bluuebunny/crossref_metadata_2025 huggingface dataset:
On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).
Authors: Chapin David A.
Published: October 2002

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.
A high‐frequency sparker source for the borehole environment
Authors: Rechtien Richard D. , Hambacker K. L. , Ballard R. F.
Published: October 2002

For tomographic investigations of shallow subsurface features of limited lateral extent, a high‐frequency, low‐cost borehole seismic source would be highly desirable, particularly for investigators with limited budgets. We constructed a simple, arc‐discharge seismic source from off‐the‐shelf items. This source consists of a salt water filled bottle containing exposed conductors of a coaxial cable, across which 100 to 300 joules of electrical power were discharged. This source produced a seismic pulse with a dominant frequency in the neighborhood of 1.5 kHz and a half‐power bandwidth in excess of 1 kHz. Repeatability of seismic signatures in a variety of environmental settings was excellent. Sufficient power was generated to observe seismic signals with at least a 35 dB signal‐to‐noise ratio at horizontal borehole separations of 100 m. For a borehole separation of 33.2 m, signals with at least a 35 dB signal‐to‐noise ratio were observed at angular ranges in the vertical plane to 68 degrees. The hydrostatic head limit for this source was determined to be approximately 430 m.
Three‐dimensional primary zero‐offset reflections
Authors: Hubral Peter , Schleicher Jorg , Tygel Martin
Published: October 2002

Zero‐offset reflections resulting from point sources are often computed on a large scale in three‐dimensional (3-D) laterally inhomogeneous isotropic media with the help of ray theory. The geometrical‐spreading factor and the number of caustics that determine the shape of the reflected pulse are then generally obtained by integrating the so‐called dynamic ray‐tracing system down and up to the two‐way normal incidence ray. Assuming that this ray is already known, we show that one integration of the dynamic ray‐tracing system in a downward direction with only the initial condition of a point source at the earth’s surface is in fact sufficient to obtain both results. To establish the Fresnel zone of the zero‐offset reflection upon the reflector requires the same single downward integration. By performing a second downward integration (using the initial conditions of a plane wave at the earth’s surface) the complete Fresnel volume around the two‐way normal ray can be found. This should be known to ascertain the validity of the computed zero‐offset event. A careful analysis of the problem as performed here shows that round‐trip integrations of the dynamic ray‐tracing system following the actually propagating wavefront along the two‐way normal ray need never be considered. In fact some useful quantities related to the two‐way normal ray (e.g., the normal‐moveout velocity) require only one single integration in one specific direction only. Finally, a two‐point ray tracing for normal rays can be derived from one‐way dynamic ray tracing.
Application of the POCS inversion method to cross‐borehole imaging
Authors: Bjarnason Ingi Th. , Menke William
Published: October 2002

Cross‐borehole tomography suffers from a well‐known problem of data incompleteness: the limited ray coverage dictated by the poor experimental geometry implies that certain features of the velocity field are not determined by the data. Construction of a tomographic image of the velocity field therefore requires the addition of prior constraints to the inversion. In the Fourier wavenumber domain (assuming straight‐line rays), the process of adding prior constraints is equivalent to specifying unmeasured wavenumber coefficients. The projection onto convex sets (POCS) algorithm can impose physically plausible constraints that allow high quality tomographic images to be produced. Each constraint is viewed as defining a set (in function space) of images that satisfy that particular constraint. The POCS method finds one or more images in the intersection of the constraining sets, which is equivalent to finding an image that simutaneously satisfies a number of constraints including the observed data. The sets of images that we employ include: those that satisfy the data in the sense of having certain known wavenumber components, those that have bounded energy in certain unmeasured wavenumber components, those that have seismic velocity bounded everywhere (e.g., non‐negative), and those in which the velocity structure is confined to the region between the boreholes. An advantage of the POCS algorithm is that it allows both space‐domain and wavenumber‐domain constraints to be imposed simultaneously. In our implementation of the POCS algorithm, we make use of the fast Fourier transform to rapidly iterate between the space and Fourier‐wavenumber domains. We test the method on synthetic data, and show that it significantly reduces the artifacts in the image, when compared to other methods. We then apply it to data from a cross‐borehole experiment in Manitoba, Canada, that were previously studied by others. We achieve a tomographic image of the velocity field that is similar in many respects to the results of others, but which possesses fewer artifacts.
Estimation of a point source wavelet in elastic media
Authors: Kagansky Alexander , Loewenthal Dan
Published: October 2002

A new method of wavelet estimation in elastic or acoustic media is presented. The method is based on the simple procedure of weighted summation of seismic traces for all the distances of source‐receivers, with a horizontal offset r as a weight. The model treated consists of a homogeneous elastic (or acoustic) layer with the free surface above and a half‐space below. The Lamé parameters and the density of the half‐space can be any function of the depth. A P‐wave point source operates in the layer, and the vertical displacement field or the vertical particle velocity field (or the pressure in the acoustic case) is measured by two horizontal lines of receivers located at two depth levels in the same layer. To obtain the wavelet‐estimation algorithm, the Fourier‐Hankel transform of the field is used. It is shown that there are two possibilities of data measuring: (1) when both the lines of the receivers are below the source and (2) when one of the lines is above the source. Numerical examples show that the proposed method gives a correct estimate of the source wavelet.
Implications of thin layers for amplitude variation with offset (AVO) studies
Authors: Juhlin Christopher , Young Roger
Published: October 2002

Amplitude variation with offset (AVO), or amplitude variation with angle (AVA), analyses of seismic reflection data are becoming increasingly popular in the exploration industry (Ostrander, 1984; Pichin and Mitchell, 1991; Mazzotti and Mirri, 1991) and also in scientific studies of the earth’s crust (Juhlin, 1990). In the exploration industry, AVO analyses are particularly suitable for the detection and mapping of gas zones since reservoirs often consist of shale with high Poisson’s ratio (high [Formula: see text]) overlying gas bearing sands with low Poisson’s ratio (low [Formula: see text]). If the gas sand has lower impedance than the overlying shale, the magnitude of the reflection coefficient will increase with increasing angle of incidence or offset. Other combinations of rock types will also show a similar increase in magnitude, such as shale over hard limestone, but the sign of the reflection coefficient will be positive in most of these cases. Therefore, if the polarity of the reflection can be determined to be negative and there is an increase in the absolute amplitude of the reflection with offset, then this is highly indicative of a gas bearing zone.
Nonuniqueness of velocity determination for one type of layered model
Authors: Sorin Valery
Published: October 2002

Recently Krey (1989) showed the nonuniqueness of interval velocity determination using the inversion method suggested by Krey (1976) and Hubral and Krey (1980). The investigated structure contains a convex spherical refractor and a horizontal reflector. The author analytically derived two velocity solutions under the spherical apex in the lower homogeneous layer. At first sight, one may suppose that the discovered nonuniqueness arises from the inversion method applied.
Wireline shear and AVO modeling: Application to AVO investigations of the Tertiary, U.K. Central North Sea
Authors: Reilly Joseph M.
Published: October 2002

Numerous examples exist in the literature of the successes and failures of the application of amplitude variation with offset (AVO) “gas effect” theory in hydrocarbon exploration. The acquisition of wireline and VSP shear data is considered critical information for accurate calibration, quantification, modeling, and successful application of AVO analysis techniques in a particular geologic environment. Wireline compressional, wireline dipole shear, well vertical seismic profiling (VSP), and surface seismic data are used to investigate the AVO behavior of the major lithologic boundaries and hydrocarbon bearing zones. Within the study area, lithologic boundaries produce significant AVO anomalies that may be easily confused with Class III AVO gas effect. In addition, the principal economic target, oil bearing sands, does not appear to produce AVO gas effect anomalies; although a Class III AVO gas effect response is observed when as little as 2 m of free gas is present at the top of the reservoir. Confirmation of an (Class I, II, or III) AVO gas effect in these Tertiary sands can be significant for detecting and delineating reservoirs; however, excessive emphasis on the importance of AVO gas effect, or high amplitudes on relative amplitude seismic sections, will result in an underestimate of (oil) hydrocarbon potential within the region.
Migration error in transversely isotropic media
Authors: Alkhalifah Tariq , Larner Ken
Published: October 2002

Most migration algorithms today are based on the assumption that the earth is isotropic, an approximation that is often not valid and thus can lead to position errors on migrated images. Here, we compute curves of such position error as a function of reflector dip for transversely isotropic (TI) media characterized by Thomsen’s anisotropy parameters δ and ε. Depending on whether the migration velocity is derived from stacking velocity or vertical root‐mean‐square (rms) velocity, we find quite contrary sensitivities of the error behavior to the values of δ and ε. Likewise error‐versus‐dip behavior depends in a complicated way on vertical velocity gradient and vertical time, as well as orientation of the symmetry axis. Moreover, error behavior is dependent on just how δ and ε vary with depth. In addition to presenting such error curves, we show migrations of synthetic data that exemplify the mispositioning that results from ignoring anisotropy for P‐wave data. When migration is done using velocities derived from stacking velocity and when medium velocity increases with depth at rates typically encountered in practice, δ alone is sufficient to describe the position error. This is fortunate since the value of δ, unlike ε, can be obtained from combined vertical seismic profile (VSP) and surface seismic data. In contrast, when the migration velocity is obtained from the vertical rms velocity, the position errors depend strongly on ε, suggesting the importance of having an accurate estimate of ε when using an anisotropic migration algorithm.
Systematics of time‐migration errors
Authors: Black James L. , Brzostowski Matthew A.
Published: October 2002

Even if the correct velocity is used, time migration mispositions events whenever the velocity changes laterally. These errors increase with lateral velocity variation, depth of burial, and dip angle θ. Our analyses of two model types, one with an implicit gradient and one with an explicit gradient, yield simple “rules of thumb” for these errors to first order in the lateral gradient. The x error is [Formula: see text], and the z error is [Formula: see text], where the quantity A = A(x, z) contains the information about depth of burial and magnitude of lateral gradient. These rules can be used to determine when depth migration is needed. Further analysis also shows that the image‐ray correction to time migration is accurate only at small dip. For dipping events, the image‐ray correction must be supplemented by a shift in x of the form [Formula: see text] and a shift in z given by [Formula: see text]. These time‐migration corrections take the same form for both the models we have studied, suggesting a general scheme for correcting time migration, which we call “remedial migration.”
DEEP CORRELATION REFLECTIONS NEAR HOSKINS MOUND SALT DOME
Authors: Campbell F. F.
Published: October 2002

Seismograph records shot north of Hoskins Mound Salt Dome are presented which show correlatable reflections beyond four seconds. Faulting and a major unconformity are suggested to explain the observed data.
GEOCHEMICAL WELL LOGGING
Authors: Ransone W. R.
Published: October 2002

The collection of well cuttings, their analysis, and subsequent plotting as a Geochemical Well Log are briefly discussed. Numerous and varied examples of actual Chemlogs are presented. These illustrate specific applications, and also may be employed to form an opinion of the usefulness of the method.
REPORT ON ORGANIZATION OF THE SOUTHERN SEISMIC WELL SHOOTING ASSOCIATION
Authors: Mower L. K.
Published: October 2002

One of the fundamental assumptions which has been used to convert the results of a reflexion seismograph survey into a subsurface structural picture has been that the vertical distribution of the velocity remained constant over the area of the survey, and that any differences in reflexion times to a given layer could be interpreted as indicating differences in depth to that layer. Fortunately, this assumption has been quite satisfactory in many cases, especially when the object of a survey has been to locate fairly pronounced structures. The actual velocity law used was sometimes just an asusmption, or may have been based on results of refraction shooting, or computed from the Δt’s of the reflexion survey itself. It was early recognized that such velocity information was not entirely satisfactory, and well geophones were designed which made it possible to carry out velocity surveys in wells. As it becomes increasingly important to map structures with small closure, it becomes increasingly necessary to know the actual velocities which should be used in seismic interpretations.
CONSIDERATIONS ON THE VERTICAL MIGRATION OF GASES
Authors: Nisle Robert G.
Published: October 2002

The vertical migration of a perfect gas saturated with aqueous vapor is studied with a view toward determining what effect it may have on the porous strata through which it passes. It is found that evaporation of water and the consequent concentration of minerals may occur at certain depths. Further, it is pointed out that the cooling due to the evaporation of water and the expanding gas may be a contributing factor in the appearance of geothermal anomalies. Suggestions for further study are included.
Soil‐embedded detector mounts for seismic monitoring
Authors: Blair Dane P.
Published: October 2002

Accurate measurements of seismic motions in soil are often required in earthquake studies and mine blasting operations at sites that have no outcropping rock. The present study shows that the most satisfactory method of coupling to soil is to attach the seismic detectors to a carefully embedded, precast mount whose shape is either cubic, or right‐cylindrical with unit aspect ratio. Furthermore, because of the competing influences of radiation and scattering, it is shown that the optimum design for the cylindrical mount is achieved only when two criteria are met simultaneously. The first criterion is given by [Formula: see text], where R is the mount radius, [Formula: see text] is the upper frequency required to be accurately detected, and [Formula: see text] is the shear‐wave velocity of the soil. The second criterion is given by b = 10, where b is the mount mass factor [Formula: see text] in which ρ is the soil density and m is the total mass of the mount and detector array. Irrespective of the above criteria, if [Formula: see text], then the ground coupling problem is negligible for all mount masses given by b < 100. All these conditions also apply to a fully embedded cubic mount of side L, provided R is replaced by 0.568L. The treatment is scale‐independent and is applicable to seismic exploration as well as to earthquake and blast vibration monitoring.
Forbidden directions for inhomogeneous pure shear waves in dissipative anisotropic media
Authors: Carcione José M. , Cavallini Fabio
Published: October 2002

In this work we investigate the wave‐propagation properties of pure shear, inhomogeneous, viscoelastic plane waves in the symmetry plane of a monoclinic medium. In terms of seismic propagation, the problem is to describe SH‐waves traveling through a fractured transversely isotropic formation where we assume that the waves are inhomogeneous with amplitudes varying across surfaces of constant phase. This assumption is widely supported by theoretical and experimental evidence. The results are presented in terms of polar diagrams of the quality factor, attenuation, slowness, and energy velocity curves. Inhomogeneous waves are more anisotropic and dissipative than homogeneous viscoelastic plane waves, for which the wavenumber and attenuation directions coincide. Moreover, the theory predicts, beyond a given degree of inhomogeneity, the existence of “stop bands” where there is no wave propagation. This phenomenon does not occur in dissipative isotropic and elastic anisotropic media. The combination of anelasticity and anisotropy activates these bands. They exist even in very weakly anisotropic and quasi‐elastic materials; only a finite value of Q is required. Weaker anisotropy does not affect the width of the bands, but increases the threshold of inhomogeneity above which they appear; moreover, near the threshold, lower attenuation implies narrower bands. A numerical simulation suggests that, in the absence of material interfaces or heterogeneities, the wavefield is mainly composed of homogeneous waves.
Crosswell seismic radial survey tomograms and the 3-D interpretation of a heavy oil steamflood
Authors: Mathisen Mark E. , Cunningham Paul , Shaw Jesse , Vasiliou Anthony A. , Justice J. H. , Guinzy N. J.
Published: October 2002

S‐wave, P‐wave, and Poisson’s ratio tomograms have been used to interpret the 3-D distribution of rock and fluid properties during an early phase of a California heavy oil sand steamflood. Four lines of good quality crosswell seismic data, with source to receiver offsets ranging from 287 to 551 ft (87 to 168 m), were acquired in a radial pattern around a high temperature cemented receiver cable in four days. Processing, first‐arrival picking, and good quality tomographic reconstructions were completed despite offset‐related variations in data quality between the long and short lines. Interpretation was based on correlations with reservoir models, log, core, temperature, and steam injection data. S‐wave tomograms define the 3-D distribution of the “high flow” turbidite channel facies, the “moderate‐low flow” levee facies, porosity, and structural dip. The S‐wave tomograms also define an area with anomalously low S‐wave velocity, which correlates with low shear log velocities and suggests that pressure‐related dilation and compaction may be imageable. P‐wave tomograms define the same reservoir lithology and structure as the S‐wave tomograms and the 3-D distribution of low compressional velocity zones formed by previous steam‐heat injection and the formation of gas. The low P‐wave velocity zones, which are laterally continuous in the “high flow” channel facies near the top of most zones, indicate that the steam‐heat‐gas distribution is controlled by stratification. The stratigraphic control of gas‐bearing zones inferred from P‐wave tomograms is confirmed by Poisson’s ratio tomograms which display low Poisson’s ratios indicative of gas (<0.35) in the same zones as the low P‐wave velocities. The interpretation results indicate that radial survey tomograms can be tied at a central well and used to develop an integrated 3-D geoscience‐engineering reservoir model despite offset‐related variations in data quality. The laterally continuous, stratification‐controlled, low P‐wave velocity zones, which extend up‐dip, suggest that significant amounts of steam‐heat are not heating the surrounding reservoir volume but are flowing updip along “high flow” channels.
High‐resolution crosswell seismic experiment with a large interwell spacing in a west Texas carbonate field
Authors: Lee Doo Sung , Lazaratos Spyros K. , Fitzgerald Gregory N. , Imayoshi Takashi
Published: October 2002

A high‐frequency crosswell seismic dataset acquired in a west Texas carbonate field has demonstrated the feasibility of the technique with a large interwell spacing. Two crosswell profiles were acquired with a well spacing of 1500 ft (460 m) and over a depth interval from 7700 ft (2350 m) to 9600 ft (2930 m) using a piezoelectric bender source. The data quality is profile and depth dependent, with the ambient noise level at the receiver position being the most important factor. Noise levels and noise characteristics among three wells were significantly different. Tube waves and gas‐ and fluid‐movement in the borehole are the dominant noise sources found in the data set. Two lithologic properties, attenuation and transmission loss controlled the data quality. Good quality and high frequency (>1000 Hz) data were acquired over most of the survey interval which contains massive limestones. However, we could not acquire any useful data within the shale layers. Transmission losses and the effects of the source radiation pattern that occurred at interfaces with large impedance contrasts limited the aperture of the useful data. There were two critical issues encountered during the reflection imaging process: (1) sparse trace spacing and poor coherency of the reflection events in common‐source gathers degraded the image in a region near the receiver well; and (2) possible lateral velocity heterogeneity in the medium and limited aperture made it difficult to build an appropriate velocity model for reflection imaging.
Inversion of reflection traveltimes for transverse isotropy
Authors: Tsvankin Ilya , Thomsen Leon
Published: October 2002

In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector depth) if only P‐wave data are included. A general analysis of the P‐wave inverse problem proves the existence of a broad set of models with different vertical velocities, all of which provide a satisfactory fit to the exact traveltimes. This strong ambiguity is explained by a trade‐off between vertical velocity and the parameters of anisotropy on gathers with a limited angle coverage. The accuracy of the inversion procedure may be significantly increased by combining both long‐spread P and SV moveouts. The high sensitivity of the long‐spread SV moveout to the reflector depth permits a less ambiguous inversion. In some cases, the SV moveout alone may be used to recover the vertical S‐wave velocity, and hence the depth. Success of this inversion depends on the spreadlength and degree of SV‐wave velocity anisotropy, as well as on the constraints on the P‐wave vertical velocity.
3-D viscoelastic anisotropic modeling of data from a multicomponent, multiazimuth seismic experiment in northeast Texas
Authors: Dong Zhengxin , McMechan George A.
Published: October 2002

Three‐component seismic data were acquired along six azimuths at a site in northeast Texas. Sources were inclined impacts combined to produce equivalent vertical and crossline horizontal components. The data were analyzed by iterative modeling using a new 3-D, staggered‐grid, finite‐differencing scheme. The 3-D model is defined in terms of spatially variable anisotropic, viscoelastic parameters (P‐velocity, S‐velocity, density, Qp, and Qs) and converted to elastic tensor components and relaxation times for computation. Simultaneous fitting of amplitudes of near‐surface reverberations, surface waves, converted waves, and deeper reflections gives an anisotropic, viscoelastic model that provides constraints on earth properties. The assumption of transverse isotropy in previous experiments is supported by the results of this experiment. The final model consists of a stack of flat layers, each of which has isotropic P‐velocity, Qp, and Qs. The Wills Point and Kincaid shales are strongly transversely isotropic, with shear propagation velocity averaging 28% higher horizontally than vertically. The geometry of the Nacatoch Sandstone is similar, with ≈19% anisotropy. The marls and chalks are essentially isotropic. Observed mixing between crossline and vertical components is incorporated by simulating a small (4°) tilt of the axis of the impact source from vertical.
High‐resolution velocity gathers and offset space reconstruction
Authors: Sacchi Mauricio D. , Ulrych Tadeusz J.
Published: October 2002

We present a high‐resolution procedure to reconstruct common‐midpoint (CMP) gathers. First, we describe the forward and inverse transformations between offset and velocity space. Then, we formulate an underdetermined linear inverse problem in which the target is the artifacts‐free, aperture‐compensated velocity gather. We show that a sparse inversion leads to a solution that resembles the infinite‐aperture velocity gather. The latter is the velocity gather that should have been estimated with a simple conjugate operator designed from an infinite‐aperture seismic array. This high‐resolution velocity gather is then used to reconstruct the offset space. The algorithm is formally derived using two basic principles. First, we use the principle of maximum entropy to translate prior information about the unknown parameters into a probabilistic framework, in other words, to assign a probability density function to our model. Second, we apply Bayes’s rule to relate the a priori probability density function (pdf) with the pdf corresponding to the experimental uncertainties (likelihood function) to construct the a posteriori distribution of the unknown parameters. Finally the model is evaluated by maximizing the a posteriori distribution. When the problem is correctly regularized, the algorithm converges to a solution characterized by different degrees of sparseness depending on the required resolution. The solutions exhibit minimum entropy when the entropy is measured in terms of Burg’s definition. We emphasize two crucial differences in our approach with the familiar Burg method of maximum entropy spectral analysis. First, Burg’s entropy is minimized rather than maximized, which is equivalent to inferring as much as possible about the model from the data. Second, our approach uses the data as constraints in contrast with the classic maximum entropy spectral analysis approach where the autocorrelation function is the constraint. This implies that we recover not only amplitude information but also phase information, which serves to extrapolate the data outside the original aperture of the array. The tradeoff is controlled by a single parameter that under asymptotic conditions reduces the method to a damped least‐squares solution. Finally, the high‐resolution or aperture‐compensated velocity gather is used to extrapolate near‐ and far‐offset traces.
Acoustic waves in finely layered media
Authors: Hovem Jens M.
Published: October 2002

The propagation of acoustic waves through a periodically stratified medium is examined theoretically and experimentally with the purpose of determining how the velocity of the composite material depends on the periodicity structure, the material properties, and frequency. A numerical simulation of a recently published experiment shows that the propagator method gives results in close agreement with the experimental observations. Using eigenvalue analysis, an expression for the sound velocity and scattering loss is calculated for all frequencies. The results show that, for frequencies lower than a certain critical (or limiting) frequency, the propagation is dispersive and no loss occurs. Above this frequency the waves are evanescent and suffer scattering loss at each interface. An expression for the limiting frequency is derived which takes into account the contrast in impedance between the two media.
Error analysis for the seismic PDA tracker
Authors: Woodham Catherine A. , Sandham William A. , Durrani Tariq S.
Published: October 2002

A new method for assessing the accuracy of a seismic event tracking algorithm is presented. Currently, the accuracy of automatic event tracking algorithms is assessed by the interpreter without the aid of any tracker error analysis. It is clear that a method for mathematically analyzing the tracker accuracy is important, and the method described here enables an accurate assessment of the tracker confidence. The tracking of seismic events through 3-D data sets using probabilistic data association (PDA) is a recently developed technique. The method requires the correlation of information from trackers working in two perpendicular directions, and diagonally, and also from trackers working forward and backward through the data set. The information contained in the covariance matrix, which forms part of the standard Kalman filter model, may be used in the tracking of seismic events using PDA. The importance of this information is two‐fold—it gives an indication of the confidence of the tracker over a particular seismic event, and it may be used to improve the correlation of the tracker information. The relevant Kalman filter theory will be presented, and its use in analyzing the tracker errors and in improving the tracker correlation will be explained. It is clear from the examples presented that the tracker correlation, and hence the overall accuracy of the tracker, may be improved, and that the tracker confidence may be obtained.
Accuracy study of velocity estimation in 3-D layered models
Authors: Sorin Valery
Published: October 2002

Velocity estimation is examined in 3-D layered structures formed by plane and curved interfaces. The applied technique of coherency inversion tests the layer velocity through the repeating sequence of ray migration/coherency measurement. The reconstructed velocity‐depth model fits zero‐offset reflection times and maximizes semblance on input common midpoint (CMP) gathers. The correctness of layer velocity analysis disregarding the three‐dimensionality of the structures is under consideration. Using the 2-D coherency inversion technique, velocity is correctly determined in the upper layer of the examined structures. Two‐dimensional analysis in the deeper layer gives biased velocity estimates. The errors in the 2-D velocity estimates vary with the profile azimuth and appear in the form of the apparent velocity anisotropy. The inaccuracy of 2-D velocity estimation is analytically considered for the profile oriented along the refractor strike direction. The derived equation relates the velocity error to structure geometry and to the velocity contrast above and below the refractor. Three‐dimensional velocity analysis in the examined structures reveals that the layer velocity resolution is affected by the refractor shape. Below the convex refractor the velocity resolution deteriorates compared with that below the plane.
Elimination of numerical dispersion in finite‐difference modeling and migration by flux‐corrected transport
Authors: Fei Tong , Larner Ken
Published: October 2002

Finite‐difference acoustic‐wave modeling and reverse‐time depth migration based on the full wave equation are general approaches that can take into account arbitrary variations in velocity and density and can handle turning waves as well. However, conventional finite‐difference methods for solving the acoustic‐ or elastic‐wave equation suffer from numerical dispersion when too few samples per wavelength are used. The flux‐corrected transport (FCT) algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite‐difference wavefield continuation. The flux‐correction procedure endeavors to incorporate diffusion into the wavefield continuation process only where needed to suppress the numerical dispersion. Incorporating the flux‐correction procedure in conventional finite‐difference modeling or reverse‐time migration can provide finite‐difference solutions with no numerical dispersion even for impulsive sources. The FCT correction, which can be applied to finite‐difference approximations of any order in space and time, is an efficient alternative to use for finite‐difference approximations of increasing order. Through demonstrations of modeling and migration on both synthetic and field data, we show the benefits of the FCT algorithm, as well as its inability to fully recover resolution lost when the spatial sampling becomes too coarse.
Fast algorithms to design discrete Wiener filters in lag and length coordinates
Authors: Porsani Milton J.
Published: October 2002

Two recursive algorithms for designing discrete Wiener filters for wavelets of different phase characteristics are the Simpson and the Manolakis recursions. Both procedures are efficient; however, both recursions work with a prefixed length filter. Two fast algorithms to design discrete Wiener filters in lag and length coordinates are presented. The recursion methods of Levinson and Manolakis are combined to generate two fast algorithms that calculate the value for the minimized total squared error (MTSE) corresponding to spiking and shaping filters. For a spiking filter of length n and a wavelet of m data points, [Formula: see text] operations are required to obtain the [Formula: see text] map of the MTSEs, (one operation is defined here as one multiplication and one addition). For a shaping filter, [Formula: see text] operations are required to obtain the corresponding m × n map. These algorithms may be seen as a Levinson recursion on two variables, length j of the filter and lag k, for the desired signal. Numerical examples for spiking and shaping filters are presented.
3-D prestack migration of common‐azimuth data
Authors: Biondi Biondo , Palacharla Gopal
Published: October 2002

In principle, downward continuation of 3-D prestack data should be carried out in the 5-D space of full 3-D prestack geometry (recording time, source surface location, and receiver surface location), even when the data sets to be migrated have fewer dimensions, as in the case of common‐azimuth data sets that are only four dimensional. This increase in dimensionality of the computational space causes a severe increase in the amount of computations required for migrating the data. Unless this computational efficiency issue is solved, 3-D prestack migration methods based on downward continuation cannot compete with Kirchhoff methods. We address this problem by presenting a method for downward continuing common‐azimuth data in the original 4-D space of the common‐azimuth data geometry. The method is based on a new common‐azimuth downward‐continuation operator derived by a stationary‐phase approximation of the full 3-D prestack downward‐continuation operator expressed in the frequency‐wavenumber domain. Although the new common‐azimuth operator is exact only for constant velocity, a ray‐theoretical interpretation of the stationary‐phase approximation enables us to derive an accurate generalization of the method to media with both vertical and lateral velocity variations. The proposed migration method successfully imaged a synthetic data set that was generated assuming strong lateral and vertical velocity gradients. The common‐azimuth downward‐continuation theory also can be applied to the derivation of a computationally efficient constant‐velocity Stolt migration of common‐azimuth data. The Stolt migration formulation leads to the important theoretical result that constant‐velocity common‐azimuth migration can be split into two exact sequential migration processes: 2-D prestack migration along the inline direction, followed by 2-D zero‐offset migration along the cross‐line direction.
2-D continuation operators and their applications
Authors: Bagaini Claudio , Spagnolini Umberto
Published: October 2002

Continuation to zero offset [better known as dip moveout (DMO)] is a standard tool for seismic data processing. In this paper, the concept of DMO is extended by introducing a set of operators: the continuation operators. These operators, which are implemented in integral form with a defined amplitude distribution, perform the mapping between common shot or common offset gathers for a given velocity model. The application of the shot continuation operator for dip‐independent velocity analysis allows a direct implementation in the acquisition domain by exploiting the comparison between real data and data continued in the shot domain. Shot and offset continuation allow the restoration of missing shot or missing offset by using a velocity model provided by common shot velocity analysis or another dip‐independent velocity analysis method.
Shear‐wave splitting in Quaternary sediments: Neotectonic implications in the central New Madrid seismic zone
Authors: Harris James B.
Published: October 2002

Determining the extent and location of surface/near‐surface structural deformation in the New Madrid seismic zone (NMSZ) is very important for evaluating earthquake hazards. A shallow shear‐wave splitting experiment, located near the crest of the Lake County uplift (LCU) in the central NMSZ, shows the presence of near‐surface azimuthal anisotropy believed to be associated with neotectonic deformation. A shallow four‐component data set, recorded using a hammer and mass source, displayed abundant shallow reflection energy on records made with orthogonal source‐receiver orientations, an indicator of shear‐wave splitting. Following rotation of the data matrix by 40°, the [Formula: see text] and [Formula: see text] sections (principal components of the data matrix) were aligned with the natural coordinate system at orientations of N35°W and N55°E, respectively. A dynamic mis‐tie of 8 ms at a two‐way traveltime of 375 ms produced an average azimuthal anisotropy of ≈2% between the target reflector (top of Quaternary gravel at a depth of 35 m) and the surface. Based on the shear‐wave polarization data, two explanations for the azimuthal anisotropy in the study area are (1) fractures/cracks aligned in response to near‐surface tensional stress produced by uplift of the LCU, and (2) faults/fractures oriented parallel to the Kentucky Bend scarp, a recently identified surface deformation feature believed to be associated with contemporary seismicity in the central NMSZ. In addition to increased seismic resolution by the use of shear‐wave methods in unconsolidated, water‐saturated sediments, measurement of near‐surface directional polarizations, produced by shear‐wave splitting, may provide valuable information for identifying neotectonic deformation and evaluating associated earthquake hazards.
Focusing analysis of seismic data with peg‐leg multiples
Authors: Maeland Einar
Published: October 2002

Seismic migration with an erroneous velocity field produces an “image” that must be interpreted to obtain reliable velocity information. Inclusion of multiples in common‐shot data makes velocity estimation more difficult. Zero‐offset migration, based on the exploding reflector model, can be used to identify peg‐leg multiples by application of an extra time shift in the imaging condition. The time and the corresponding position when reflected energy focuses must be detected by inspection of the migrated data set. Formulas are derived and the method is tested on synthetic data from a multilayered medium.
Prestack multicomponent migration
Authors: Zhe Jingping , Greenhalgh Stewart A.
Published: October 2002

Prestack elastic migration by displacement potential extrapolation is a mixed, systematic, and function‐blocked vector wavefield migration algorithm. A new wavefield extrapolation method for inhomogeneous media is introduced here according to the following sequence: displacements ← potentials ← extrapolation of the potentials ← displacements, which is relatively accurate and not computer‐time intensive. Traveltimes of both direct downgoing P‐ and S‐waves, which are necessary in elastic migration, are calculated with a modified convolutional acoustic forward modeling program applicable to complex structures. A new image condition based on the time consistent principle is developed. It involves first obtaining an image condition section. Then two images (P P and S S) are obtained from the product of the extrapolated and decomposed P P‐ and S S‐wave displacement amplitudes and the image condition section. All P P‐, P S‐, S P‐ and S S‐waves are considered when the image condition section is calculated. The image condition section minimizes cross‐talk between modes. Compared to previous treatments, the newly developed image condition formula is superior since it allows migration of multicomponent seismic data produced using a combined P and S source. Numerical test results are very encouraging and clearly demonstrate the robustness of the technique. Further work is continuing so as to overcome ray angle and polarity problems in the image condition.
Implicit interpolation in reverse‐time migration
Authors: Zhu Jinming , Lines Larry R.
Published: October 2002

Reverse‐time migration applies finite‐difference wave equation solutions by using unaliased time‐reversed recorded traces as seismic sources. Recorded data can be sparsely or irregularly sampled relative to a finely spaced finite‐difference mesh because of the nature of seismic acquisition. Fortunately, reliable interpolation of missing traces is implicitly included in the reverse‐time wave equation computations. This implicit interpolation is essentially based on the ability of the wavefield to “heal itself” during propagation. Both synthetic and real data examples demonstrate that reverse‐time migration can often be performed effectively without the need for explicit interpolation of missing traces.
Seeing through seismically difficult rocks unconventionally
Authors: Ryu Jisoo V.
Published: October 2002

Two wide‐aperture, seismic profiles from traditionally poor‐record or no‐record areas are presented here—one acquired using an aperture of 12 km and the other acquired using an aperture of 9.6 km. Both seismic profiles were recorded with in‐line geometry in a common‐offset profiling mode. The wide‐aperture sections with an aperture of longer than 5 km are far superior in data quality to the conventional 5-km aperture sections, which rarely show any interpretable events in the deep zones of major exploration interest. The wide‐aperture recording technique can provide a viable alternative to conventional recording techniques in the poor‐record or no‐record terranes where the poor quality of conventional seismic data hampers exploration. Such poor‐record or no‐record areas commonly occur where upper layers of high seismic velocity overlie target layers of lower velocity.
Far‐field phase extrapolation for marine source signatures
Authors: Duren Richard E. , Andersen Kenneth D.
Published: October 2002

The convolutional model expresses seismic data as a time convolution of the radiated source pulse and the impulse response function of the geological formation. Except for ghosting effects associated with the streamer in the marine environment, a recorded seismic trace, [Formula: see text], may be represented as a function of time by the following equation [Formula: see text]where * denotes convolution, s(t) is the source pulse, [Formula: see text] is the impulse response of the geogical formation, subscripts s and r indicate dependence on the source and receiver positions, respectively. Since the radiated source pulse and impulse response are independent, the seismic reflection data may be deconvolved to remove the source pulse. However, to accurately perform this task the source pulse applied to the deconvolution process must be accurate.
On: “Magnetotelluric delineation of the Trillabelle massive sulfide body in Sudbury, Ontario” (D. Livelybrooks, M. Mareschal, E. Blais, and J. T. Smith, GEOPHYSICS, 61, 4, 971–986)
Authors: Corry Charles E.
Published: October 2002

Livelybrooks et al. (1996) propose that measuring magnetotelluric (MT) currents generated by naturally occurring electromagnetic fields can be used to locate deep, 2–4 km, ore bodies where other electrical methods fail. However, I find a number of difficulties with both their survey and the analysis.
Use of the slant stack for geologic or geophysical map lineament analysis
Authors: Pawlowski Robert S.
Published: October 2002

The slant‐stack technique (also known as Radon transform, τ-p transform, and plane‐wave decomposition) used in seismic data processing for discriminating between and separating seismic events of differing dips (or moveout) is applied here to the problem of geologic or geophysical map lineament analysis. The latter problem is analogous to the seismic coherent noise problem in the sense that lineaments associated with one geologic event or episode are often underprinted by the lineaments of preceding geologic disturbances and overprinted by the lineaments of subsequent disturbances. Consequently, it can be difficult to distinguish between the individual lineament sets.
Effect of cable capacitance on in‐situ borehole geophone calibration
Authors: Liu Hsi‐Ping , Warrick Richard E.
Published: October 2002

Using 2-Hz electromagnetic moving‐coil geophones as sensing elements, we have constructed and deployed three‐component seismometers in boreholes at various sites for wave‐propagation studies associated with earthquake hazards (Liu et al., 1991). For example, one such seismometer has been deployed in a 88-m deep borehole reaching bedrock in the Marina District of San Francisco since 1990 (Liu et al., 1992) for the purpose of comparing ground motions in the bedrock and those at the surface. Periodic calibrations for such geophones are necessary to check if the geophone parameters have changed because of decreased magnetization of the geophone ferro‐magnet. For example, the coil transductance of the vertical‐component geophone of the borehole seismometer mentioned above was calibrated to be 121 V-s/m using phase‐ellipse test and step test before deployment. Sixty six months after the deployment, the coil transductance, when calibrated in situ and with a 100-m intervening cable between the geophone and the calibration instrument, was found to be 114 V-s/m.