bluuebunny/crossref_metadata_2025 huggingface dataset:
Permeability relation with other petrophysical parameters for periodic porous media
Authors: Dunn Keh‐Jim , LaTorraca Gerald A. , Bergman David J.
Published: October 2002

We modeled permeability (k) estimation based on porosity (ϕ), electrical formation factor (F), and nuclear magnetic resonance (NMR) relaxation time (T), using periodic structures of touching and overlapping spheres. The formation factors for these systems were calculated using the theory of bounds of bulk effective conductivity for a two‐component composite. The model allowed variations in grain consolidation (degree of overlap), scaling (grain size), and NMR surface relaxivity. The correlation of the permeability (k) with the predictor a [Formula: see text] was slightly higher than [Formula: see text] (i.e., a correlation coefficient of 0.98 versus 0.95). The exponent b ranged from 1.4 for a pure grain consolidation system to 2 for a pure scaling system. Variations in surface relaxivity are shown to cause significant scatter in the correlations.
Effective elastic properties of heavily faulted structures
Authors: Hudson John A. , Liu Enru
Published: October 2002

Recent results have shown how to construct the smoothed transmission properties of a plane fault from the parameters of its microstructure in two particular cases. In the first, the fault is modelled as a plane distribution of approximately circular cracks while elsewhere the faces of the fault are held together by the ambient pressure and friction. In the second, the model consists of a plane distribution of approximately circular stuck regions within an area where the faces are separated as for a crack. The averaging method for a sequence of such slip planes enables the construction of overall properties of a material weakened by a series of parallel faults. With the first model, where the distribution of cracks is sparse, this approach leads to exactly the same expressions to first order in the number density as for dilute volume distributions of cracks. The higher‐order terms do not agree since they refer to crack‐crack interactions and in the Schoenberg‐Douma averaging process only the overall interactions between faults are allowed for, not individual interactions between cracks on different faults. Application of this procedure to the second model, in which the fracture density is high, gives for the first time an exact first‐order formula for the overall properties of heavily cracked material, the cracks being aligned and confined to the fault planes. These expressions are first order in the (small) parameter, denoting the proportion of each slip plane that is welded. The unwelded part may be free (any cracks) or filled with an incompressible inviscid fluid. An alternative approach in either case is to replace each fault or slip plane by an equivalent thin layer of material whose properties are related, at least in part, to the structure of the fault. The corresponding process of averaging over the layers is, in this case, the original Backus method. Comparison between the properties of the equivalent layers for dilute cracks and for extended cracking leads to an extension of the slip relations on a single heavily cracked fault to cases where the cracks contain secondary material with arbitrary elastic properties. Finally, results for a stack of parallel, heavily cracked faults is identical, to first order in the number density of the contact regions on the faults, to those for a cubical packing of spheres. This further reveals the insensitivity of first‐order results to many of the details of the microstructure.
Fresnel zone effect on seismic velocity resolution
Authors: Thore Pierre D. , Juliard Corrine
Published: October 2002

For impedance, velocity resolution depends on Fresnel zone considerations. A change of velocity can be distinguished only if its size is greater than the Fresnel zone. This is demonstrated on synthesized examples where a single velocity anomaly is introduced in a homogeneous medium. (Although unrealistic, this model was designed to exhibit the physical phenomenon in its simplest configuration.) The presence of the velocity anomaly breaks the wavefront into two main parts. The first part, which travels through the anomaly, corresponds to the specular ray and gives rise to an event which we call the ray event since it can be predicted by standard ray‐tracing techniques. The second, which emanates from outside the anomaly, does not correspond to a ray event. Therefore, we call it the nonray event. It travels at the speed of the background medium. The relative amplitude of the two events depends upon the size of the anomaly compared to the size of the Fresnel zone. When the anomaly is larger than the Fresnel zone, then the ray event dominates and the velocity variation is detectable. On the other hand, when the anomaly is smaller than the Fresnel zone, then the nonray event dominates and everything occurs as if there were velocity variation, leading to the wrong velocity model. The physical phenomenon underlying the presence of the nonray event is very pervasive and does not depend on the velocity contrast. It has already been referred to as wavefront healing, but its consequences in terms of velocity resolution have not been outlined in the domain of seismic reflection. The paper is organized in the following way. First, we present the phenomenon and its consequences on velocity analysis on a single model. Then, by changing the model parameters, we show how the respective amplitudes of the nonray event and the ray event and, therefore, the detectability of velocity variations depends on the size of the anomaly. Finally, we present two approaches to describe the physics of the phenomenon: (1) geometrical considerations based on Huyghen’s principle to explain the wave‐front healing phenomenon and (2) a discussion on the Kirchhoff integral to explain how the amplitude ratio of the ray event to the nonray event (and in turn the detectability of the velocity variation) depends on the size of the anomaly compared to the size of the Fresnel zone. In the final part of the paper we give two potential applications of this theory: (1) the use of the Fresnel zone diameter as the minimum length for smoothing velocity horizons and (2) a theoretical scheme for velocity analysis that should improve the velocity resolution: a combination of velocity estimation and wave equation redatuming. No implementation of this scheme has yet been tested.
On: “What is noise?,” (J. A. Scales and R. Snieder, GEOPHYSICS, 63, 1122–1124)
Authors: Grubb Howard
Published: October 2002

With reference to Scales and Snieder’s (1998) discussion of “what is noise,” I would like to offer a statistical interpretation of this question. Any experiment involving measurement will have variation—this is what allows us to make inference upon the results—and it is the partition of this variation which is key to the noise question. From an experimenter’s point of view, noise may be “that part of the data (variation) which we choose not to explain,” although Scales and Snieder are correct to point out that we must then have a model to explain the rest, since a purely statistical one (i.e., assuming that the remainder is in some way “random”) may not be adequate. From a statistical viewpoint however, noise may be better described as “that part of the variation which we cannot explain with a parsimonious deterministic model” and the signal is then the interesting part of the overall model.
Reply by the author to the discussion by Gijs J. O. Vermeer
Authors: Wisecup R. Daniel
Published: October 2002

I wish to thank Dr. Vermeer for his letter about my paper on RSI2 imaging. I feel the work stands on its own merits, but as we appear to disagree on some points, I would like to comment on them.
Smooth inversion of VSP traveltime data
Authors: Lizarralde Daniel , Swift Steve
Published: October 2002

Vertical seismic profile (VSP) direct arrivals provide an insitu measurement of traveltime with depth into the earth. In this note, we describe a weighted, damped least‐squares inversion of VSP traveltimes for a smooth velocity/depth function that inherently reveals the resolution of the data. Smooth velocity/depth profiles of this type are suitable for migration or as a starting models for waveform inversion or tomography. The application of this inversion is particularly simple, requiring only the value of the damping parameter to be determined, and this value is determined from residual statistics.
Imaging through gas‐filled sediments using marine shear‐wave data
Authors: Granli John R. , Arntsen Børge , Sollid Anders , Hilde Eilert
Published: October 2002

Marine multicomponent sea‐floor data of excellent quality have been acquired over the Tommeliten Alpha field. The most dominating wave modes are interpreted to be conventional compressional PP-waves and converted PS-waves. The most important geophysical problem associated with the Tommeliten Alpha field is the presence of a gas chimney obscuring the conventional 3-D seismic image of the reservoir zone. The converted PS-waves effectively undershoot the gas chimney, leading to substantially improved images of the reservoir. Subsequent interpretation indicates the Tommeliten Alpha structure is a faulted dome.
Converted‐wave reflection seismology over inhomogeneous, anisotropic media
Authors: Thomsen Leon
Published: October 2002

Converted‐wave processing is more critically dependent on physical assumptions concerning rock velocities than is pure‐mode processing, because not only moveout but also the offset of the imaged point itself depend upon the physical parameters of the medium. Hence, unrealistic assumptions of homogeneity and isotropy are more critical than for pure‐mode propagation, where the image‐point offset is determined geometrically rather than physically. In layered anisotropic media, an effective velocity ratio [Formula: see text] (where [Formula: see text] is the ratio of average vertical velocities and γ2is the corresponding ratio of short‐spread moveout velocities) governs most of the behavior of the conversion‐point offset. These ratios can be constructed from P-wave and converted‐wave data if an approximate correlation is established between corresponding reflection events. Acquisition designs based naively on γ0instead of [Formula: see text] can result in suboptimal data collection. Computer programs that implement algorithms for isotropic homogeneous media can be forced to treat layered anisotropic media, sometimes with good precision, with the simple provision of [Formula: see text] as input for a velocity ratio function. However, simple closed‐form expressions permit hyperbolic and posthyperbolic moveout removal and computation of conversion‐point offset without these restrictive assumptions. In these equations, vertical traveltime is preferred (over depth) as an independent variable, since the determination of the depth is imprecise in the presence of polar anisotropy and may be postponed until later in the flow. If the subsurface has lateral variability and/or azimuthal anisotropy, then the converted‐wave data are not invariant under the exchange of source and receiver positions; hence, a split‐spread gather may have asymmetric moveout. Particularly in 3-D surveys, ignoring this diodic feature of the converted‐wave velocity field may lead to imaging errors.
A side‐by‐side test of four land gravity meters
Authors: Chapin David A. , Crawford Michael F. , Baumeister Max
Published: October 2002

Four different land gravity meters were run side by side on a test range in eastern Texas. This test range was designed to duplicate typical field survey conditions encountered in gravity measurements on 3-D land seismic surveys. A profile of 270 stations was acquired with a station spacing of 33.5 m (110 ft). The four meters were Scintrex CG-3, Sodin, LaCoste & Romberg (L&R) G-meter, and Edcon/L&R Super-G meter. The purpose of this study was to determine which of the four meters had the best balance of accuracy, convenience, and speed of measurement for these specialized surveys. All four meters had their limitations, and no single meter was greatly superior to the others. The CG-3 was awkward in leveling, had a large (368 μGal per day) drift rate, and had some quirks in its user interface. The Sodin meter had problems controlling its temperature and, at one point, had a very high 935 μGal per day drift rate. It had the poorest accuracy of the four. The G-meter lacked a convenient digital user interface; thus, it was susceptible to operator blunder in misreading or recording the data. The Super-G meter also had some problems in its user interface, had only a 6-mGal range without a range change, and was the heaviest of the field instruments. An unbiased statistical estimator was developed to analyze the data. The technique determined the best three meters at each station. Both the G-meter and the Super-G meter produced the most accurate data. They had an average absolute deviation from the mean of 20 and 23 μGal, respectively. In comparison, the two quartz meters—the CG-3 and the Sodin—had an average absolute deviation from the mean of 31 and 46 μGal, respectively. We would like to see the manufacturers improve (or add, in the case of the G-meter and the Sodin) their digital interfaces. Additionally, we would like to see upgrades in the thermal control systems in all the meters. The single largest amount of station time was devoted to leveling (rather than reading) the meters. Significant advances can be envisioned to create fast, automated leveling systems in all the meters.
Multiparameter 𝓁1norm waveform fitting: Interpretation of Gulf of Mexico reflection seismograms
Authors: Djikpéssé Hugues A. , Tarantola Albert
Published: October 2002

Estimation of the elastic properties of the crust from surface seismic recordings is of great importance for the understanding of lithology and for the detection of mineral resources. Although in marine reflection experiments only P-waves are recorded, information on shear properties of the medium is contained in multioffset reflection seismograms. Being able to retrieve both dilatational and shear properties gives stronger constraints on the lithology. It is therefore desirable to recover isotropic elastic parameters from multioffset seismograms. Unfortunately, most classical waveform fitting methods used for extracting shear properties of the subsurface are based on a 1-D earth model assumption and on linear approximations of the wave equations. In this paper, a 2.5-D elastic waveform inversion method is used to extract the variations of acoustic impedance and Poisson’s ratio from marine multioffset reflection seismograms collected in the Gulf of Mexico area. A complete seismic profile is interpreted, including complex physical phenomena apparent in the data, such as unconsolidated sediment reflections and seismic refraction events. The amplitude of the reflections cannot be explained by one parameter related to the dilatational properties (P-impedance) only, when trying to minimize the least absolute fit between observed and synthetic seismograms. When adding an additional parameter related to shear properties (Poisson’s ratio), the fit between observed and synthetic seismograms improves. The resulting 2-D models of P-impedance and Poisson’s ratio contrasts are anticorrelated almost everywhere in depth, except where hydrocarbons are present. The estimation of physical P-impedance and Poisson’s ratio models by a full waveform fitting allows lithology characterization and, therefore, the delineation of a shale‐over‐gas sand reservoir.
Analyzing operators of 3-D imaging software with impulse responses
Authors: Schneider William A.
Published: October 2002

No processing step changes seismic data more than 3-D imaging. Imaging techniques such as 3-D migration and dip moveout (DMO) generally change the position, amplitude, and phase of reflections as they are converted into reflector images. Migration and DMO may be formulated in many different ways, and various algorithms are available for implementing each formulation. These algorithms all make physical approximations, causing imaging software to vary with algorithm choice. Imaging software also varies because of additional implementation approximations, such as those that trade accuracy for efficiency. Imaging fidelity, then, generally depends upon algorithm, implementation, specific software parameters (such as aperture, antialias filter settings, and downward‐continuation step size), specific acquisition parameters (such as nominal x- and y-direction trace spacings and wavelet frequency range), and, of course, the velocity model. Successfully imaging the target usually requires using appropriate imaging software, parameters, and velocities. Impulse responses provide an easy way to quantitatively understand the operators of imaging software and then predict how specific imaging software will perform with the chosen parameters. (An impulse response is the image computed from a data set containing only one nonzero trace and one arrival on that trace.) I have developed equations for true‐amplitude impulse responses of 3-D prestack time migration, 3-D zero‐offset time migration, 3-D exploding‐reflector time migration, and DMO. I use these theoretical impulse responses to analyze the operators of actual imaging software for a given choice of software parameters, acquisition parameters, and velocity model. The procedure is simple: compute impulse responses of some software; estimate position, amplitude, and phase of the impulse‐response events; and plot these against the theoretical values. The method is easy to use and has proven beneficial for analyzing general imaging software and for parameter evaluation with specific imaging software.
Special section on azimuthal dependence ofP-wave seismic signatures—Introduction
Authors: Tsvankin, Ilya , Lynn, Heloise B.
Published: October 2002

This special issue is based on papers presented at the post‐convention SEG workshop on azimuthal dependence of P-wave signatures held in Dallas in 1997. The main motivation for analyzing the azimuthal variation of seismic traveltimes, amplitudes, attenuation, etc. is to obtain reliable information about azimuthal anisotropy in the subsurface. Another potential application of multiazimuth techniques is in finding and mapping desirable lateral heterogeneities that could “masquerade” as azimuthal anisotropy. The last topic has not yet been fully discussed (and is not addressed in the special issue), but several exploration and development scenarios contain oriented lateral heterogeneities (sand channels, etc.) that at the right scale length could be highly visible in properly processed wide‐azimuth 3-D data.
Moveout inversion ofP-wave data for horizontal transverse isotropy
Authors: Contreras Pedro , Grechka Vladimir , Tsvankin Ilya
Published: October 2002

The transversely isotropic model with a horizontal symmetry axis (HTI media) has been extensively used in seismological studies of fractured reservoirs. In this paper, a parameter‐estimation technique originally developed by Grechka and Tsvankin for the more general orthorhombic media is applied to horizontal transverse isotropy. Our methodology is based on the inversion of azimuthally‐dependent P-wave normal‐moveout (NMO) velocities from horizontal and dipping reflectors. If the NMO velocity of a given reflection event is plotted in each azimuthal direction, it forms an ellipse determined by three combinations of medium parameters. The NMO ellipse from a horizontal reflector in HTI media can be inverted for the azimuth β of the symmetry axis, the vertical velocity [Formula: see text], and the Thomsen‐type anisotropic parameter δ(V). We describe a technique for obtaining the remaining (for P-waves) anisotropic parameter η(V)(or ε(V)) from the NMO ellipse corresponding to a dipping reflector of arbitrary azimuth. The interval parameters of vertically inhomogeneous HTI media are recovered using the generalized Dix equation that operates with NMO ellipses for horizontal and dipping events. High accuracy of our method is confirmed by inverting a synthetic multiazimuth P-wave data set generated by ray tracing for a layered HTI medium with depth‐varying orientation of the symmetry axis. Although estimation of η(V)can be carried out by the algorithm developed for orthorhombic media, for more stable results the HTI model has to be used from the outset of the inversion procedure. It should be emphasized that P-wave conventional‐spread moveout data provide enough information to distinguish between HTI and lower‐symmetry models. We show that if the medium has the orthorhombic symmetry and is sufficiently different from HTI, the best‐fit HTI model cannot match the NMO ellipses for both a horizontal and a dipping event. The anisotropic coefficients responsible for P-wave moveout can be combined to estimate the crack density and predict whether the cracks are fluid‐filled or dry. A unique feature of the HTI model that distinguishes it from both vertical transverse isotropy and orthorhombic media is that moveout inversion provides not just zero‐dip NMO velocities and anisotropic coefficients, but also the true vertical velocity. As a result, reflection P-wave data acquired over HTI formations can be used to build velocity models in depth and perform anisotropic depth processing.
P-wave andS-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell‐Altamont Field, Utah
Authors: Lynn Heloise B. , Beckham Wallace E. , Simon K. Michele , Bates C. Richard , Layman M. , Jones Michael
Published: October 2002

Reflection P- and S-wave data were used in an investigation to determine the relative merits and strengths of these two data sets to characterize a naturally fractured gas reservoir in the Tertiary Upper Green River formation. The objective is to evaluate the viability of P-wave seismic to detect the presence of gas‐filled fractures, estimate fracture density and orientation, and compare the results with estimates obtained from the S-wave data. The P-wave response to vertical fractures must be evaluated at different source‐receiver azimuths (travelpaths) relative to fracture strike. Two perpendicular lines of multicomponent reflection data were acquired approximately parallel and normal to the dominant strike of Upper Green River fractures as obtained from outcrop, core analysis, and borehole image logs. The P-wave amplitude response is extracted from prestack amplitude variation with offset (AVO) analysis, which is compared to isotropic‐model AVO responses of gas sand versus brine sand in the Upper Green River. A nine‐component vertical seismic profile (VSP) was also obtained for calibration of S-wave reflections with P-wave reflections, and support of reflection S-wave results. The direction of the fast (S1) shear‐wave component from the reflection data and the VSP coincides with the northwest orientation of Upper Green River fractures, and the direction of maximum horizontal in‐situ stress as determined from borehole ellipticity logs. Significant differences were observed in the P-wave AVO gradient measured parallel and perpendicular to the orientation of Upper Green River fractures. Positive AVO gradients were associated with gas‐producing fractured intervals for propagation normal to fractures. AVO gradients measured normal to fractures at known waterwet zones were near zero or negative. A proportional relationship was observed between the azimuthal variation of the P-wave AVO gradient as measured at the tops of fractured intervals, and the fractional difference between the vertical traveltimes of split S-waves (the “S-wave anisotropy”) of the intervals.
Comparison of gravimetric formulas for uniform polyhedra
Authors: Holstein Horst , Schürholz Peter , Starr Andrew J. , Chakraborty Mausumi
Published: October 2002

The gravitational anomaly of a polyhedral target of uniform density is amenable to analytical solution and has received wide attention. We analyze a number of apparently dissimilar solutions for consistency and comment on their suitability for numeric computation. Consistency is determined by evaluating a method over a special contour for which all methods must agree. Numerical performance is assessed through operation counts and algorithm classification into vertex, line, or surface type, each type having a known accuracy bound for a given floating‐point precision. We verify performance predictions through model calculations. In particular, we demonstrate the effectiveness of revised vertex and line algorithms and of a new analytical surface method. Our scheme of analysis and classification has general application. It provides criteria by which existing and novel solutions may be examined for consistency and numerical performance.
A new kinematic method for mapping seismic reflectors
Authors: Zhe Jingping , Greenhalgh Stewart A.
Published: October 2002

This paper presents a modern version of an old technique of common tangent reflection migration. Rather than using the graphical method of swinging arcs and looking for the envelope of touching tangents on widely separated geophones, we use a numerical scheme of searching along each isochron, constructed by a wave‐equation‐based modeling scheme for arbitrary velocity media, to find the common tangent points. The assumption is made that the receivers are close together so that the interface can be locally approximated by a straight line, although different pairs of receivers permit different tangents to be found, enabling a curved boundary to be migrated. The technique can be extended to several shot gathers to map multiple curved boundaries. Synthetic examples are used to illustrate the capabilities of the method and the effect of using an erroneous velocity distribution.
Reflectivity randomness revisited
Authors: Dey Ayon K. , Lines Larry R.
Published: October 2002

In seismic exploration, statistical wavelet estimation and deconvolution are standard tools. Both of these processes assume randomness in the seismic reflectivity sequence. The validity of this assumption is examined by using well‐log synthetic seismograms and by using a procedure for evaluating the resulting deconvolutions. With real data, we compare our wavelet estimations with the in‐situ recording of the wavelet from a vertical seismic profile (VSP). As a result of our examination of the randomness assumption, we present a fairly simple test that can be used to evaluate the validity of a randomness assumption. From our test of seismic data in Alberta, we conclude that the assumption of reflectivity randomness is less of a problem in deconvolution than other assumptions such as phase and stationarity.
Time‐varying effects in magnetic mapping: Amphidromes, doldrums, and induction hazard
Authors: Lilley F. E. M. , Hitchman Adrian P. , Wang Lie Jun
Published: October 2002

A magnetic amphidrome is defined as a place where changes of the magnetic field over time, as measured by a total‐field magnetometer, are reduced to the point of being negligible. The reduction is caused by destructive interference between the vertical and horizontal components of the time‐varying field. At an ideal amphidrome, variations with time are suppressed completely and the total‐magnetic‐field magnitude is steady. Such a phenomenon may be expected to depend on the frequency content of the time variations in the vertical and horizontal components. The subject is treated first in terms of the quiet daily variation, [Formula: see text], which is studied on a global basis. It is seen that there are magnetic latitude bands, north and south of the equator, where the quiet daily variation is minimal. These zones are called the “diurnal doldrums.” In addition to this global pattern, the magnetic daily variation is modified by Earth’s conductivity structure locally, and [Formula: see text] amphidrome behavior may be aided or obstructed locally. The second part of the paper treats the magnetic “rapid fluctuations.” A simple condition for an amphidrome is that the direction of Earth’s main magnetic field be parallel to the normal of the “preferred plane” in which the small vector changes of rapid magnetic fluctuations tend to lie. Examples are given of observed data for Australia, and a numerical model of Australian electrical‐conductivity structure is used to predict amphidromes regionally. Formal treatment of the preferred‐plane concept involves taking the out‐of‐phase (or quadrature) part of the induction phenomenon into account as well, and a parameter is proposed which may be contoured to show an amphidrome minimum. The phenomena of amphidromes are fundamental for magnetic mapping procedures. Near amphidromes, the fluctuating magnetic fields of Earth are suppressed, and their capacity for introducing error into magnetic survey data is reduced correspondingly. The case of a “complete” or “ultimate” amphidrome, applying to both diurnal and rapid fluctuations, may be expected to be rare. None is known at present. The reason is that the diurnal doldrums, favoring [Formula: see text] amphidromes, occur at low latitudes. Rapid‐fluctuation amphidromes, however, are more likely to occur at mid‐ to high latitudes.
Display of residual profiles versus gridded image data in aeromagnetic study of sedimentary basins: A case history
Authors: Skilbrei Jan Reidar , Kihle Ola
Published: October 2002

High‐pass filtered aeromagnetic profiles from the Mid‐Norwegian continental shelf, displayed as shaded relief versions of color stripes, provide a lucid picture of sedimentary layering and structure not easily displayed by proper application of modern enhancement techniques to images of the gridded aeromagnetic data. We show that when the aim is to analyze anomalies related to sedimentary features, it is more useful to study shaded relief versions of the profile data than to study digitally enhanced images of high‐pass filtered or calculated gradient data; a reason for this is probably the loss of high‐wavenumber, very low amplitude, information in the gridding process. The reprocessed data sets reveal anomaly patterns that are interpreted to originate from the following magnetic sources: (1) Quaternary overburden and bathymetric features, (2) magnetic sedimentary rocks, the subcropping sedimentary rock units, (3) magnetic basement in the structural highs and in the coastal zone, and (4) igneous intrusives at relatively deep levels within sedimentary basins. West of the basement rocks along the coast, the subcropping wedge of Mesozoic to Tertiary sediments is characterized by a distinct set of subparallel anomalies. Also, sedimentary layering within the Tertiary can be resolved. Short to intermediate wavelength anomalies correlate with the Late Jurassic faults of the Halten Terrace.
The link of Kirchhoff migration and demigration to Kirchhoff and Born modeling
Authors: Jaramillo Herman H. , Bleistein Norman
Published: October 2002

The Kirchhoff approximation provides a representation of seismic data as a summation of imaged data along isochron surfaces (demigration). The asymptotic inversion of this representation provides a migration as a summation of seismic data along diffraction surfaces. We replace Born inversion techniques with Kirchhoff inversion techniques and further show the link between the Kirchhoff and Born representations after the Born linearized reflection coefficient is replaced by the Kirchhoff reflection coefficient.
Model‐based removal of water‐layer multiple reflections
Authors: Lu Guochun , Ursin Bjørn , Lutro Jan
Published: October 2002

We have developed a procedure to attenuate water‐layer multiple reflections. We estimate the sea‐bottom reflectivity function and use it plus calculated amplitude functions to model all order water‐layer multiple reflections, taking into account both amplitude and waveform shape. We model the primary and multiple reflections from the sea bottom in the frequency‐slowness domain. The amplitude function in the data modeling includes the source directivity function, source ghost response, receiver array directivity function, receiver ghost response, and offset‐dependent geometrical spreading. For small offsets we can assume that the seabed reflectivity depends only on frequency, and it is estimated using a least‐squares algorithm. An unknown scaling constant in the data is estimated using the amplitude of the primary and first multiple reflection from the sea bed. The composite sea‐bottom reflectivity is estimated as a function of frequency for each common midpoint (CMP) position. We apply the algorithm to high‐resolution seismic data from the North Sea. The modelled data match the recorded data well, and the estimated primary reflectivity is more geologically meaningful than the stacked trace. By comparison with Radon transform multiple removal applied to the same data, the model‐based method was more computationally efficient and left less residual multiple energy.
High‐frequency reflections in granite? Delineation of the weathering front in granodiorite at Piñon Flat, California
Authors: Radzevicius Stanley J. , Pavlis Gary L.
Published: October 2002

We analyze data from two orthogonal seismic lines 336 m in length collected at Piñon Flat, California, over weathered granodiorite bedrock. Each line was made up of 10 reversed segments 84 m in length. We analyzed the first arrivals from these data and found dramatic variations in velocity along the profiles. An upper layer (approximately 2-m thick) known from trenching to be composed of soil and sandy grus had measured velocities ranging from 400 to 700 m/s. Velocities inferred from refraction analysis of first arrivals of the reversed lines revealed a heterogeneous lower layer below the soil with measured velocities of 1600–2700 m/s by a depth of 15 m. We interpret these data to be measuring velocities of a deeply weathered unit characterized by granodiorite corestones embedded in a matrix of saprolite. The most remarkable feature of these data emerged from attempting to process the same data as reflection data. Simple bandpass filtering in the 250–400 Hz band revealed a bright, impulsive arrival with three characteristic properties: (1) irregular velocity moveout that is inconsistent with that expected from a layered earth model, (2) the arrival is at a nearly constant time‐depth on all data, and (3) the arrival tends to be followed by a ringing coda whose frequency varies from trace to trace. This arrival ties exactly with a velocity discontinuity measured in a borehole located on one of the profiles that we interpret as the base of the weathered layer. We suggest this arrival is a specular reflection from a weathering front that occurs along horizontal sheeting joints at a fixed depth below the surface. This surface acts as an effective mirror for high‐frequency seismic waves which are then channeled upward through an intact, high-Q path of unaltered blocks of granodiorite to define the observed signals at the surface.
3-D ray modeling by wavefront construction in open models
Authors: Vinje Vetle , Åstebøl Ketil , Iversen Einar , Gjøystdal Håvar
Published: October 2002

A synthesis of two newly developed concepts in 3-D modeling is developed in this paper: (1) The open, (noncomplete) seismic model, and (2) the ray tracing based wavefront (WF) construction method. The open model may contain interfaces with holes and other missing parts, which simplifies model building considerably because the input horizon data from standard interpretation and processing packages are often incomplete. A set of volumes is defined in the model. A volume is a logical unit that points to a set of property functions, e.g., P-velocity, S-velocity, and density. The properties are represented either as constants or as B-spline functions of the spatial coordinates (x, y) or (x, y, z). The volumes of the model are assigned to opposing sides of each interface and not to specific spatial areas of the model, which is the case in most (blocky) model representations. The interfaces are given explicitly by triangular grids where the sizes of the triangles are determined locally by the curvature of the interface. We show how modeling by WF construction is both possible and computationally efficient in open models, but only after some modifications to deal with the ambiguity of the model representation. It is not possible to find a unique volume for the spatial positions in an open model. Instead, the volumes (with associated velocities, etc.) are determined from the last interface encountered by each ray in the WF. To find an arrival in a receiver, the volume associated to the receiver has to match the volume of the WF hitting the receiver.
Depth to bedrock using gravimetry in the Reno and Carson City, Nevada, area basins
Authors: Abbott Robert E. , Louie John N.
Published: October 2002

Sedimentary basins can trap earthquake surface waves and amplify the magnitude and lengthen the duration of seismic shaking at the surface. Poor existing gravity and well‐data coverage of the basins below the rapidly growing Reno and Carson City urban areas of western Nevada prompted us to collect 200 new gravity measurements. By classifying all new and existing gravity locations as on seismic bedrock or in a basin, we separate the basins’ gravity signature from variable background bedrock gravity fields. We find an unexpected 1.2-km maximum depth trough below the western side of Reno; basin enhancement of the seismic shaking hazard would be greatest in this area. Depths throughout most of the rest of the Truckee Meadows basin below Reno are less than 0.5 km. The Eagle Valley basin below Carson City has a 0.53-km maximum depth. Basin depth estimates in Reno are consistent with depths to bedrock in the few available records of geothermal wells and in one wildcat oil well. Depths in Carson City are consistent with depths from existing seismic reflection soundings. The well and seismic correlations allow us to refine our assumed density contrasts. The basin to bedrock density contrast in Reno and Carson City may be as low as −0.33 g/cm3. The log of the oil well, on the deepest Reno subbasin, indicates that Quaternary deposits are not unusually thick there and suggests that the subbasin formed entirely before the middle Pliocene. Thickness of Quaternary fill, also of importance for determining seismic hazard below Reno and Carson City may only rarely exceed 200 m.
Dipole dispersion crossover and sonic logs in a limestone reservoir
Authors: Sinha Bikash K. , Kane Michael R. , Frignet Bernard
Published: October 2002

Analyses of sonic logs in a horizontal well provide new information about mechanical properties of rocks, made possible by recent developments in our understanding of acoustic wave propagation in prestressed formations. Most sections of this horizontal well exhibit azimuthal shear isotropy, indicating isotropic stresses in the plane perpendicular to the well trajectory, leading to stable wellbore conditions. However, two sections show dipole dispersion crossovers that confirm the presence of stress‐induced shear anisotropy caused by a difference between the maximum and minimum stresses in the plane perpendicular to the well trajectory. The two dipole dispersions are obtained by processing the recorded waveforms by a modified matrix pencil algorithm. The fast‐shear direction is estimated from Alford rotation of the cross‐dipole waveforms. One section of the well exhibits the fast‐shear direction parallel to the overburden stress as the maximum stress direction, whereas the other section has the fast‐shear direction parallel to the horizontal stress that is larger than the overburden stress. The cause of this change in the fast‐shear direction is believed to be the well’s penetration into a 3-ft-thick bed with lower porosity and permeability and significantly higher elastic stiffnesses than those in the other part of the homogeneous, high‐permeability reservoir. A stiff bed is likely to have greater stresses in its plane than perpendicular to it, which would make the horizontal stresses greater than the vertical.
Airborne resistivity and susceptibility mapping in magnetically polarizable areas
Authors: Huang Haoping , Fraser Douglas C.
Published: October 2002

The apparent resistivity technique using half‐space models has been employed in helicopter‐borne resistivity mapping for twenty years. These resistivity algorithms yield the apparent resistivity from the measured in‐phase and quadrature response arising from the flow of electrical conduction currents for a given frequency. However, these algorithms, which assume free‐space magnetic permeability, do not yield a reliable value for the apparent resistivity in highly magnetic areas. This is because magnetic polarization also occurs, which modifies the electromagnetic (EM) response, causing the computed resistivity to be erroneously high. Conversely, the susceptibility of a magnetic half‐space can be computed from the measured EM response, assuming an absence of conduction currents. However, the presence of conduction currents will cause the computed susceptibility to be erroneously low. New methods for computing the apparent resistivity and apparent magnetic permeability have been developed for the magnetic conductive half‐space. The in‐phase and quadrature responses at the lowest frequency are first used to estimate the apparent magnetic permeability. The lowest frequency should be used to calculate the permeability because this minimizes the contribution to the measured signal from conduction currents. Knowing the apparent magnetic permeability then allows the apparent resistivity to be computed for all frequencies. The resistivity can be computed using different methods. Because the EM response of magnetic permeability is much greater for the in‐phase component than for the quadrature component, it may be better in highly magnetic environments to derive the resistivity using the quadrature component at two frequencies (the quad‐quad algorithm) rather than using the in‐phase and quadrature response at a single frequency (the in‐phase‐quad algorithm). However, the in‐phase‐quad algorithm has the advantage of dynamic range, and it gives credible resistivity results when the apparent permeability has been obtained correctly.
Simultaneous use of electrostatic quadrupole and GPR in urban context: Investigation of the basement of the Cathedral of Girona (Catalunya, Spain)
Authors: Dabas Michel , Camerlynck Christian , Camps Pere Freixas i
Published: October 2002

There is a growing demand for nondestructive geophysical investigation in archaeology, especially in an urban context. This is a result of taking our heritage more seriously than in the past. Since excavations are possible only over a very limited area, any a priori information brought by geophysical methods can help to focus these excavations. The classical geophysical methods used in archaeology (resistivity, magnetism) are not applicable in an urban context with problems of accessibility and inherent electromagnetic noise. The potential of the combined use of ground‐penetrating radar (GPR) and electrostatic (ES) quadrupole data is demonstrated in the investigation of the floor of the cathedral of Girona in northern Spain. A 1.3 × 1.3 m electrostatic quadrupole was towed continuously over a set of parallel profiles to produce a resistivity map for a 20 × 60 m area. A set of resistive anomalies corresponds with known structures (probably graves). The largest observed anomalies appear to be related to foundations of former buildings. A set of 450-MHz GPR profiles were collected and common midpoint (CMP) soundings were performed to convert from time to depth. The time slice centered at 14 ns (at 0.9-m depth) shows anomalies similar to those in the resistivity map. Two different physical properties are measured (electrical resistivity and a reflectivity coefficient that is mainly a function of the contrast in dielectric permittivity); both methods may be sensitive mainly to the water content in the volume under investigation. The improved confidence in an interpretation obtained by combining these two sets of data enables us to infer the location and geometry of the Romanesque building which stood previously on the site of the present cathedral of Girona. Excavations support the interpretation.
Seismic velocities and Poisson’s ratio of shallow unconsolidated sands
Authors: Bachrach Ran , Dvorkin Jack , Nur Amos M.
Published: October 2002

We determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three‐component surface seismic data. P- and S-wave velocity profiles were calculated from traveltime measurements of vertical and tangential component seismograms, respectively. The results reveal two discrepancies between theory and data. Whereas both velocities were found to be proportional to the pressure raised to the power of 1/6, as predicted by the Hertz‐Mindlin contact theory, the actual values of the velocities are less than half of those calculated from this theory. We attribute this discrepancy to the angularity of the sand grains. Assuming that the average radii of curvature at the grain contacts are smaller than the average radii of the grains, we modify the Hertz‐Mindlin theory accordingly. We found that the ratio of the contact radius to the grain radius is about 0.086. The second disparity is between the observed Poisson’s ratio of 0.15 and the theoretical value (0.008 for random pack of quartz spheres). This discrepancy can be reconciled by assuming slip at the grain contacts. Because slip decreases the shearing between grains, Poisson’s ratio increases.
Separation of signal and coherent noise by migration filtering
Authors: Nemeth Tamas , Sun Hongchuan , Schuster Gerard T.
Published: October 2002

A key issue in wavefield separation is to find a domain where the signal and coherent noise are well separated from one another. A new wavefield separation algorithm, called migration filtering, separates data arrivals according to their path of propagation and their actual moveout characteristics. This is accomplished by using forward modeling operators to compute the signal and the coherent noise arrivals. A linearized least‐squares inversion scheme yields model estimates for both components; the predicted signal component is constructed by forward modeling the signal model estimate. Synthetic and field data examples demonstrate that migration filtering improves separation of P-wave reflections and surface waves, P-wave reflections and tube waves, P-wave diffractions, and S-wave diffractions. The main benefits of the migration filtering method compared to conventional filtering methods are better wavefield separation capability, the capability of mixing any two conventional transforms for wavefield separation under a general inversion framework, and the capability of mitigating the signal and coherent noise crosstalk by using regularization. The limitations of the method may include more than an order of magnitude increase in computation costs compared to conventional transforms and the difficulty of selecting the proper modeling operators for some wave modes.
Wave propagation near a fluid‐solid interface: A spectral‐element approach
Authors: Komatitsch Dimitri , Barnes Christophe , Tromp Jeroen
Published: October 2002

We introduce a spectral‐element method for modeling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as for instance in offshore seismic experiments. The problem is formulated in terms of displacement in elastic regions and a velocity potential in acoustic regions. Matching between domains is implemented based upon an interface integral in the framework of an explicit prediction‐multicorrection staggered time scheme. The formulation results in a mass matrix that is diagonal by construction. The scheme exhibits high accuracy for a 2-D test case with known analytical solution. The method is robust in the case of strong topography at the fluid‐solid interface and is a good alternative to classical techniques, such as finite differencing.