bluuebunny/crossref_metadata_2025 huggingface dataset:
Wave‐equation velocity replacement of the low‐velocity layer for overthrust‐belt data
Authors: Schneider William A. , Phillip Lindy D. , Paal Ernest F.
Published: October 2002

Seismic land data are commonly plagued by nonhyperbolic distortions induced by a variable near‐surface, low‐velocity layer (LVL). First‐arrival refraction analysis is conventionally employed to estimate the LVL geometry and velocities. Then vertical static time shifts are used to replace the LVL velocities with the more uniform, faster velocities that characterize the underlying refracting layer. This methodology has earned a good reputation as a geophysical data processing tool; however, velocity replacement with static shifts assumes that no ray bending occurred at the LVL base and that waves propagated vertically through the LVL (even though conventional refraction analysis methods, which are used to derive LVL models from seismic data, are less restrictive). These assumptions often are inadequate in thick, complex LVL situations, where resulting errors may considerably hamper a statics‐based velocity replacement procedure. Wave‐equation datuming may be used to perform LVL velocity replacement when statics are inadequate. This method extrapolates the seismic data from the surface to the LVL base with the LVL velocities. Then it extrapolates the data from the LVL base to an arbitrary datum, with the replacement velocity field. The marine analog of such a procedure has been well documented in the geophysical literature, where the object is to remove distortions caused by an irregular water layer. Application of wave‐equation datuming to land data is more difficult because of certain common characteristics of land data (irregular shooting, large data gaps, and crooked line geometry, combined with lower signal/noise) and because the LVL estimation procedure is considerably more difficult. We demonstrate wave‐equation velocity replacement on land data from a western U.S. overthrust belt. The LVL in this region was particularly thick and complicated and ideal for a wave‐theoretical velocity‐replacement procedure. Standard refraction analysis techniques were employed to estimate the LVL, then wave‐equation datuming was used to perform the velocity replacement. Our derived LVL model was not perfect, so some imaging errors were expected because wave‐equation datuming is highly dependent upon the LVL model. Nevertheless, our results show that wave‐equation datuming generally allowed better shallow reflector imaging than could be achieved with conventional statics processing.
A least‐squares minimization approach to shape determination from gravity data
Authors: Abdelrahman El‐Sayed M. , Sharafeldin Sharafeldin M.
Published: October 2002

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function of both shape (shape‐factor) and depth‐related variables with an amplitude coefficient related to mass (Abdelrahman and El‐Araby, 1993). Few methods have been developed to determine the shape of the buried geologic structure from residual gravity anomaly profiles. These methods include a Walsh transform approach (Shaw and Agarwal, 1990) and the employment of a correlation factor between successive least‐squares residuals (Abdelrahman and El‐Araby 1993). In the present note, a least‐squares minimization approach to shape‐factor determination from a residual gravity anomaly profile is presented. The problem of the shape‐factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0.
Time‐lapse crosswell seismic tomogram interpretation: Implications for heavy oil reservoir characterization, thermal recovery process monitoring, and tomographic imaging technology
Authors: Mathisen Mark E. , Vasiliou Anthony A. , Cunningham Paul , Shaw J. , Justice J. H. , Guinzy N. J.
Published: October 2002

Time‐lapse crosswell seismic data acquired with a cemented receiver cable have been processed into P‐ and S‐wave tomograms which image heavy oil sand lithofacies and changes as a result of steam injection. Twenty‐seven crosswell surveys were acquired between two wells over a 3.5 month period before, during, and after a 34‐day, 30 MBBL [Formula: see text] steam injection cycle. Interpretation was based on correlations with reservoir data and models, observation well data, and engineering documentation of the production history and steam cycle. Baseline S‐ and P‐wave tomograms image reservoir sand flow units and areas affected by past cyclic steam injection. S‐wave tomograms define lithology and porosity contrasts between the excellent reservoir quality, “high flow” turbidite channel facies and the interbedded “low to moderate flow” bioturbated levee facies. The reservoir dip of approximately 20° is defined by the velocity contrast between lithofacies. P‐wave baseline tomograms image lithology, porosity, structure, and several low velocity zones caused by past steam injection. Previous steam‐heat injection caused the formation of gas which reduced velocities as much as several thousand ft/s (600 m/s), an amount which obscures the velocity contrast between lithofacies and smaller velocity reductions as a result of temperature alone. Time‐lapse and difference P‐wave tomograms document several areas with small decreases in velocity during steam injection and larger decreases after cyclic steam injection. Velocity reductions range from 300 to 900 ft/s (90 to 270 m/s) adjacent to and above injectors located 20 to 50 feet (6 to 15 m) from the tomogram cross‐section. Poisson’s ratio tomograms show a significant decrease (.10) in the same area, and include low values indicative of gas saturation. Continuous injectors located 50 to 350 feet (15 to 100 m) from the survey area also caused a progressive decrease in velocity of the “high flow” channel sands during the time‐lapse survey. Interdisciplinary interpretation indicates that tomograms not only complement other borehole‐derived reservoir characterization and temperature monitoring data but can be used to quantitatively characterize interwell reservoir properties and monitor changes as a result of the thermal recovery process. Monitoring results over 3.5 months confirms that stratification has controlled the flow of steam, in contrast to gravity override. This suggests that tomographic images of reservoir flow‐units and gas‐bearing high temperature zones should be useful for positioning wells and optimizing injection intervals, steam volumes, and producing well completions.
High‐resolution crosswell imaging of a west Texas carbonate reservoir: Part 5—Core analysis
Authors: Nolen‐Hoeksema Richard C. , Wang Zhijing , Harris Jerry M. , Langan Robert T.
Published: October 2002

We conducted a core analysis program to provide supporting data to a series of crosswell field experiments being carried out in McElroy Field by Stanford University’s Seismic Tomography Project. The objective of these experiments is to demonstrate the use of crosswell seismic profiling for reservoir characterization and for monitoring [Formula: see text] flooding. For these west Texas carbonates, we estimate that [Formula: see text] saturation causes P‐wave velocity to change by −1.9% (pooled average, range = −6.3 to +0.1%), S‐wave velocity by +0.6% (range = 0 to 2.7%), and the P‐to‐S velocity ratio by −2.4% (range = −6.4 to −0.3%). When we compare these results to the precisions we can expect from traveltime tomography (about ±1% for P‐ and S‐wave velocity and about ±2% for the P‐to‐S velocity ratio), we conclude that time‐lapse traveltime tomography is sensitive enough to resolve changes in the P‐wave velocity, S‐wave velocity, and P‐to‐S velocity ratio that result from [Formula: see text] saturation. We concentrated here on the potential for [Formula: see text] saturation to affect seismic velocities. The potential for [Formula: see text] saturation to affect other seismic properties, not discussed here, may prove to be more significant (e.g., P‐wave and S‐wave impedance).
Sensitivity analysis of crosswell electromagnetics
Authors: Spies B. R. , Habashy T. M.
Published: October 2002

Sensitivity studies for low‐frequency crosswell electromagnetics (EM) show that the region contributing to the response is quasi‐ellipsoidal in shape and encompasses both source and receiver. The strongest response originates from the immediate vicinity of the source and receiver, but measurable contributions are also produced in the interwell region. Side lobes of opposite sign are present outside the interwell region. The interwell contribution increases markedly for elongated (2-D) geological features and for increasing frequency. The horizontal magnetic‐field component as a result of a vertical source is sensitive to vertical changes in conductivity in the vicinity of the receiver well and, when source and receivers are aligned, is relatively insensitive to any conductivity distribution at the transmitter well. Spatial resolution of crosswell electromagnetics, as inferred from the sensitivity patterns, is highest near the source and receiver and decreases away from the wells. Interpretation is improved by combining measurements at different frequencies and by using multicomponent receivers. The highest resolution is obtained at the highest frequencies, when the crosswell sensitivity pattern approaches the shape of a relatively narrow, focused beam.
Improved Fourier terrain correction, Part I
Authors: Parker Robert L.
Published: October 2002

A description of a new Fourier technique is given for calculating the gravitational attraction of a layer with an irregular top surface for application in the terrain correction of marine gravity surveys in shallow water. An earlier Fourier‐based algorithm fails or becomes inaccurate when the peaks of the topography approach the sea surface too closely. The new approach divides the attraction into two parts: a local contribution from the material within a cylinder around each observation point and the attraction from the matter outside the cylinder. A special quadrature rule, optimized for the actual data distribution, evaluates the local contribution. The calculation of the exterior component represents the bulk of the numerical effort. Fortunately, the exterior integral possesses an expansion as a series of convolutions, and by evaluating these in the Fourier domain, the procedure can take advantage of the efficiency of the fast Fourier transform. Chebychev economization of the convolution series provides further significant improvements in computational speed. Two examples, one artificial and the other based on a survey around Guadalupe Island, illustrate the application of the new technique. Estimates of the errors from computation sources and from the inadequacies of the topographic model confirm the general accuracy of the approach, except in regions of very steep terrain.
Distortion in resistivity logging at shallow depth
Authors: Lee Tien‐Chang , Damiata Brian N.
Published: October 2002

Owing to the proximity of an insulating ground surface, normal resistivity logging at shallow depths (less than 30 m) can yield an apparent resistivity that exceeds 200% of the formation resistivity for a homogeneous medium. The distortion is more acute for long‐normal than for short‐normal logging. Three examples from a landfill site in southern California are presented to show such distortion. The patterns of distortion are similar for logging devices consisting of either two point‐source electrodes or one point‐source and one finite length, line‐source electrode. The former electrode array is a generally accepted approximation of the latter. However, the simulated apparent resistivity for the line‐source array is greater than that for the point‐source array at any given depth. A resistivity contrast between the formation and the borehole fluid can shift the magnitude of the background apparent resistivity but does not significantly alter the pattern of distortion. The magnitude of the distortion can be reduced by placing the reference‐ground potential electrode at a radial distance that is about equal to the spacing between the downhole upper potential electrode and the upper current electrode. It can also be removed by including the radial distance in an array‐dependent geometric factor that accounts for the resistivity of the borehole fluid and the proximity of the logging device to the ground surface.
A simple, effective‐medium model for water saturation in porous rocks
Authors: Berg Charles R.
Published: October 2002

A general equation for water saturation is derived from effective‐medium theory. A simpler low‐frequency equation is also derived. Both equations are directly solvable for water saturation. The model should be applicable to any granular, water‐wet formation. Additional relationships are derived specifically for application to shaly sandstones, but the model should be applicable to a wide range of rock types, water conductivities, and tool frequencies. In the derivation, hydrocarbons are included in the matrix component of the equation and the combined “matrix” elements are treated as resistors in parallel. The low‐frequency equation is compared to various approaches to calculation of water saturation, such as Dual‐Water, Waxman‐Smits, and Bussian. The general equation is compared to three‐component effective medium, porosity index, and complex refractive index models (CRIM). The model is proven to work on experimental data under a wide range of frequencies and water conductivities. It is recommended that the new saturation model be used for nearly all types of electrical saturation calculation, whether the measurements are from standard resistivity tools or from dielectric tools.
Examination of the optimum XY value by ray tracing
Authors: Leung Tak Ming
Published: October 2002

The ability to recognize undetected layers in the generalized reciprocal method (GRM) depends on the optimum XY value. The determination of the optimum XY value, in turn, requires that some lateral variations exist in the refractor. Since lateral subsurface variations may not be just on the refractor, different locations and aspects of lateral variations may invalidate the usefulness of the optimum XY value. The optimum XY value is examined through velocity models having different types of lateral variations. Accurate traveltime data are generated by a first‐arrival ray‐tracing routine. The results of the study indicate that the integrity of the optimum XY value may be violated because of the various types of lateral variation.
On the distribution of seismic reflection coefficients and seismic amplitudes
Authors: Painter Scott , Beresford Greg , Paterson Lincoln
Published: October 2002

Reflection coefficient sequences from 14 wells in Australia have a statistical character consistent with a non‐Gaussian scaling noise model based on the Lévy‐stable family of probability distributions. Experimental histograms of reflection coefficients are accurately approximated by symmetric Lévy‐stable probability density functions with Lévy index between 0.99 and 1.43. These distributions have the same canonical role in mathematical statistics as the Gaussian distribution, but they have slowly decaying tails and infinite moments. The distribution of reflection coefficients is independent of the spatial scale (statistically self‐similar), and the reflection coefficient sequences have long‐range dependence. These results suggest that the logarithm of seismic impedance can be modeled accurately using fractional Lévy motion, which is a generalization of fractional Brownian motion. Synthetic seismograms produced from our model for the reflection coefficients also have Lévy‐stable distributions. These simulations include transmission losses, the effects of reverberations, and the loss of resolution caused by band‐limited wavelets, and suggest that actual seismic amplitudes with sufficient signal‐to‐noise ratio should also have a Lévy‐stable distribution. This prediction is verified using poststack seismic data acquired in the Timor Sea and in the continental USA. However, prestack seismic amplitudes from the Timor Sea are nearly Gaussian. We attribute the difference between prestack and poststack data to the high level of measurement noise in the prestack data. Many of the basic statistical techniques upon which seismic deconvolution and wavelet estimation are based presume implicitly that the underlying probability distribution has finite variance. Sample variance, autocorrelation, and even sample means are not reliable for infinite‐variance Lévy‐distributed variables. Although the seismic amplitudes and reflection coefficients are bounded and cannot truly have a Lévy‐stable distribution, some of their statistical properties are similar to those of Lévy‐stable variables. In other words, they behave as if they were following a Lévy‐stable distribution, which suggests that methods developed for Gaussian or near‐Gaussian variables may not be the most appropriate. The highly non‐Gaussian nature of the seismic amplitudes and the reflection coefficients should be considered in the design of seismic deconvolution and inversion techniques.
Finite‐difference modeling of faults and fractures
Authors: Coates Richard T. , Schoenberg Michael
Published: October 2002

For the purposes of seismic propagation, a slip fault may be regarded as a surface across which the displacement caused by a seismic wave is discontinuous while the stress traction remains continuous. The simplest assumption is that this slip and the stress traction are linearly related. Such a linear slip interface condition is easily modeled when the fault is parallel to the finite‐difference grid, but is more difficult to do for arbitrary nonplanar fault surfaces. To handle such situations we introduce equivalent medium theory to model material behavior in the cells of the finite‐ difference grid intersected by the fault. Virtually identical results were obtained from modeling the fault by (1) an explicit slip interface condition (fault parallel to the grid) and (2) using the equivalent medium theory when the finite‐difference grid was rotated relative to the fault and receiver array. No additional computation time is needed except for the preprocessing required to find the relevant cells and their associated moduli. The formulation is sufficiently general to include faults in and between arbitrary anisotropic materials with slip properties that vary as a function of position.
Some analytic aspects of a 2.5-D wave equation
Authors: Liner Christopher L.
Published: October 2002

A recently proposed 2.5-D wave equation is transformed to the frequency domain where WKBJ analysis is applied. This analysis assumes a general c(x, z) velocity field. Eikonal and transport equations are derived and compared to their 2-D and in‐plane 3-D counterparts. The implied eikonal equation is shown to be identical to the 2-D and in‐plane 3-D eikonal. This assures traveltime accuracy of the 2.5-D wave equation for any velocity model. The implied transport equation is shown to be consistent with 3-D theory in a constant velocity region containing a point source.
VSP normal moveout stretch
Authors: Owusu John C. , Spencer Terry W.
Published: October 2002

The vertical seismic profiling, common depth‐point (VSPCDP) transformation is a technique used to image the reflected waves in an offset VSP. This coordinate transformation procedure maps reflection amplitudes from receiver depth and reflection times to lateral offset and reflector depth (Wyatt and Wyatt, 1981). The process involves the application of moveout correction followed by stacking. This moveout correction results in a distortion of the original waveform and a smear of the reflection event that consequently degrades the lateral resolution of the transformation (Owusu, 1991). Therefore, to determine the optimum processing parameters for the transformation we need to understand the effects of the VSP moveout stretch.
Properties of the kernel function in electric stratified problems
Authors: Straub André
Published: October 2002

The kernel function plays an important role in the 1-D problem because of the spectral representation of the electric potential for a stratified model with a point source. Functional analysis establishes the equivalence between the differential equation (which governs the kernel function) and a boundary integral equation, called a jump summation equation for the 1-D case. In this equation, the jumps of the weighted Wronskian of two distinct models are summed over all the singular points. Numerous applications of this general equation demonstrate its flexibility. An appropriate choice of models and of the weight function leads to two splitting theorems and two imbedding theorems. The basic idea is to split the stratification into two models for the splitting theorems and into three models for the imbedding theorems. An application of these theorems concerns the handling of underground and underwater sounding measurements. Three possible configurations are examined and their performances are compared. With these examples, a simple method of layer stripping is introduced in the kernel space. These theorems are also used to establish the shift properties for a given set of layers surrounded by two homogeneous half‐spaces. The consequences of these shift properties especially concern electrical tomography, where a case of equivalence is shown. The general character of these theorems may generate other applications.
2-D depth migration in transversely isotropic media using explicit operators
Authors: Uzcategui Omar
Published: October 2002

Stable, explicit depth‐extrapolation filters can be used to propagate plane waves corresponding to the qP and qSV (quasi‐P and quasi‐SV propagation) modes for transversely isotropic (TI) media. Here, I discuss and compare results of two different methods for obtaining the filters for TI media with a vertical axis of symmetry (VTI). The first, a modified Taylor series method, is used to calculate the N‐coefficients of a finite‐length filter such that the Taylor expansion around vertical propagation matches the spatial Fourier transform of the downward‐continuation operator for VTI media. Second, a least‐squares method is used to calculate the filter coefficients such that the amplitude and phase departures from the ideal response of the downward‐continuation operator for VTI media are minimized over a range of frequencies and propagation angles. In both methods, the amplitude response of the filter is forced to be less than unity in the evanescent region to achieve stability. In general, as exemplified in all the cases studied here, the constrained least‐squares method produced filters with accurate wavefield extrapolation for a wider range of propagation angles than that obtained for the modified Taylor series method. In both methods, the maximum angle that can be accurately propagated depends on the ratio of frequency to vertical phase velocity [Formula: see text], and on the length of the filter. However, for a fixed filter length and for a given ratio [Formula: see text], the maximum angle propagated with accuracy depends on the elastic constants of the medium. The accuracy of the filters degrades as the degree of anisotropy becomes more extreme.
Gravimetric analysis of uniform polyhedra
Authors: Holstein Horst , Ketteridge Ben
Published: October 2002

Analytical formulas for the gravity anomaly of a uniform polyhedral body are subject to numerical error that increases with distance from the target, while the anomaly decreases. This leads to a limited range of target distances in which the formulas are operational, beyond which the calculations are dominated by rounding error. We analyze the sources of error and propose a combination of numerical and analytical procedures that exhibit advantages over existing methods, namely (1) errors that diminish with distance, (2) enhanced operating range, and (3) algorithmic simplicity. The latter is achieved by avoiding the need to transform coordinates and the need to discriminate between projected observation points that lie inside, on, or outside a target facet boundary. Our error analysis is verified in computations based on a published code and on a code implementing our methods. The former requires a numerical precision of one part in [Formula: see text] (double precision) in problems of geophysical interest, whereas our code requires a precision of one part in [Formula: see text] (single precision) to give comparable results, typically in half the execution time.
2-D magnetic interpretation using the vertical integral
Authors: Silva João B. C.
Published: October 2002

A magnetic interpretation method is presented which numerically computes the vertical integral of the observed total‐field anomaly along a profile. This transformed field is fitted by the vertical integral (also computed numerically) of the total‐field anomaly of an interpretation model using a standard, nonlinear, least‐squares estimation routine. The vertical integral transformation used here is similar to using a spatial domain pseudogravity operator after reducing the magnetic anomaly to the pole. The difference is that the reduction to the pole is not needed, so that the knowledge of the magnetization direction is not required. This method estimates the depth to a weakly magnetized basement that is intruded by strongly magnetized rocks. This method is best suited for the case where sills cut the overlying sediments and interfere with the magnetic signal from basement. Attempts to interpret isolated anomalies of stocks in the basement should take into account this kind of interference. The proposed method attenuates the effect of the shallow sources and produces a better lateral resolution than the upward continuation filter. Synthetic examples show that in interpreting the total‐field anomaly, the presence of shallow sources leads to underestimated depths to the basement. By using the vertical integral of the total‐field anomaly, on the other hand, depth estimates closer to the true values are obtained. The method is applied to aeromagnetic data from Amazon Basin, Brazil, and produces estimates for the basement depths that are consistent with the geological knowledge and with previous magnetic interpretations.
A matched‐filter approach to impedance estimation
Authors: Simmons James L. , Backus Milo M.
Published: October 2002

Stacked seismic data are modeled as a superposition of simple‐interface and thin layer reflections. This parameterization permits a parsimonious blocky model of the impedance. The method is an alternative to the classical least‐mean‐squared‐error approach and is similar in spirit to minimum‐entropy deconvolution and sparse‐spike inversion, although much different, and simpler, in implementation. A specified number of events on a seismic trace are modeled (inverted) independently. The selected set of basis functions used to represent the data includes a simple interface and a suite of high and low impedance layers covering a range of layer thickness. The simple interface basis function is the seismic wavelet, which is presumed to be known. Each event is classified using a normalized zero‐lag crosscorrelation of the basis functions with the seismic trace. Modeled events are prevented from overlapping, thereby ensuring a sparse earth model. Real data results show that a portion of a shallow‐marine data set can be well modeled in the context of a sparse earth model. A maximum of 30 simple‐interface and thin‐layer reflections (per trace) model 65 stacked traces over the time range of 0.8–1.9 s. We use a time and space invariant, statistically derived, autoregressive, seismic wavelet estimate. Wavelet polarity is chosen such that the inversion correctly models the fluid anomaly signals as low impedance layers. For wavelet A, we make the common assumption of white reflectivity and achieve a data misfit that is 7.8 dB down. For wavelet B, we assume a blue reflectivity that has a 3 dB/octave increase with frequency and achieve an improved fit to the data. Wavelet B also produces a more accurate estimate of the layer thickness of a known gas reservoir (10–12 ms average thickness) than does wavelet A (15–17 ms average thickness). Our results are competitive with other approaches to impedance estimation and are obtained in a much simpler fashion.
2-D acoustic wave equation inversion combining plane‐wave seismograms with well logs
Authors: Wang Shoudong , Liu Jiaqi , Xie Ganquan
Published: October 2002

Seismic waves can be described approximately by an acoustic wave equation. An inversion procedure for obtaining velocities using well logs and plane‐wave reflection seismograms is described. The forward problem is based on the 2-D acoustic wave equation. The inversion is performed by minimizing the difference between the calculated data and the observed data using the least‐squares regularization method. The numerical example shows that the stability and the robustness of the algorithm to noisy data is improved by introducing well logs into the inversion process.
Nonlinear waveform tomography applied to crosshole seismic data
Authors: Reiter Delaine Thompson , Rodi William
Published: October 2002

The acoustic inverse problem of crosshole seismology is nonlinear in the medium velocities and ill‐posed because of the lack of complete data coverage surrounding the area of interest. In light of these facts, this paper develops a new nonlinear waveform tomography technique for imaging acoustic velocities from crosshole seismic data. The technique, based on Tikhonov regularization, defines solution models that minimize the normed misfit between observed and modeled data subject to a constraint on the spatial roughness of the model. This type of regularization produces minimum structure velocity models which can vary in their degree of smoothness versus fit to the data. We solve the Tikhonov minimization condition numerically using a conjugate gradient algorithm. To accurately calculate the components of the forward problem, we use a frequency‐domain integral equation method with sinc basis functions. The integral equation method discretizes the integral form of the acoustic wave equation over a 2-D area and produces a two‐part matrix problem that we solve for Green’s functions and total fields in the medium using general matrix decomposition techniques. We successfully apply nonlinear waveform tomography to a scale‐model data set obtained from an ultrasonic modeling tank. This data set comes from a mostly plane‐layered, epoxy‐resin model, and the data exhibit elastic effects and other complicated wave phenomena. We invert this data set for the lateral variations in the model using a smoothed 1-D starting model to demonstrate the usefulness and efficacy of nonlinear waveform tomography.
On: “Apparent resistivity curves in controlled‐source electromagnetic sounding directly reflecting true resistivities in a layered earth”, by U. C. Das (January‐February 1995 GEOPHYSICS, 60, 53–60).
Authors: Spies Brian R. , Wait James R.
Published: October 2002

Das has made a number of fundamental errors in his paper on apparent resistivity in controlled‐source EM sounding, and has ignored the previous literature.
High‐resolution velocity determination: Statistical phase correlation and image processing
Authors: Morozov Igor B. , Smithson Scott B.
Published: October 2002

We address three areas of the problem of the stacking velocity determination: (1) the development of a new high‐resolution velocity determination technique, (2) the choice of an optimal velocity trial scenario, and (3) a unified approach to the comparison of time‐velocity spectra produced by various methods. We present a class of high‐resolution coherency measures providing five‐eight times better velocity resolution than conventional measures. The measure is based on the rigorous theory of statistical hypothesis testing and on the statistics of directional data. In its original form, our method analyzes only the phase distributions of the data, thus making unnecessary careful spherical divergence corrections and other normalization procedures. Besides the statistical one, we develop an “instantaneous” version of the conventional coherency measure. This measure is based on the concept of the trace envelope, thus eliminating the need for an averaging procedure. Finally, we design a hybrid high‐resolution coherency measure, incorporating the latter and the statistical one. Carrying out a systematic comparison of various measures of coherency, we present a simple estimate of an attainable velocity resolution. Based on this estimate, we define an optimal velocity grid, providing uniform coverage of all details of the time‐velocity spectrum. To facilitate quantitative comparisons of different coherency functions, we develop a unified normalization approach, based on techniques known in image processing. Described methods are tested on synthetic and field data. In both cases, we obtained a remarkable improvement in the time‐velocity resolution. The methods are general, very simple in implementation, and robust and reliable in application.
Seismogram synthesis for radially layered media using the generalized reflection/transmission coefficients method: Theory and applications to acoustic logging
Authors: Chen Xiaofei , Quan Youli , Harris Jerry M.
Published: October 2002

A new method based on generalized reflection and transmission coefficients is proposed to calculate the synthetic seismograms in radially multilayered media. This method can be used to efficiently simulate full waveform acoustic logs and crosswell seismic profiles in situations where we need to consider borehole effects. The new formulation is tested by comparing our numerical results with previous available work and shows excellent agreement. Because of the use of the normalized Hankel functions and the normalization factors, this new algorithm for computing seismograms is stable numerically even for high‐frequency problems. To show the applicability of this new approach to full waveform sonic logging, we apply it to investigate the effects of complex invaded zones on the geometrical spreading and attenuation estimation for P‐waves. We find that a damaged zone (its velocity is slower than the unperturbed formation velocity) exhibits a convergence effect on the P‐waves, and a flushed zone (velocity is faster than the unperturbed formation velocity) exhibits a divergence effect on the P‐waves.
3-D seismic imaging and seismic attribute analysis of genetic sequences deposited in low‐accommodation conditions
Authors: Hardage B. A. , Carr D. L. , Lancaster D. E. , Simmons J. L. , Hamilton D. S. , Elphick R. Y. , Oliver K. L. , Johns R. A.
Published: October 2002

A multidisciplinary team, composed of stratigraphers, petrophysicists, reservoir engineers, and geophysicists, studied a portion of Boonsville gas field in the Fort Worth Basin of North‐Central Texas to determine how modern geophysical, geological, and engineering techniques could be combined to understand the mechanisms by which fluvio‐deltaic depositional processes create reservoir compartmentalization in a low‐ to moderate‐accommodation basin. An extensive database involving well logs, cores, production, and pressure data from 200‐plus wells, [Formula: see text] [Formula: see text] of 3-D seismic data, vertical seismic profiles (VSPs), and checkshots was assembled to support this investigation. The reservoir system we studied was the Bend Conglomerate, a productive series of gas reservoirs composed of Middle Pennsylvanian fluvio‐deltaic clastics 900 to 1300 ft (275 to 400 m) thick in our project area. We were particularly interested in this reservoir system because evidence suggested that many of the sequences in this stratigraphic interval were deposited in low‐accommodation conditions (that is, in an environment where there was limited vertical space available for sediment accumulation), and our objective was to investigate how fluvio‐deltaic reservoirs were compartmentalized by low‐accommodation depositional processes. Using an extensive well log database (200 plus wells) and a core‐calibrated calculation of rock facies derived from these logs, we divided the Bend Conglomerate interval into ten genetic sequences, with each sequence being approximately 100 ft (30 m) thick. We then used local VSP and checkshot control to transform log‐measured depths of each sequence boundary to seismic two‐way time coordinates and identified narrow seismic data windows encompassing each sequence across the [Formula: see text] [Formula: see text] 3-D seismic grid. A series of seismic attributes was calculated in these carefully defined data windows to determine which attributes were reliable indicators of the presence of productive reservoir facies and which attributes could, therefore, reveal distinct reservoir compartments and potentially show where infield wells should be drilled to reach previously uncontacted gas reservoirs. Our best success was the seismic attribute correlations we found in the Upper and Lower Caddo sequences, at the top of the Bend Conglomerate. These sequences were deposited in a low‐accommodation setting, relative to other Boonsville sequences, and we found that reflection amplitude and instantaneous frequency, respectively, were reliable indicators of the areal distribution of reservoir facies in these low‐accommodation sequences.
Explicit 3-D migration using equiripple polynomial expansion and Laplacian synthesis
Authors: Soubaras Robert
Published: October 2002

In f-x explicit finite‐difference depth migration schemes, wavefield downward extrapolation is carried out through spatial convolution using finite‐length filters. Existing methods for computing these filters are based on nonlinear least‐squares, with a high computational cost, or on Taylor series expansion, which is suboptimal. In the 3-D case, the physics of wavefield extrapolation requires 2-D extrapolation filters with circular symmetry. Recently, McClellan transformation has been used to design circularly symmetric extrapolation operators. But this approach exhibits artifacts when the data are not spatially oversampled. We describe an alternative method to take advantage of the circular symmetry: the radial response of the filter is expanded as a polynomial in the Laplacian, which is synthesized as the sum of two 1-D second‐derivative filters. Using the Laplacian rather than the McClellan transform yields an artifact‐free impulse response for wavenumbers much closer to the Nyquist wavenumber at the same computational cost. Other advantages of the proposed method are the easy extension to a rectangular grid and the possibility of time‐migration implementation. The coefficients of the polynomials are optimized in the [Formula: see text] norm, because the stability condition is expressed more easily with this norm. The Remez exchange algorithm, which is a fast [Formula: see text] norm spectral synthesis algorithm, is adapted to obtain these [Formula: see text] coefficients of the polynomials, as well as the coefficients of the second derivative filters.
Anatomy of diving waves
Authors: Levin Franklyn K.
Published: October 2002

When velocity increases linearly with depth, rays are arcs of circles and reflections can come from the upper or lower surface (turning rays) of a dipping plane. In this paper, I examine the behavior of both types of reflections as a function of dip and azimuth. Reflections from the upper surface of a plane behave much like those for a constant velocity medium, the principal difference being movement downdip of a reflection point when the profile is in the strike direction. Reflections from the lower surface of a plane have no constant velocity analog. In addition to downdip movement of a reflection point for a strike line, the turning ray reflections have negative time stepout for a dip line and zero stepout for a profile near 45° from dip.
Fourier transform approximations for sweeps and phase‐encoded sweeps
Authors: Ha Stephen T. T. , Zhou Hau‐wei , Sheriff Robert E. , McDonald John A.
Published: October 2002

The Fourier transform of a real sweep is often approximated by a complex exponential. This approximation fails under certain conditions related to taper length and bandwidth. Our intuitive graphical explanation using the Cornu spiral is supported by rigorous proof that the radius of the spiral decreases monotonically to zero. This proof is also useful elsewhere in diffraction study and other Fourier analyses of sweeps. With this approach, we found that the Fourier phase function of an approximate formulation of a phase‐encoded sweep is affected in the same manner by the sweep parameters and the length of the taper. If the mean phase value is computed over the bandwidth, this mean phase agrees better with the ideal encoded phase. This simple phase‐encoded sweep can also be improved computationally so that its individual phase component approximates more closely with the ideal. We conclude that, other than some time‐compressed phase‐encoded wavelets known to be useful in direction determination, our approximate and improved phase‐encoded sweeps are equally applicable as well.
Precise detection of a P‐wave in low S/N signal by using time‐frequency representations of a triaxial hodogram
Authors: Moriya Hirokazu , Niitsuma Hiroaki
Published: October 2002

We have developed a signal processing technique for three‐component microseismic data that allows the precise determination of P‐wave arrival times. The method is based on a time‐frequency representation of the signal that allows the evaluation of the 3-D particle motion from seismic waves in both time and frequency domains. A spectral matrix is constructed using the time‐frequency distributions. A crosscorrelation coefficient for the three‐component signal is derived through eigenvalue analysis of the spectral matrix. The P‐wave arrival time is determined through a statistical test of hypotheses using the crosscorrelation coefficient. This signal processing method is evaluated using a synthetic signal and it is compared to the local stationary autoregressive method for determining P‐wave arrival times. We also show that the proposed method is capable of determining the arrival time of a synthetic P‐wave to within 1 ms (five points in the discrete time series) in the presence of a signal‐to‐noise ratio of −5dB. The method can detect the arrival time of different frequency components of the P‐wave, which is a possibility for the evaluation of velocity dispersion of the seismic wave. We demonstrate the feasibility of the method further by applying it to microseismic data from a geothermal field.
Multidomain Chebyshev spectral method for 3-D dc resistivity modeling
Authors: Zhao Shengkai , Yedlin Matthew J.
Published: October 2002

We use the multidomain Chebyshev spectral method to solve the 3-D forward direct current (dc) resistivity problem. We divided the whole domain into a number of subdomains and approximate the potential function by a separate set of Chebyshev polynomials in each subdomain. At an interface point, we require that both the potential and the flux be continuous. Numerical results show that for the same accuracy the multidomain Chebyshev spectral method is 2 to 260 times faster than the finite‐difference method.
Modeling of broadband airborne electromagnetic responses from saline environments
Authors: Buselli G. , Williamson D. R.
Published: October 2002

The removal of vegetation for the development of nonirrigated agriculture and the associated increase in groundwater recharge and discharge has caused significant areas of salinization of surface soil and water resources in Australia. At least three types of salt profiles are known to indicate the relative magnitude of recharge. These profiles may be differentiated by their resistivity structure. Since a broadband airborne electromagnetic (AEM) method offers the possibility of readily obtaining resistivity soundings, modeling was carried out to investigate the ability of a broadband AEM system to distinguish different salt profile types. Salt profile types may be represented by a four‐layer resistivity model. The use of a broadband AEM system to distinguish the relative magnitude of the resistivity of a layer of high salt accumulation and the underlying layer forms the basis for efficiently identifying areas of high or low recharge. Where the resistivity of the underlying layer is greater than that of the salt accumulation, high recharge is indicated, and a lower resistivity of this layer implies low recharge. The response of each of the salt profile models was calculated in the frequency domain and then inverted back to a layered model. With noise added to the calculated responses, the inversion results show that the depth, thickness, and resistivity of a layer of high salt accumulation can be resolved by AEM measurements. Furthermore, the resistivity of this layer can be distinguished from the resistivity of the underlying layer. A high‐recharge profile may therefore be differentiated from a low‐recharge profile with AEM measurements. Since the quadrature component of the AEM response is relatively unaffected by noise caused by the primary field, the effect of using solely the quadrature component of the response was examined briefly as a second part of the AEM modeling investigation. It is found that simultaneous inversion of the quadrature part of the spatial components measured along the line of flight and in a vertical direction gives results similar to those when both the in‐phase and quadrature parts of these components are used in the inversion.
Robust statistical methods for reducing sferics noise contaminating transient electromagnetic measurements
Authors: Buselli G. , Cameron Murray
Published: October 2002

The transient electromagnetic (TEM) method is used extensively for mineral exploration and other applications such as geothermal soundings, oil exploration, groundwater pollution, soil salinity and geological mapping. Sferics pulses produced by lightning strokes propagating in the ionosphere‐earth waveguide cavity induce noise in a bandwidth of a few Hz to tens of kHz. The usual method of stacking and calculating the mean of a given stack cannot effectively reduce the spike‐like noise induced by high‐amplitude sferics pulses. To reduce this type of noise, a number of different ways of stacking data were investigated and compared. Noise data were stacked by using robust estimators such as the median, trimmed mean, and a range of M‐estimators. Since storage of all the samples of a given stack can take up a prohibitively large amount of microprocessor memory, recursive algorithms for the M‐estimators and their standard error were developed for the real‐time reduction of sferics pulses. The recursive algorithms have been demonstrated to work effectively on windowed data, and thus the memory normally required to obtain the mean is sufficient for calculation of the M‐estimate. In the recursive calculation of the robust estimate of the transient response, the spread of the background noise distribution (known as the scale of the data) needs to be known or calculated. In the algorithm that has been developed, the scale of the data is derived from a noise run carried out before pulsing the transmitter loop with current. It has been assumed that the presence of a signal does not change the scale of the data. This value of the scale of the data has been used to obtain a robust estimate of the transient response itself. To allow for possible changes in the background noise level during a given survey, the estimate of the scale of the data is updated throughout the survey. Many tests of the performance of the recursive algorithms have been carried out with both simulated noise data and sferics data that have been recorded previously on magnetic tape. The results show that for sferics activity as high as that observed in northern latitudes of Australia in summer, a noise reduction by a factor of about 5 (when compared with simple stacking) should be obtained. In areas where sferics noise predominates over geological background signal, such a reduction should lead to an increase in target detection depth by approximately 50%.