to a nonlinear world. However, in many cases, excellent results can be achieved by suitable postprocessing of the output of the basic linear inversion algorithm. Although a certain degree of helpful postprocessing can be and has been performed by straightforward consideration of the linearization process, we present here a substantially improved postprocessing algorithm. The basis for these improvements is a more accurate scattering model due to Lahlou et al where, among other things, a WKB analysis of the wave equation led to a much more accurate accounting of the geometric spreading of the scattered wave. These notions plus an effective use of traveltime are used in the new algorithm to improve both the estimate of the reflector locations and the estimate of amplitude (velocity or acoustic impedance) change across the reflectors. The basic idea is to insert this idealized scattering data into the original linear algorithm, and then use the result of this computation as a guide in the interpretation of the numerical output of the algorithm. We demonstrate the result of computer implementation of this algorithm on synthetic data, with and without noise, and verify that the postprocessing algorithm produces dramatically improved reflector locations and speed estimates. Moreover, the new algorithm adds only very modest cost to the basic processing, which is, in turn, very competitive in cost to other multidimensional algorithms.
Effect of well casings on surface electrical surveys
Authors: Holladay J. Scott , West G. F.
Published: October 2002

Surface electrical surveys are being used as alternative oil exploration tools in both developed and frontier areas. We have examined the resistivity‐IP response of steel oil well casings, which are common in developed oil fields. Two numerical models were constructed: a solution of Laplace’s equation in the spatial wavenumber domain, and an integral equation approach using the Galerkin weighted residual technique, which simulate hollow, infinite‐length cylinders and finite‐length cylindrical shells, respectively, embedded in a uniform half‐space. Induced‐polarization effects can be simulated in these models by including a complex, frequency‐dependent surface impedance on the outer surface of the cylinder. Significant anomalies are generated by pipes having physically realistic dimensions and conductivities. Important parameters governing the response are the longitudinal conductance, length and radius of the pipe, and the number of pipes and their distances from the survey line. Comparison of field data with model results suggests that a significant part of the observed response may be due to well casings. However, more complicated models including electrical connections at the surface and earth layering are required before accurate modeling of many situations will be possible.
Poststack estimation of three‐dimensional crossline statics
Authors: Schultz Philip S. , Lau August
Published: October 2002

In three‐dimensional land data acquisition, the crossline dimension of the receiver spread is often much smaller than the inline dimension, typically for reasons of economy. Because of fundamental wavenumber limitations in the estimation of residual statics by prestack surface consistent methods, unresolved static errors will persist through processing to the stack data, particularly in the crossline direction. The present method involves an analysis of poststack 3-D data through the creation of a correlation time surface from crosscorrelations of adjacent stack data traces. This time surface is decomposed in the wavenumber domain to isolate and correct some of the spectral components of residual static errors which are beyond the resolution of prestack approaches. Assumptions are implicit within the method regarding the expected 2-D wavenumber nature of the wave field response of true geologic structure. The method is proposed as an additional procedure to the standard 3-D processing sequence for land data.
Survey design for multicomponent electromagnetic systems
Authors: Macnae James C.
Published: October 2002

A roving coil receiver is employed by several modern EM exploration systems to measure various spatial components of the time derivative of the magnetic field set up by a fixed transmitter. The absolute instantaneous secondary field measured above the surface of the earth is a potential field in this case, and, using well‐established potential field theory, it is known to be possible to predict the response of both horizontal components on any plane from a complete knowledge of the vertical component on the same plane. The required operation is simply performed in the wavenumber domain and is an amplitude invariant quadrature phase translation. In practice, errors are introduced in this transformation by spatial aliasing effects which depend upon the sampling density and by windowing effects which depend upon the areal extent of data coverage. The major source of noise in EM survey data collected in remote areas is sferic activity, which arises from the worldwide distribution of lightning discharges. Sferic noise, although time‐varying, is predominantly uniform in a spatial sense, with local spatially varying anomalies near conductive inhomogeneities. Since the horizontal component noise amplitude is typically an order of magnitude greater than the vertical component noise amplitude, a strong case can be made that it is advantageous in routine surveys to increase the spatial coverage of vertical component data rather than to read both horizontal components.