bluuebunny/crossref_metadata_2025 huggingface dataset:
A strategy for nonlinear elastic inversion of seismic reflection data
Authors: Tarantola Albert
Published: October 2002

The problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory. In its roughest formulation, the inverse problem consists of obtaining the Earth model for which the predicted data best fit the observed data. If an adequate forward model is used, this best model will give the best images of the Earth’s interior. Three parameters are needed for describing a perfectly elastic, isotropic, Earth: the density ρ(x) and the Lamé parameters λ(x) and μ(x), or the density ρ(x) and the P-wave and S-wave velocities α(x) and β(x). The choice of parameters is not neutral, in the sense that although theoretically equivalent, if they are not adequately chosen the numerical algorithms in the inversion can be inefficient. In the long (spatial) wavelengths of the model, adequate parameters are the P-wave and S-wave velocities, while in the short (spatial) wavelengths, P-wave impedance, S-wave impedance, and density are adequate. The problem of inversion of waveforms is highly nonlinear for the long wavelengths of the velocities, while it is reasonably linear for the short wavelengths of the impedances and density. Furthermore, this parameterization defines a highly hierarchical problem: the long wavelengths of the P-wave velocity and short wavelengths of the P-wave impedance are much more important parameters than their counterparts for S-waves (in terms of interpreting observed amplitudes), and the latter are much more important than the density. This suggests solving the general inverse problem (which must involve all the parameters) by first optimizing for the P-wave velocity and impedance, then optimizing for the S-wave velocity and impedance, and finally optimizing for density. The first part of the problem of obtaining the long wavelengths of the P-wave velocity and the short wavelengths of the P-wave impedance is similar to the problem solved by present industrial practice (for accurate data interpretation through velocity analysis and “prestack migration”). In fact, the method proposed here produces (as a byproduct) a generalization to the elastic case of the equations of “prestack acoustic migration.” Once an adequate model of the long wavelengths of the P-wave velocity and of the short wavelengths of the P-wave impedance has been obtained, the data residuals should essentially contain information on S-waves (essentially P-S and S-P converted waves). Once the corresponding model of S-wave velocity (long wavelengths) and S-wave impedance (short wavelengths) has been obtained, and if the remaining residuals still contain information, an optimization for density should be performed (the short wavelengths of impedances do not give independent information on density and velocity independently). Because the problem is nonlinear, the whole process should be iterated to convergence; however, the information from each parameter should be independent enough for an interesting first solution.
Weak elastic anisotropy
Authors: Thomsen Leon
Published: October 2002

Most bulk elastic media are weakly anisotropic. The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted δ) controls most anisotropic phenomena of importance in exploration geophysics, some of which are nonnegligible even when the anisotropy is weak. The critical parameter δ is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.
Deep‐water peg legs and multiples: Emulation and suppression
Authors: Berryhill J. R. , Kim Y. C.
Published: October 2002

This paper discusses a two‐step method for predicting and attenuating multiple and peg‐leg reflections in unstacked seismic data. In the first step, an (observed) seismic record is extrapolated through a round‐trip traversal of the water layer, thus creating an accurate prediction of all possible multiples. In the second step, the record containing the predicted multiples is compared with and subtracted from the original. The wave‐equation method employed to predict the multiples takes accurate account of sea‐floor topography and so requires a precise water‐bottom profile as part of the input. Information about the subsurface below the sea floor is not required. The arrival times of multiple reflections are reproduced precisely, although the amplitudes are not accurate, and the sea floor is treated as a perfect reflector. The comparison step detects the similarities between the computed multiples and the original data, and estimates a transfer function to equalize the amplitudes and account for any change in waveform caused by the sea‐floor reflector. This two‐step wave‐equation method is effective even for dipping sea floors and dipping subsurface reflectors. It does not depend upon any assumed periodicity in the data or upon any difference in stacking velocity between primaries and multiples. Thus it is complementary to the less specialized methods of multiple suppression.
Borehole field calibration and measurement of low‐concentration manganese by decay gamma rays
Authors: Mikesell J. L. , Senftle F. E. , Lloyd T. A. , Tanner A. B. , Merritt C. T. , Force E. R.
Published: October 2002

The manganese concentration in the Arundel clay formation, Prince Georges County, Maryland, was determined from a borehole by using delayed neutron activation. The neutrons were produced by a [Formula: see text] source. The 847 keV gamma ray of manganese was detected continuously, and its counting rate was measured at intervals of 15 s as the measuring sonde was moved at a rate of 0.5 cm/s. The technique measured the concentration ratio of manganese to aluminum. This ratio, when combined with an estimate of the aluminum concentration of the clay, made it possible to determine the percentage concentration of manganese without using a test‐pit calibration facility. The measurements were made by using an NaI(Tl) scintillation detector and a Ge(HP) solid‐state detector cooled by solid propane. A two‐pass technique had to be used with the scintillation detector because Compton background from the 1 779 keV photopeak of aluminum masked the manganese line. The Compton background did not interfere when the solid‐state detector was used. The borehole measurements compared favorably with a chemical core analysis and were unaffected by water in the borehole.
Robust iterative inversion for the one‐dimensional acoustic wave equation
Authors: Gersztenkorn Adam , Bednar J. Bee , Lines Larry R.
Published: October 2002

Seismic inversion can be formulated by considering a linearized integral relation which is deduced from the wave equation. This Born inversion approach is equivalent to linear least‐squares inversion for a particular parameterization of the medium. The least‐squares solution is a member of a family of generalized LP norm solutions which are deduced from a maximum‐likelihood formulation. This formulation allows design of various statistical inversion solutions. We present two iterative solutions to the one‐dimensional (1-D) seismic inverse problem: the iterative least‐squares (ILS) and the iterative reweighted least‐squares (IRLS) methods. The ILS method involves solving a distorted background velocity problem after the initial least‐squares solution is obtained. The IRLS method is used as a robust regression technique which is better suited for dealing with certain types of noise and is computationally faster than ILS. Several numerical examples demonstrate that the IRLS method accurately estimates impedance profiles despite the presence of large‐amplitude noise spikes in the seismic traces. Numerical experiments suggest that the IRLS inversion can also be insensitive to noise bursts which are of a lower frequency band than noise spikes.
Ground‐penetrating radar surveys used in archaeological investigations
Authors: Vaughan C. J.
Published: October 2002

During 1982 and 1983, two ground‐penetrating radar surveys were carried out in conjunction with archaeological investigations in Canada. The first survey was a detailed, high‐resolution radar survey at the site of a sixteenth century Basque whaling station on the Labrador coast designed to locate the graves of the Basques. The second was a rapid, low‐resolution reconnaissance survey as part of a prehistory impact assessment program at the site of the new National Museum of Man in Hull, Quebec. Both surveys were experimental and were designed to see whether ground‐penetrating radar would be useful for identifying and locating anomalies of archeological significance. Radar was successful in detecting archeological anomalies several meters in size at both locations, and the high‐resolution survey was moderately successful in identifying Basque graves. Ongoing work involves comparing radar results with the archaeological investigations to increase the understanding of how radar can be applied to archaeology and to improve interpretation of radar responses to artifacts.
Display of archaeological magnetic data
Authors: Scollar Irwin , Weidner Bernd , Segeth Karel
Published: October 2002

Magnetic data from archaeological sites have traditionally been displayed by contour, isometric, and dot‐density plotting, or by simulated gray‐scale techniques using symbol overprinting. These methods do not show fine linear structures in the data which are of great interest to archaeologists. If true gray‐scale methods using a modern video display, followed by film recording for hard copy are employed, image processing techniques can be applied to enhance the geometric structures of archaeological interest. Interpolation techniques for enlarging data to full screen size, along with compression methods to keep data within gray‐scale capabilities, are needed. Such techniques would introduce minimum distortion and allow faint details to be seen in the vicinity of strong anomalies. Postprocessing methods based on rapid image spatial filtering and enhancement algorithms could then be applied in an interactive environment.
The scatter of magnetic directions in archaeomagnetic studies
Authors: Tarling D. H. , Hammo N. B. , Downey W. S.
Published: October 2002

Early studies of kiln structures suggested that magnetic refraction could be a major source of error in archaeomagnetic studies of large, strongly magnetized structures. Recent studies of the directions of magnetization of samples from four British and two Cretan kilns and furnaces do not show clear evidence for such effects, although only two show the level of scatter predicted from an assessment of the errors in orientation and measurement. There is also some evidence for systematic distortion of either declination or inclination around the circumference of some of these structures. These systematic deviations do not appear to be related to the intensity of magnetization, and the magnitude of scatter tends to decrease with increasing intensity of magnetization of the structure. The magnitude of scatter appears to be largest where the magnetic materials are inhomogeneous, but it is not clear how this can account for systematic variations. Evaluation of both earlier and newer observations indicates that floors are not necessarily the optimum parts of a structure for sampling, but instead walls can be considered at least as reliable if not more so. In both cases, differential subsistence may be the main source of error. It is recommended that, until more is known about the cause of scatter, sampling should incorporate both floors and walls, and that the azimuth of the sampling relative to the structure should be noted.
Seismic reflection profiling studies of a buried Precambrian rift beneath the Wabash Valley fault zone
Authors: Sexton John L. , Braile L. W. , Hinze W. J. , Campbell M. J.
Published: October 2002

Sixty‐eight kilometers of 12-fold seismic reflection data were collected in the Wabash River Valley of southwestern Indiana and southeastern Illinois to investigate the configuration of a basement structure inferred from regional gravity and magnetic anomaly data. The seismic profiles were also positioned to cross faults of the Wabash Valley fault system in a number of locations. Interpretation of the seismic reflection profiles and detailed gravity and magnetic profile data provides evidence for a series of northeasterly trending grabens in the basement. These grabens are filled with pre‐Mt. Simon layered rocks and are overlain by Paleozoic sedimentary rocks of the Illinois basin. Beneath the Wabash River near Grayville, Illinois, an interpreted graben (the Grayville graben) is approximately 15 km wide and contains about 3 km of fill. Individual boundary faults for the graben cut prominent reflectors within pre‐Mt. Simon rocks and display offsets of up to 500 m. The interpreted configuration of basement faults and thickness of pre‐Mt. Simon layered rocks provide evidence of a late Precambrian rift inferred to be one arm of the New Madrid rift complex. Post‐Pennsylvanian faulting of the Wabash Valley fault system is visible on the seismic reflection record sections as small offsets (less than 100 m) on steeply dipping normal faults. The downward projection of these faults intersects the older large‐offset faults within the pre‐Mt. Simon rocks suggesting that the Wabash Valley faults represent a post‐Pennsylvanian reactivation of the rift system.
Acoustic response of manganese nodule deposits
Authors: Ma Y. , Magnuson A. H. , Varadan V. K. , Varadan V. V.
Published: October 2002

Backscattered acoustic intensities are studied analytically for manganese nodule deposits excited by a normally incident plane wave. The primary objective is to use this remote‐sensing technique to infer the nodule concentration as well as its size distribution from the frequency spectrum of the acoustic response. For sparse distributions of scatterers, multiple scattering theory has been used to obtain the coherent reflection and transmission coefficients from the sea floor covered with manganese nodules. The derived equations can also be used for densely distributed configurations when considering higher‐order statistics between scatterers. The validity of the formalism is examined by using the principle of conservation of energy and considering both the coherent and the incoherent intensities. Numerical results of acoustic intensities are highly frequency‐dependent, especially when the nondimensional frequency ka is greater than 1. The strength of the acoustic intensity is proportional to nodule concentration. Different size distributions of nodules can be distinguished through use of the intensity measurements. However only a minor difference is observed in the low‐frequency range between uniform and Rayleigh size distributions.
A comparison of electromagnetic exploration systems
Authors: McCracken K. G. , Oristaglio M. L. , Hohmann G. W.
Published: October 2002

Electromagnetic (EM) exploration systems fall into three distinct classes, (1) frequency domain, (2) impulse response, and (3) step response, and have overall frequency responses that approximate [Formula: see text], [Formula: see text], and [Formula: see text]. To examine further these three classes, the transfer function of a frequency‐domain system, and the step and impulse response functions of ideal time‐domain EM systems (TEM), are derived in terms of a single set of target‐specific parameters. The inductive time constants of practical exploration targets extend over three orders of magnitude, imposing severe constraints on practical exploration systems. Field data demonstrate that the impulse TEM response from a conductive half‐space may show a 100‐fold spatial variability at early times (≲1 ms) and then will decrease to a two‐fold variability at late times ( ⩾4 ms). This differential variability influences the ability of an EM system to detect an exploration target. For a half‐space where the impulse response varies as [Formula: see text], an inductive target of time constant τ exhibits the greatest contrast to the half‐space at a delay time of kτ for an impulse‐response system, and at [Formula: see text] for a step‐response system.
P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method
Authors: Virieux Jean
Published: October 2002

I present a finite‐difference method for modeling P-SV wave propagation in heterogeneous media. This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid. The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson’s ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson’s ratio. Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid‐solid interface. Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results. The weathered‐layer and corner‐edge models show in seismograms the same converted phases obtained by previous authors. This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half‐space. The head wave preserves the correct amplitude. Finally, the corner‐edge model illustrates a more complex geometry for the liquid‐solid interface. As the Poisson’s ratio v increases from 0.25 to 0.5, the shear converted phases are removed from seismograms and from the time section of the wave field.
A slant‐stack procedure for point‐source data
Authors: Brysk Henry , McCowan Douglas W.
Published: October 2002

The proper implementation of the τ-p method for surface data excited by a point source requires a cylindrical slant stack. Usually the common (Cartesian) slant stack is computed instead as an approximation to the geometrically correct procedure. Here we describe a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks; our cylindrical slant stack is computationally efficient to perform. We show how, although the usefulness of the slant stack is most easily seen with Cartesian coordinates, it can also be used with Fourier‐Bessel transforms. An example of the method shows results computed from data recorded on the West Florida Shelf. Severe edge‐effect noise which overwhelms the Cartesian slant stack is attenuated by the cylindrical slant‐stacking. Applications of the cylindrical slant stack to other seismological calculations, such as Lamb’s problem, are also discussed. In particular, we prove that the plane‐wave reflection coefficients apply exactly in the τ-p domain; hence an amplitude‐versus‐offset analysis is unambiguous in that domain.
Shallow seismic reflection investigations of coal in the Sydney Basin
Authors: Greenhalgh S. A. , Suprajitno M. , King D. W.
Published: October 2002

Surface reflection profiling with the Mini‐SOSIE technique successfully mapped shallow coal seam structure in the western Sydney Basin, New South Wales. Several minor faults and zones of fracturing were detected. In regions of thick Triassic sandstone cover, data quality was poor and unsuitable for geologic interpretation. Synthetic seismograms based on nearby borehole and petrophysical control show excellent agreement with the Mini‐SOSIE sections and illustrate the deleterious filtering effects of coal seams and sequences. To establish a phenomenological basis for seismic wave propagation in shallow coal measures, two vertical seismic profiles (VSPs) which used small explosive charges were recorded with high spatial and temporal sampling. Numerous multiple reflections were observed in the downgoing wave display. The isolated upgoing waves were migrated to yield blurred images of the main coal seams. The subsurface velocity function, also deduced from the VSP, shows broad correlation with the geologic log. The VSP seismograms are not simple because of the combined effects of wave absorption, scattering, and interference. Such problems impede recovery of fine structural detail from seismic data in the shallow environment, particularly when a surface energy source is used.
An empirical study of instability and improvement of absorbing boundary conditions for the elastic wave equation
Authors: Mahrer Kenneth D.
Published: October 2002

One of the persistent problems with numerical solutions to the elastic wave equation is the finite size of the numerical grid. As with a physical body, the grid boundaries will reflect incident energy. If not eliminated or reduced substantially, these reflections will invade the grid interior and interfere with the desired solution. One method for eliminating reflections is creating a large and/or expanding grid. This method may be impractical since it can be quite costly in both computer time and memory. Another method is making the grid boundary “transparent” to outgoing energy. This method is ideally done by designing absorbing or nonreflecting boundaries which are mathematically equivalent to a one‐way, or outgoing, elastic wave equation only. In practice, an outgoing elastic wave equation is an approximation since the wave equation is not generally separable into outgoing and incoming parts. Two absorbing boundary condition approximations commonly used are those from Reynolds (Reynolds, 1978) and Clayton and Engquist, (Clayton and Engquist, 1977).
Transient electromagnetic response of a three‐dimensional body in a layered earth
Authors: Newman Gregory A. , Hohmann Gerald W. , Anderson Walter L.
Published: October 2002

The three‐dimensional (3-D) electromagnetic scattering problem is first formulated in the frequency domain in terms of an electric field volume integral equation. Three‐dimensional responses are then Fourier transformed with sine and cosine digital filters or with the decay spectrum. The digital filter technique is applied to a sparsely sampled frequency sounding, which is replaced by a cubic spline interpolating function prior to convolution with the digital filters. Typically, 20 to 40 frequencies at five to eight points per decade are required for an accurate solution. A calculated transient is usually in error after it has decayed more than six orders in magnitude from early to late time. The decay spectrum usually requires ten frequencies for a satisfactory solution. However, the solution using the decay spectrum appears to be less accurate than the solution using the digital filters, particularly after early times. Checks on the 3-D solution include reciprocity and convergence checks in the frequency domain, and a comparison of Fourier‐transformed responses with results from a direct time‐domain integral equation solution. The galvanic response of a 3-D conductor energized by a large rectangular loop is substantial when host currents are strong near the conductor. The more conductive the host, the longer the galvanic responses will persist. Large galvanic responses occur if a 3-D conductor is in contact with a conductive overburden. For a thin vertical dike embedded within a conductive host, the 3-D response is similar in form but differs in magnitude and duration from the 2-D response generated by two infinite line sources positioned parallel to the strike direction of the 2-D structure. We have used the 3-D solution to study the application of the central‐loop method to structural interpretation. The results suggest variations of thickness of conductive overburden and depth to sedimentary structure beneath volcanics can be mapped with one‐dimensional inversion. Successful 1-D inversions of 3-D transient soundings replace a 3-D conductor by a conducting layer at a similar depth. However, other possibilities include reduced thickness and resistivity of the 1-D host containing the body. Many different 1-D models can be fit to a transient sounding over a 3-D structure. Near‐surface, 3-D geologic noise will not permanently contaminate a central‐loop apparent resistivity sounding. The noise is band‐limited in time and eventually vanishes at late times.
An analysis of the magnetotelluric impedance for three‐dimensional conductivity structures
Authors: LaTorraca G. A. , Madden T. R. , Korringa J.
Published: October 2002

The eigenstate analysis of Lanczos, also known as singular value decomposition (SVD), is used to define eight parameters which uniquely describe the magnetotelluric impedance Z. These parameters are independent of a priori assumptions about Z and can be interpreted in terms of three‐dimensional conductivity structures. Through SVD, the impedance is represented by two characteristic states. These states consist of two pairs (E and H) of complex vectors and two corresponding, real, singular values which together describe the extremal properties of Z. The singular values are the maximum and minimum |E|/|H| ratios possible at the observation site and therefore yield the true maximum and minimum apparent resistivities. We use a variation of SVD analysis by incorporating phases in the singular values, which are then called characteristic values. These phases reflect the delay (caused by the earth’s conductivity) of the electric fields relative to their associated magnetic fields. In this analysis of Z, the characteristic values contain four parameters, two singular values and two phases. The characteristic vectors contain the remaining four parameters, two principal axis directions and two ellipticities. The principal axis directions for the E and H vectors need not be at right angles as in biorthogonal analysis. The deviation of these axes from orthogonality is called the “skew angle” S. From a model by Park, we have found S to be closely related to distortions in the telluric current system caused by current gathering due to a good conductor. From the same model, we have found the ellipticity parameters to be the largest in regions of high current distortion and at the shorter periods. Consequently, we speculate that the ellipticity parameters are associated with local induction.
On: “A geophone subarray beam‐steering process” by D. E. Biswell, L. F. Konty, and A. L. Liaw (Geophysics, 49, 1838–1849, November 1984).
Authors: Savit Carl H.
Published: October 2002

Please note that the beam‐steering process described in this paper is disclosed and claimed in United States patent 4 319 347 issued March 9, 1982. The application upon which this patent is based was filed March 8, 1976.
Two‐dimensional velocity inversion and synthetic seismogram computation
Authors: Zhu Tianfei , Brown Larry D.
Published: October 2002

A traveltime inversion scheme has been developed to estimate velocity and interface geometries of two‐dimensional media from deep reflection data. The velocity structure is represented by finite elements, and the inversion is formulated as an iterative, constrained, linear least‐squares problem which can be solved by either the singular value truncation method or the Levenberg‐Marquardt method. The damping factor of the Levenberg‐Marquardt method is chosen by the model‐trust region approach. The traveltimes and derivative matrix required to solve the least‐squares problem are computed by ray tracing. To aid seismic interpretation, we also include in the inversion scheme a fast algorithm based on asymptotic ray theory for calculating synthetic seismograms from the derived velocity model. Numerical tests indicate that the inversion scheme is effective, and that the accuracy of inversion results depends upon both noise in the data and the aperture of recording used in data acquisition. Two real examples demonstrate that the new inversion scheme produces velocity models fitting the data better than those estimated by other approaches.
Fault slicing—A new approach to the interpretation of fault detail
Authors: Brown Alistair R. , Edwards G. Serpell , Howard Robert E.
Published: October 2002

The manner in which a fault intersects a hydrocarbon reservoir affects production characteristics and thus must be understood in great detail. A 3-D seismic data volume can be sliced interactively to yield seismic sections parallel to a fault plane. These fault slices can then be used in several ways for the study of faults. Tracking of correlative horizons on fault slices provides a map of fault throw and permits study of the throw as a function of vertical traveltime and horizontal position. Because a fault slice remains within one major fault block, the study of growth relationships in that block is facilitated. Splinter faults, which are also significant in development and production, can be studied effectively on fault slices because of the uniform proximity of these sections to the parent fault. We conclude that there is some uniformity in azimuth between splinter faults and their parent.
Comparison of plane‐wave decomposition and slant stacking of point‐source seismic data
Authors: Mithal Rakesh , Vera Emilio E.
Published: October 2002

The plane‐wave decomposition and slant stacking of point‐source seismic data are not identical processes; they are, however, related. We have found that the algorithm for slant stacking can be used for plane‐wave decomposition if we apply a weighting function (depending on frequency and offset, and including a π/4 phase shift) before slant stacking, and a p-dependent correction after the slant stacking. This procedure requires only a small extra effort to incorporate the geometrical spreading and phase shift not accounted for by the slant stacking. In this process we use the asymptotic approximation for the zeroth‐order Bessel function. This approximation reduces the number of computations significantly, but it is valid only for ωpx greater than 2 or 3. Using this approximation, we have been able to obtain the correct plane‐wave decomposition of expanding spread profile data for ray parameters as low as 0.03 s/km; for smaller p, the exact Bessel function should be used. We have performed model studies to compare plane‐wave decomposition and slant stacking. Using a possible velocity model for the North Atlantic Transect (NAT) expanding spread profile (ESP 5), we computed synthetic seismograms at a 50 m spacing using the reflectivity method, and then computed the plane‐wave decomposition and slant stacks of these seismograms. On comparing these with the exact τ-p seismograms for this model, we found that the waveforms, the frequency content, and the amplitudes were exactly reproduced in the plane‐wave decomposition, but were significantly different in the slant stacks. We also computed the plane‐wave decomposition and slant stacks of real data (NAT ESP 5). The results in this case show that the amplitudes of deep crustal arrivals in plane‐wave decomposition are higher than in slant stacks, and therefore these arrivals can be identified much better in the plane‐wave decomposition.
The paraxial ray method
Authors: Beydoun Wafik B. , Keho Timothy H.
Published: October 2002

The paraxial ray method is an economical way of computing approximate Green’s functions in heterogeneous media. The method uses information from the standard dynamic ray‐tracing method to extrapolate the seismic wave field at receivers in the neighborhood of a ray so that two‐point ray tracing is not required. Applicability conditions are explicit: they define where asymptotic (high‐frequency) methods are valid, and how far away from the ray the extrapolation remains accurate. Increasing the density of the ray fan improves accuracy but increases computation time. However, since reasonable accuracy is obtained with relatively few rays, the method yields results similar to the two‐point ray‐tracing method, but at a fraction of the cost. Examples of wave‐field extrapolation from a ray to neighboring receivers show that traveltime extrapolation is more accurate than amplitude extrapolation. Accuracy, robustness, and efficiency tests, comparing paraxial ray synthetic seismograms with acoustic finite‐difference and elastic discrete‐wavenumber synthetics, are judged very satisfactory.
The radiation characteristics of an arbitrary antenna positioned on a polar ice sheet
Authors: West James C. , Demarest Kenneth R.
Published: October 2002

The radiation pattern of an arbitrarily shaped antenna system placed directly on the surface of a polar ice sheet (a configuration often used for ice‐probing radars) may be determined at any depth within the ice sheet using a two‐step process. The distribution of the radiated field just beneath the surface may be determined first using the method of moments, and geometric optics can then be used to calculate the effects of the exponential density gradient of the ice. Closed‐form solutions of the ray‐tracing equation, valid at any depth within the ice sheet, allow rapid calculation of the effective look angles and gain increases of any antenna mounted on the surface. These solutions asymptotically approach previously determined relations which are valid only at great depths. A numerical example demonstrates the use of this procedure in the design of a practical ice‐probing radar antenna system.
Estimating the thickness of shallow salt from seismic refractions
Authors: Ebeniro Joseph O. , Nakamura Yosio , Sawyer Dale S.
Published: October 2002

The presence of shallow, tectonized salt is a major impediment to exploration efforts in many sedimentary basins, including the northern Gulf of Mexico. The salt there forms a shallow tongue of high‐velocity material emplaced between lower‐velocity Tertiary and Quaternary sediments. Using conventional seismic reflection techniques, explorationists often have difficulty identifying the base of the salt tongue. Only in a very few instances (e.g., Buffler, 1983; Buffler et al., 1978; Watkins et al., 1978) have they been able to identify the base of the shallow salt. Interfaces below the salt are even more rarely observed.
Seismic noise‐reduction techniques for use with vertical stacking: An empirical comparison
Authors: Klemperer Simon L.
Published: October 2002

A systematic comparison of a wide range of noise‐reduction techniques applied to a single data set collected for this purpose was attempted. The study includes a comparison of the relative benefits of noise‐reduction schemes for very different noise levels. The comparisons use computer simulations of field techniques for noise reduction as applied to deep crustal, 48-fold VIBROSEIS® data. The noise‐reduction techniques involve amplitude scaling (diversity stacking and automatic gain control), noise editing (the use of fixed‐gain and self‐updating noise‐rejection systems with and without buffered memory for recursive editing), and reduced numbers of recording bits (mantissa‐only and sign‐bit‐only formats). The effectiveness of each noise‐reduction procedure is assessed by a study of its effects on noise levels seen on source‐point gathers and on both true‐amplitude and amplitude‐balanced common‐midpoint (CMP) stacks. For low levels of ambient noise, true‐amplitude CMP stacks can be substantially improved by the appropriate noise‐reduction techniques, but CMP stacks incorporating gain control before CMP stacking show only minor improvements. In contrast, when a high level of ambient noise is present, both true‐amplitude and gain‐controlled CMP stacks can be greatly improved by appropriate noise‐reduction processing before vertical stacking. Of procedures involving zeroing of noise bursts, self‐updating noise‐rejection systems were more effective than fixed‐gain noise‐rejection systems for all the conditions simulated here. A system incorporating recursive editing techniques is still more effective at low levels of ambient noise, but this system tends to edit recorded traces too severely at very high noise levels. Mantissa‐only and sign‐bit‐only recording give very similar results, and show an effect comparable to that given by self‐updating editing systems. Diversity stacking produced significant noise reduction in all conditions studied, and may be the most widely applicable and most generally useful of the noise‐reduction methods studied here. ®Trade and service mark of Conoco Inc.
Downhole seismic source
Authors: Hardee H. C. , Elbring G. J. , Paulsson B. N. P.
Published: October 2002

A prototype model of a downhole controlled seismic source has been built and field tested. This instrument is a swept‐frequency, penumatically powered seismic source that operates in the 10 to 100 Hz range. This particular version is a vertical‐dipole source and generates vertically polarized shear waves. The instrument is an improved version of a downhole monofrequency source first tested in the crust of Kilauea Lava Lake, Hawaii, in 1981. The present prototype source was field tested recently at the Chevron Oil Field Research facility in La Habra, California. Data from this test, combined with calculations for a full‐scale instrument, indicate that considerable amounts of energy can be coupled into the ground with this type of downhole source. Signals from these prototype sources are easily detectable at distances of 150 m or more. A larger version of the source is currently being designed and fabricated for use in 0.20 m diameter holes, and it will theoretically have a range 30 times greater than the current prototype model. This new seismic source has applications in scientific studies related to the Continental Scientific Drilling Program. The source also has applications in locating magma bodies for the Magma Energy Program and in evaluating oil reservoirs.
Introduction to the Special Issue on remote sensing
Authors: Watson Kenneth
Published: October 2002

In 1977, the first Special Issue on remote sensing published by Geophysics contained papers selected from two special sessions at the 45th Annual International SEG Meeting, October 12–16, 1975, in Denver, Colorado. That first Special Issue consisted of eight papers: four are primarily tutorial (image processing, spectral signatures in the visible and near infrared, microwave spectra of layered media, and factor analysis of gamma‐ray spectrometry), two involve structural interpretations with implications for mineral exploration and seismicity, and two examine multispectral reflectance data for detecting hydrothermal alteration and for uranium exploration. Although these papers indicate the importance of physical properties and models in the interpretation of remote sensing data, the studies were constrained by the instruments that collected the data and by the availability of image‐processing software. Circumstances have changed significantly in the intervening decade, as illustrated in recent review papers (Watson, 1985; Goetz et al., 1983) and demonstrated by the papers in this Special Issue.
Vertical seismic profile reflectivity: Ups over downs
Authors: Ross W. S. , Shah P. M.
Published: October 2002

The idea of designing a deconvolution operator for the vertical seismic profile (VSP) based on its downgoing waves is well known (Anstey, 1976; Gaiser et al., 1984; Hubbard, 1979; Lee and Balch, 1983; Kennett et al., 1980). Many variations of the scheme exist. Anstey (1976) recommends the average of the downgoing wave from all levels as the basis for designing an inverse operator. Lee and Balch (1983) use the downgoing wave from a single level to deconvolve all the VSP traces. Gaiser et al. (1984) and Hubbard (1979) recommend doing the deconvolution independently at each depth level. As observed by Hubbard, there are similar disparities in the literature about whether all or only part of the downgoing wave train should be used in the design of an inverse operator. Although all of the above approaches are identical if multiples are generated in a limited zone near the sea bottom, they differ for more complex media. We recommend, and in this note we explore the theoretical properties of, the level‐by‐level deconvolution based on the entire downgoing wave train. The expressions we develop apply to the general case of the vertical VSP response to any number of horizontal layers with any degree of complexity in the process that generates multiples.
Subsurface imaging using magnetotelluric data
Authors: Levv S. , Oldenburg D. , Wang J.
Published: October 2002

A linear programming approach is developed to construct a pseudo‐impulse response for magnetotelluric (MT) data. The constructed time function is made up of discrete pulses whose amplitudes depend upon the electromagnetic reflection and transmission coefficients at various layer interfaces. The arrival time of an individual pulse corresponds to the time for a reference signal to travel a particular raypath from the surface to a reflector and back. The display of the impulse responses recovered from many stations produces an MT reflectivity section which is analogous to the image ray section regularly interpreted in reflection seismology. Application of linear programming inversion to one‐dimensional conductivity models shows the viability of the method and validates the physical interpretation of the pseudo‐impulse response function. Using a number of simple two‐dimensional geologic models, we show that a line of MT stations acquired perpendicular to strike produces a reflectivity section which is an image of the explored target. The interpretation of the MT image section follows the conventional guidelines used in reflection seismology; features such as traveltime pullup, primary and multiple reflections, and diffraction events are evident on the final section.
Datum correction by wave‐equation extrapolation
Authors: Shtivelman V. , Canning A.
Published: October 2002

Seismic sections are usually datum corrected by static shifting. For small differences in elevation and slow velocity variations between the input datum and the output datum, static shifting is a sufficiently accurate datum correction procedure. However, for significant differences in elevations and a more complicated velocity model, the accuracy of the static solution may prove to be insufficient; and a more exact method should be used. In this paper, we study the limitations of the static method of datum correction and develop simple and effective extrapolation schemes based on the wave equation, schemes which lead to more accurate datum correction. The distortions of seismic events caused by static correction are illustrated by a number of simple examples. To reduce the distortions, we propose a number of extrapolation schemes based on the asymptories of the Kirchhoff integral solution of the 2-D scalar wave equation. Application of the extrapolation algorithms to synthetic data shows that they provide accurate datum corrections even for a nonplanar input datum and vertical and lateral velocity variations. The algorithms have been successfully applied to real data.
On the problem of estimating the depth to the magnetic basement
Authors: Tarlowski C. , Koch I.
Published: October 2002

In many applications in aeromagnetics, the estimation of the depth to the crystalline magnetic basement is of great importance. Of many approaches to this problem, the most widely applied appear to be based upon Fourier analysis (see Ruotoistenmäki, 1987) or on fitting hypothetical models to observed data using a least‐squares principle (for example, Leite and Leão, 1985). Recently, some interest has been focused on direct approaches to the problem (Strakhov and Brodsky, 1986; Koch and Tarlowski, 1986; and Jonca and Vogel, 1987).
Paraxial ray Kirchhoff migration
Authors: Keho T. H. , Beydoun W. B.
Published: October 2002

A rapid nonrecursive prestack Kirchhoff migration is implemented (for 2-D or 2.5-D media) by computing the Green’s functions (both traveltimes and amplitudes) in variable velocity media with the paraxial ray method. Since the paraxial ray method allows the Green’s functions to be determined at points which do not lie on the ray, two‐point ray tracing is not required. The Green’s functions between a source or receiver location and a dense grid of thousands of image points can be estimated to a desired accuracy by shooting a sufficiently dense fan of rays. For a given grid of image points, the paraxial ray method reduces computation time by one order of magnitude compared with interpolation schemes. The method is illustrated using synthetic data generated by acoustic ray tracing. Application to VSP data collected in a borehole adjacent to a reef in Michigan produces an image that clearly shows the location of the reef.
A new algorithm for finite‐difference migration of steep dips
Authors: Guan‐quan Zhang , Shu‐lun Zhang , Ying‐xiang Wang , Chau‐ying Liu
Published: October 2002

One‐way wave propagation is formulated in the (x, t) domain as an integro‐differential equation and is applied to the migration of stacked data. A key step is to replace the phase‐shift square root in the frequency‐domain representation by an integral of a rational function; the resulting expression is interpreted in the space‐time domain. Approximating the integral by a finite sum leads to a number of practical approximations, the lowest order being Claerbout’s 15 degree equation and others being various high‐order equations in the literature. Optimal mth‐order quadrature formulas based upon Chebychev criteria suggest a second‐order approximation which takes 20 percent more time than the 15 degree equation but is accurate to over 50 degrees.
On the theory of air‐gun bubble interactions
Authors: Bailey R. C. , Garces P. B.
Published: October 2002

Calculation of the seismic signatures of marine air‐gun arrays often requires that the interactions among the bubbles from air guns be taken into account. The standard method of doing this is to use the Giles‐Johnston approximation in which a time‐dependent effective ambient pressure is calculated for each bubble as the sum of the true ambient pressure and the local pressure signals of all the other bubbles in the array. These effects of interaction have a relative importance in the dynamics proportional to (R/D), where R and D are the typical bubble radius and interbubble separation, respectively. To ensure that current methods of calculating signatures are accurate, it is necessary to know how good this approximation is. This paper shows that there are no interaction terms in the full dynamical equations proportional to [Formula: see text] or [Formula: see text], and that the errors of the Giles‐Johnston approximation are only of order [Formula: see text]. The Giles‐Johnston approximation is therefore justified even for fairly accurate signature calculations for noncoalescing bubbles. The analysis here also shows how to incorporate bubble motions and deformations into the dynamical equations, so that the errors can be reduced to order [Formula: see text] if desired.
Vertical seismic profile sonde coupling
Authors: Gaiser James E. , Fulp Terrance J. , Petermann Steve G. , Karner Gary M.
Published: October 2002

P-wave and S-wave displacements occur at high angles of incidence in vertical seismic profiles (VSPs). Therefore, the coupling of a geophone sonde to the borehole wall must be rigid in all directions. A sonde that is well coupled should have no resonant frequency within the seismic band and should provide geophone outputs that accurately represent the earth’s ground motion. An in‐situ coupling response experiment conducted under normal VSP field conditions provides a measure of the sonde‐to‐borehole wall coupling. The sonde is locked in the borehole and a surface source is excited at different offsets and azimuths. An analysis of the P-wave direct arrivals enhances damped oscillations that represent an estimate of the coupling impulse response. This response is characterized by the viscoelastic behavior of a Kelvin model related to the complex compliance [Formula: see text], where κ is the elastic spring constant, η is the damping constant, and ω is the angular frequency. The complex modulus κ−iωη is proportional to the contact width of the sonde with the borehole wall. Increasing the width by a factor of 4.5 causes a similar increase in κ−iωη where the resonant frequency and initial amplitude of the coupling impulse response increase by a factor of two. Also, the initial amplitude of the coupling impulse response appears to be inversely proportional to the locking force of the sonde. For a constant contact width, increasing the locking force by a factor of 1.37 decreases the amplitude of the response by 3.5 dB.