bluuebunny/crossref_metadata_2025 huggingface dataset:
Theoretical response of vertical coincident and horizontal coplanar coils when operated over steeply dipping conductors located below a conductive overburden
Authors: Duckworth Ken , Krebes Edward S.
Published: October 2002

Theory for the electromagnetic response of a single‐turn, loaded‐coil target conductor located below a conductive overburden is developed for the case of moving source electromagnetic systems. Application of this theory to a comparative study of the horizontal coplanar and vertical coincident coil configurations demonstrates that the secondary magnetic field detected by a vertical coincident coil configuration over a steeply dipping tabular target located in free space is significantly stronger than the secondary field detected by the separated horizontal coplanar coil system over that same target for all target depths. In the presence of an overburden, this relative strength of anomaly magnitude is retained. In addition, the response of the coil target to the vertical coincident coil system is found to be less distorted by the presence of the overburden than when detected by the separated horizontal coplanar coils.
3-D localization of buried objects by nearfield electromagnetic holography
Authors: Guo Yanping , Ko Harvey W. , White David M.
Published: October 2002

We present a practical method of localizing underground objects with low‐frequency electromagnetic fields. The method uses spatial information from the field measured on the ground, and a nearfield “holographic” theory to reconstruct the field image of buried objects. Both numerical simulations and field tests demonstrate that buried metallic objects can be resolved and individually localized in 3-D space even if the measurement field shows only a single peak as might be indicative of a single object.
Comparison of the Krief and critical porosity models for prediction of porosity and VP/VS
Authors: Mavko Gary , Mukerji Tapan
Published: October 2002

[Formula: see text] relations are key to the determination of lithology from seismic or sonic log data, as well as for direct seismic identification of pore fluids using, for example, amplitude variation with offset (AVO) analysis. While there are a variety of published [Formula: see text] relations and [Formula: see text] prediction techniques, most reduce to two simple elements: (1) for each lithology, establish empirical relations among [Formula: see text], [Formula: see text], and porosity for one reference fluid—usually water—and (2) use Gassmann’s (1951) relations to map these to other pore fluid states. In this short note we point out similarities between the critical porosity models of Nur (1992) and Krief et al. (1990) for predicting [Formula: see text]. Both are useful, primarily because they incorporate the above two robust elements. Although derived from different directions, they are nearly identical.
Shear‐wave studies in glacial till
Authors: Carr Bradley J. , Hajnal Zoltan , Prugger Arnfinn
Published: October 2002

Within a high‐resolution shallow reflection survey program in Saskatchewan, Canada, S-waves were produced using a single seismo‐electric blasting cap and were found to be distinguishable from surface wave phases. The local glacial deposits have average velocities of 450 m/s. [Formula: see text] ratios average 3.6 in these sequences, but they vary laterally, according to the velocity analyses done in two boreholes drilled along the seismic line. Vertical resolution for S-wave reflections are 0.75 m [in the vertical seismic profiling (VSP) data] and 1.5 m (in the CDP data). Yet, the S-wave CDP results are still better than corresponding P-wave data, which had a vertical resolution of 2.6 m. S-wave anisotropy is inferred in the glacial deposits on the basis of particle motion analysis and interpretations of S-wave splitting. However, the amount of observed splitting is small (∼2–6 ms over 5–10 m) and could go undetected for seismic surveys with larger sampling intervals. VSPs indicate that S-wave reflectivity is caused by both distinct and subtle lithologic changes (e.g., clay/sand contacts or changes in clay percentage within a particular till unit) and changes in bulk porosity. Migrated S-wave sections from line 1 and line 2 image reflections from sand layers within the tills as well as the first “bedrock” sequence (known as the Judith River Formation). Shear wave images are not only feasible in unconsolidated materials, but provide additional information about structural relationships within these till units.
Shallow 3-D seismic reflection surveying: Data acquisition and preliminary processing strategies
Authors: Büker Frank , Green Alan G. , Horstmeyer Heinrich
Published: October 2002

A comprehensive strategy of 3-D seismic reflection data acquisition and processing has been used in a study of glacial sediments deposited within a Swiss mountain valley. Seismic data generated by a downhole shotgun source were recorded with single 30-Hz geophones distributed at 3 m × 3 m intervals across a 357 m × 432 m area. For most common‐midpoint (CMP) bins, traces covering a full range of azimuths and source‐receiver distances of ∼2 to ∼125 m were recorded. A common processing scheme was applied to the entire data set and to various subsets designed to simulate data volumes collected with lower density source and receiver patterns. Comparisons of seismic sections extracted from the processed 3-D subsets demonstrated that high‐fold (>40) and densely spaced (CMP bin sizes ⩽ 3 m × 3 m) data with relatively large numbers (>6) of traces recorded at short (<20 m) source‐receiver offsets were essential for obtaining clear images of the shallowest (<100 ms) reflecting horizons. Reflections rich in frequencies >100 Hz at traveltimes of ∼20 to ∼170 ms provided a vertical resolution of 3 to 6 m over a depth range of ∼15 to ∼150 m. The shallowest prominent reflection at 20 to 35 ms (∼15 to 27 m depth) originated from the boundary between a near‐surface sequence of clays/silts and an underlying unit of heterogeneous sands/gravels.
Improving seismic data quality in the Gippsland Basin (Australia)
Authors: Dunne Jarrod , Beresford Greg
Published: October 2002

Deep seismic exploration in the Gippsland Basin is hindered by strong noise below the Latrobe Group coal sequence. The reflectivity method provides a means for constructing detailed and accurate synthetic seismograms, often from little more than a partial sonic log. The noise contributions to the synthetics can then be interpreted using additional synthetics computed from variations upon the depth model and by exercising control over the wave types modeled. This approach revealed three types of persistent noise in progressively deeper parts of the subcoal image: (1) mode‐converted interbed multiples (generated within the coal sequence), (2) S-wave reflections and long‐period multiples (generated between the coal sequence and the Miocene carbonates), and (3) surface‐related multiples. The noise interpretation can also be performed upon semblance analyses of the elastic synthetics to guide a velocity analysis away from a well. This procedure helped to avoid picking the interformation long‐period multiples, whose stacking velocities were only 5 to 10% below those of the weak target zone primaries. An improve subcoal image was obtained by making full use of the versatile noise suppression offered by a τ-p domain processing stream. By separating the strong linear events at the far offsets, it is possible to stack a larger portion of the target zone reflections, provided hyperbolic velocity filtering (HVF) is applied to suppress the transform artifacts. Hyperbolic velocity filtering can be incorporated into a point‐source τ-p transform to suppress S-wave reflections and guided waves while preserving plane‐wave amplitudes to assist the subsequent deconvolution of the mode‐converted interbed multiples. Stacking in the τ-p domain is achieved using an elliptical moveout correction that reduces wavelet stretch and approximates the exact reflection traveltime better than NMO. Two regional seismic lines were reprocessed in this manner and cointerpreted with the modeling studies performed at nearby wells to avoid the noise events that still remained. Several new events appeared in the immediate target zone, passing the low‐frequency character expected following transmission through a coal sequence.
3-D seismic imaging and interpretation of Brushy Canyon slope and basin thin‐bed reservoirs, northwest Delaware Basin
Authors: Hardage B. A. , Simmons J. L. , Pendleton V. M. , Stubbs B. A. , Uszynski B. J.
Published: October 2002

A study was done at Nash Draw field, Eddy County, New Mexico, to demonstrate how engineering, drilling, geologic, geophysical, and petrophysical technologies should be integrated to improve oil recovery from Brushy Canyon reservoirs at depths of approximately 6600 ft (2000 m) on the northwest slope of the Delaware basin. These thin‐bed reservoirs were deposited in a slope‐basin environment by a mechanism debated by researchers, a common model being turbidite deposition. In this paper, we describe how state‐of‐the‐art 3-D seismic data were acquired, interpreted, integrated with other reservoir data, and then used to improve the sitting of in‐field wells and to provide facies parameters for reservoir simulation across this complex depositional system. The 3-D seismic field program was an onshore subsalt imaging effort because the Ochoan Rustler/Salado, a high‐velocity salt/anhydrite section, extended from the surface to a depth of approximately 3000 ft (900 m) across the entire study area. The primary imaging targets were heterogenous siltstone and fine‐grained sandstone successions approximately 100 ft (30 m) thick and comprised of complex assemblages of thin lobe‐like deposits having individual thickness of 3 to 6 ft (1 to 2 m). The seismic acquisition was complicated further by (1) the presence of active potash mines around and beneath the 3-D grid that were being worked at depths of 500 to 600 ft (150 to 180 m), (2) shallow salt lakes, and (3) numerous archeological sites. We show that by careful presurvey wave testing and attention to detail during data processing, thin‐bed reservoirs in this portion of the Delaware basin can be imaged with a signal bandwidth of 10 to 100 Hz and that siltstone/sandstone successions 100 ft (30 m) thick in the basal Brushy Canyon interval can be individually detected and interpreted. Further, we show that amplitude attributes extracted from these 3-D data are valuable indicators of the amount of net pay and porosity‐feet in the major reservoir successions and of the variations in the fluid transmissivity observed in production wells across the field. Relationships between seismic reflection amplitude and reservoir properties determined at the initial calibration wells have been used to site and drill two production wells. The first well found excellent reservoir conditions; the second well was slightly mispositioned relative to the targeted reflection‐amplitude trend and penetrated reservoir facies typical of that at other producing wells. Relationships between seismic reflection amplitude and critical petrophysical properties of the thin‐bed reservoirs have also allowed a seismic‐driven simulation of reservoir performance to be initiated.
Weighted Euler deconvolution of gravity data
Authors: Keating Pierre B.
Published: October 2002

Euler deconvolution is used for rapid interpretation of magnetic and gravity data. It is particularly good at delineating contacts and rapid depth estimation. The quality of the depth estimation depends mostly on the choice of the proper structural index and adequate sampling of the data. The structural index is a function of the geometry of the causative bodies. For gravity surveys, station distribution is in general irregular, and the gravity field is aliased. This results in erroneous depth estimates. By weighting the Euler equations by an error function proportional to station accuracies and the interstation distance, it is possible to reject solutions resulting from aliasing of the field and less accurate measurements. The technique is demonstrated on Bouguer anomaly data from the Charlevoix region in eastern Canada.
Seismic system analysis—A case study from the Gulf of Mexico
Authors: Hornbostel Scott C.
Published: October 2002

It is often difficult to predict the effects of change in seismic acquisition or processing on data quality. To address this difficulty, ensemble averaging can be used to estimate the final stacked‐trace effects of altering aspects of the seismic acquisition or processing. This method of studying the seismic system begins by modeling of an ensemble of data gathers based on some geological region of interest. The model gathers are subsequently processed to create stacked traces that are compared with related reference traces to make signal‐to‐noise ratio (SNR) or bandwidth measurements. The ensemble average of these stacked‐trace measurements can then be examined while some aspect of the simulated acquisition or processing is adjusted. The result of this analysis is a plot illustrating the sensitivity of the seismic system (i.e., the stacked‐trace quality) to the selected parameter under investigation. This ensemble averaging approach was used to study system sensitivities for a data set collected in the Gulf of Mexico. The specific issues examined in this analysis include source and receiver parameters, ambient noise levels, spatial sampling, velocity picking, velocity errors, and stretch muting. Of the parameters studied, the final system output was most sensitive to velocity errors. Even differences of 1–2% in the stacking velocity led to noticeable degradation of the stacked‐trace bandwidth and SNR. This velocity sensitivity was evident in both the model and field data. Certain parameters, such as gun volumes, were less important for typical values. The ambient noise level and spatial sampling effects were similarly less important except in the deeper portions of the data (where the unstacked SNR was fairly low). These insensitivities are interesting because they imply potential cost savings. The percent stretch‐mute study was interesting because SNR and bandwidth were optimized with different mutes. All study results by design, are, tied to a specific data area. Nonetheless, these findings may provide an initial direction for system studies in other areas.
PP-wave reflection coefficients in weakly anisotropic elastic media
Authors: Vavryuk Václav , Peník Ivan
Published: October 2002

Approximate PP-wave reflection coefficients for weak contrast interfaces separating elastic, weakly transversely isotropic media have been derived recently by several authors. Application of these coefficients is limited because the axis of symmetry of transversely isotropic media must be either perpendicular or parallel to the reflector. In this paper, we remove this limitation by deriving a formula for the PP-wave reflection coefficient for weak contrast interfaces separating two weakly but arbitrarily anisotropic media. The formula is obtained by applying the first‐order perturbation theory. The approximate coefficient consists of a sum of the PP-wave reflection coefficient for a weak contrast interface separating two background isotropic half‐spaces and a perturbation attributable to the deviation of anisotropic half‐spaces from their isotropic backgrounds. The coefficient depends linearly on differences of weak anisotropy parameters across the interface. This simplifies studies of sensitivity of such coefficients to the parameters of the surrounding structure, which represent a basic part of the amplitude‐versus‐offset (AVO) or amplitude‐versus‐azimuth (AVA) analysis. The reflection coefficient is reciprocal. In the same way, the formula for the PP-wave transmission coefficient can be derived. The generalization of the procedure presented for the derivation of coefficients of converted waves is also possible although slightly more complicated. Dependence of the reflection coefficient on the angle of incidence is expressed in terms of three factors, as in isotropic media. The first factor alone describes normal incidence reflection. The second yields the low‐order angular variations. All three factors describe the coefficient in the whole region, in which the approximate formula is valid. In symmetry planes of weakly anisotropic media of higher symmetry, the approximate formula reduces to the formulas presented by other authors. The accuracy of the approximate formula for the PP reflection coefficient is illustrated on the model with an interface separating an isotropic half‐space from a half‐space filled by a transversely isotropic material with a horizontal axis of symmetry. The results show a very good fit with results of the exact formula, even in cases of strong anisotropy and strong velocity contrast.
Joint inversion ofP- andPS-waves in orthorhombic media: Theory and a physical modeling study
Authors: Grechka Vladimir , Theophanis Stephen , Tsvankin Ilya
Published: October 2002

Reflection traveltimes recorded over azimuthally anisotropic fractured media can provide valuable information for reservoir characterization. As recently shown by Grechka and Tsvankin, normal moveout (NMO) velocity of any pure (unconverted) mode depends on only three medium parameters and usually has an elliptical shape in the horizontal plane. Because of the limited information contained in the NMO ellipse of P-waves, it is advantageous to use moveout velocities of shear or converted modes in attempts to resolve the coefficients of realistic orthorhombic or lower‐symmetry fractured models. Joint inversion of P and PS traveltimes is especially attractive because it does not require shear‐wave excitation. Here, we show that for models composed of horizontal layers with a horizontal symmetry plane, the traveltime of converted waves is reciprocal with respect to the source and receiver positions (i.e., it remains the same if we interchange the source and receiver) and can be adequately described by NMO velocity on conventional‐length spreads. The azimuthal dependence of converted‐wave NMO velocity has the same form as for pure modes but requires the spatial derivatives of two-way traveltime for its determination. Using the generalized Dix equation of Grechka, Tsvankin, and Cohen, we derive a simple relationship between the NMO ellipses of pure and converted waves that provides a basis for obtaining shear‐wave information from P and PS data. For orthorhombic models, the combination of the reflection traveltimes of the P-wave and two split PS-waves makes it possible to reconstruct the azimuthally dependent NMO velocities of the pure shear modes and to find the anisotropic parameters that cannot be determined from P-wave data alone. The method is applied to a physical modeling data set acquired over a block of orthorhombic material—Phenolite XX-324. The inversion of conventional‐spread P and PS moveout data allowed us to obtain the orientation of the vertical symmetry planes and eight (out of nine) elastic parameters of the medium (the reflector depth was known). The remaining coefficient (c12or δ(3)in Tsvankin’s notation) is found from the direct P-wave arrival in the horizontal plane. The inversion results accurately predict moveout curves of the pure S-waves and are in excellent agreement with direct measurements of the horizontal velocities.
Least‐squares migration of incomplete reflection data
Authors: Nemeth Tamas , Wu Chengjun , Schuster Gerard T.
Published: October 2002

A least‐squares migration algorithm is presented that reduces the migration artifacts (i.e., recording footprint noise) arising from incomplete data. Instead of migrating data with the adjoint of the forward modeling operator, the normal equations are inverted by using a preconditioned linear conjugate gradient scheme that employs regularization. The modeling operator is constructed from an asymptotic acoustic integral equation, and its adjoint is the Kirchhoff migration operator. We tested the performance of the least‐squares migration on synthetic and field data in the cases of limited recording aperture, coarse sampling, and acquisition gaps in the data. Numerical results show that the least‐squares migrated sections are typically more focused than are the corresponding Kirchhoff migrated sections and their reflectivity frequency distributions are closer to those of the true model frequency distribution. Regularization helps attenuate migration artifacts and provides a sharper, better frequency distribution of estimated reflectivity. The least‐squares migrated sections can be used to predict the missing data traces and interpolate and extrapolate them according to the governing modeling equations. Several field data examples are presented. A ground‐penetrating radar data example demonstrates the suppression of the recording footprint noise due to a limited aperture, a large gap, and an undersampled receiver line. In addition, better fault resolution was achieved after applying least‐squares migration to a poststack marine data set. And a reverse vertical seismic profiling example shows that the recording footprint noise due to a coarse receiver interval can be suppressed by least‐squares migration.
Seismic reflection imaging over a massive sulfide deposit at the Matagami mining camp, Québec
Authors: Calvert Andrew J. , Li Yexu
Published: October 2002

A 2-D seismic reflection profile was shot across the southern flank of the Matagami mining camp, almost directly above the recently discovered Bell Allard massive sulfide deposit, now estimated at more than 6 million metric tons. All orebodies found in the southern part of the mining camp, including Bell Allard, are located at the contact between the primarily basaltic Wabassee Group and the underlying rhyolitic Watson Lake Group. Seismic reflections were recorded from the basalt‐rhyolite contacts of the lower Wabassee Group, as well as from gabbro sills that intrude much of the volcanic stratigraphy. A strong reflection from the top of the Bell Allard orebody was also detected, but the reflection does not extend over the full width of the deposit as defined by drilling, appearing to correlate with the lower pyrite‐rich zone. Faulting, which can be interpreted from discontinuities in the observed reflections, probably controlled the formation of the Bell Allard deposit. If the interpreted gabbro sills are accepted as isotime markers, then faulting of the deeper sill complex defines a series of half grabens within the rhyolitic Watson Lake Group. The Bell Allard deposit is found at the intersection of one of these apparently low‐angle normal faults with the top of the Watson Lake Group, indicating that sulfide mineralization may have been associated with fluid flow along the fault, which likely penetrates to the underlying mafic intrusion. Although the precise geometry of subsurface faulting cannot be estimated from a single 2-D seismic profile, these results indicate that a full 3-D seismic survey should allow the mapping of many of the subsurface fault systems and the verification of hypotheses of fault‐controlled deposit formation.
Seismic signal band estimation by interpretation of f-x spectra
Authors: Margrave Gary F.
Published: October 2002

The signal band of reflection seismic data is that portion of the temporal Fourier spectrum which is dominated by reflected source energy. The signal bandwidth directly determines the spatial and temporal resolving power and is a useful measure of the value of such data. The realized signal band, which is the signal band of seismic data as optimized in processing, may be estimated by the interpretation of appropriately constructed f-x spectra. A temporal window, whose length has a specified random fluctuation from trace to trace, is applied to an ensemble of seismic traces, and the temporal Fourier transform is computed. The resultant f-x spectra are then separated into amplitude and phase sections, viewed as conventional seismic displays, and interpreted. The signal is manifested through the lateral continuity of spectral events; noise causes lateral incoherence. The fundamental assumption is that signal is correlated from trace to trace while noise is not. A variety of synthetic data examples illustrate that reasonable results are obtained even when the signal decays with time (i.e., is nonstationary) or geologic structure is extreme. Analysis of real data from a 3-C survey shows an easily discernible signal band for both P-P and P-S reflections, with the former being roughly twice the latter. The potential signal band, which may be regarded as the maximum possible signal band, is independent of processing techniques. An estimator for this limiting case is the corner frequency (the frequency at which a decaying signal drops below background noise levels) as measured on ensemble‐averaged amplitude spectra from raw seismic data. A comparison of potential signal band with realized signal band for the 3-C data shows good agreement for P-P data, which suggests the processing is nearly optimal. For P-S data, the realized signal band is about half of the estimated potential. This may indicate a relative immaturity of P-S processing algorithms or it may be due to P-P energy on the raw radial component records.
A finite element method for computation of the regional gravity anomaly
Authors: Mallick K. , Sharma K. K.
Published: October 2002

A regional gravity anomaly, based on element shape functions used in finite element analysis, is developed. The regional gravity is approximated by a weighted sum of discrete gravity values at eight stations coinciding with the eight nodes of a second‐order or at twelve stations coinciding with the twelve nodes of a third‐order isoparametric element superimposing the map space. The computations are carried out on a reference space with the shape functions acting as weighting factors, and subsequently translated to the real map space. In this technique, no observed gravity data lying inside the survey area enter into the regional computation. Tests on the gravity field in Harris County, Texas, a well known hydrocarbon prospect during the 1940s, and the Klamath Mountains and the Cascade Range in California confirmed the efficacy of this method.
An optimal true‐amplitude least‐squares prestack depth‐migration operator
Authors: Chavent Guy , Plessix René‐Edouard
Published: October 2002

In order to define an optimal true‐amplitude prestack depth migration for multishot and multitrace data, we develop a general methodology based on the least‐squares data misfit function associated with a forward model. The amplitude of the migrated events are restored at best for any given geometry and any given preliminary filtering and amplitude correction of the data. The migrated section is then the gradient of the cost function multiplied by a weight matrix. A study of the Hessian associated with this data misfit shows how efficiently to find a good weight matrix via the computation of only few elements of this Hessian. Thanks to this matrix, the resulting migration operator is optimal in the sense that it ensures the best possible restoration of the amplitudes among the large class of least‐squares migrations. Applied to a forward model based on Born, ray tracing, and diffracting points approximation, this optimal migration outperforms or at least equals the classic Kirchhoff formula, since the latter belongs to the class of least‐squares migrations and is only optimal for one shot and an infinite aperture. Numerical results illustrate this construction and confirm the above expectations.
Ground roll supression using the Karhunen‐Loeve transform
Authors: Liu Xuewei
Published: October 2002

Ground roll is the main type of coherent noise in land seismic surveys, and is commonly much stronger in amplitude than the reflection signals. Standard methods for suppressing ground roll include 1-D high‐pass filtering and 2-D f-k filtering. High‐pass filtering is based on the low‐frequency nature of ground roll, but has the disadvantage that it also eliminates low‐frequency reflection signals which contribute to the character of reflection events and are very important in inversion for acoustic impedance. When the amplitude of the ground roll is much stronger than the reflection signals, f-k filters cause serious distortion of the signal.
3-D seismic stratal‐surface concepts applied to the interpretation of a fluvial channel system deposited in a high‐accomodation environment
Authors: Hardage Bob A. , Remington Randy L.
Published: October 2002

A fundamental thesis of seismic stratigraphy is that seismic reflections follow impedance contrasts that coincide with stratal surfaces, which are surfaces where depositional processes occur at a fixed moment in geologic time. This stratal‐surface concept is used in this paper to image a narrow (width ∼300 ft or 90 m), thin, fluvial channel system that is embedded within a seismic reflection peak that reflects from a large (about 2 × 2 mi or 3.2 × 3.2 km) area of nonchannel facies that dominate the waveshape of the reflection peak. The targeted channel facies are confined to an interval that vertically spans less than 30 ft. According to principles of seismic stratigraphy, four conformable seismic stratal surfaces that pass through the interior of this channel sequence were constructed across a 2 × 2-mi (3.2 × 3.2-km) (approximately) area of a 3-D seismic‐data volume. The channel images portrayed on these seismic horizons, which were spaced at vertical increments of 2 ms, illustrate the principle that seismic attributes viewed on seismic stratal surfaces provide valuable images of facies distributions within thin‐bed sequences and help seismic interpreters segregate channel facies from nonchannel facies. These stratal‐surface interpretations of the fluvial system were then integrated to create a thin (8-ms-thick), stratal‐bounded seismic‐data window that spans the short geologic time period during which the targeted fluvial depositional system was active. Seismic‐attribute calculations within this stratal‐bounded analysis window improve parts of the channel image by integrating the facies information from all stratal surfaces into a unified seismic attribute that vertically spans the total depositional sequence. A comparison is made between channel images on seismic stratal surfaces that are conformable to two different reference surfaces, one reference surface being positioned below the targeted fluvial system and the second reference surface being above the thin‐bed channels. This comparison supports the premise that seismic interpreters should extrapolate stratal surfaces both upward and downward across a thin‐bed target to optimize the image of that target.
Doubling the effective skin depth with a local source
Authors: Reid James E. , Macnae James C.
Published: October 2002

The depth at which the amplitude of the frequency‐domain electromagnetic fields due to dipole and square loop sources over a homogeneous half‐space fall to 1/e of their value at the surface is compared to the conventional plane‐wave skin depth. The skin depth due to a local source depends on the transmitter frequency, half‐space conductivity, transmitter altitude, and transmitter‐receiver offset, and may range from a fraction of to more than twice the plane‐wave skin depth. Unlike the plane‐wave skin depth, the “local‐source skin depth” is different for electric and magnetic fields, and may be nonunique for some transmitter geometries and field components. For all transmitter geometries, however, the local‐source skin depth approaches the plane‐wave skin depth as the transmitter altitude and/or receiver offset increase. The concept of the local‐source skin depth has direct application to survey design and data interpretation. A theoretical example demonstrates that it is possible to predict, for a given survey geometry and frequency range, whether or not an electromagnetic sounding can detect a conductive basement below a thick overburden layer.
Diagnosing high‐porosity sandstones: Strength and permeability from porosity and velocity
Authors: Dvorkin Jack , Brevik Ivar
Published: October 2002

Nonuniqueness in relating velocity to porosity in core and well‐log data complicates interpretation of sonic and seismic measurements. One reason for this nonuniqueness in sandstones is clay (e.g., Han, 1986). Another reason is textural variability among samples. Dvorkin and Nur (1996) examine two relatively clay‐free sandstone groups in the same porosity range, but whose velocities significantly differed (Figure 1a). By comparing the data with effective‐medium theories, they interpret this velocity difference as resulting from the difference in the position of diagenetic cement. The explanation is that in the “fast” (Oseberg) rocks (contact) cement is located predominantly at the grain contacts, whereas in the “slow” (Troll) rocks (noncontact) cement is located predominantly away from these contacts.
Effects of vector attenuation on AVO of offshore reflections
Authors: Carcione J. M.
Published: October 2002

Waves transmitted at the ocean bottom have the characteristic that, for any incidence angle, the attenuation vector is perpendicular to the ocean‐bottom interface (assuming water a lossless medium). Such waves are called inhomogeneous; in this case, the inhomogeneity angle coincides with the propagation angle. The vector character of this transmitted pulse affects the amplitude variation with offset (AVO) response of deeper reflectors. The analysis of the reflection coefficient is performed for a shale (the ocean‐bottom sediment) overlying a chalk, assuming no loss in the sea floor and loss with an incident homogeneous wave and an incident inhomogeneous wave. Beyond the elastic critical angle the differences are important, mainly for the incident homogeneous wave. These differences depend not only on the properties of the media but also on the inhomogeneity of the wave.
Seismic depth migration with the Dirac equation
Authors: Hokstad Ketil , Mittet Rune
Published: October 2002

We demonstrate the applicability of the Dirac equation in seismic wavefield extrapolation by presenting a new explicit one‐way prestack depth migration scheme. The method is in principle accurate up to 90° from the vertical, and it tolerates lateral velocity variations. This is achieved by performing the extrapolation step of migration with the Dirac equation, implemented in the space‐frequency domain. The Dirac equation is an exact linearization of the square‐root wave equation and is equivalent to keeping infinitely many terms in a Taylor series or continued‐fraction expansion of the square‐root operator. An important property of the new method is that the local velocity and the spatial derivatives decouple in separate terms within the extrapolation operator. Therefore, we do not need to precompute and store large tables of convolutional extrapolator coefficients depending on velocity. The main drawback of the explicit scheme is that evanescent energy must be removed at each depth step to obtain numerical stability. We have tested two numerical implementations of the migration scheme. In the first implementation, we perform depth stepping using the Taylor series approximation and compute spatial derivatives with high‐order finite difference operators. In the second implementation, we perform depth stepping with the Rapid expansion method and numerical differentiation with the pseudospectral method. The imaging condition is a generalization of Claerbout’s U / D principle. For both implementations, the impulse response is accurate up to 80° from the vertical. Using synthetic data from a simple fault model, we test the depth migration scheme in the presence of lateral velocity variations. The results show that the proposed migration scheme images dipping reflectors and the fault plane in the correct positions.
Simultaneous deconvolution and wavelet inversion as a global optimization
Authors: Wood Warren T.
Published: October 2002

Estimates of the source wavelet and band‐limited earth reflectivity are obtained simultaneously from an optimization of deconvolution outputs, similar to minimum‐entropy deconvolution (MED). The only inputs required beyond the observed seismogram are wavelet length and an inversion parameter (cooling rate). The objective function to be minimized is a measure of the spikiness of the deconvolved seismogram. I assume that the wavelet whose deconvolution from the data results in the most spike‐like trace is the best wavelet estimate. Because this is a highly nonlinear problem, simulated annealing is used to solve it. The procedure yields excellent results on synthetic data and disparate field data sets, is robust in the presence of noise, and is fast enough to operate in a desktop computer environment.
In quest of the grid
Authors: Böhm Gualtiero , Vesnaver Aldo L.
Published: October 2002

The possible nonuniqueness and inaccuracy of tomographic inversion solutions may be the result of an inadequate discretization of the model space with respect to the acquisition geometry and the velocity field sought. Void pixels and linearly dependent equations are introduced if the grid shape does not match the spatial distribution of rays, originating the well‐known null space. This is a common drawback when using regular pixels. By definition, the null space does not depend on the picked traveltimes, and so we cannot eliminate it by minimising the traveltime residuals. We show that the inversion quality can be improved by following a trial and error approach, that is, by adapting the pixels’ shape and distribution to the layer interfaces and velocity field. The resolution can be increased or decreased locally to search for an optimal grid, although this introduces a personal bias. On the other hand, we can so decide where, why, and which a priori information is introduced in the sought velocity field, which is hardly feasible by managing other stabilising tools such as damping factors and smoothing filters.
A refraction‐seismic field study to determine the anisotropic parameters of shales
Authors: Leslie Jennifer M. , Lawton Don C.
Published: October 2002

Shales are known to be transversely isotropic (TI), which can lead to incorrect subsurface imaging if isotropic behavior is assumed. By knowing the anisotropic parameters of the shales, it is possible to correct for the anisotropic effects in seismic data, thereby obtaining a more correct subsurface image. Two P-wave refraction‐seismic field studies were undertaken in areas of steeply dipping marine shales of the Wapiabi Formation to determine the anisotropic parameters of these shales in situ. The first survey was located in Jumpingpound Creek, Alberta, Canada, and the other location was west of Longview, Alberta, Canada. Seismic lines were laid out parallel, perpendicular, and 45° to the local strike directions. At both locations, the compressional headwave velocities along strike were determined to be faster than the velocities perpendicular to strike. Analysis of the Jumpingpound Creek data location yielded anisotropic parameters of ε = 0.14 ± 0.05 and δ = 0.00 ± 0.08, whereas at Longview, the anisotropic parameters were determined to be ε = 0.25 ± 0.06 and δ = 0.00 ± 0.06. The difference in ε is attributed to variations in the shale facies between the two sites.
Fracture detection in a carbonate reservoir using a variety of seismic methods
Authors: Pérez Maria A. , Grechka Vladimir , Michelena Reinaldo J.
Published: October 2002

We combine various methods to estimate fracture orientation in a carbonate reservoir located in southwest Venezuela. The methods we apply include the 2-D rotation analysis of 2-D P-S data along three different azimuths, amplitude‐variation‐with‐offset (AVO) of 2-D P-wave data along the same three azimuths, normal‐moveout (NMO) analysis of the same 2-D data, and both 3-D azimuthal AVO and NMO analysis of 3-D P-wave data recorded in the same field. The results of all methods are compared against measures of fracture orientation obtained from Formation microScanner logs recorded at four different locations in the field, regional and local measures of maximum horizontal stress, and the alignment of the major faults that cross the field. P-S data yield fracture orientations that follow the regional trend of the maximum horizontal stress, and are consistent with fracture orientations measured in the wells around the carbonate reservoir. Azimuthal AVO analysis yields a similar regional trend as that obtained from the P-S data, but the resolution is lower. Local variations in fracture orientation derived from 3-D AVO show good correlation with local structural changes. In contrast, due to the influence of a variety of factors, including azimuthal anisotropy and lateral heterogeneity in the overburden, azimuthal NMO analysis over the 3-D P-wave data yields different orientations compared to those obtained by other methods. It is too early to say which particular method is more appropriate and reliable for fracture characterization. The answer will depend on factors that range from local geological conditions to additional costs for acquiring new information.
Modeling detector response in airborne gamma‐ray spectrometry
Authors: Billings Stephen , Hovgaard Jens
Published: October 2002

A geometrical detector model of airborne gamma‐ray spectrometry is presented for data acquired using a rectangular detector of arbitrary dimensions. The detector response is modeled by calculating variations in solid angle and detector thickness for sources at different orientations. This gives the total count rate, which is then multiplied by a factor, assumed independent of orientation, to give the peak count rate. The model shows excellent agreement with experimental data collected using a 4.2-liter detector and with Monte Carlo simulations of a 16.8-liter detector. Results for the 4.2-liter crystal showed significant asymmetry. However, for a typical airborne system, with a 16.8-liter crystal, the asymmetry was weak because the detector had about the same solid angle and thickness at any azimuthal angle. The point spread function for the geometrical detector model differed significantly from a uniform detector model, the latter predicting a lower spatial resolution. This implies that surveys designed on the uniform assumption may undersample the signal between flight lines. For example, at 60 m elevation, the area that contributes 90% of the thorium signal is predicted to be 10.9 hectares (ha) for the uniform model and only 7.6 ha for the geometrical model. The model can be extended to incorporate aircraft velocity by convolving the stationary model with a rectangular function. Aircraft velocity can have a substantial influence on the modeled response if long integration times permit significant displacement of sources relative to the height of the aircraft.
Simultaneous inversion of formation shear‐wave anisotropy parameters from cross‐dipole acoustic‐array waveform data
Authors: Tang Xiaoming , Chunduru Raghu K.
Published: October 2002

This study presents an effective technique for obtaining formation azimuthal shear‐wave anisotropy parameters from four‐component dipole acoustic array waveform data. The proposed technique utilizes the splitting of fast and slow principal flexural waves in an anisotropic formation. First, the principal waves are computed from the four‐component data using the dipole source orientation with respect to the fast shear‐wave polarization azimuth. Then, the fast and slow principal waves are compared for all possible receiver combinations in the receiver array to suppress noise effects. This constructs an objective function to invert the waveform data for anisotropy estimates. Finally, the anisotropy and the fast shear azimuth are simultaneously determined by finding the global minimum of the objective function. The waveform inversion procedure provides a reliable and robust method for obtaining formation anisotropy from four‐component dipole acoustic logging. Field data examples are used to demonstrate the application and features of the proposed technique. A comparison study using the new and conventional techniques shows that the new technique not only reduces the ambiguity in the fast azimuth determination but also improves the accuracy of the anisotropy estimate. Some basic quality indicators of the new technique, along with the anisotropy analysis results, are presented to demonstrate the practical application of the inversion technique.
A quasi‐Monte Carlo approach to efficient 3-D migration: Field data test
Authors: Zhou Changxi , Chen Jing , Schuster Gerard T. , Smith Brackin A.
Published: October 2002

The quasi‐Monte Carlo migration algorithm is applied to a 3-D seismic data set from West Texas. The field data were finely sampled at approximately 220-ft (67-m) intervals in the in‐line direction but were sampled coarsely at approximately 1320-ft (402-m) intervals in the cross‐line direction. The traces at the quasi‐Monte Carlo points were obtained by an interpolation of the regularly sampled traces. The subsampled traces at the quasi‐Monte Carlo points were migrated, and the resulting images were compared to those obtained by migrating both regular and uniform grids of traces. Results show that, consistent with theory, the quasi‐Monte Carlo migration images contain fewer migration aliasing artifacts than the regular or uniform grid images. For these data, quasi‐Monte Carlo migration apparently requires fewer than half the number of the traces needed by regular‐grid or uniform‐grid migration to give images of comparable quality. These results agree with related migration tests on synthetic data computed for point scatterer models. Our results suggest that better migration images might result from data recorded on a coarse quasi‐random grid compared to regular or uniform coarse grids.
Tomographic imaging by reflected and refracted arrivals at the North Sea
Authors: Vesnaver Aldo L. , Böhm G. , Madrussani G. , Petersen S. A. , Rossi G.
Published: October 2002

We discuss some processing steps of a marine 3-D data set from the Oseberg field, North Sea. We compare the prestack depth‐migrated images obtained by the velocity fields provided by different tools: velocity spectra, reflection tomography, and joint tomographic inversion of reflected and refracted arrivals. The last ones are definitely better. We also produced a synthetic example by modeling the estimated earth structure and the actual recording geometry, and we reached similar conclusions. The correlation between reflected and refracted signals may be unclear for later arrivals because of their reciprocal interference and multiple reflections. We adopt a technique based on a surgical mute in the τ-p domain, which allows coupling the signals coming from the same elastic interface.