bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear velocity inversion by a two‐step Monte Carlo method.
Authors: Jin Side , Madariaga Raul
Published: October 2002

Seismic reflection data contain information on small‐scale impedance variations and a smooth reference velocity model. Given a reference velocity model, the reflectors can be obtained by linearized migration‐inversion. If the reference velocity is incorrect, the reflectors obtained by inverting different subsets of the data will be incoherent. We propose to use the coherency of these images to invert for the background velocity distribution. We have developed a two‐step iterative inversion method in which we separate the retrieval of small‐scale variations of the seismic velocity from the longer‐period reference velocity model. Given an initial background velocity model, we use a waveform misfit‐functional for the inversion of small‐scale velocity variations. For this linear step we use the linearized migration‐inversion method based on ray theory that we have recently developed with Lambaré and Virieux. The reference velocity model is then updated by a Monte Carlo inversion method. For the nonlinear inversion of the velocity background, we introduce an objective functional that measures the coherency of the short wavelength components obtained by inverting different common shot gathers at the same locations. The nonlinear functional is calculated directly in migrated data space to avoid expensive numerical forward modeling by finite differences or ray theory. Our method is somewhat similar to an iterative migration velocity analysis, but we do an automatic search for relatively large‐scale 1-D reference velocity models. We apply the nonlinear inversion method to a marine data set from the North Sea and also show that nonlinear inversion can be applied to realistic scale data sets to obtain a laterally heterogeneous velocity model with a reasonable amount of computer time.
Elastic constants of transversely isotropic media from constrained aperture traveltimes
Authors: Michelena Reinaldo J.
Published: October 2002

The elastic constants that control P‐ and SV‐wave propagation in a transversely isotropic media can be estimated by using P‐ and SV‐wave traveltimes from either crosswell or VSP geometries. The procedure consists of two steps. First, elliptical velocity models are used to fit the traveltimes near one axis. The result is four elliptical parameters that represent direct and normal moveout velocities near the chosen axis for P‐ and SV‐waves. Second, the elliptical parameters are used to solve a system of four equations and four unknown elastic constants. The system of equations is solved analytically, yielding simple expressions for the elastic constants as a function of direct‐ and normal‐moveout velocities. For SH‐waves, the estimation of the corresponding elastic constants is easier because the phase velocity is already elliptical. The procedure, introduced for homogeneous media, is generalized to heterogeneous media by using tomographic techniques.
Inverse scattering of surface waves: A new look at surface Consistency
Authors: Blonk Bastian , Herman Gérard C.
Published: October 2002

A method is presented for eliminating near‐surface scattered noise from seismic data. Starting from an appropriately chosen background model, a surface‐consistent scattering model is determined using linearized elastodynamic inverse scattering theory. This scattering model does not necessarily equal the actual scatterer distribution, but it enables one to calculate, approximately, the near‐surface scattered part of the data. The method honors at least some of the complexity of the near‐surface scattering process and can be applied in cases where traditional methods, like wavenumber‐frequency filtering techniques and methods for static corrections, are ineffective. From a number of tests on synthetic data, we conclude that the method is rather robust; its main sensitivity is because of errors in the determination of the background Rayleigh‐wave velocity.
The application of map migration to 2-D migrated data
Authors: Whitcombe David N. , Carroll Randall J.
Published: October 2002

Two‐dimensional migrated time interpretations are used in a novel application of map migration. This is done by following the seismic migration along the 2-D lines by a map migration in a direction orthogonal to the lines, thus achieving a fully 3-D migrated representation of the subsurface. In addition to modifying the 2-D times and positions, this approach corrects the amplitudes of the 2-D migrated data, which suffer from being corrupted by focusing or defocusing because of the reflector curvature orthogonal to the line direction. A Gulf of Mexico case study illustrates how this map migration technique simplifies the time structure map and explains anomalous amplitude variations.
Measurements of cable shape in a cross current
Authors: Krail Paul M.
Published: October 2002

In a previous paper, Krail and Brysk (1989), we gave a theory for the curve shape of a streamer in a constant cross current. The curve shape predicted by this theory was compared with the shape of a towed streamer cable determined from a small number of field measurements. The agreement was judged to be fair. At the conclusion of the paper we promised to do a more extensive comparison with field measurements.
An integrated target‐oriented prestack elastic waveform inversion: Sensitivity, calibration, and application
Authors: Pan Gee Shang , Young Chi. Y. , Castagna John P.
Published: October 2002

An integrated target‐oriented prestack elastic waveform inversion procedure is implemented to estimate lithology, fluid type, and pay thickness of a layered target zone from surface seismic PP reflection data. The integrated inversion procedure consists of three parts: data processing and preparation, iterative seismic inversion, and rock property integration. In the data processing and preparation, the seismic field gathers are processed and transformed into plane‐wave seismograms, and the well‐logs are prepared for establishing a well tie. The well tie is established using synthetics from a layered model obtained from blocking sonic, shear sonic, and density logs. The layered model is later used as the a priori starting model for the iterative seismic inversion. Based on the a priori starting model and using the processed plane‐wave seismograms as input, P‐wave velocity ( [Formula: see text]), S‐wave velocity ([Formula: see text]), density ρ, and thickness (h) of each layer in the layered target zone are estimated at each CDP location in the iterative seismic inversion. Through the rock property integration, the inverted seismic parameters are related to the reservoir properties: the lithology/fluid contents, and the net pay thickness. Synthetic examples of gas‐related bright spot models are used to illustrate the functionality of the procedure. The sensitivity and the vertical resolution of the inversion procedure are investigated. Under favorable conditions, the inversion procedure is able to estimate the net pay thickness down to a tenth of a wavelength. In noisy situations, the inversion tends to break down where the thickness of target is approximately equal to the tuning thickness. The procedure was successfully applied to a gas‐related shallow bright spot prospect offshore Gulf of Mexico. The lithology (sand shale distribution), [Formula: see text] ratio, and the net pay thickness of gas‐sand were derived for the prospect. The estimated net pay thickness of gas‐sand was within acceptable error range when compared with the actual net pay thickness measured from well logs.
A NUMERICAL METHOD OF COMPUTING DIP DATA USING WELL‐VELOCITY INFORMATION
Authors: Waters Kenneth H.
Published: October 2002

A method of computation for calculating steeply dipping strata is presented. It takes full advantage of the velocity information afforded by well shooting and is simple in application. Charts are derived from the velocity data which will give depth and position of the reflecting point together with angle of dip and azimuth of dip immediately from the time and differential time of a reflection taken from a seismic record.
A TRANSFORMED WAVE‐FRONT CHART
Authors: Peterson Raymond A.
Published: October 2002

In seismograph computations assuming a uniform rate of velocity increase with depth, a “wave front‐wave path” chart consisting of sets of orthogonal circles is often used. The present paper describes a transformation by which the wave fronts become a set of concentric circles with the wave paths as radii, while the cartesian coordinates representing vertical and horizontal distances in the ground become orthogonal circles.
TIDAL GRAVITY OBSERVATIONS
Authors: Wolf A.
Published: October 2002

Last August I sent you the manuscript of a paper on tidal gravity variations. Since that time, we made another test run of the gravimeter with very similar results. I am sending you a chart of the curves of gravity variation which we obtained.
THE EFFECT OF THE PLACEMENT OF A SEISMOMETER ON ITS RESPONSE CHARACTERISTICS
Authors: Washburn Harold , Wiley Harold
Published: October 2002

A group of experiments were performed to determine the effect of the plant of a seismometer on the motion imparted to it by the ground. It was found experimentally that a seismometer and the ground form a resonant system. The characteristics of this system depend on the type and condition of the ground surface, the method of planting the seismometer and the seismometer weight and base area. Methods were devised for obtaining a satisfactory seismometer plant in areas where ordinary surface plants introduce distortion into seismic records. The mathematical expression of Seismometer Response and Ground Admittance in terms of experimentally measurable quantities is given in the appendix.
NETWORK ADJUSTMENT BY LEAST SQUARES—ALTERNATIVE FORMULATION AND SOLUTION BY ITERATION
Authors: Gibson M. O.
Published: October 2002

Given a network, as in a gravity survey, comprising observed differences in the values of adjacent points, any adjustment of the network, however obtained, is shown to be a least square adjustment if (1) the sum of the corrected observations around any circuit is zero and (2) the sum of the weighted corrections at any junction is zero. This principle provides a means of controlling necessary approximations such as the subdivision of a large network, and simplifies subsequent adjustments made necessary by extension or revision of the observations. It also serves in some cases to reduce the number of equations and in others to eliminate the equations entirely. The paper outlines a time‐saving trial and error method of solving network equations, applicable to electric circuits as well as observational network problems.
SEISMIC RECEPTORS
Authors: Prescott H. R.
Published: October 2002

Development of equations of seismic receptor for both the steady state and dynamic case, illustrated by curves of steady state lag and steady state response for various degrees of damping, and also illustrated by graphs of response to transient impulses. A simple method of accurately obtaining the steady state displacement response and degree of damping is given.
NOTES ON REFRACTION PROSPECTING
Authors: Dix Charles Hewitt
Published: October 2002

This is a series of notes dealing with several aspects of the problem of the interpretation of refraction data. A method of dealing with unreversed refraction lines is outlined. The case of a high velocity section with an overburden having a linear increase of velocity with depth is discussed. We show how the accuracy of the relative depth calculations depends upon the difference between the upper and lower velocities at the interface in question. A method of computing tables for the linear velocity depth case is given which is well adapted to machine calculation. Finally, reflections at the ground‐air interface and the formation of shadows by such obstacles as high or low velocity layers are considered.
Migration velocity analysis: Theory and an iterative algorithm
Authors: Liu Zhenyue , Bleistein Norman
Published: October 2002

Imaging complex structures inside the earth requires reasonable velocities that can be provided by applying prestack depth migration to multichannel seismic data. Migration velocity analysis is based on the principle that the images in the migrated data will be distorted when an erroneous velocity is used, and the difference of the imaged depths (residual moveout) at a common image gather is a measure of the error in the velocity. The imaging equations that we derive from Snell’s law describe a general, quantitative relationship between migration images and migration velocity. Based on the imaging equations, we analyze properties of common‐image gathers and derive analytical formulas to represent residual moveout in some cases. These formulas show what factors affect the sensitivity of velocity analysis, which is useful to assess errors involved in velocity estimates. In addition, we develop a simple‐iteration algorithm to correct the layer velocities from residual moveout. The algorithm presented here is applicable to a medium that consists of constant‐velocity layers separated by arbitrary smooth interfaces. Some computer implementations are presented for both synthetic data and physical‐tank data. They demonstrate the effectiveness of our velocity analysis approach.
Extraction of the normal component of the particle velocity from marine pressure data
Authors: Amundsen Lasse , Secrest Bruce G. , Arntsen Børge
Published: October 2002

We present a general wave theoretical method for extracting the normal component of the particle velocity from marine pressure data. A possible use of the normal component of the particle velocity and the pressure is the separation of upgoing and downgoing waves at the receivers. For one special acquisition geometry, the source wavelet can also be estimated. The method in principle is exact. No information about the properties of the elastic earth is required. When the pressure data are recorded on a single surface, it is necessary to know the source signatures if the source array location is above the receiver surface. If the sources are located below, the signatures need not be known. The locations of the individual receivers must be specified, and the reflecting properties of the sea surface must be known. When the receiver surface is plane and horizontal, the extraction process can be performed in the frequency‐horizontal wavenumber domain. The normal component of the particle velocity can furthermore be extracted from pressure data recorded at two surfaces at different depths. In this case the reflectivity of the sea surface does not come into play; it is only the medium properties between the two receiver surfaces that enter the problem. The actual depths of the receivers need not be known, only their relative distances. If the sources are located above the uppermost receiver surface, the source signatures can also be estimated. A simple synthetic data example demonstrates the extraction of the normal component of the pressure from the pressure field recorded along a dipping receiver line below a free surface.
Frequency‐ and time‐domain electromagnetic responses of layered earth—A multiseparation, multisystem approach
Authors: Das Umesh C.
Published: October 2002

EM depth soundings by controlled‐source electromagnetic methods (CSEM) are made to determine the vertical resistivity distribution of the earth. The two variations of soundings, namely frequency sounding and geometric sounding, are used for exploring the subsurface. Although in field applications electromagnetic (EM) sounding has relative advantages over direct current resistivity sounding, quantitative use of EM depth sounding has not been used as much as direct current resistivity sounding (Mundry and Bohlm, 1987). Mundry and Bohlm (1987) have pointed out that one of the problems in the application of frequency EM sounding is the lack of sophisticated interpretational tools. The interpretation of the mutual coupling ratio (MCR) from the EM field component measurements, [Formula: see text], invariably relies on numerical inversion routines. However, unlike the direct current (DC) or magnetotelluric (MT) apparent resistivity curves, MCR curves do not reflect the subsurface resistivity distributions, and an initial guess model from MCR required for its inversion is difficult. Conversion of single component EM measurements into apparent resistivity is ambiguous because for a single measurement, two apparent resistivity values are obtained. Combining the general expressions for MCR obtained from the quasi‐static tangential electric and vertical magnetic field components of a vertical magnetic dipole source on the surface of a half‐space, Das (1995) defined an apparent resistivity for the use of the CSEM. The CSEM apparent resistivity curves show features similar to DC and MT apparent resistivity curves and they greatly enhance the interpretation. I refer to this paper (Das, 1995, published in this issue) as Paper I. In the present paper, difficult measurements of the electric field have been avoided by combining [Formula: see text] and [Formula: see text] obtained from the magnetic field measurements of two different configurations, i.e., the horizontal coplanar loops (HCP) and vertical coplanar loops (VCP) systems, respectively. This combination of measurements provides operational simplicity in the field and gives the same CSEM apparent resistivity described in Paper I. However, complementary behavior of the two combinations would be realized.
Borehole seismic‐source radiation pattern in transversely isotropic media
Authors: Dong Wenjie , Toksöz M. Nafi
Published: October 2002

We extend previous discussions on crosswell tomography in anisotropic formations by deriving the radiation patterns of three typical downhole seismic sources (impulsive air gun or dynamite, wall‐clamped vertical vibrators, and cylindrical bender) inside a fluid‐filled borehole embedded in a transversely isotropic (TI) formation. The method of steepest descents, in conjuncture with the low‐frequency and far‐field assumptions, is applied to the exact displacement integrals of these sources to obtain their radiation patterns asymptotically. In spite of complications caused by quasi‐P‐ and quasi‐SV‐wave coupling and wavefront triplication in homogeneous TI media, the final results can still be expressed in slowness components determined by a ray direction, which is desired when source radiation effects are to be accounted for by ray‐based tomography techniques. Tests with the radiation patterns show that while the effect of anisotropy on P‐waves is moderate, its effect on the S‐wave pattern is significant even for slightly anisotropic formations. One can predict the S‐wave pattern from the sign of the Thomsen’s measure δ*.
Attenuation of P‐ and S‐waves as a method of distinguishing gas and condensate from oil and water
Authors: Klimentos Theodoros
Published: October 2002

Compressional‐ and shear‐wave attenuation data were calculated from sonic waveforms in three wells. The results show that at similar porosities and at in‐situ conditions, gas and condensate sandstone reservoirs exhibit higher P‐wave attenuation (lower P‐wave quality factor, [Formula: see text]) than either fully‐water or partially “oil + water” saturated sandstones. However, S‐wave attenuation and quality factor [Formula: see text] do not show such a strong dependence on pore fluids. Furthermore, [Formula: see text] indicates presence of gas or condensate, while [Formula: see text] indicates “full water” or “oil + water” saturation. These field data are consistent with laboratory data and theoretical predictions by various researchers. The crossovers of P-S‐wave attenuation and [Formula: see text] quality factors proved useful for distinguishing gas and condensate from oil and water reservoirs. They may be used in conjunction with [Formula: see text] and other logs as an aid in formation evaluation for the detection of gas, condensate, and oil. Several case studies in the literature report high P‐wave energy absorption at seismic frequencies below gas and condensate pools. This suggests that it is not unreasonable to assume that this method could also be used in seismic exploration as an aid for distinguishing gas and condensate from oil and water formations.
High‐resolution crosswell imaging of a west Texas carbonate reservoir: Part 3—Wavefield separation of reflections
Authors: Rector James W. , Lazaratos Spyros K. , Harris Jerry M. , Van Schaack Mark
Published: October 2002

Using crosswell data collected at a depth of about 3000 ft (900 m) in west Texas carbonates, one of the first well‐to‐well reflection images of an oil reservoir was produced. The P and S brute stack reflection images created after wavefield separation tied the sonic logs and exhibited a vertical resolution that was comparable to well log resolution. Both brute stacks demonstrated continuity of several reflectors known to be continuous from log control and also imaged an angular unconformity that was not detected in log correlations or in surface seismic profiling. The brute stacks, particularly the S‐wave reflection image, also exhibited imaging artifacts. We found that multichannel wavefield separation filters that attenuated interfering wavemodes were a critical component in producing high‐resolution reflection images. In this study, the most important elements for an effective wavefield separation were the time‐alignment of seismic arrivals prior to filter application and the implementation of wavefield‐separation filters in multiple domains, particularly in common offset domain. The effectiveness of the multichannel filtering was enhanced through the use of extremely fine wellbore sampling intervals. In this study, 2.5 ft (0.76 m) vertical sampling intervals for both source and receiver were used, whereas most previous crosswell data sets were collected with much coarser sampling intervals, resulting in spatial aliasing and limiting the utility of the data for reflection processing. The wavefield separation techniques employed in this study used data volumes and associated filtering operations that were several orders of magnitude larger than those encountered in conventional VSP data analysis.
Numerical calculations of the thermal conductivities of composites—A 3-D model
Authors: Jones F. Walter , Pascal Florica
Published: October 2002

A 3-D numerical finite‐difference model to calculate the thermal conductivity of a composite with two or more constituents has been developed to better understand how the relative quantities and distributions of the component materials within a sample affect the whole sample conductivity. It is found that different distributions of similar components within a sample can yield whole sample conductivity differences greater than a factor of 2. Comparisons are made between the numerical model results and the geometric and real‐space renormalization group theory (RSRG) models and the effective medium approximation (EMA) for random distributions. Although good agreement exists between the numerical model and the EMA for the ranges of constituent conductivities considered, the geometric and RSRG models give lower values.
Robust and efficient upwind finite‐difference traveltime calculations in three dimensions
Authors: Schneider William A.
Published: October 2002

First‐arrival traveltimes in complicated 3-D geologic media may be computed robustly and efficiently using an upwind finite‐difference solution of the 3-D eikonal equation. An important application of this technique is computing traveltimes for imaging seismic data with 3-D prestack Kirchhoff depth migration. The method performs radial extrapolation of the three components of the slowness vector in spherical coordinates. Traveltimes are computed by numerically integrating the radial component of the slowness vector. The original finite‐difference equations are recast into unitless forms that are more stable to numerical errors. A stability condition adaptively determines the radial steps that are used to extrapolate. Computations are done in a rotated spherical coordinate system that places the small arc‐length regions of the spherical grid at the earth’s surface (z = 0 plane). This improves efficiency by placing large grid cells in the central regions of the grid where wavefields are complicated, thereby maximizing the radial steps. Adaptive gridding allows the angular grid spacings to vary with radius. The computation grid is also adaptively truncated so that it does not extend beyond the predefined Cartesian traveltime grid. This grid handling improves efficiency. The method cannot compute traveltimes corresponding to wavefronts that have “turned” so that they propagate in the negative radial direction. Such wavefronts usually represent headwaves and are not needed to image seismic data. An adaptive angular normalization prevents this turning, while allowing lower‐angle wavefront components to accurately propagate. This upwind finite‐difference method is optimal for vector‐parallel supercomputers, such as the CRAY Y-MP. A complicated velocity model that generates turned wavefronts is used to demonstrate the method’s accuracy by comparing with results that were generated by 3-D ray tracing and by an alternate traveltime calculation method. This upwind method has also proven successful in the 3-D prestack Kirchhoff depth migration of field data.
Analytical solution of the borehole resistivity casing problem
Authors: Wait James R.
Published: October 2002

There has been a strong interest in understanding how direct current flow is influenced by the presence of a metal casing in boreholes. In particular, when the current electrode is within the cylindrical borehole, the resulting potential in the external region is severely shielded. Nevertheless, it is possible to exploit the external potential, even though it is very weak. Basic investigations have been carried out by Kaufman (1990), and Kaufman and Wightman (1993) employing simplified analytical procedures and by Schenkel and Morrison (1990) using more complicated numerical schemes.
An analytical solution to separate P‐waves and S‐waves in VSP wavefields
Authors: Amano Hiroshi
Published: October 2002

An analytical solution to separate P‐waves and S‐waves in vertical seismic profile (VSP) wavefields is derived using combinations of certain terms of the formal solution for forward VSP modeling. Some practical applications of this method to synthetic seismograms and field data are investigated and evaluated. Little wave distortion is recognized, and the weak wavefield masked by dominant wavetrains can be extracted with this method. The decomposed wavefield is expressed in the frequency‐depth (f-z) domain as a linear combination of up to the third‐order differential of traces, which is approximated by trace differences in the practical separation process. In general, five traces with single‐component data are required in this process, but the same process is implemented with only three traces in the acoustic case. Two‐trace extrapolation is applied to each edge of the data gather to enhance the accuracy of trace difference. Since the formulas are developed in the f-z domain, the influence of anelasticity can be taken into account, and the calculation is carried out fast enough with the benefit of the fast Fourier transform (FFT).
Advances of geophysical prospecting for petroleum in marine carbonate areas of the upper Yangtze region, southern China
Authors: Ou Qingxian , Deng Dumming
Published: October 2002

In the marine carbonate area of the upper Yangtze region, southern China, including parts of Guizhou and Sichuan Provinces, complex subsurface structures and undulating surface terrain exist because of multiple tectonic events. Various geophysical prospecting methods have been conducted in local areas in an attempt to map these structures. In the Guizhou Plateau, a carbonate‐exposed area, crooked seismic lines were acquired using vibrators as the main source, supplemented with dynamite. In Sichuan Province, a mountainous area, regional seismic profiles, wide‐line profiling, and 3-D seismic surveys were conducted. These were accomplished with portable air drills and human transport. Data processing techniques were designed to improve data quality in the presence of noise and to image complex structures. In central Sichuan Province, high‐resolution and converted‐wave seismic surveys were carried out for imaging complex structures and for collecting lithologic parameters. These methods have enabled us to get effective information from complex structural, mountainous, and carbonate‐exposed hilly areas in the upper Yangtze region of southern China. These collective efforts have produced a database appropriate for sedimentology, tectonic, and prospective area evaluation studies.
3-D resistivity forward modeling and inversion using conjugate gradients
Authors: Zhang Jie , Mackie Randall L. , Madden Theodore R.
Published: October 2002

We have developed rapid 3-D dc resistivity forward modeling and inversion algorithms that use conjugate gradient relaxation techniques. In the forward network modeling calculation, an incomplete Cholesky decomposition for preconditioning and sparse matrix routines combine to produce a fast and efficient algorithm (approximately 2 minutes CPU time on a Sun SPARC‐station 2 for 50 × 50 × 20 blocks). The side and bottom boundary conditions are scaled impedance conditions that take into account the local current flow at the boundaries as a result of any configuration of current sources. For the inversion, conjugate gradient relaxation is used to solve the maximum likelihood inverse equations. Since conjugate gradient techniques only require the results of the sensitivity matrix [Formula: see text] or its transpose [Formula: see text] multiplying a vector, we are able to bypass the actual computation of the sensitivity matrix and the inversion of [Formula: see text], thus greatly decreasing the time needed to do 3-D inversions. We demonstrate 3-D resistivity tomographic imaging using pole‐pole resistivity data collected during an experiment for a leakage monitoring system near evaporation ponds at the Mojave Generating Station in Laughlin, Nevada.
Recognizing surface scattering in ground‐penetrating radar data
Authors: Sun Jingsheng , Young Roger A.
Published: October 2002

Ground‐penetrating radar (GPR) data may show strong noise events as a result of scattering by surface objects on the ground or above the survey line. The relative strength of these events can be large in comparison to reflections from geologic features, because radar signals in the ground attenuate exponentially whereas signals that travel in the air attenuate geometrically. Migration of GPR field data from clastic and carbonate sequences in central Oklahoma distinguishes between scattered events and geologic events because the former are focused at the air‐wave velocity, while the latter are focused at the ground‐wave velocity. Forward modeling using locations of scatterers derived from migration confirms the presence of scattered events, and common midpoint (CMP) gathers are helpful in identifying surface scattering. Scattered events displayed at a horizontal/vertical scale of 1:1 are easily mistaken for subhorizontal, geologic reflections. Methods of recognizing scattered events and removing them, if possible, are therefore crucial to correct geological interpretation of GPR data.
Estimation of sea‐floor wave velocities and density from pressure and particle velocity by AVO analysis
Authors: Amundsen Lasse , Reitan Arne
Published: October 2002

Sea‐bottom properties play an important role in fields as diverse as underwater acoustics, earthquake and geotechnical engineering, and marine geophysics. Water‐column acousticians study shear and interface waves in the nearbottom sediments with the aim of inferring sea‐bed geoacoustic parameters for predicting reflection and absorption of waves at the sea floor. On the other hand, geotechnical engineers working on design and siting of offshore structures focus on these waves to characterize soil and rock properties. In the field of geophysics, sea‐bottom parameters are of interest for several reasons. In conventional marine acquisition, these parameters determine the partitioning of the incident P‐wave energy from the source into transmitted P‐waves and mode‐converted S‐waves (Tatham and Goolsbee, 1984; Kim and Seriff, 1992). The sea‐floor P‐ and S‐wave velocities and density are also necessary inputs for decomposing multicomponent sea‐floor data into P‐ and S‐waves (Amundsen and Reitan, 1995a and b), as well as in the numerical study of wave propagation phenomena.
General formulation of the electric stratified problem with a boundary integral equation
Authors: Straub André
Published: October 2002

The electric potential created by a point source in a stratified model is usually written, in a spectral representation, in terms of a Hankel transform because of the cylindrical symmetry of the model. The solution in the radial wavenumber domain is called the kernel function. This kernel function, as a function of the depth coordinate, is the solution of a 1-D differential equation. The conventional procedure for the calculation of the kernel function consists in applying a recursive scheme. This procedure is effective from a computational point of view but becomes cumbersome from an analytical point of view, especially in the case of an arbitrary number of layers for arbitrary positions of the source and measurement points. I reformulate the problem of the kernel function by establishing the equivalence between the 1-D differential equation and a set of two boundary integral equations. This equivalence lowers the dimension of the problem by one unit so that the integration is performed over a space of dimension zero. The equations thus obtained are called jump summation equations. They are derived from a weighted product of two distinct models. The explicit form of these equations with the use of Green’s kernel (i.e., the kernel function for a homogeneous reference model) leads to the introduction of two basic representations, monopolar and dipolar. Each representation is related to a specific integral operator, but the basic representations are equivalent. The kernel function is computed by solving a linear system of equations. Our formulation is also well adapted to the inverse problem. The relationship between a perturbation of the model and the resulting perturbation of the kernel function is expressed by a Fréchet derivative. This sensitivity quantity is obtained by means of the jump summation equation, and its computation appears straightforward with the basic representations. An application to a novel evaluation of the depth of investigation for usual arrays is given.
The detection of monumental tombs buried in tumuli by seismic refraction
Authors: Tsokas Gregory N. , Papazachos C. B. , Vafidis Antonis , Loukoyiannakis M. Z. , Vargemezis G. , Tzimeas K.
Published: October 2002

A tumulus is a construction erected to cover a tomb. Some tumuli are impressively massive and may conceal architectural masterpieces. Seismic refraction is employed to locate the tomb and to allow selective excavation without destroying the tumulus. The detectors are spread along a circular profile on the periphery of the tumulus, and acoustic waves are generated on its top. Time delays observed in the arrivals of the headwaves reveal the position of the monument. The delays are not caused by the monument itself, but are an effect caused by the presence of a ramp that was dug in the undisturbed soil to help in the construction of the tomb. Three case histories in Northern Greece establish the efficiency of the technique. In the first example, an experiment was conducted at a previously excavated tumulus, and time delays attributed to the revealed ramp are observed. The second case study led to the discovery of an impressive monument; 3-D modeling by finite difference verifies the interpretation. A third study is also reported; where, for the most promising portion of the data, 3-D modeling has been performed.
Seismic pore space compressibility and Gassmann’s relation
Authors: Mavko Gary , Mukerji Tapan
Published: October 2002

The pore space compressibility of a rock provides a robust, model‐independent descriptor of porosity and pore fluid effects on effective moduli. The pore space compressibility is also the direct physical link between the dry and fluid‐saturated moduli, and is therefore the basis of Gassmann’s equation for fluid substitution. For a fixed porosity, an increase in pore space compressibility increases the sensitivity of the modulus to fluid substitution. Two simple techniques, based on pore compressibility, are presented for graphically applying Gassmann’s relation for fluid substitution. In the first method, the pore compressibility is simply reweighted with a factor that depends only on the ratio of fluid to mineral bulk modulus. In the second technique, the rock moduli are rescaled using the Reuss average, which again depends only on the fluid and mineral moduli.
3-D prestack full‐wavefield inversion
Authors: Xu Tong , McMechan George A. , Sun Robert
Published: October 2002

A full‐wavefield inversion algorithm for direct imaging of a 3-D compressional wave velocity distribution is based on the full 3-D scalar wave equation and operates on common‐source data recorded by areal arrays. For each source, the method involves reverse‐time extrapolation of the residual wavefield. Application of the image condition by crosscorrelation with the source wavefield at each time step produces a 3-D image whose amplitude at each point is proportional to the required velocity update at that point. Convergence to local minima is mitigated against by gradually increasing the wavenumber bandwidth in the estimated 3-D velocity distribution as iterations proceed, starting from the smallest wavenumber. The algorithm is illustrated by successful application to synthetic data for a multilayered monocline, and for a multilayered structure with the geometry of the standard French model. The latter demonstrates good performance with noisy, unequally spaced data with significant elevation statics.
Sponge boundary condition for frequency‐domain modeling
Authors: Shin Changsoo
Published: October 2002

Several techniques have been developed to get rid of edge reflections from artificial boundaries. One of them is to use paraxial approximations of the scalar and elastic wave equations. The other is to attenuate the seismic waves inside the artificial boundary by a gradual reduction of amplitudes. These techniques have been successfully applied to minimize unwanted seismic waves for time‐domain seismic modeling. Unlike time‐domain seismic modeling, suppression of edge reflections from artificial boundaries has not been successful in frequency‐domain seismic modeling. Rayleigh waves caused by coupled motions of P‐ and S‐waves near the surface have been a particularly difficult problem to overcome in seismic modeling. In this paper, I design a damping matrix for frequency‐ domain modeling that damps out seismic waves by adding a diffusion term to the wave equation. This technique can suppress unwanted seismic waves, including Rayleigh waves and P‐ and S‐waves from an artificial boundary.
Frequency‐time decomposition of seismic data using wavelet‐based methods
Authors: Chakraborty Avijit , Okaya David
Published: October 2002

Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency‐time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time‐ frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale‐translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive‐source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet‐based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.
Simplified anisotropy parameters for transversely isotropic sedimentary rocks
Authors: Sayers Colin M.
Published: October 2002

Sedimentary rocks frequently possess an anisotropic structure resulting, for example, from fine scale layering, the presence of oriented microcracks or fractures, or the preferred orientation of nonspherical grains or anisotropic minerals. For many rocks the anisotropy may be described, to a good approximation, as being transversely isotropic. The purpose of this note is to present simplified anisotropy parameters for these rocks that are valid when the P‐wave normal moveout (NMO) and vertical velocities differ by less than 25%. This condition appears reasonable since depths calculated from P‐wave stacking velocities are often within 10% of actual depths (Winterstein, 1986). It is found that when this condition is satisfied the elastic constants [Formula: see text] and [Formula: see text] affect the P‐wave NMO velocity and anellipticity only through the combination [Formula: see text], a combination of elastic constants that can be determined using walkaway VSP data (Miller et al., 1993). The anellipticity quantifies the deviation of the P‐phase slowness from an ellipse and also determines the difference between the vertical and NMO velocities for SV‐waves. Helbig (1983) has shown that a time‐migrated section for which elliptical anisotropy has been taken into account is identical to one that has been determined under the assumption of isotropy. The anellipticity is therefore the important anisotropy parameter for anisotropic time migration. The results given are of interest for anisotropic velocity analysis, time migration, and time‐to‐depth conversion.
Stress sensitivity of sandstones
Authors: Dvorkin Jack , Nur Amos , Chaika Caren
Published: October 2002

Our observations made on dry‐sandstone ultrasonic velocity data relate to the variation in velocity (or modulus) with effective stress, and the ability to predict a velocity for a rock under one effective pressure when it is known only under a different effective pressure. We find that the sensitivity of elastic moduli, and velocities, to effective hydrostatic stress increases with decreasing porosity. Specifically, we calculate the difference between an elastic modulus, [Formula: see text], of a sample of porosity ϕ at effective pressure [Formula: see text] and the same modulus, [Formula: see text], at effective pressure [Formula: see text]. If this difference, [Formula: see text], is plotted versus porosity for a suite of samples, then the scatter of ΔM is close to zero as porosity approaches the critical porosity value, and reaches its maximum as porosity approaches zero. The dependence of this scatter on porosity is close to linear. Critical porosity here is the porosity above which rock can exist only as a suspension—between 36% and 40% for sandstones. This stress‐sensitivity pattern of grain‐supported sandstones (clay content below 0.35) practically does not depend on clay content. In practical terms, the uncertainty of determining elastic moduli at a higher effective stress from the measurements at a lower effective stress is small at high porosity and increases with decreasing porosity. We explain this effect by using a combination of two heuristic models—the critical porosity model and the modified solid model. The former is based on the observation that the elastic‐modulus‐versus‐porosity relation can be approximated by a straight line that connects two points in the modulus‐porosity plane: the modulus of the solid phase at zero porosity and zero at critical porosity. The second one reflects the fact that at constant effective stress, low‐porosity sandstones (even with small amounts of clay) exhibit large variability in elastic moduli. We attribute this variability to compliant cracks that hardly affect porosity but strongly affect the stiffness. The above qualitative observation helps to quantitatively constrain P‐ and S‐wave velocities at varying stresses from a single measurement at a fixed stress. We also show that there are distinctive linear relations between Poisson’s ratios (ν) of sandstone measured at two different stresses. For example, in consolidated medium‐porosity sandstones [Formula: see text], where the subscripts indicate hydrostatic stress in MPa. Linear functions can also be used to relate the changes (with hydrostatic stress) in shear moduli to those in compressional moduli. For example, [Formula: see text], where [Formula: see text] is shear modulus and [Formula: see text] is compressional modulus, both in GPa, and the subscripts indicate stress in MPa.
A prestack residual time migration operator
Authors: Stolt Robert H.
Published: October 2002

Larner and Beasley (1987) present cascaded migration as a way to increase the power and effectiveness of relatively simple migration methods. In particular, f-k migration (Stolt, 1978) can be made to accommodate a depth‐dependent velocity as a cascade of constant‐velocity migrations. The core concept is that data which have been migrated with an approximate velocity can be effectively migrated to their true velocity by migrating with a velocity that is equal to the square root of the difference between the squares of the true and approximate velocities.
Lithologic analysis from multispectral thermal infrared data of the alkalic rock complex at Iron Hill, Colorado
Authors: Watson Ken , Rowan Lawrence C. , Bowers Timothy L. , Anton‐Pacheco Carmen , Gumiel Pablo , Miller Susanne H.
Published: October 2002

Airborne thermal‐infrared multispectral scanner (TIMS) data of the Iron Hill carbonatite‐alkalic igneous rock complex in south‐central Colorado are analyzed using a new spectral emissivity ratio algorithm and confirmed by field examination using existing 1:24 000‐scale geologic maps and petrographic studies. Color composite images show that the alkalic rocks could be clearly identified and that differences existed among alkalic rocks in several parts of the complex. An unsupervised classification algorithm defines four alkalic rock classes within the complex: biotitic pyroxenite, uncompahgrite, augitic pyroxenite, and fenite + nepheline syenite. Felsic rock classes defined in the surrounding country rock are an extensive class consisting of tuff, granite, and felsite, a less extensive class of granite and felsite, and quartzite. The general composition of the classes can be determined from comparisons of the TIMS spectra with laboratory spectra. Carbonatite rocks are not classified, and we attribute that to the fact that dolomite, the predominant carbonate mineral in the complex, has a spectral feature that falls between TIMS channels 5 and 6. Mineralogical variability in the fenitized granite contributed to the nonuniform pattern of the fenite‐nepheline syenite class. The biotitic pyroxenite, which resulted from alteration of the pyroxenite, is spatially associated and appears to be related to narrow carbonatite dikes and sills. Results from a linear unmixing algorithm suggest that the detected spatial extent of the two mixed felsic rock classes was sensitive to the amount of vegetation cover. These results illustrate that spectral thermal infrared data can be processed to yield compositional information that can be a cost‐effective tool to target mineral exploration, particularly in igneous terranes.