bluuebunny/crossref_metadata_2025 huggingface dataset:
Simultaneous velocity filtering of hyperbolic reflections and balancing of offset‐dependent wavelets
Authors: Harlan William S.
Published: October 2002

Hyperbolic reflections and convolutional wavelets are fundamental models for seismic data processing. Each sample of a “stacked” zero‐offset section can parameterize an impulsive hyperbolic reflection in a midpoint gather. Convolutional wavelets can model source waveforms and near‐surface filtering at the shot and geophone positions. An optimized inversion of the combined modeling equations for hyperbolic traveltimes and convolutional wavelets makes explicit any interdependence and nonuniqueness in these two sets of parameters. I first estimate stacked traces that best model the recorded data and then find nonimpulsive wavelets to improve the fit with the data. These wavelets are used for a new estimate of the stacked traces, and so on. Estimated stacked traces model short average wavelets with a superposition of approximately parallel hyperbolas; estimated wavelets adjust the phases and amplitudes of inconsistent traces, including static shifts. Deconvolution of land data with estimated wavelets makes wavelets consistent over offset; remaining static shifts are midpoint‐consistent. This phase balancing improves the resolution of stacked data and of velocity analyses. If precise velocity functions are not known, then many stacked traces can be inverted simultaneously, each with a different velocity function. However, the increased number of overlain hyperbolas can more easily model the effects of inconsistent wavelets. As a compromise, I limit velocity functions to reasonable regions selected from a stacking velocity analysis—a few functions cover velocities of primary and multiple reflections. Multiple reflections are modeled separately and then subtracted from marine data. The model can be extended to include more complicated amplitude changes in reflectivity. Migrated reflectivity functions would add an extra constraint on the continuity of reflections over midpoint. Including the effect of dip moveout in the model would make stacking and migration velocities equivalent.
Gravity interpretation using correlation factors between successive least‐squares residual anomalies
Authors: Abdelrahman E. M. , Bayoumi A. I. , Abdelhady Y. E. , Gobashy M. M. , El‐Araby H. M.
Published: October 2002

The correlation factors between successive least‐squares residual (or regional) gravity anomalies from a buried sphere, a two‐dimensional (2‐D) horizontal cylinder, and a vertical cylinder and the first horizontal derivative of the gravity from a 2‐D thin faulted layer are computed. Correlation values are used to determine the depth to the center of the buried structure, and the radius of the sphere or the cylinder and the thickness of the fault are estimated. The method can be applied not only to residuals but also to the Bouguer‐anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order. The method is easy to apply and may be automated if desired. It can also be applied to the derivative anomalies of the gravity field. The validity of the method is tested on two field examples from the United States and Denmark.
In‐situ holographic elastic moduli measurements from boreholes
Authors: Schmitt Douglas R. , Smither Catherine , Ahrens Thomas J.
Published: October 2002

We have developed a unique technique employing optical holography to measure the static Young’s modulus (E) from a borehole. In the experiment, a known point force induces micron scale displacements on the borehole wall which are recorded by a double‐exposure hologram. Raw data consist of dark fringes superimposed on the three‐dimensional image whose pattern is modeled to find E directly. In the laboratory, the holographic technique determined E on rock and metal samples to an uncertainty better than 10 percent. For example, double exposure holograms of a saw‐cut sample of dolomitic marlstone gave an E of 16.8 ± 2.8 GPa in agreement with 17.2 ± 2.0 GPa predicted by published density‐modulus relationships. Field tests of a holographic tool in a horizontal mine pillar borehole gave in‐situ Es which range from 26.9 to 36.0 GPa. Although these data could be interpreted as localized elastic heterogeneity within the rock mass, elastic anisotropy of the rock is a possible explanation for this variation.
Spherical divergence correction for seismic reflection data using slant stacks
Authors: Wang David Y. , McCowan Douglas W.
Published: October 2002

We have developed a method for the spherical divergence correction of seismic reflection data based on normal moveout and stacking of cylindrical slant stacks. The method is illustrated on some Gulf of Mexico data. The results show that our method yields essentially the same traveltime information as does conventional processing. Our amplitudes, however, are more interpretable in terms of reflectivity than are those obtained by using an empirical spherical divergence correction.
On: “Reduction of magnetic and gravity data on an arbitrary surface acquired in a region of high topographic relief” by B. K. Bhattacharyya and K. C. Chan (GEOPHYSICS, 42, 1411–1430, December, 1977).
Authors: Pedersen Laust B.
Published: October 2002

When attempting to get an overview of continuation of potential fields in exploration geophysics, one cannot avoid reading the much quoted article by Bhattacharyya and Chan (hereafter referred to as BC). However, it is unfortunate that the article is unclear on some fundamental points, which this comment attempts to clarify.
In quest of the flank
Authors: Larner Ken , Beasley Craig J. , Lynn Walt
Published: October 2002

Primarily through synthetic and field data examples, this paper reviews the benefits of recent developments in time migration of seismic data and reveals limitations, some of them fundamental, that keep elusive the goal of imaging steep events with full accuracy. Even where velocity varies only with depth and, hence, time migration should suffice, accurate imaging of very steep events requires that the velocity structure be known with considerable precision and be finely sampled in depth. This sensitivity of migration accuracy to detail in velocity structure is attributable to the sensitivity of ray bending for wide‐angle rays to detail in the velocity structure. Also, interestingly, the presence of ray bending at interfaces is seen to enhance the steep‐event accuracy of some algorithms (e.g., phase shift and cascaded finite‐difference) while it degrades the accuracy of others (for example, conventional Kirchhoff summation and the frequency‐wavenumber domain method of Stolt). Of the various time‐migration schemes, a cascading of the Stolt method is the most efficient while having steep‐event accuracy in the presence of significant vertical velocity variation. Its behavior in the presence of even mild lateral velocity variation, however, differs greatly from that of the other methods and must be taken into account. A case involving 3-D migration of 3-D survey data shows how different issues in imaging of the subsurface (two‐pass versus single‐pass 3-D migration and algorithm choice in the presence of mild lateral velocity variation) can become intertwined in practice and lead to confusion as to which of the issues is essential for accurate imaging of the subsurface.
Full‐wave acoustic logging in an irregular borehole
Authors: Bouchon Michel , Schmitt Denis P.
Published: October 2002

A new boundary integral equation formulation for wave propagation in a borehole of irregular cross‐section represents the wave field diffracted at the borehole‐rock interface by the radiation from a distribution of surface sources applied along the borehole wall. The wave fields in the borehole fluid and in the elastic rock are then expressed using the discrete wavenumber method. Application of boundary conditions at discretized locations along the borehole wall leads to a linear system of equations, whose inversion yields the required source distribution. We have used the method to investigate the effect of changes in borehole diameter on the pressure wave field inside the borehole. When the change is smooth, records obtained ahead of the discontinuity location are not affected by its presence. In the case of a steep variation, however, a significant amount of the Stoneley‐wave energy is reflected. When the borehole diameters are different at the source and receiver levels, the microseismograms obtained are somewhat of an average of those that would have been recorded in constant‐radius source and receiver boreholes, respectively. Small‐scale fluctuations in borehole diameter decrease the velocity of the Stoneley wave and of the pseudo‐Rayleigh wave.
Inverse extrapolation of primary seismic waves
Authors: Wapenaar C. P. A. , Peels G. L. , Budejicky V. , Berkhout A. J.
Published: October 2002

Forward wave‐field extrapolation operators simulate propagation effects from one depth level to another. Inverse wave‐field extrapolation operators eliminate those propagation effects. Since forward wave‐field extrapolation can be described in terms of spatial convolution, inverse wave‐field extrapolation can be described in terms of spatial deconvolution. A simple approximation to a stable, spatially band‐limited deconvolution operator is obtained by taking the complex conjugate of the convolution operator. A one‐way version of the Kirchhoff integral that contains the conjugate complex Green’s function is derived. Unlike the situation with respect to the forward problem, the modification of the closed surface integral into an open boundary integral involves an approximation that is identical to the approximation in the conjugate complex deconvolution approach. This approximation neglects the evanescent field and causes a second‐order amplitude error. For a plane acquisition surface, the one‐way Kirchhoff integral is transformed into a one‐way Rayleigh integral. For media with small to moderate contrasts, the one‐way Rayleigh integral with the conjugate complex Green’s function describes true amplitude inverse extrapolation of primary waves. This is illustrated with an example, in which the Green’s function has been modeled with the Gaussian beam method.
Retrieving both the impedance contrast and background velocity: A global strategy for the seismic reflection problem
Authors: Snieder R. , Xie M. Y. , Pica A. , Tarantola A.
Published: October 2002

Recorded seismic reflection waveforms contain information as to the small‐scale variations of impedance and the large‐scale variations of velocity. This information can be retrieved by minimizing the misfit between the recorded waveforms and synthetic seismograms as a function of the model parameters. Because of the different physical characters of the velocity and the impedance, we update these parameters in an alternating fashion, which amounts to a relaxation approach to the minimization of the waveform misfit. As far as the impedance is concerned, this minimization can be performed efficiently using gradient algorithms. For the inversion for seismic velocities, gradient methods do not work nearly as well; therefore, we use different minimization methods for determining impedances and velocities. However, the determination of the impedance and the determination of the velocity are strongly coupled; relaxation is most effective when this coupling is as weak as possible. Weak coupling can be achieved partially by parameterizing the impedances not as a function of depth but as a function of traveltime. A nonlinear, nonlocal method is presented for determining the smooth reference velocity from seismic reflection data. This technique is applied both to synthetic seismograms and to real marine data. In both cases, the velocity information implicitly contained in the curvature of the reflection hyperbolas was fully retrieved using nonlinear waveform optimization. In this way, it is possible to reconstruct both the impedance contrast and the smooth reference velocity from band‐limited seismic reflection data using a single waveform‐fit criterion.
Seismic tomography at a fire‐flood site
Authors: Bregman N. D. , Hurley P. A. , West G. F.
Published: October 2002

A crosshole seismic experiment was conducted to locate and characterize a firefront at an enhanced oil recovery (EOR) pilot project. The reservoir engineers involved in the project were interested in finding out why the burnfront apparently had stalled between two wells 51 m apart. In a noisy producing environment, good quality seismic data were recorded at depths ranging from 710 to 770 m. The frequency range of the data, 500 to 1500 Hz, allows resolution of the velocity structure on a scale of several meters. The moveout of first arrivals indicates that there are large velocity variations in the study region; a high‐amplitude, late arriving channel wave points to the existence of a low‐velocity channel connecting the boreholes. Using an iterative, nonlinear scheme which incorporates curved ray tracing and least‐squares inversion in each iteration, the first‐arrival times were inverted to obtain a two‐dimensional model of the compressional seismic velocity between the boreholes. The velocities range from 1.5 km/s to 3.2 km/s, with a low‐velocity channel at the depth of the producing oil sand. Sonic, core, and temperature logs lead us to conclude that the extremely low velocities in the model are probably due to gases produced by the burn. Increased velocities in an adjacent shale may be a secondary effect of the burn. The velocity model also indicates an irregularity in the topography at the bottom of the reservoir, an irregularity which may be responsible for blocking the progress of the burnfront.
The nonuniqueness of the determination of interval velocities from moveout velocities
Authors: Krey Theodor C.
Published: October 2002

In earlier papers (Krey, 1976; Hubral and Krey, 1980) I described how to obtain an equation for [Formula: see text], the nth interval velocity in an isovelocity layered earth having interfaces with arbitrary dips and curvatures, provided the velocities [Formula: see text], [Formula: see text], … to [Formula: see text] for the first n − 1 layers and the depths of the first n − 1 interfaces [Formula: see text], K = 1, 2, …, n − 1, are known and have continuous derivatives. Moreover, we assume that the zero‐offset time for the reflection from the base of the nth layer and gradient of the traveltime with respect to the horizontal coordinates are known. Finally, the normal moveout (NMO) velocity [Formula: see text] for the nth interface is observed in one arbitrary azimuth (one only), defined by ϕ, the angle between the x‐axis and the seismic profile.
Gravity terrain corrections calculated using digital elevation models
Authors: Cogbill Allen H.
Published: October 2002

Corrections for terrain effects are required for virtually all gravity measurements acquired in mountainous areas, as well as for high‐precision surveys, even in areas of low relief. Terrain corrections are normally divided into two parts, one part being the correction for terrain relatively close to the gravity station (the “inner‐zone” correction) and the other part being the correction for more distant, say, >2 km, terrain. The latter correction is normally calculated using a machine procedure that accesses a digital‐terrain data set. The corrections for terrain very close to the gravity station are done manually using Hammer’s (1939) procedures or a similar method, are guessed in the field, or simply are neglected. Occasionally, special correction procedures are used for the inner‐zone terrain corrections (e.g., LaFehr et al., 1988); but such instances are uncommon.
An iterative approach to seismic skeletonization
Authors: Lu Shin‐yee , Cheng Yoa‐chou
Published: October 2002

In this paper pattern recognition techniques are applied to the automatic tracking of seismic reflectors. We call this procedure seismic skeletonization, since it reduces a seismic section into a line drawing corresponding to seismic reflectors. The procedure uses an iterative approach. Strong reflectors are tracked first; weaker reflectors are tracked at later iterations. At any iteration, the tracking is confined to the areas delineated by the reflectors already tracked in a previous iteration. Reflectors are tracked by correlating neighboring seismic traces. An algorithm called the binary consistency‐checking (BCC) scheme is used to correlate three traces at a time. The combined use of the iterative approach and the BCC scheme is efficient, emulating human interpretation and incorporating “geologic trend” into the results.
An algorithm for the plane‐wave decomposition of point‐source seismograms
Authors: Dietrich M.
Published: October 2002

The correct formulation of the plane‐wave decomposition of point‐source seismograms involves a sequence of Fourier and Hankel transforms which can be evaluated in several ways. The procedure which is proposed here exploits the fact that the plane‐wave response is bandlimited along the horizontal slowness axis. This property permits to expand the Hankel transform into a Fourier‐Bessel series. In practice, this algorithm requires an interpolation in distance of the recorded dataset, but allows a considerable reduction of Bessel functions calculations. Numerical applications performed with synthetic and real data show that the Fourier‐Bessel summation technique yields results which are equivalent to a discrete integration of the Hankel transform.
The migrator’s equation for anisotropic media
Authors: Uren N. F. , Gardner G. H. F. , McDonald J. A.
Published: October 2002

The migrator’s equation, which gives the relationship between real and apparent dips on a reflector in zero‐offset reflection seismic sections, may be readily implemented in one step with a frequency‐domain migration algorithm for homogeneous media. Huygens’ principle is used to derive a similar relationship for anisotropic media where velocities are directionally dependent. The anisotropic form of the migrator’s equation is applicable to both elliptically and nonelliptically anisotropic media. Transversely isotropic media are used to demonstrate the performance of an f-k implementation of the migrator’s equation for anisotropic media. In such a medium SH-waves are elliptically anisotropic, while P-waves are nonelliptically anisotropic. Numerical model data and physical model data demonstrate the performance of the algorithm, in each case recovering the original structure. Isotropic and anisotropic migration of anisotropic physical model data are compared experimentally, where the anisotropic velocity function of the medium has a vertical axis of symmetry. Only when anisotropic migration is used is the original structure recovered.
On: “Gravity and magnetic inversion with minimization of a specific functional” by A. Guillen and V. Menichetti (GEOPHYSICS, 49, 1354–1360, August 1984).
Authors: Ivan Marian
Published: October 2002

The following errors have been detected on p. 1356, equations (14), (15), (16), and (18).
Iterative trace deconvolution and noncausal transform for processing band‐limited data
Authors: Carrion Philip , Braga A. de Pinto
Published: October 2002

In 1983, Carrion and Patton showed that if recorded seismic data do not have low frequencies in their spectrum, inversion for acoustic impedance is unstable. This concept is commonly accepted. Here, we infer acoustic impedance from band‐limited data without low frequencies using iterative trace deconvolution with the so‐called “noncausal projection” which moves initial data samples corresponding to small eigenvalues to negative times. We show that this procedure can solve ill‐posed problems by migrating large residuals (uncertainties in the trend of the recovered impedance) to the bottom of the model. An important property of the proposed method is that it converges to the true solution independently of the chosen initial model. Another advantage of the proposed algorithm is that, unlike conventional dynamic deconvolution (characteristic‐integration schemes), it increases neither errors nor the condition number with depth. The method is illustrated on synthetic and real data.
Magnetic variations in the reconnaissance of sedimentary basins: Field procedure and generalized inversion of short‐period data from the Rio Grande rift
Authors: Hermance J. F. , Neumann G. A.
Published: October 2002

The magnetic variation (MV) technique employs magnetic transients from natural sources in the magnetosphere to delineate geologic structures in the earth’s interior based on their electrical properties. By measuring only the magnetic field at each site, and not the electric field as required for magnetotelluric (MT) studies, a site can be set up quickly, and often in places which might be quite unsuitable for MT measurements. This generally allows one to execute MV surveys in culturally developed areas or in rugged and logistically difficult terrain at much closer site spacings than those used for conventional MT surveys. Procedures for acquiring and processing MV field data are straightforward, as are methods for inverting data to obtain plausible geophysical models. Using a new 2-D generalized inverse algorithm which employs singular value damping of the Lanczos (or SVD) inverse, we apply the MV technique to determine the basement topography beneath a sequence of 11 remote referenced MV sites from an east‐west profile transecting one of the sedimentary basins of the Rio Grande rift—the San Antonio graben in the southern portion of the Socorro Basin in central New Mexico. Band‐limited data at 50 and 63 s were adequate to delineate the major features of the basin: its lateral margins, its asymmetrical cross‐section with basement dipping sharply to the west, and a large vertical displacement along the western boundary fault of the graben. Our results suggest, therefore, that reconnaissance surveys can be optimized to capture only those data needed to resolve such features. This strategy significantly affects the cost‐effectiveness of the method as a complement to other geophysical techniques.
Experimental studies on downhole seismic sources
Authors: Chen S. T. , Eriksen E. A. , Miller M. A.
Published: October 2002

Reversed vertical seismic profiling (RVSP) and crosshole seismology can produce detailed images around a well since they record higher frequency data than surface seismic. The key issue, however, is whether or not a source can be constructed that can deliver enough energy downhole and yet do no significant damage to the borehole. We have investigated various candidate downhole sources for reversed vertical seismic profiling and crosshole seismology. The potential sources studied included explosive charges, a perforating gun, an air gun, and a water gun. The studies were conducted in both open and cased holes in various lithologies. We found that an explosive charge or an air gun can be a viable direct source in both open and cased wells (cemented or free casing). In an open borehole or in a cased well (with new casing), neither explosive charges nor air gun produced damage that was detectable by the borehole televiewer. However, the long‐spaced sonic logging tool indicated that both sources may cause a deterioration of the cement bond between the formation and the casing where the cement is new and its integrity is questionable. The direct P-wave signal is found to be approximately linearly proportional to the amount of explosives used. The signal amplitude decreases as the transmitting distance increases approximately as the power law (−2.14).
Nonlinear inversion of seismic reflection data in a laterally invariant medium
Authors: Pica A. , Diet J. P. , Tarantola A.
Published: October 2002

Interpretation of seismic waveforms can be expressed as an optimization problem based on a non‐linear least‐squares criterion to find the model which best explains the data. An initial model is corrected iteratively using a gradient method (conjugate gradient). At each iteration, computation of the direction of the model perturbation requires the forward propagation of the actual sources and the reverse‐time propagation of the residuals (misfit between the data and the synthetics); the two wave fields thus obtained are then correlated. An extra forward propagation is required to compute the amplitude of the perturbation along the conjugate‐gradient direction. The number of propagations to be simulated numerically in each iteration equals three times the number of shots. Since a 2-D finite‐difference code is employed to solve forward‐ and backward‐propagation problems, the method is general and can handle arbitrary 2-D source‐receiver configurations and lateral heterogeneities. Using conventional velocity analysis to derive an initial velocity model, the method is implemented on a real marine data set. The data set which has been selected corresponds approximately to a horizontally stratified medium. Consequently, a single‐shot gather has been used for inversion. In spite of some simplifying assumptions used for wave‐field propagation (acoustic approximation, point source), and using synthetics generated by a nearby sonic log to calibrate amplitudes, our final synthetics match the input data very well and the inversion result has clear similarities to the log.
Deep subpermafrost thermal regime in the Mackenzie Delta basin, northern Canada—Analysis from petroleum bottom‐hole temperature data
Authors: Majorowicz J. A. , Jones F. W. , Judge A. S.
Published: October 2002

In our studies of the thermal regime of sediments of the young Mackenzie Delta in the southeastern part of the Beaufort-Mackenzie basin of northern Canada, we used thermal data from the base of the permafrost layer, together with temperature data from petroleum wells. By analyzing bottom-hole temperature (BHT) data, we found that the percentage correction, i.e., the percentage difference between BHT and equilibrium temperature, is less than 10% ((with 67% probability) for times exceeding 10 hours after circulation ended, regardless of circulation time. No correlation exists between the percentage correction and depths for the BHT data. Theoretical temperature-depth profiles were constructed from the individual heat flow Q, Q [Formula: see text] and [Formula: see text] values (δQ is error of estimate of Q), the interval thermal conductivities, and a permafrost base temperature of 0°C. Estimates of Q were based on the maximum BHTs from depths >2.7 km. The measured and corrected BHT values for depths less than 1.5 km lie outside the range defined by the predicted temperature and temperature at the base of permafrost. Therefore, the temperature gradient based on interval‐temperature difference between deep and shallow BHTs or ground‐surface temperature and shallow BHTs may not represent the thermal field accurately within the sedimentary strata. The temperature data from the maximum depths, the permafrost base temperature of 0 °C from the 10 deep wells, and estimated thermal conductivities for the sedimentary column give an average heat flow [Formula: see text] of [Formula: see text] (error of estimate of the individual Q value, [Formula: see text]), which is comparable to the values found in the region of the Canada basin.
Accounting for limited spatial aperture in the waveform inversion of p-τ seismograms
Authors: Dobbs S. L. , Wilson C. R. , Backus M. M.
Published: October 2002

The finite length of seismic arrays results in smeared estimates of the plane‐wave decomposition of the recorded wave field. The smearing is a fundamental property of plane‐wave decomposition; it can be reduced but not eliminated. If not accounted for, this smearing can have a significant effect upon the waveform inversion of plane‐wave seismograms. This paper illustrates the effects of limited spatial aperture on the plane‐wave decomposition and demonstrates that these truncation artifacts can be described by a linear ray parameter‐dependent filter. Experiments with synthetic data indicate that including the effects of limited aperture in the forward model of an iterative inversion produces a stable inversion result without significantly reducing the information content of the data. The method is illustrated with synthetic data derived for an earth consisting of elastic, isotropic, flat layers.
A simultaneous inversion for background velocity and impedance maps
Authors: Cao D. , Beydoun W. B. , Singh S. C. , Tarantola A.
Published: October 2002

Full‐waveform inversion of seismic reflection data is highly nonlinear because of the irregular form of the function measuring the misfit between the observed and the synthetic data. Since the nonlinearity results mainly from the parameters describing seismic velocities, an alternative to the full nonlinear inversion is to have an inversion method which remains nonlinear with respect to velocities but linear with respect to impedance contrasts. The traditional approach is to decouple the nonlinear and linear parts by first estimating the background velocity from traveltimes, using either traveltime inversion or velocity analysis, and then estimating impedance contrasts from waveforms, using either waveform inversion or conventional migration. A more sophisticated strategy is to obtain both the subsurface background velocities and impedance contrasts simultaneously by using a single least‐squares norm waveform‐fit criterion. The background velocity that adequately represents the gross features of the medium is parameterized using a sparse grid, whereas the impedance contrasts use a dense grid. For each updated velocity model, the impedance contrasts are computed using a linearized inversion algorithm. For a 1-D velocity background, it is very efficient to perform inversion in the f-k domain by using the WKBJ and Born approximations. The method performs well both with synthetic and field data.
Estimated pay mapping using three‐dimensional seismic data and incremental pay thickness modeling
Authors: Neff Dennis B.
Published: October 2002

Better estimates of hydrocarbon pay thickness and reservoir distribution are achieved if forward modeling is combined with crossplot cluster analysis before the seismic amplitude and isochron data are converted into estimates of pay thickness. To facilitate this process, an enhanced convolutional modeling technique that incorporates petrophysical data and equations into the synthetic seismogram generation process was developed. These incremental pay thickness (IPT) forward models provide the pertinent seismic and petrophysical values required for crossplot analysis. The crossplot analyses then define which seismic variables (trough amplitude, peak amplitude, time structure, isochron, etc.) are most uniquely related to a pay thickness parameter (gross thickness, net thickness, net porosity thickness, or hydrocarbons in place). Work to date, mostly in offshore Gulf Coast gas sands, has shown significant variation in the crossplot transforms required to convert seismic data to estimated pay maps. As such, an interactive, model‐based, interpretive approach is recommended as an appropriate means to integrate petrophysical, geologic, and 3-D seismic data in the creation of reservoir pay maps.
On: “Observations of the air‐coupled waves as a function of depth,” by R. W. Knapp (GEOPHYSICS, 51, 1853–57, September 1986)
Authors: Lomnitz Cinna , de Souza J. Adauto
Published: October 2002

Body waves critically refracted at the free surface may be the cause of the poor record quality in dry sandy loams, such as those of the extensive areas covered by the Barreiras formation in northeastern Brazil (Gomes and Souza, 1986). Records in these areas are corrupted by strong noise cones with a velocity of 340 m/s, usually identified as air‐coupled Rayleigh waves. The velocity at the top of the weathered layer should probably be at least 1.78 times the speed of sound in air for effective coupling between air waves and Rayleigh waves to take place. However, these so‐called “no‐record areas” are characterized by P-wave velocities less than the speed of sound in air.
Dip moveout in anisotropic media
Authors: Uren N. F. , Gardner G. H. F. , McDonald J. A.
Published: October 2002

When a common‐midpoint gather is collected above a dipping reflector, the point at which reflection occurs moves updip as the source‐receiver offset increases. Stacking velocity is constant, but it is a function of dip. Hence a stacked trace is not equivalent to a zero‐offset recorded trace. Dip moveout (DMO) is a processing step which converts traces to the equivalent of true zero‐offset records, making migration after stack (MAS) equivalent to migration before stack (MBS). The theory of velocity‐independent Gardner DMO is extended to triaxially elliptically anisotropic media in this paper. It is shown that the transformation is exact for homogeneous elliptically anisotropic media and that, after DMO, the stacking velocity is the horizontal component of the elliptically anisotropic velocity function. By taking three distinct seismic lines, three of the six constants of triaxial elliptical anisotropy may be determined. The remaining three cannot be obtained from surface seismic measurements. A simple numerical model of a point scatterer in a transversely isotropic medium with a tilted axis of symmetry is used to generate examples. The DMO process works when the velocity function is elliptical, but is not exact when the velocity function is nonelliptical.
Bouguer density determination by fractal analysis
Authors: Thorarinsson Freyr , Magnusson Stefan G.
Published: October 2002

Density values for the Bouguer reduction of two gravity data sets from Iceland are determined using a new method based on minimization of the roughness of the Bouguer anomaly surface. The fractal dimension of the surface is used as a gauge of the roughness. The analysis shows the size of topographic features supported by crust without isostatic compensation to be 25 to 30 km in southwest Iceland and 9 to 10 km inside the active rifting zone. The densities selected for these areas are 2490 and [Formula: see text], respectively.
Seismic velocity models for heat zones in Athabasca tar sands
Authors: Lines Larry R. , Jackson Ronald , Covey James D.
Published: October 2002

Recent laboratory and field studies indicate that the P-wave velocity in Athabasca tar sands decreases when temperature increases during steam injection. In this paper we derive time variant velocity models from seismic traveltime inversions of both reflection and borehole data. Prior to steam injection, three‐dimensional (3-D) reflector velocity‐depth models are established using image‐ray conversions of traveltimes to depth. The changes in velocity due to steam injection are modeled by inverting traveltime data from seismic monitor surveys after steam injection and comparing these results to velocities computed prior to steam injection. Velocity models are essentially determined by traveltimes from the 3-D seismic reflection survey. The surface‐to‐wellbore data traveltimes show the expected delay caused by steam injection but do not significantly alter the velocity model produced by reflection traveltimes. For seismic monitor surveys, low‐velocity zones show a very good correlation with zones of temperature increase at injector well positions. The results indicate that velocity models obtained from seismic traveltimes may prove useful in detecting steam fronts in tar sands.
A computer program to convert SEG-2 data to SEG-Y
Authors: Bennett Brett
Published: October 2002

Recent introduction of the SEG-2 data format to the geophysical community creates compatibility problems with existing seismic data formats. Presented here is a computer program (SEG2SEGY.C) that converts seismic data from SEG-2 format to SEG-Y format. The discussion of the program architecture assumes the reader has a working knowledge of SEG-2, SEG-Y, and C programming language.
Estimating SV‐wave stacking velocities for transversely isotropic solids
Authors: Berge Patricia A.
Published: October 2002

Conventional seismic experiments can record converted shear waves in anisotropic media, but the shear‐wave stacking velocities pose a problem when processing and interpreting the data. Methods used to find shear‐wave stacking velocities in isotropic media will not always provide good estimates in anisotropic media. Although isotropic methods often can be used to estimate shear‐wave stacking velocities in transversely isotropic media with vertical symmetry axes, the estimations fail for some transversely isotropic media even though the anisotropy is weak. For a given anisotropic medium, the shear‐wave stacking velocity can be estimated using isotropic methods if the isotropic Snell’s law approximates the anisotropic Snell’s law and if the shear wavefront is smooth enough near the vertical axis to be fit with an ellipse. Most of the 15 transversely isotropic media examined in this paper met these conditions for short reflection spreads and small ray angles. Any transversely isotropic medium will meet these conditions if the transverse isotropy is weak and caused by thin subhorizontal layering. For three of the media examined, the anisotropy was weak but the shear wave-fronts were not even approximately elliptical near the vertical axis. Thus, isotropic methods provided poor estimates of the shear‐wave stacking velocities. These results confirm that for any given transversely isotropic medium, it is possible to determine whether or not shear‐wave stacking velocities can be estimated using isotropic velocity analysis.
Kinematics of crossline prestack migration
Authors: Berryhill John R.
Published: October 2002

Among the reasons for considering optional seismic processes such as dip moveout (DMO) or prestack migration is the fact that two reflections with the same arrival time may require different stacking velocities in order to produce an acceptable image. For example, inline dip tends to increase the required stacking velocity, and DMO can be applied to correct this effect. Crossline dip has no direct effect on stacking velocity, but, because average velocity tends to increase with depth, a dipping reflection broadside to a seismic line will tend to require a lower stacking velocity than an in‐plane reflection with the same time of arrival. This problem is not addressed by DMO, but it can be handled by what I call “crossline prestack migration.”
A rapid method for three‐dimensional modeling of magnetic anomalies
Authors: Rao D. Bhaskara , Babu N. Ramesh
Published: October 2002

A computer program has been developed for three‐dimensional analysis of total field magnetic anomalies due to arbitrary polarization suitable for present‐day personal computers. A vertical sided prism with arbitrary polarization is used as a basic model. A nonlinear optimization technique based on Marquardt’s algorithm is used to estimate all parameters of the model. A combination of prisms is used to analyze more complex magnetic fields. Analytical methods are used to estimate the derivatives required in the simultaneous solutions of the normal equations. Methods have been developed to minimize the computing time in forward calculation as well as in inversion. Approximate equations have been derived for rapid calculation of magnetic anomalies and partial derivatives of anomalies of prismatic bodies, which are valid beyond short distances from the sources. The algorithm has been developed in such a way that the use of the exact and approximate equations may be efficiently monitored as a trade‐off between accuracy and speed. The method is applied to analyze a synthetic anomaly contour map and the total field aeromagnetic anomalies in the offshore region of Mahanadi basin, Orissa, India.
Seismic mis‐tie resolution technique
Authors: Harper Michael D.
Published: October 2002

Efficient resolution of seismic time mis‐ties within a survey can be critical to the successful generation of a prospect. A mathematical technique for the automatic resolution of mis‐ties is presented that determines an optimal set of bulk time corrections to be applied to each line in a survey. A bulk time correction for a seismic line is a static time shift that is applied to every point on the line, thus preserving the dip of each seismic line. Dynamic time shifts that can vary over a seismic line are not addressed here. Solutions are presented for both the fully determined case and the over‐determined case where the squared error (or squared mis‐tie) is minimized. A mathematical weight, associated with each seismic line, is utilized within the technique to reflect line quality, desirability, vintage, or some other line attribute. The utilization of this technique extends beyond merely obtaining a set of optimal corrections for each seismic line. Problem lines may be identified for closer scrutiny, bulk time corrections for a group of lines as a function of vintage can be estimated, and statistical analyses can be performed on the results due to the least‐squares nature of the technique.
High‐resolution three‐dimensional seismic survey of a thin sand at depth
Authors: Kinsland G. L. , McDonald J. A. , Gardner G. H. F.
Published: October 2002

A thin sand has been successfully imaged at great depth using a carefully designed, high‐resolution, three‐dimensional (3-D), seismic survey. The area of the survey was along a portion of the boundary between northeastern Vermilion Parish and southern Lafayette Parish about twelve miles south of Lafayette, Louisiana. Surface terrain was typically flat farmland at the southern edge of the Pleistocene Prairie Terrace and was ideal for this type of high‐resolution survey. The greatest elevation difference between any two source or receiver locations was about 6 ft (1.8 m). The target for this survey was the Cib jeff sand at a depth of about 13,400 ft (4084 m). The Cib jeff sand is within massive shales and is within a geopressured zone. Relative isolation of the Cib jeff sand by the surrounding shales makes the sand a good candidate for seismic imaging. After some preliminary field tests a survey was designed which used the crossed‐array method in which the source and receiver lines are at some angle to one another, usually orthogonal. Data were collected using a 1024-channel recording system with vibrators as sources. Receiver arrays were not used as it was possible to sweep with frequencies outside the frequency range of the ground roll. A total of [Formula: see text] seismic traces was collected. Many tests were also carried out in the processing of these data and it was found that large variations of offsets in the data volume resulted in deterioration in the quality of stacked data due to nonhyperbolic moveout. The migrated data volume was restricted to traces with less than 7500 ft (2286 m) source‐to‐receiver offset, and to the time window containing the Cib jeff sand, namely from 2.5 to 5.0 s. The Cib jeff sand was successfully imaged and the migrated data volume was interpreted using paper sections. As one would expect, the interpretation based on the total volume is more complex than the interpretation using available conventional two‐dimensional (2-D) lines. In particular the fault pattern interpretation based on 2-D seismic data and well logs is believed to be in error. The western bounding fault is placed further west and other faults were delineated through the reservoir when the interpretation was based on the total 3-D volume. Overall, we believe that this reservoir was mapped with more control than was possible with 2-D data.
A proof for the convergence of 15‐degree cascaded migration
Authors: Cambois Guillaume
Published: October 2002

Larner and Beasley (1987) introduced cascaded migrations and showed, without proving it rigorously, that iterating a 15-degree migration with proper choice of migration velocity was equivalent to a 90-degree migration. In this paper, I will give a proof based on a power series expansion that makes it possible to compare this method with other migration methods. This analysis shows, for example, that cascaded 45-degree migrations yield higher accuracy than cascaded 15-degree migrations with fewer iterations.
Seismic reflection amplitude versus angle variations over a thermally enhanced oil recovery site
Authors: Tsingas C. , Kanasewich E. R.
Published: October 2002

In recent years it has become increasingly important to develop a capability for monitoring enhanced oil recovery (EOR) processes as they are occurring within any reservoir. An amplitude‐versus‐angle (AVA) analysis over a steam injection location showed encouraging results and established that seismic reflection methods, when well designed and carefully processed, can be used to map the invaded steam zones in steam stimulation EOR operations. The results are imaged on a new type of display called ARPA (amplitude‐ratio for partial angle), which illustrates reflection zones with low or high Poisson’s ratio or equivalently high or low gas saturation with a CMP stack section plotted as the background. A seismic experiment consisting of three reflection lines was carried out by Esso Resources in February, 1984 over a steam injection site near Cold Lake, Alberta. Analysis of the field data showed that large variations in reflected scattered energy were a function of angle of incidence in areas affected by the steam zone.
Acoustic modeling in fluid‐saturated porous media
Authors: Hassanzadeh Siamak
Published: October 2002

An acoustic modeling method with possible application to enhanced hydrocarbon reservoir characterization is presented. The method involves numerical simulation of two‐dimensional (2‐D), low‐frequency transient acoustic‐wave propagation in porous media and is based on the explicit finite‐difference formulation of Biot’s system of equations in a fluid‐saturated poroacoustic medium. The scheme is second‐order accurate in space and time. Synthetic seismograms computed using this approach indicate that transient acoustic‐wave propagation in unbounded fluid‐filled porous media and in the presence of fluid viscosity closely mimics that in an equivalent nonporous (single‐phase) solid. However, in the presence of heterogeneities, such as layering, inclusions, and discontinuities, the results show that acoustic‐wave characteristics are affected by spatial variations in reservoir parameters such as porosity, permeability, and fluid content as well as the fluid‐solid interaction. The effects of permeability and fluid viscosity are discernible in dispersion and dissipation of the compressional wave, whereas porosity affects the compressional velocity as well. The results of this study suggest that no equivalent single‐phase model can adequately describe the effects of permeability and porosity on seismic waves propagating through heterogeneous fluid‐filled porous media.
Migration analysis with an extra time shift
Authors: Maeland Einar
Published: October 2002

Migration of single‐shot data with an erroneous velocity yields an “image” of the true reflector which is distorted. Associated with this image is a virtual source, a wavefront of geometrical optics, orthogonal to the rays. The position of the caustics or focal regions, enveloped by the reflected rays, indicates where very high amplitudes can be expected. In order to compensate for the erroneous velocity, the imaging condition is relaxed to allow for an extra time‐shift. If the position of a “focus” can be detected by inspection of the migrated output, this approach provides the correct velocity. A synthetic example is used to illustrate the results of the analysis.
Analytic synthetic seismograms for depth migration testing
Authors: Gray Samuel H. , Jacewitz Chester A. , Epton Michael E.
Published: October 2002

By using the fact that raypaths in a linear acoustic velocity field are circular arcs, we analytically generate a number of distinct nontrivial synthetic seismograms. The seismograms yield accurate traveltimes from reflection events, but they do not give reflection amplitudes. The seismograms are useful for testing seismic migration programs for both speed and accuracy, in settings where lateral velocity variations can be arbitrarily high and dipping reflectors arbitrarily steep. Two specific examples are presented as illustrations.