bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of three‐dimensional interactive modeling in gravity and magnetics
Authors: Götze H. ‐J. , Lahmeyer Bernd
Published: October 2002

Three‐dimensional (3-D) interactive modeling permits integrated processing and interpretation of gravity and magnetic data, yielding an improved geologic interpretation. 3-D model bodies are constructed from polyhedra of suitable geometry and physical parameters (density and susceptibility), input on an interactive graphics terminal that is tied to a host computer. The method is especially designed for concurrent processing and interpretation in an interactive mode. The effect on gravity of a homogeneous polyhedron is calculated by transforming a volume integral into a sum of line integrals. Magnetic effects can be modeled by using either Poisson’s theorem or a slight modification of the formulas derived for gravity modeling. The interactive modeling program allows the user to change the geometry as well as the density and/or susceptibility of the elementary polyhedra and to observe results quickly during the course of processing. This capability enables the interpreter to decide immediately if and where a tentative geologic structure must be changed for the modeled effect to fit that of a field survey. He is able to drive the device‐dependent process by clear menu functions without any knowledge of the rather complicated data structure and the interaction between the main program and its many subroutines. In addition, application of this method requires considerably less computing time than conventional methods based on the direct evaluation of volume integrals.
On: “Computing the gravitational and magnetic anomalies due to a polygon: Algorithms and Fortran subroutines” by I. J. Won and Michael Bevis (GEOPHYSICS, 52, 232–238, February 1987)
Authors: Dasgupta S. P.
Published: October 2002

I thank the authors of this article for their nice investigation. In addition, I would like to add a few observations on the comlex representation for gravity and magnetic anomalies of a 2-D polygonal body. These observations lead to considerable simplication in the mathematical forms of the anomalies, providing a straightforward computing procedure.
Improved interface detection for vertical seismic profile inversion
Authors: Dillon William G. , Spencer Terry W.
Published: October 2002

Grivelet (1985) presented an interface detection scheme as part of his iterative modeling approach to vertical seismic profile (VSP) inversion. In his scheme and those like it (Dillon, 1985), the interfaces which produce major reflections must be identified for reasons of stability and uniqueness. In general, Grivelet’s detection algorithm works well, though it sometimes fails when two events of the same polarity and amplitude overlap. By extending his detection algorithm, we obtain more robust interface detection.
Statistically perturbed geophone array responses
Authors: Aldridge David F.
Published: October 2002

Seismic‐receiver arrays implemented under typical field conditions are subject to a variety of perturbing influences. The array responses that are actually achieved differ, perhaps substantially, from the nominal response associated with ideal conditions (precise positioning, vertical plants, identical geophones, perfect ground coupling, etc.). Variations in receiver array response may degrade the effectiveness of multichannel processing and analysis schemes that rely upon channel‐to‐channel waveform constancy. In effect, array‐response variation is a form of noise added to recorded waveforms and is thus potentially harmful. A rigorous physical treatment of the response of a geophone array to incident plane‐wave elastic radiation forms the point of departure for assessing the importance of response perturbations. The hard‐wired multiple seismometer group, long transmission line, and recording‐system input impedance are considered an electromechanical system. An individual geophone may have arbitrarily specified position and axial orientation and is modeled as a ground‐motion transducer that incorporates, to first order, the effect of compliant coupling to the earth. Elastic waves (of either vibratory mode) can be incident from any direction. This generality built into the mathematical description of receiver‐array response allows numerous array types (including those designed to record shear waves) to be analyzed. All parameters that determine the response value are then subjected to controlled random perturbations in order to evaluate the statistical variability of the complex valued array‐response function. Transformation of the perturbed responses to the time domain indicates the extent of waveform variability induced by geophone‐array diversity. Computational studies indicate that, for vertical or near‐vertical plane P‐wave incidence, reasonable variations in the controlling parameters do not reduce waveform coherence by any major amount. Peak times of reflection signal recorded on well planted geophone arrays typically vary by up to 4 ms. As the angle of incidence increases or the quality of the field‐array implementation degrades, the wavelets exhibit increasing amplitude loss, wave‐shape alteration, and incoherence that may affect an interpretation.
A direct method for determining the altitude variation of the uranium stripping ratio in airborne gamma‐ray surveys
Authors: Raghuwanshi S. S. , Bhaumik B. K. , Tewari S. G.
Published: October 2002

In airborne gamma‐ray spectrometric surveys, it is essential to calculate the net counts in the thorium, uranium, and potassium channels for quantitative analysis. The net uranium, thorium, and potassium counts are given by [Formula: see text], (1a) [Formula: see text] (1b) and [Formula: see text], (1c) where [Formula: see text], [Formula: see text], and [Formula: see text] are the background corrected counts per second for uranium, thorium, and potassium channels, respectively; α and β are the Compton contributions of thorium gamma rays in the uranium and potassium windows, respectively; and γ is the contribution of uranium gamma rays in the potassium window. In some countries, such as the U.S., Canada, and India, it is common practice to compute the stripping ratios by taking measurements over a set of calibration pads with known and varying amounts of uranium, thorium, and potassium (Grasty and Darnley, 1971; Grasty, 1975; Lovborg, 1984). These factors are determined by keeping the detector system inside the survey aircraft over the calibration pads. The stripping coefficients do not have fixed values but vary with source‐detector distance. Because most airborne surveys are conducted at about 120 m above ground level, the stripping ratios measured over the pads should be corrected for variations with ground clearance. In practice, the ground clearance in airborne gamma‐ray surveys may vary from about 40 m to 200 m depending upon the topography of the area flown. It is, therefore, necessary to know the values of the stripping coefficients as a function of ground clearance at least within the range of investigations. If this is known, it is possible to apply proper corrections while converting all data to a uniform datum of 122 m.
Anisotropic velocity analysis for lithology discrimination
Authors: Byun B. S. , Corrigan D. , Gaiser J. E.
Published: October 2002

A new velocity analysis technique is presented for analyzing moveout of signals on multichannel surface seismic or VSP data. An approximate, skewed hyperbolic moveout formula is derived for horizontally layered, transversely isotropic media. This formula involves three measurement parameters: the average vertical velocity and horizontal and skew moveout velocities. By extending Dix‐type hyperbolic moveout analysis, we obtain improved coherence over large source‐geophone offsets for more accurate moveout correction. Compared with the stacking velocity obtained by simple hyperbolic analysis methods, the three velocity parameters estimated by this technique contain more physically meaningful geologic information regarding the anisotropy and/or velocity heterogeneity of the subsurface. Synthetic P‐wave model experiments demonstrate that the skewed hyperbolic moveout formula yields an excellent fit to time‐distance curves over a wide range of ray angles. Consequently, the measurement parameters are shown to reflect adequately the characteristics of velocity dependence on ray angle, i.e., velocity anisotropy. The technique is then applied to two field offset VSP data sets to measure and analyze the velocity parameters. The results show that the apparent anisotropy, defined as the ratio between the horizontal moveout velocity and average vertical velocity, correlates reasonably well with lithology. Highly anisotropic shale and chalk exhibit higher horizontal‐to‐vertical velocity ratios and sandstones show lower ratios.
Reduction to the pole at low latitudes by Wiener filtering
Authors: Hansen R. O. , Pawlowski R. S.
Published: October 2002

Using simple estimates of the signal and noise power from gridded magnetic data, we design regulated frequency‐domain operators for reduction to the pole at low magnetic latitudes. These operators suppress the artifacts along the direction of the magnetic declination associated with the conventional reduction‐to‐the‐pole procedure, with negligible increase in computational load. The new procedure is applied to produce high‐quality reductions to the pole for noisy low‐latitude synthetic data and for magnetic data from the Dixon Seamount.
On: “Seismic contouring: A unique skill” by P. M. Tucker (GEOPHYSICS, 53, 741–749, June 1988).
Authors: Stone Donald S.
Published: October 2002

As a happy owner of the popular SEG monographs by Tucker and Yorston (1973) and Tucker (1982), the appearance of Tucker (1988) as the leadoff article in the June, 1988 issue of Geophysics caught my attention, and I began reading with high expectations. Admitting that the paper was chiefly about the philosophy and mechanics of contouring seismic data, I nevertheless found it disappointing, primarily because in describing his unique seismic contouring skill, Tucker never mentions migration or its importance in the conversion of raw seismic times to three‐dimensional (3-D) geologic structure. Also, many of the statements in his paper can be challenged on the grounds of imprecision or omission in terms of real structural interpretation.
Ground‐roll suppression by the stackarray
Authors: Morse Peter F. , Hildebrandt George F.
Published: October 2002

For 2-D common‐midpoint (CMP) seismic data acquisition, ground roll can be highly attenuated and, under ideal circumstances, virtually eliminated from the stacked data if care is taken to adjust the field geometry so that the long array formed by summing the traces of a CMP gather (i.e., the stackarray) is continuous and evenly weighted. In this paper, we use synthetic field data to quantify the improvement in signal‐to‐noise ratio that can be achieved by the stackarray and to determine if such processing steps as normal moveout (NMO) correction affect the stackarray’s effectiveness. We demonstrate that, while the beneficial effects of the stackarray are mitigated somewhat by NMO correction, source‐receiver coupling variations, and static corrections, acquisition geometries that result in a discontinuous or unevenly weighted stackarray have a much more pronounced negative effect. We also compare real field data recorded with geometries that do and do not satisfy the stackarray criterion. On the basis of both synthetic and real field data examples, we conclude that proper acquisition geometry is of prime importance in the effective implementation of the stackarray strategy.
The shape of a marine streamer in a cross current
Authors: Krail P.M. , Brysk H.
Published: October 2002

A serious problem in marine data collection (particularly 3‐D) is the necessity to assign to each hydrophone a precise location on the surface of the earth. The data available for this purpose can come from the vessel’s navigation system, a radio beacon (at the tail buoy), an acoustic transponder (at the head of the streamer and occasionally elsewhere), and magnetic compasses distributed over the length of the cable. The shape of the streamer is commonly reconstructed by fitting a curve’s tangents to the compass readings. The shape deduced in this fashion is highly sensitive to compass errors. As an alternative to the ad hoc numerical fit, we have derived the shape of the streamer in a cross current from physical principles. The mechanical equilibrium of tension and drag forces leads to differential equations which we integrate analytically to obtain a formal solution for the tension. A further analytic integration yields an equation (containing two integration constants) that relates arc length along the cable to the tangent angle. This equation can be matched to compass readings (for stability and minimum error) by a least‐squares estimation of the integration constants. A satisfactory fit is obtained with a representative data set. Parametric equations are also obtained for x and y along the cable (with the x-axis in the fluid flow direction), as functions of the tangent angle; they contain the same integration constants (evaluated by the previous procedure). Elimination of the angle between the two parametric equations yields the equation of the cable shape in Cartesian coordinates.
A case history of velocity problems in the shadow of a large growth fault in the Frio formation, Texas Gulf Coast
Authors: Allen James L. , Bruso J. M.
Published: October 2002

False structures can appear on seismic data in the shadow of normal growth faults, with the upthrown time structure appearing to roll into the fault where no such roll exists in depth. This phenomenon was encountered in a prospect in the Frio formation of the Texas Gulf Coast, where a large growth fault expanded a thick, low‐velocity shale above the Frio. Two check‐shot velocity surveys, one at either end of the seismic control, demonstrated a severe average velocity gradient across the prospect at the level of the objective geologic formation. Assuming first one and then the other velocity survey was valid over the entire area for conversion of well data to time produced a drastic difference in the structural interpretation of the seismic data. The more obvious interpretation required a down‐to‐the‐northwest fault with a downthrown rollover anticline at the objective formation. This interpretation had been previously tested with a dry hole on the crest of the time structure. This interpretation also contradicted a dipmeter in this “crestal” well. Using a model derived from interval velocities from the nearby check‐shot surveys, we were able to demonstrate that over 200 ms of apparent seismic dip in the shadow of the growth fault was false. When we used stacking velocities to perform a depth conversion of the seismic time section, both the apparent dip direction of the formation and interpreted throw direction of the fault were reversed. Based on these results, a well was drilled which demonstrated the qualitative success of our model. We also discovered that minor buried faulting mapped behind the major fault was a false effect caused by velocity contrasts across the growth fault. This case history proves that the recognition and proper use of velocity gradients can be extremely important in the Gulf Coast.
Automatic algorithm for triaxial hodogram source location in downhole acoustic emission measurement
Authors: Nagano K. , Niitsuma H. , Chubachi N.
Published: October 2002

An automatic acoustic emission (AE) source location algorithm has been developed for downhole AE measurement of subsurface cracks by using the triaxial hodogram method. The P-wave arrival time is detected by analyzing crosscorrelation coefficients among three components of AE signal energy; the P-wave direction is determined by the method of least squares. For detection of S-wave arrival time, a maximum‐likelihood method analyzes a distribution of instantaneous values of the SH-wave component amplitude. This algorithm can locate an AE source as accurately as human analysis. For field measurements, it takes less than 4 s to locate an AE source using a 16-bit personal computer with a program in C language. Automatic AE source location by the triaxial hodogram method has been realized with this algorithm.
Effect of conductive host rock on borehole transient electromagnetic responses
Authors: Newman Gregory A. , Anderson Walter L. , Hohmann Gerald W.
Published: October 2002

Transient electromagnetic (TEM) borehole responses of 3-D vertical and horizontal tabular bodies in a half‐space are calculated to assess the effect of a conductive host. The transmitter is a large loop at the surface of the earth, and the receiver measures the time derivative of the vertical magnetic field. When the host is conductive (100 Ω ⋅ m), the borehole response is due mainly to current channeled through the body. The observed magnetic‐field response can be visualized as due to galvanic currents that pass through the conductor and return in the half‐space. When the host resistivity is increased, the magnetic field of the conductor is influenced more by vortex currents that flow in closed loops inside the conductor. For a moderately resistive host (1000 Ω ⋅ m), the magnetic field of the body is caused by both vortex and galvanic currents. The galvanic response is observed at early times, followed by the vortex response at later times if the body is well coupled to the transmitter. If the host is very resistive, the galvanic response vanishes; and the response of the conductor is caused only by vortex currents. The shapes of the borehole profiles change considerably with changes in the host resistivity because vortex and galvanic current distributions are very different. When only the vortex response is observed, it is easy to distinguish vertical and horizontal conductors. However, in a conductive host where the galvanic response is dominant, it is difficult to interpret the geometry of the body; only the approximate location of the body can be determined easily. For a horizontal conductor and a single transmitting loop, only the galvanic response enables one to determine whether the conductor is between the transmitter and the borehole or beyond the borehole. A field example shows behavior similar to that of our theoretical results.
Amplitude‐versus‐offset variations in gas sands
Authors: Rutherford Steven R. , Williams Robert H.
Published: October 2002

Seismic reflections from gas sands exhibit a wide range of amplitude‐versus‐offset (AVO) characteristics. The two factors that most strongly determine the AVO behavior of a gas‐sand reflection are the normal incidence reflection coefficient [Formula: see text] and the contrast in Poisson’s ratio at the reflector. Of these two factors, [Formula: see text] is the least constrained. Based on their AVO characteristics, gas‐sand reflectors can be grouped into three classes defined in terms of [Formula: see text] at the top of the gas sand. Class 1 gas sands have higher impedance than the encasing shale with relatively large positive values for [Formula: see text]. Class 2 gas sands have nearly the same impedance as the encasing shale and are characterized by values of [Formula: see text] near zero. Class 3 sands have lower impedance than the encasing shale with negative, large magnitude values for [Formula: see text]. Each of these sand classes has a distinct AVO characteristic. An example of a gas sand from each of the three classes is presented in the paper. The Class 1 example involves a Hartshorn channel sand from the Arkoma Basin. The Class 2 example considers a Miocene gas sand from the Brazos offshore area of the Gulf of Mexico. The Class 3 example is a Pliocene gas sand from the High Island offshore area of the Gulf of Mexico.
High‐resolution velocity spectra using eigenstructure methods
Authors: Biondi Biondo L. , Kostov Clement
Published: October 2002

Stacking spectra provide maximum‐likelihood estimates for the stacking velocity, or for the ray parameter, of well separated reflections in additive white noise. However, the resolution of stacking spectra is limited by the aperture of the array and the frequency of the data. Despite these limitations, parametric spectral estimation methods achieve better resolution than does stacking. To improve resolution, the parametric methods introduce a parsimonious model for the spectrum of the data. In particular, when the data are modeled as the superposition of wavefronts, the properties of the eigenstructure of the data covariance matrix can be used to obtain high‐resolution spectra. The traditional stacking spectra can also be expressed as a function of the data covariance matrix and directly compared to the eigenstructure spectra. The superiority of the latter in separating closely interfering reflections is then apparent from a simple geometric interpretation. Eigenstructure methods were originally developed for use with narrow‐band signals, while seismic reflections are wide‐band and transient in time. Taking advantage of the full bandwidth of seismic data, we average spectra from several frequency bands. We choose each frequency band wide enough, so that we can average over time estimates of the covariance matrix. Thus, we obtain a robust estimate of the covariance matrix from short data sequences. A field‐data example shows that the high‐resolution estimators are particularly attractive for use in the estimation of local spectra in which short arrays are considered. Several realistic synthetic examples of stacking‐velocity spectra illustrate the improved performance of the new methods in comparison with conventional processing.
Depth of investigation in electromagnetic sounding methods
Authors: Spies Brian R.
Published: October 2002

The time or frequency at which the electromagnetic (EM) response of a buried inhomogeneity can first be measured is determined by its depth of burial and the average conductivity of the overlying section; it is relatively independent of the type of source or receiver and their separation. The ability to make measurements at this time or frequency, however, depends on the sensitivity and accuracy of the instrumentation, the signal strength, and the ambient noise level. These factors affect different EM sounding systems in surprisingly different ways. For the magnetotelluric (MT) method, it is possible to detect a buried half‐space under about 1.5 skin depths of overburden. The maximum depth of investigation is virtually unbounded because of high signal strengths at low frequencies. Transient electromagnetic (TEM) soundings, on the other hand, have a limited depth of penetration, but are less affected by static shift errors. For TEM, a buried inhomogeneity can be detected under about one diffusion depth of overburden. For conventional near‐zone sounding in which induced voltage is measured (impulse response), the depth of investigation is proportional to the [Formula: see text] power of the source moment and ground resistivity. By contrast, if the receiver is a magnetometer (step response system), the depth of investigation is proportional to the [Formula: see text] power of source moment and is no longer a function of resistivity. Magnetic‐field measurements may, therefore, be superior for exploration in conductive areas such as sedimentary basins. Far‐zone, or long‐offset, TEM soundings are traditionally used for deep exploration. The depth of investigation for a voltage receiver is proportional to the [Formula: see text] power of source moment and resistivity and is inversely proportional to the source‐receiver separation. Magnetic‐field measurements are difficult to make at long offsets because instrumental accuracy limits the measurement of the very slow decay of the magnetic field. Frequency‐domain controlled‐source systems are ideally suited for sounding at the very shallow depths needed for engineering, archaeological, and groundwater applications because of the relative ease of extending the measurements to arbitrarily high frequencies, and also because geometric soundings can be made at low induction numbers.
Numerical experiments with a salt dome
Authors: Mufti Irshad R.
Published: October 2002

A salt dome is a familiar example of a three‐dimensional (3-D) geologic structure. Surprisingly, most of the literature devoted to the investigation of salt domes deals only with cross‐sectional views of the domes. This is particularly true for seismic work. A notable exception is the work of French (1974) which discusses inaccuracies in focusing introduced by performing two‐dimensional (2-D) migration of data obtained over a 3-D model structure.
A test of a controlled downhole seismic source
Authors: Elbring G. J. , Hardee H. C. , Paulsson B. N. P.
Published: October 2002

With the growing interest in borehole seismic investigations such as vertical seismic profiling and crosshole surveys, the need for new instrumentation has arisen, especially in the area of seismic sources. An ideal seismic downhole source should be nondestructive to the well, provide enough energy to be recorded at useful distances, produce a broad band of seismic frequencies, and create a reproducible signal. A prototype of a source that fits these requirements has been constructed and was described in a previous paper (Hardee et al., 1987).
On: “Application of three‐dimensional interactive modeling in gravity and magnetics” by H.-J. Götze and Bernd Lahmeyer (GEOPHYSICS, 53, 1096–1108, August 1988).
Authors: Starostenko V. I.
Published: October 2002

Götze and Lahmeyer present the main principles and results new automatic system for the interactive modeling of three‐dimensional (3-D) gravity and magnetic fields. The high efficiency of the system is demonstrated convincingly on a practical example of a geologic study in the northwest German Basin. The importance and timeliness of this work are beyond doubt. Nonetheless, a few remarks on the analytical results seem to be appropriate.
The electrical field in a borehole with a casing
Authors: Kaufman Alexander A.
Published: October 2002

The electric field on the borehole axis in the presence of a casing can be divided into three zones: the near, intermediate, and far zones. Within the intermediate zone, determination of the second derivative of the potential allows me to define the formation resistivity. Outside the casing, the electric field, at large distances from the borehole, has a radial direction that provides a sufficient depth of investigation in this direction. The measurement requires knowledge of the casing conductance. Application of transmission line theory is based on the fact that the electric field in the formation is radial within the intermediate zone, resulting in the conclusion that the vertical resolution of such a measurement would depend only upon the spacing of the electrodes required to estimate the second derivative of the potential.
Three‐component sonde orientation in a deviated well
Authors: Becquey M. , Dubesset M.
Published: October 2002

In well seismics, when operating with a three‐component tool, particle velocities are measured in the sonde coordinate system but are often needed in other systems (e.g., source‐bound or geographic). When the well is vertical, a change from the three orthogonal components of the sonde to another orthogonal coordinate system can be performed through one rotation around the vertical axis and, if necessary, another one around a horizontal axis (Hardage, 1983). If the well is deviated, the change of coordinate system remains easy in the case when the source is located at the vertical of the sonde, or in the case when the source stands in the vertical plane defined by the local well axis. In the general case (offset VSPs or walkaways) or when looking for unknown sources (such as microseismic emissions induced by hydraulic fracturing), coordinate rotation may still be performed, provided that we first get back to a situation in which one of the axes is vertical.
The use of the Hartley transform in geophysical applications
Authors: Saatcilar R. , Ergintav S. , Canitez N.
Published: October 2002

The Hartley transform (HT) is an integral transform similar to the Fourier transform (FT). It has most of the characteristics of the FT. Several authors have shown that fast algorithms can be constructed for the fast Hartley transform (FHT) using the same structures as for the fast Fourier transform. However, the HT is a real transform and for this reason, since one complex multiplication requires four real multiplications, the discrete HT (DHT) is computationally faster than the discrete FT (DFT). Consequently, any process requiring the DFT (such as amplitude and phase spectra) can be performed faster by using the DHT. The general properties of the DHT are reviewed first, and then an attempt is made to use the FHT in some seismic data processing techniques such as one‐dimensional filtering, forward seismic modeling, and migration. The experiments show that the Hartley transform is two times faster than the Fourier transform.
Approximate Fréchet derivatives in inductive electromagnetic soundings
Authors: Boerner D. E. , Holladay J. S.
Published: October 2002

Fréchet derivatives play dual roles in electromagnetic (EM) methods as averaging functions relating conductivity to EM fields and as sensitivity functions relating conductivity perturbations to changes in these fields. For one‐dimensional EM inductive sounding, the Fréchet derivatives are not strongly model‐dependent, even for quite diverse earth models. In fact, using a scaled version of the Fréchet derivative for a uniform half‐space to approximate the exact Jacobian in a layered earth inversion program can actually improve the convergence to an acceptable model. This lack of a strong model dependence makes it possible to consider the capabilities and limitations of EM “imaging” methods from the perspective of Fréchet derivatives. Of particular interest is that noninductive Fréchet derivatives are strongly model‐dependent and hence the EM fields generated by this mode are less amenable to imaging techniques.
Reduction to the pole of the North American magnetic anomalies
Authors: Arkani‐Hamed J. , Urquhart W. E. S.
Published: October 2002

Magnetic anomalies of North America are reduced to the pole using a generalized technique which takes into account the variations in the directions of the core field and the magnetization of the crust over North America. The reduced‐to‐the‐pole magnetic anomalies show good correlations with a number of regional tectonic features, such as the Mid‐Continental rift and the collision zones along plate boundaries, which are also apparent in the vertical gravity gradient map of North America. The magnetic anomalies do not, however, show consistent correlation with the vertical gravity gradients, suggesting that magnetic and gravity anomalies do not necessarily arise from common sources.
On computing ray‐synthetic seismograms for anelastic media using complex rays
Authors: Hearn D. J. , Krebes E. S.
Published: October 2002

A plane wave propagating in a viscoelastic medium is generally inhomogeneous, meaning that the direction in which the spatial rate of amplitude attenuation is maximum is generally different from the direction of travel. The angle between these two directions, which we call the “attenuation angle,” is an acute angle. In order to trace the ray corresponding to a plane wave propagating between a source point and a receiver point in a layered viscoelastic medium, one must know both the initial propagation angle (the angle that the raypath makes with the vertical) and the initial attenuation angle at the source point. In some recent literature on the computation of ray‐synthetic seismograms in anelastic media, values for the initial attenuation angle are chosen arbitrarily; but this approach is fundamentally unsatisfactory, since different choices lead to different results for the computed waveforms. Another approach, which is more deterministic and physically acceptable, is to deduce the value of the initial attenuation angle from the value of the complex ray parameter at the saddle point of the complex traveltime function. This value can be obtained by applying the method of steepest descent to evaluate approximately the integrals giving the exact wave field at the observation point. This well‐known technique results in the ray‐theory limit. The initial propagation angle can also be determined from the saddle point. Among all possible primary rays between source and receiver, each having different initial propagation and attenuation angles, the ray determined by the saddle point, which we call a “stationary ray,” has the smallest traveltime, a result which is consistent with Fermat’s principle of least time. Such stationary rays are complex rays, i.e., the spatial (e.g., Cartesian) coordinates of points on stationary raypaths are complex numbers, whereas the arbitrarily determined rays mentioned above are usually traced as real rays. We compare examples of synthetic seismograms computed with stationary rays with those from some arbitrarily determined rays. If the initial value of the attenuation angle is arbitrarily chosen to be a constant for all initial propagation angles, the differences between the two types of seismograms are generally small or negligible in the subcritical zone, except when the constant is relatively large in value, say, within 10 degrees or so of its upper bound of 90 degrees. In that case, the differences are significant but still not large. However, if the surface layer is highly absorptive, the differences can be quite large and pronounced. For larger offsets, i.e., in the supercritical zone, large phase discrepancies can exist between the waveforms for the stationary rays and those for the arbitrarily determined rays, even if the constant initial attenuation angle is not large and even for moderate absorptivity in the surface layer.
Robust elastic nonlinear waveform inversion: Application to real data
Authors: Crase E. , Pica A. , Noble M. , McDonald J. , Tarantola A.
Published: October 2002

Nonlinear elastic waveform inversion has advanced to the point where it is now possible to invert real multiple‐shot seismic data. The iterative gradient algorithm that we employ can readily accommodate robust minimization criteria which tend to handle many types of seismic noise (noise bursts, missing traces, etc.) better than the commonly used least‐squares minimization criteria. Although there are many robust criteria from which to choose, we have tested only a few. In particular, the Cauchy criterion and the hyperbolic secant criterion perform very well in both noise‐free and noise‐added inversions of numerical data. Although the real data set, which we invert using the sech criterion, is marine (pressure sources and receivers) and is very much dominated by unconverted P waves, we can, for the most part, resolve the short wavelengths of both P impedance and S impedance. The long wavelengths of velocity (the background) are assumed known. Because we are deriving nearly all impedance information from unconverted P waves in this inversion, data acquisition geometry must have sufficient multiplicity in subsurface coverage and a sufficient range of offsets, just as in amplitude‐versus‐offset (AVO) inversion. However, AVO analysis is implicitly contained in elastic waveform inversion algorithms as part of the elastic wave equation upon which the algorithms are based. Because the real‐data inversion is so large—over 230,000 unknowns (340,000 when density is included) and over 600,000 data values—most statistical analyses of parameter resolution are not feasible. We qualitatively verify the resolution of our results by inverting a numerical data set which has the same acquisition geometry and corresponding long wavelengths of velocity as the real data, but has semirandom perturbations in the short wavelengths of P and S impedance.
Efficient tau‐p hyperbolic velocity filtering
Authors: Mitchell Alan R. , Kelamis Panos G.
Published: October 2002

Time and offset varying velocity filtering can be achieved by limiting the data input to forward tau‐p transforms. This limiting procedure, called hyperbolic velocity filtering (HVF), suppresses transform‐related artifacts as well as coherent and noncoherent noise while retaining elliptical (reflection) events. We show that HVF can be viewed as a muting process in the slant‐stack domain. Based on this simple but physical interpretation of HVF, a more efficient computer implementation is proposed. We further examine possible applications of HVF for processing seismic reflection data and illustrate the results using both synthetic and real data examples.
Acoustic pulse diffraction by step discontinuities on a plane
Authors: Zhang Q. , Jull E. V. , Yedlin M. J.
Published: October 2002

High‐frequency acoustic pulse diffraction of a point source by step discontinuities in a hard plane boundary is analyzed with the uniform geometrical theory of diffraction. Proper treatment of source and receiver locations at shadow boundaries provides a more complete analysis than before for the 90-degree step as evidenced by frequency‐domain numerical values. Time‐domain results for the 90-degree step, for a 30-degree inclined step, and for two offset half‐planes illustrate the significance of corner reflection and double diffraction missing from earlier numerical models based on Kirchhoff diffraction theory. Advantages in accuracy, computational efficiency, and scope of application of geometrical over Kirchhoff diffraction theory are indicated.
Ground roll: Rejection using adaptive phase‐matched filters
Authors: Herrmann R. B. , Russell D. R.
Published: October 2002

The technique of phase‐matched filtering dispersive surface waves is extended to permit an adaptive, iterative process by which the signal itself in a seismic trace designs a filter to remove the surface wave. The technique is robust and well‐behaved and requires the specification of only simple parameters for its operation. The technique is applied to data sets from three regions, representing a wide range in the ratio of surface‐wave noise to exploration signal. The technique works very well with poor data sets and also improves good data sets. Since the technique is applied to individual traces, it works in situations for which f‐k filtering might not be feasible due to poor spatial sampling. The technique is computationally more intensive than recursive digital band‐pass filtering of individual traces, but is less intensive than filtering in the f‐k domain.
Stratigraphic mapping of sedimentary formations in southern Ontario by ground electromagnetic methods
Authors: Sinha Ajit K.
Published: October 2002

Multifrequency and transient electromagnetic (EM) soundings were done at several locations in southern Ontario to evaluate the possibility of stratigraphic mapping of gently dipping sedimentary formations by ground EM techniques. The possibility of detecting structural features such as folds, faults, and grabens in the formations was also explored. The two EM techniques were used to map a buried river valley near the village of Copetown, about 75 km southwest of Toronto. The valley, buried under fairly resistive glacial till and dolomite formations was mapped at depths ranging from 100 to 200 m. The interpreted shape and depth of the valley agreed well with information from a high resolution seismic reflection survey and data from wells penetrating the bedrock. Transient EM (TEM) data, using square transmitter loops with side dimensions comparable to the transmitter‐receiver separation for the multifrequency system, was found to be less affected by the presence of shallow conductors and lateral inhomogeneities than the multifrequency data, and had greater depth of investigation. TEM soundings were made on five additional profiles in the area. Lithologic logs from old oil and gas wells located near the profiles provided information for comparison with EM sounding interpretations. The depths to various dolomite, shale, and limestone formations interpreted from EM data agreed well with drillhole information. The EM soundings also detected structures in the Paleozoic formations such as faults and folds that were not previously known. The soundings confirmed the existence of a graben at one site at a depth of 100 m, which was postulated from logs from a cluster of closely spaced drillholes by geologists. The survey results indicated that EM sounding methods can be used for stratigraphic mapping in areas where detailed geological information is unavailable either because the bedrock is concealed by overburden, or when drillholes are sparsely distributed.
A comparison of tau‐p transform methods
Authors: Kappus Mary E. , Harding Alistair J. , Orcutt John A.
Published: October 2002

Many τ-p transform methods are available to seismic data analysts; selection of the appropriate method should depend on the nature of the source excitation, the intended use of the transformed data, limits imposed by sampling parameters, and computational cost. Using these criteria, we compare five methods on marine multichannel data and similar synthetic profiles. On fully sampled synthetic profiles, methods that handle the three‐dimensional (3-D) nature of the point source provide correct amplitude and phase information even at small slownesses, whereas 2-D and asymptotic approximate methods do not. When data from small ranges are not available, aliasing and truncation distort the amplitude of small slowness traces produced by all methods, but are most severe in the 3-D results. Transformation of data with increased input trace spacing or decreased depth to the reflector results in increased aliasing effects. When the intended use of the transformed data depends on correct arrival times only, and not on accurate amplitudes of small‐slowness traces, we recommend an asymptotic approximate method for its relative computational efficiency and comparative robustness with respect to aliasing and truncation. Uses that depend on correct amplitudes demand a τ-p transform method which honors the source geometry of the experiment.
Angle‐dependent reflectivity by means of prestack migration
Authors: de Bruin C. G. M. , Wapenaar C. P. A. , Berkhout A. J.
Published: October 2002

Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent reflectivity in the imaging we must not only add all frequency contributions but we should extend the imaging principle by adding along lines of constant angle in the wavenumber‐frequency domain. This procedure is carried out for each grid point. The resulting amplitude information provides a rigorous approach to amplitude‐versus‐offset related methods. The new imaging technique has been tested on media with horizontal layers. However, with our shot‐record oriented algorithm it is possible to handle any subsurface geometry. The first tests show excellent results up to high angles, both in the acoustic and in the elastic case. With angle‐dependent reflectivity information it becomes feasible to derive detailed velocity and density information in a subsequent stratigraphic inversion step.
Gravity inversion using seminorm minimization: Density modeling of Jasper Seamount
Authors: Hammer P. T. C. , Hildebrand J. A. , Parker R. L.
Published: October 2002

A gravity inversion algorithm for modeling discrete bodies with nonuniform density distributions is presented. The algorithm selects the maximally uniform model from the family of models which fit the data, ensuring a conservative and unprejudiced estimate of the density variation within the body. The only inputs required by the inversion are the gravity anomaly field and the body shape. Tests using gravity anomalies generated from synthetic bodies confirm that seminorm minimizing inversions successfully represent mass distribution trends but do not reconstruct sharp discontinuities. We apply the algorithm to model the density structure of seamounts. Inversion of the seasurface gravity field observed over Jasper Seamount suggests the edifice has a low average density of [Formula: see text] and contains a dense body within its western flank. These results are consistent with seismic, magnetic, and petrologic studies of Jasper Seamount.
Compensating finite‐difference errors in 3-D migration and modeling
Authors: Li Zhiming
Published: October 2002

One‐pass three‐dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two‐pass 3-D migration for variable velocity media. Conventional one‐pass 3-D migration, using the method of finite‐difference inline and crossline splitting, however, creates large errors in the image of complex structures. These errors are due to paraxial wave‐equation approximation of the one‐way wave equation, inline‐crossline splitting, and finite‐difference grid dispersion. To compensate for these errors, and still preserve the efficiency of the conventional finite‐difference splitting method, a phase‐correction operator is derived by minimizing the difference between the ideal 3-D migration (or modeling) and the actual, conventional 3-D migration (or modeling). For frequency‐space 3-D finite‐difference migration and modeling, the compensation operator is implemented using either the phase‐shift, or phase‐shift‐plus‐interpolation method, depending on the extent of lateral velocity variations. The compensation operator increases the accuracy of handling steep dips, suppresses the inline and crossline splitting error, and reduces finite‐difference grid dispersions.
Seismic noise cancellation in a geothermal field
Authors: Harris D. B. , Jarpe S. P. , Harben P. E.
Published: October 2002

High background seismic noise due to process machinery in production oil or geothermal fields can present a major problem for active seismic studies such as reflection and refraction surveys and passive seismic studies such as microearthquake monitoring. The general noise suppression problem is a difficult one since process noise may be due to a large number of sources distributed over a large region. In some situations, one or a few sources may dominate the noise field locally, presenting an opportunity for noise suppression by cancellation. In this note we describe an application of adaptive noise cancellation (Widrow, et al., 1975) in which we attempt to suppress noise recorded at a primary monitoring site using reference noise recorded at a major nearby noise source.
Diffraction‐based velocity estimates from optimum offset seismic data
Authors: Cross Guy M. , Knoll Michael D.
Published: October 2002

A graphical method is characterized for estimating seismic velocity directly from diffraction patterns observed on common offset records. The nature of the resulting estimate is examined by illustrating the connection between the graphical approach and a related method used by practitioners of ground penetrating radar. While the latter provides only a crude stacking velocity, the graphical technique yields the generalized rms velocity for stratified media. Associated interval velocities can be derived from two or more diffraction events having their sources within the plane of survey. Where there is a lack of geological evidence to suggest that scatterers reside in‐plane, we propose a simple strategy for locating a scatterer from its expression on two or more independent records. Error in the resulting location is directly related to subsurface velocity heterogeneity. Finally, since the diffraction‐based velocity estimates assume that source and receiver are coincident, the error stemming from nonzero offset is characterized.