bluuebunny/crossref_metadata_2025 huggingface dataset:
Full‐wave acoustic logging: synthetic microseismograms and frequency‐wavenumber analysis
Authors: Schmitt Denis P. , Bouchon Michel
Published: October 2002

The discrete wavenumber method is used to compute synthetic full‐waveform acoustic logs in axisymmetric multilayered boreholes and to perform the frequency‐wavenumber analysis of the radiated wave field. The stress‐displacement vector is propagated through the layers using a numerically improved formulation of the Thomson‐Haskell method. In the time domain, all the trapped and interface modes overlap. On the contrary, the representations of the spectral energy density of the scattered wave field in the frequency axial‐wavenumber domain, for various radial positions of observation, allow the recognition and identification of the different wave types as well as their repartition of energy. In particular, these diagrams show the close relation between the resonance frequencies of the borehole and the significant low‐frequency energy of the pseudo‐Rayleigh modes. They also facilitate the interpretation of some of the physical phenomena which occur during the propagation in a complex borehole environment. We present the configurations of a well‐bonded and unbonded cased hole, an invaded zone, and a mudcake. For all of these models, we consider a “fast” formation in which the S-wave velocity is higher than the bore fluid velocity and a “slow” formation. The presence of an elastic tool at the center of the borehole is also investigated. The associated microseismograms, computed for a series of source‐receiver spacings, characterize in the time domain the observations previously made.
On: “Comparison of P‐ and S‐wave seismic data: A new method for detecting gas reservoirs” by R. A. Ensley (GEOPHYSICS, 49, 1420‐1431, September, 1984).
Authors: Winterstein D. F.
Published: October 2002

Ensley’s paper was based on data of the Conoco Shear Wave Group Shoot of 1977–1978; hence, many companies besides Exxon, including my own, have the Putah Sink data he showed. The stacked sections he showed look identical to the Conoco brute stacks furnished to group shoot participants. The brute stacks had no residual statics or stacking velocity corrections. Those of us who have processed S-wave data often have been pleasantly surprised at how much improvement can come from careful application of residual statics and stacking velocity corrections. Our experience shows that it is unwise to interpret stacked S-wave data that have not had benefit of such refinements.
Physical characterization of rock masses using borehole methods
Authors: Dyck Alfred V. , Young R. Paul
Published: October 2002

A convenient view of geophysical phenomena is based on the categorization of techniques according to the governing partial differential equation: the Laplace, diffusion, or wave equation. Each category is examined (nonmathematically) in the context of those borehole methods used to investigate large volumes of a rock mass away from the borehole in which the instrumentation is deployed. The published literature reflects the variety of applications, some of which occur more frequently than others. Our discussion of the physics focuses on electric‐potential, electromagnetic‐induction, and seismic methods, respectively, as representatives of each category. Choice of a single technique for characterization of rock masses involves a compromise which depends upon the geophysical problem and the type of information desired. The complementary nature of the information means, however, that integrated studies using two or more types of methods may be worthwhile.
Surface‐consistent residual statics estimation by stack‐power maximization
Authors: Ronen Joshua , Claerbout Jon F.
Published: October 2002

Application of incorrect static shifts will decrease the power of the common‐depth‐point stack. Conversely, static shifts can be estimated by maximizing the stack power. We tried it and it worked well enough that we recommend it in routine practice for data with low signal‐to‐noise ratio. Likewise, stack power was maximized by adjustment of surface‐consistent phase correction.
Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit
Authors: Thomsen Leon
Published: October 2002

The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the “Self‐Consistent” (S-C) model (developed to deal with finite concentrations of heterogeneities) violates these predictions and hence is not consistent with the underlying Biot‐Gassmann theory. [The special case of S-C theory, corresponding to pores only (no cracks), is consistent with the B-G model.] A new formulation of the model theory, for finite concentrations of heterogeneities of ideal shape, is developed so as to be explicitly consistent with B-G. This “Biot‐consistent” (B-C) formalism is the first theory truly suitable for modeling most sedimentary rocks at seismic frequencies, in terms of porosity and pore shape.
Spontaneous polarization associated with porphyry sulfide mineralization
Authors: Corry Charles E.
Published: October 2002

In the years 1978 through 1981, many spontaneous polarization (SP) surveys of porphyry sulfide deposits and prospects were done in the western United States. Effective depth of exploration using SP was found to exceed 1 km for large porphyry sulfide orebodies. The relationship between depth of erosion since time of emplacement and the spontaneous polarization observed on the surface, together with the effects of weathering, are presented from field surveys over known deposits. Successful use of the spontaneous polarization technique in porphyry sulfide exploration led to an investigation of the causative mechanism. The field data do not support the electrochemical model first proposed in Sato and Mooney (1960). The measured potential appears to be simply the oxidation potential ΔE between a reference electrode outside the mineralization and a roving electrode within the mineralization. The ΔE measured in the field is dominated by the difference in Eh (ΔEh) potential between the two electrodes, but it is not equivalent due to the unavoidable inclusion of other potentials in the field measurement. Without a wire connecting the electrodes, current between the sulfide mineralization and the surrounding country rock is sensibly zero, as evidenced by the persistence of the sulfides through geologic time.
Computational and asymptotic aspects of velocity inversion
Authors: Bleistein Norman , Cohen Jack K. , Hagin Frank G.
Published: October 2002

We discuss computational and asymptotic aspects of the Born inversion method and show how asymptotic analysis is exploited to reduce the number of integrations in an f-k like solution formula for the velocity variation. The output of this alternative algorithm produces the reflectivity function of the surface. This is an array of singular functions—Dirac delta functions which peak on the reflecting surfaces—each scaled by the normal reflection strength at the surface. Thus, imaging of a reflector is achieved by construction of its singular function and estimation of the reflection strength is deduced from the peak value of that function. By asymptotic analysis of the application of the algorithm to the Kirchhoff representation of the backscattered field, we show that the peak value of the output estimates the reflection strength even when the condition of small variation in velocity (an assumption of the original derivation) is violated. Furthermore, this analysis demonstrates that the method provides a migration algorithm when the amplitude has not been preserved in the data. The design of the computer algorithm is discussed, including such aspects as constraints due to causality and spatial aliasing. We also provide O‐estimates of computer time. This algorithm has been successfully implemented on both synthetic data and common‐midpoint stacked field data.
Ridge regression applied to the inversion of two‐dimensional aeromagnetic anomalies
Authors: Leite Lourenildo W. B. , Leão Jorge W. D.
Published: October 2002

The methodology presented was developed for processing and mathematical interpretation of aeromagnetic data derived from two‐dimensional sources. The inversion is based on the ridge regression technique as extended in Marquardt (1963) to nonlinear problems. The mathematical formulation provides a statistical approach for study of the efficiency of the solution. A procedure for data preparation is presented which includes a critical evaluation of the digital data obtained during the aerosurvey, joining of flight segments into a single line, and regional‐residual separation for profile analysis to set up the initial model approximation. The forward model is analyzed using predictive diagnostics called sensitivity coefficients and parameter correlation matrix. The parameter confidence intervals take into account the measurements of the nonlinearity of the quadratic approximation to the object function. The initial approximation is determined by profile analysis and by the geologic information that defines the forward model and its constraints. The nonuniqueness of the solution results in an interpretation that can be refined as new geologic information is applied for additional model constraints. Synthetic models are used to test and study the convergence and statistical properties of the solution, and to show the ability of the method to resolve anomalies due to various sources. The procedure is also applied to data obtained from aerosurveys over an oil exploration area of the upper Amazon sedimentary basin of Brazil. The validity of the solution is discussed in terms of its compatibility with the geologic information and constraints, and in terms of the statistical properties of the model parameters used to explain the observed data.
Transient electromagnetic response of a thin conducting plate embedded in conducting host rock
Authors: Rai S. S.
Published: October 2002

The transient response of a thin, rectangular conducting plate in a conductive host medium is presented for a horizontal‐loop electromagnetic (EM) system considering both a step and pulse EM method (PEM) excitation. For a shallow plate‐like conductor, the current‐gathering effect is preceded by a blanking effect. However, for deeper plates, current gathering was not observed. The effect of increasing plate depth, the ratio of the time constant of the plate to that of the host, and the plate time constant on the temporal characteristics of blanking and current gathering are investigated. The onset time for current gathering is independent of the plate time constant and is essentially a property of the host medium. At later observations (⩾5 ms) the decay of the plate in the host resembles the decay of the plate in free air. An interpretation scheme is proposed to determine plate parameters for Crone PEM measurements using the responses in two relatively late time channels.
Deconvolution of noisy seismic data—A method for prestack wavelet extraction
Authors: Newman Barry J.
Published: October 2002

The presence of random additive noise is the most important degrading factor in the deconvolution of seismic data. Noise‐induced distortion of signal phase and amplitude produces severe stack attenuation, makes poststack recovery difficult with spectral enhancement techniques, and leaves the stratigraphic imprint unclear. The random noise component in the data is estimated from trace segments before the first arrivals and at the bottom of the record beyond seismic basement. An autocorrelation of this noise is used to adjust the signal autocorrelation prior to Wiener‐Levinson deconvolution filter design. To improve the robustness of the technique, an iterative surface‐consistent wavelet solution (common source, receiver, and offset) is used in preference to a single‐channel operation. Use of this deconvolution technique is shown by synthetic and case examples to result in correct phase alignment, enhanced stacking fidelity, and extended signal bandwidth even on very noisy data. The improvement, coupled with sensible handling of coherent noise energy, is crucial for the interpretation of subtle statigraphic plays in many areas.
Reconstruction of reflecting structures from vertical seismic profiles with a moving source
Authors: Köhler K. , Koenig M.
Published: October 2002

When a vertical seismic profile (VSP) is recorded, the illuminated part of a reflector depends upon the shape and position of the reflector itself as well as on the seismic velocities and the positions of sources and receivers. A preferable arrangement for the investigation of structures of reflectors is to fix the receiver(s) at constant depth(s) in the well and move the source horizontally along a line at the Earth’s surface, usually called a “multioffset VSP” (MSP) or “walkaway VSP.” As a test of the resolution power of this survey geometry, synthetic records were generated from a subsurface model by inverse Kirchhoff migration. Three different methods were applied for the reconstruction. Wavefront construction leads to the correct shape of the reflectors, thus assuring the validity of the modeling method applied. Reflection‐point mapping delivered a near similarity to the model, but without focusing fault edges. Kirchhoff migration resulted in a detailed image of the reflectors with fault edges focused. Application of reflection‐point mapping and Kirchhoff migration to a real survey delivered results consistent with results from a survey at the Earth’s surface.
Inversion of aeromagnetic data for multilayered crustal models
Authors: Pilkington Mark , Crossley D. J.
Published: October 2002

A common problem in interpreting aeromagnetic data involves mapping of a single magnetic crystalline basement interface overlain by nonmagnetic sedimentary rocks. The solution of this problem, as discussed in Pilkington and Crossley (1986), provides important geologic information. However, difficulties arise where the magnetic effects of the crystalline magnetic interface are obscured by intrusives or volcanic flows within the sedimentary sequence. The resulting problem in the interpretation requires separation of the two effects, so that the modeling problem will be tractable. Unfortunately, in view of the spectral overlap of fields from sources at different depths (e.g., Bhattacharyya, 1966), a perfect separation is not possible. This condition has led to the subjective approach of simply dividing the observed field into low‐wavelength and high‐wavelength parts and interpreting each one independently (Lehmann, 1970; Sprenke and Kanasewich, 1982). An alternative method has been advocated by Spector and Parker (1979) who separate the two effects based on power spectral analysis of the observed field.
A simple method for determining the S80 water gun depth
Authors: Safar M. H.
Published: October 2002

The water gun, which is becoming a popular seismic source, has proven to be an important development in marine oil prospecting. The principal reason is that, unlike the air gun, the pressure signature radiated by the water gun consists of a single bubble pulse and contains a high level of high‐frequency signal. These important features make the water gun a suitable seismic source for high‐resolution surveys. Water guns currently used are the S80, which has been used by Horizon since 1977, and the P400, introduced in 1983. The S80 and P400 water guns were developed by Sodera.™
Transient electromagnetic response of the Teutonic Bore orebody
Authors: Buselli G. , McCracken K. G. , Thorburn M.
Published: October 2002

Transient electromagnetic (TEM) measurements have been made with SIROTEM on four separate surveys over the Teutonic Bore orebody (Western Australia), both before mining operations began and subsequently during different stages of stripping overburden from the mineral deposit. In the late stage of the transient decay the target response was relatively free of the overburden and host‐rock response. Beyond ∼ 6 ms, the maximum anomalous response was a factor of 8 to 10 greater than the combined overburden and host‐rock response. Analog modeling with a copper plate in free space shows that the TEM response of the target consists of a single peak at early delay times, while at delay times beyond ∼ 4.2 ms, the response becomes a double‐peak anomaly with a low directly over the top of the plate. Mathematical modeling of the TEM response with a free‐space infinitely thin plate produces profile characteristics similar to those obtained by analog modeling beyond a delay time of ∼ 4.2 ms. Inversion of premining survey profiles in the delay time range 7.0 to 13.2 ms gives values of 82 m for target depth d, and 86 degrees for dip angle θ. These agree well with the values d = 86 m and θ = 82 degrees derived from drilling data. A target conductance value in the range 250 to 320 S is obtained from the TEM data, indicating that the massive sulfide target is highly conductive. Responses calculated for surveys made during overburden stripping are lower than corresponding field values at early delay times because of the absence of overburden response in the model measurements. At delay times beyond 8.5 ms, the model values are consistent with the field values. These results indicate that for a case similar to the Teutonic Bore orebody, where the maximum anomalous late‐time response is a factor of 8 to 10 times greater than the background response, important target parameters may be derived from free‐space models.
Gravity inversion using open, reject, and “shape‐of‐anomaly” fill criteria
Authors: René R. M.
Published: October 2002

A gravity inversion method is developed by iteratively applying open, reject, and fill (O-R-F) criteria within a model space comprising a great many rectangular prisms. Each prism is assigned a density contrast. The modeling procedure consists of filling some prisms while leaving others empty. Only one element is filled for each pass. Generally, elements are added only to the periphery of the growing model. Models can be allowed to grow in any combination of directions, or in all directions. By application of a “shape‐of‐anomaly” fill criterion, the model rapidly attains a form which yields gravity approximating the given gravity scaled down by some constant factor. As the model continues to grow, this scale factor approaches unity. The method readily yields inverse models comprising several thousand individual prisms. Examples presented here give applications to 2-D problems. The method is readily applicable to [Formula: see text] and 3-D problems as well. Overhanging elements are obtained by appropriate use of model constraints. Initial density models are not required but they are allowed. An “expanding seed” method is explained which efficiently generates sets of inverse models by using dense models to initiate development of less dense models. The method is applied to inversion of several synthetic gravity profiles from known density models. A density model is also derived from gravity across the Troodos massif in Cyprus. Using a density contrast of [Formula: see text], the resultant model extends from the surface to a depth of 20.6 km and has a center of mass distribution displaced approximately 7 km to the northeast of the anomaly peak.
Signal penetration In the COCORP Basin and Range‐Colorado Plateau survey
Authors: Mayer James R. , Brown Larry D.
Published: October 2002

Seismic sections from COCORP’s 1982 survey from the eastern Basin and Range to the Colorado Plateau of central Utah exhibit distinct cutoff times after which reflections are rare to nonexistent. In the eastern Basin and Range, this cutoff time is approximately 11 s (33 km), but beneath the central Colorado Plateau it exceeds 15 s (45 km). These depths appear to correspond to the base of the crust (Moho), with the lack of reflections from greater depths indicating mantle homogeneity. In general, absence of deeper reflections may be due either to geologic homogeneity or to lack of signal penetration. COCORP line 3 in the Colorado Plateau‐Basin and Range transition zone shows that variations in penetration are significant. On line 3 few reflections are evident below the structurally complex sedimentary cover, which extends to only 4 s (8 km), and virtually none are identifiable later than 7 s (21 km). Lateral variations in the temporal decay of source‐generated energy, together with estimates of corresponding ambient noise levels, infer that limited signal penetration, rather than geologic homogeneity, causes the lack of subsedimentary reflections within the transition zone. Deep reflections, if any, from beneath the westernmost Colorado Plateau appear to be masked by unusually high local environmental noise. In contrast, continued decay of source‐generated energy at traveltimes significantly greater than Moho arrival times within the Basin and Range and Colorado Plateau suggests (though it cannot confirm) that the underlying mantle is seismically transparent. Variations in signal penetration, such as those documented here, severely constrain interpretations of nonreflective zones in deep reflection data and should be a standard estimation in any interpretational procedure.
Simultaneous pre‐normal moveout and post‐normal moveout deconvolution
Authors: Claerbout Jon F.
Published: October 2002

Wave theory justifies both pre‐ and post‐NMO deconvolution, but the filters should be estimated simultaneously, not sequentially. A linearized theory enables simultaneous estimation of the two filters. The theory incorporates spherical divergence independently from statistical weighting. Field data test cases show the expected interaction between NMO and deconvolution. The tests were not able to establish that simultaneous estimation is superior to sequential estimation. The difficulty is ascribed to the inadequacy of NMO as a downward continuation process.
Prestack layer replacement
Authors: Yilmaz Oz , Lucas Darran
Published: October 2002

We present a method of layer replacement based on the Kirchhoff integral solution to the scalar wave equation. The term “layer replacement” refers to replacing the overburden velocity with the velocity of the substratum, thereby eliminating raypath bendings at the interface between the overburden and the substratum. It is the raypath bendings that induce distortions and disruptions on reflections beneath a complex structure. When implemented before stack, layer replacement provides an opportunity to revise velocity estimates after correcting for the nonhyperbolic moveout on CMP data caused by a complex overburden. As a result, layer replacement also yields an improved unmigrated stack section. Imaging can then be completed by time migration after stack. We demonstrate the layer‐replacement technique on field data with irregular water‐bottom topography.
Submarine canyons: Velocity replacement by wave‐equation datuming before stack
Authors: Berryhill John R.
Published: October 2002

Submarine canyons incised into the continental slope interfere with the quality of common‐midpoint (CMP) stacked seismic data obtainable from reflectors beneath the sea floor. The interference problem is caused by rough topography in conjunction with the contrast between the acoustic velocity of sea water and the velocity of the exposed rock layers. Geophysicists have long recognized that part of the solution is to replace the traveltimes of raypaths through the water by their traveltimes through an identical thickness of rock. However, use of wave‐equation datuming to effect velocity replacement yields an additional correction for the change in raypath direction that occurs in crossing from rock to sea water; the wave‐equation datuming implementation of velocity replacement is more comprehensive and complete. The wave‐equation datuming method requires an accurate sea‐floor profile as part of the input, along with values of replacement velocity; it does not require knowledge of geology or velocities at depths much greater than the sea floor. Unstacked common‐source and common‐receiver records are processed to appear as if sources and receivers were moved to the water bottom; the velocity of water is replaced; and the sources and receivers are moved back to the sea surface through the replacement medium. The computational method is well‐suited to the irregular surfaces and laterally variable velocities inherent in the problem of submarine canyons. The advantage of this method is that the corrected seismic records accurately emulate the data that would actually be observed if the acoustic velocity of water could be changed physically. The normal‐moveout (NMO) velocity for optimum CMP stacking becomes the root mean square of the layer velocities, including the velocity substituted for that of water. The spurious lateral variation of stacking velocity in the original data is eliminated. Processing of the corrected data through velocity analysis, stacking, migration, and conversion to depth is therefore more reliable.
Dip moveout in shot profiles
Authors: Biondi Biondo , Ronen Joshua
Published: October 2002

All the known dip‐moveout (DMO) algorithms that are not integral methods require the seismic data to be sorted in regularly sampled constant‐offset sections. In contrast, the dip‐moveout method proposed here can be applied directly to recorded shot profiles and thus can handle data that cannot be sorted in regular constant‐offset sections. The definition of the shot‐DMO operator is analogous to that of the dip‐moveout operator for constant‐offset sections. The two operators have impulse responses with the same projection on the zero‐offset plane, i.e., the stacking plane; therefore, the application of dip moveout in constant‐offset sections or in shot profiles gives the same stacked section. Dip moveout transforms shot profiles to zero‐offset data, to which any poststack migration can be applied. The shot‐DMO operator is space‐variant and time‐ variant; thus direct application of the operator would be computationally expensive. Fortunately, after a logarithmic transformation of both the time and the space coordinates, the operator becomes time‐invariant and space‐invariant; then dip moveout can be performed efficiently as a multiplication in the Fourier domain. Shot dip moveout is also a useful tool for improving the accuracy of residual velocity analysis performed after the DMO process. Field‐data examples show that the shot‐profile dip‐moveout method yields stacked sections similar to those from Hale’s (1984) dip moveout for constant‐offset sections.
Fast frequency‐wavenumber migration for depth‐dependent velocity
Authors: Müller G. , Temme P.
Published: October 2002

Fast frequency‐wavenumber migration for a constant‐velocity medium is generalized for a medium with depth‐dependent velocity and density. As in the constant‐velocity case, the migrated section is obtained with one inverse Fourier transformation of the modified spectrum of the observed wave field. The migrated section is exact in a preselected focusing depth (in the case of common‐midpoint and plane‐wave migration) or in a preselected focusing point (in the case of single‐shot migration) and in the vicinity of this depth or point. Elsewhere the migrated section is distorted. The method is in essence a constant‐velocity migration with the velocity [Formula: see text] at the target depth [Formula: see text] (not with an average velocity), extended by a phase‐shift operation which takes account of the true velocity‐depth function v(z) between z = 0 and [Formula: see text]. If the focusing depth or point is located in a layer with constant velocity and density, the migrated section is exact throughout the layer (for CMP and plane‐wave migration) or along the segment of the ray from shot to focusing point, running through the layer (for single‐shot migration). Examples are given for the successful migration of the plane‐wave response of a horizontally layered medium at vertical and oblique incidence and for the single‐shot response of a horizontally layered structure with embedded reflector elements. The method appears to be particularly useful for the investigation of subsurface structures with restricted dimensions; because of its speed, interactive data interpretation is possible.
Use of ground‐probing radar and resistivity surveys for archaeological investigations
Authors: Imai Tsuneo , Sakayama Toshihiko , Kanemori Takashi
Published: October 2002

In Japan, geophysical methods are normally used to estimate the distribution of cultural relics before digging. Objects of archaeological interest are usually located within a few meters of the surface. Therefore, geophysical methods suitable for archaeological exploration are those which provide high resolution at shallow depths. The most commonly used geophysical methods are ground‐probing radar, resistivity, and magnetometry. Of these methods, we used mainly ground‐probing radar and resistivity surveys in archaeological investigations at four sites. Three of the sites were in Gumma Prefecture (Japan); they were covered with volcanic deposits (loam or pumice). Using ground‐probing radar, we were able to locate ancient dwellings, burial mounds, and a distribution of archaeologically significant “culture layers.” At the other site, in Nara Prefecture, we located part of the remains of an ancient city. In this investigation, the resistivity method and ground‐probing radar were combined to determine the location of an underground water course within the ancient city.
Permeability determination in crystalline rocks by standard geophysical logs
Authors: Katsube T. J. , Hume J. P.
Published: October 2002

The formation factor (ratio of bulk resistivity of rock to resistivity of formation fluid) obtained from the focused‐electrode log can be used to estimate the hydraulic conductivity of the unfractured granitic rock matrix [Formula: see text], using an empirical relationship developed between laboratory measurements of formation factor and permeability. The ratio of the formation factor derived from the focused‐electrode log [Formula: see text] to the formation factor derived from the density log [Formula: see text] may be used to estimate the hydraulic conductivity of fractured zones [Formula: see text], because of the following empirical relationship between the transmissivity [Formula: see text] obtained from the in situ hydrogeologic tests and the ratio of the two formation factors, namely, [Formula: see text] where A and s are coefficients [Formula: see text]. This empirical relationship confirms the usefulness of geophysical logs for identifying intervals of potentially high permeability in boreholes drilled in granitic rock. Estimates of hydraulic conductivity derived using these relationships can help obtain a qualitative understanding of hydrological conditions in a crystalline rock mass.
Smoothing spectral gamma logs: A simple but effective technique
Authors: Mathis Gary L.
Published: October 2002

Spectral gamma‐ray logs suffer from unusually poor counting statistics because of the extremely low counting rates used to compute the concentrations of potassium (K), uranium (U), and thorium (T). Filtering is therefore a prerequisite to interpretation. Kalman filtering has been suggested, but this approach is complex and involves uncertain assumptions. Simple weighted averaging, on the other hand, fails to take into account abrupt changes that can occur in geologic response. Effective filtering of real logging data is possible, however, by a simple adaptive filter which uses the total gamma responses of a gamma‐ray tool to compute filter weights based on the error function. This filter is mathematically and computationally simple to implement for real time or postprocessing of spectral gamma logs.
On: “When reflection coefficients are zero,” by F. K. Levin (GEOPHYSICS, 51, 736–741, March 1986).
Authors: Ursin Bjørn
Published: October 2002

In an interesting recent paper, Levin discusses when the PP reflection coefficient is zero for plane P-SV waves at an interface between two homogeneous half‐spaces. The expression for the reflection coefficient is given as a ratio between a numerator and a denominator, and the zeros are obtained by setting the numerator equal to zero.
Seismic wave synthesis by Gaussian beam summation: A comparison with finite differences
Authors: George Th. , Virieux J. , Madariaga R.
Published: October 2002

We apply Gaussian beam summation to the calculation of seismic reflections from complex interfaces, introducing several modifications of the original method. First, we use local geographical coordinates for the representation of paraxial rays in the vicinity of the recording surface. In this way we avoid the time‐consuming evaluation of the ray‐centered coordinates of the observation points. Second, we propose a method for selecting the beams that ensures numerical stability of the synthetic seismograms. Third, we introduce a simple source wave packet that simplifies and stabilizes the calculations of inverse Fourier transforms. We compare reflection seismograms computed using the Gaussian beam‐summation method with those calculated by finite differences. Two simple models are used. The first is a continuous curved interface separating an elastic layer from a free half‐space. A double caustic, or degenerate focal point, appears due to the crossing of reflected rays. In this instance the finite‐difference simulation and the Gaussian beam summation are in excellent agreement. Both phase and amplitude are modeled correctly for both the direct and reverse branches. When compared to geometrical ray theory, Gaussian beam summation provides a good approximation of the field near the caustics while geometrical ray theory does not. The second, more complex, model we consider is a trapezoidal dome with sharp corners in the interface. The corners of the dome in this model produce rather strong diffractions. Also, creeping head waves propagate along the interface. The results compare well with the finite‐difference simulation except for the diffracted branches, where the traveltime of diffracted waves is poorly approximated by the Gaussian beam‐summation method.
Local Fourier transform of the Helmholtz wave equation
Authors: Hildebrand Steve
Published: October 2002

A local Fourier transform of a wave field is an integral transformation from space‐time coordinate space to phase space, i.e., ray parameter, spatial coordinate, and intercept‐ time space. McMechan (1983) introduced the concept of a local slant‐stack/Fourier transform. Using this integral transform, he was able to define a wave field in phase space. By projecting the resulting wave field to the spatial coordinate space, he obtained a representation of the wave field in the ray‐parameter and the spatial‐coordinate plane. In this paper, the local Fourier method is used to transform the Helmholtz wave equation into a phase‐space coordinate system. The resulting wave equation is then written in a state‐variable form of coupled first‐order differential equations. A propagator solution is then shown.
Determination of the coherent condition for the scattering of an acoustic wave with an arbitrarily shaped wavefront by a curved area
Authors: Ewaida M. A.
Published: October 2002

The investigation of wave scattering has become one of the most important and urgent problems of seismology and seismic prospecting. Layered media, the traditional objects of seismic investigations, have physical properties which slowly change across certain smooth and extended surfaces.
Fracture detection using P-wave and S-wave vertical seismic profiling at The Geysers
Authors: Majer E. L. , McEvilly T. V. , Eastwood F. S. , Myer L. R.
Published: October 2002

In a pilot vertical seismic profiling study, P-wave and cross‐polarized S-wave vibrators were used to investigate the potential utility of shear‐wave anisotropy measurements in characterizing a fractured rock mass. The caprock at The Geysers geothermal field was found to exhibit about an 11 percent velocity variation between SH-waves and SV-waves generated by rotating the S-wave vibrator orientation to two orthogonal polarizations for each survey level in the well. The effect is generally consistent with the equivalent anisotropy expected from the known fracture geometry.
Constraint criteria for adjustment of potential field surveys
Authors: Peters Mary F. , Brozena John M.
Published: October 2002

In airorne gravity surveys, as well as in airborne magnetics and shipboard gravity and magnetics surveys, discrepancies between measurements on different tracks may exist at the intersections of those tracks. Advances in navigational systems, such as the implementation of the Global Positioning System, reduce discrepancies due to mislocation; but discrepancies from other sources remain. These misties should be removed before procedures such as contouring the data set or performing two‐dimensional (2-D) analyses are performed. Various approaches have been used to remove misties, but the most reasonable is to estimate the most likely error and subsequently adjust the data. The procedure is to hypothesize the “shape” of the error along the tracks and then to find errors that minimize[Formula: see text]Error minimization has been carried out for various types of surveys with different error models (e.g., Zurflueh, 1968; Yarger et al., 1978, Sander and Mrazek, 1982). The general method is applicable to airborne gravity surveys but requires some changes from applications to other types of surveys. Based on techniques we have used for airborne gravity surveys, we propose modifications which should also be useful in applying the method to a wider class of adjustment problems.
Numerical verification and extension of an analytic generalized inverse for common‐depth‐point and vertical‐seismic‐profile traveltime equations
Authors: Schuster Gerard T. , Johnson Daniel P. , Trentman Daniel J.
Published: October 2002

This paper empirically establishes the range of validity for an analytic generalized inverse (assuming negligible ray bending) associated with one‐dimensional vertical seismic profiles (VSP) or common‐depth‐point (CDP) traveltime equations. Computer tests show that the analytic inverse closely predicts the condition number of [Formula: see text] and roughly predicts some features of the unit covariance matrix for a source offset‐to‐well depth ratio less than 1. The analytic inverse is invalid for offset‐to‐depth ratios greater than 1; i.e., when ray bending becomes severe enough to violate the assumption of negligible ray bending. To overcome the restriction of negligible ray bending, we extend the analytic inverse to traveltime equations which honor Snell’s law. Computer tests show this extended inverse is a good approximation to the actual generalized inverse. The extended inverse appears to be valid for any practical source‐receiver offset and any layered velocity structure. The important implication is that, prior to their execution, VSP or CDP experiments (over approximately one‐dimensional structures) can now be designed for optimal velocity resolution. No numerical inverses need to be computed and the condition number, covariance matrix, resolution matrix, and inverse matrix are closely approximated by analytic formulas. This development promises to allow accurate and efficient velocity analysis of VSP data or CDP gathers by least‐squares traveltime inversion.
On: “Weak elastic anisotropy,” by L. Thomsen (GEOPHYSICS, 52, 1954–1966, October, 1986).
Authors: Levin Franklyn K.
Published: October 2002

In a paper whose importance seems to have escaped notice, Thomsen (1) derived equations that give the moveout velocities of P, SV, and SH-waves when solids are weakly transversely isotropic and (2) tabulated experimentally determined elastic constants for a large number of rocks, crystals, and a few other solids. For rocks, one of the constants, delta, differed from zero by as much as 0.73 and −0.27. Delta is the fraction by which P-wave moveout velocity deviates from the vertical velocity [Thomsen’s equation (27a)]. Although some deltas indicated deviations from the vertical velocity smaller than 1 or 2 percent, most were larger and positive. Until the publication of Thomsen’s data, most of us concerned with elastic waves traveling in earth sections that act as transversely isotropic solids because the sections consist of thin beds had assumed the individual beds were isotropic solids, all with the same Poisson’s ratios. That assumption results in a zero value for delta and a moveout velocity equal to the vertical velocity. The validity of the assumption is now doubtful.
The reconstruction of the magnetotelluric impedance tensor: An adaptive parametric time‐domain approach
Authors: Yee E. , Kosteniuk P. R. , Paulson K. V.
Published: October 2002

Magnetotelluric (MT) data processing for the estimation of the impedance tensor is usually carried out in the frequency domain using nonparametric methods of spectral analysis. In this paper, the impedance tensor is reconstructed using an adaptive parametric time‐domain approach, whereby the observed MT data are used directly in the estimation process without the need for a frequency‐domain transformation. In such a reconstruction, the impedance tensor is represented by a rational‐form or matrix‐fraction model. The parameters for this model are determined using a recursive instrumental variables (RIV) adaptation algorithm, allowing on‐line real‐time application. This adaptation algorithm is capable of providing consistent estimates for the impedance tensor from only the observed (i.e., noisy) MT field data and auxiliary information in the form of measurements of the contemporaneous components of the magnetic field at some remote site. Hence, the RIV algorithm provides a time‐domain implementation of the remote‐reference MT method, which has been applied with good success for unbiased impedance tensor determination in the frequency domain for moderate‐to‐high‐level noise conditions.
Three‐dimensional elastic modeling by the Fourier method
Authors: Reshef Moshe , Kosloff Dan , Edwards Mickey , Hsiung Chris
Published: October 2002

Earlier work on three‐dimensional forward modeling is extended to elastic waves using the equations of conservation of momentum and the stress‐strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In addition to arbitrary compressional (or P‐wave) velocity and density variation in lateral and vertical directions, elastic modeling permits shear (or S‐wave) velocity variation as well. The elastic wave equation is solved using a generalization of the method for the acoustic case. Computation of each time step begins by computing six strain components by performing nine spatial partial differentiation operations on the three displacement components from the previous time step. The six strains and two Lamé constants are linearly combined to yield six stress components. Nine spatial partial differentiation operations on the six stresses, three body forces, and density are used to compute second partial time derivatives of the three displacement components. Time stepping to obtain the three displacement components for the current time step is performed with second‐order difference operators. The modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. This modeling scheme is implemented on a four‐processor CRAY X‐MP computer system using the solid‐state storage device (SSD). Using parallel processing with four CPUs, a reasonable geologic model can be computed within a few hours. The modeling scheme provides a variety of seismic source types and many possible output displays. These features enable the modeling of a wide range of seismic surveys. Numerical and analytic results are presented.
Iterative deconvolution using generalized “positivity”
Authors: Hornbostel Scott C.
Published: October 2002

In some cases a real signal may be known a priori to be always positive. If this positive signal is later band‐limited, the knowledge of its original positivity can be used to help in recovering the lost frequencies. Specifically, the frequency‐domain values for members of this special class of signals have the interesting property that they are related to each other via the self‐convolution of Hermitian functions. This relationship is the basis for some current deconvolution approaches and can be generalized for the case of a signal of arbitrary sign. A steepest descent formulation in the frequency domain can determine these Hermitian functions while maximizing the fit to the known in‐band data and to estimated dc values. This formulation allows for the explicit calculation of the step size and is also easily modified to include finite support or penalty/reward constraints. Simulated data tests indicate good bandwidth extension for this method, while actually sometimes improving the signal‐to‐noise ratio of the in‐band values.
Multiple suppression by optimized fold reduction
Authors: Yang Mai
Published: October 2002

Fold reduction for high‐fold data is often necessary due to cost considerations. In the presence of multiples, fold reduction can also improve multiple suppression. By keeping the differences between adjacent squared offsets constant, hyperbolic moveouts are approximately transformed to linear moveouts after fold reduction; dip filtering can then remove multiples more effectively. This approach to multiple suppression is especially attractive if fold must be reduced anyway to save the cost of dip moveout (DMO) or prestack migration. Usually fold is reduced by partial stacking. Approximately, mis‐stacking due to moveout error and reflection‐point smearing in partial stacking are proportional to squared offset. Therefore to a good approximation, optimal partial stacking for multiple suppression, as well as DMO or prestack migration, can be accomplished in the same processing step.