bluuebunny/crossref_metadata_2025 huggingface dataset:
Simultaneous estimation of residual static and crossdip corrections
Authors: Larner Kenneth L. , Gibson Bruce R. , Chambers Ron , Wiggins Ralph A.
Published: October 2002

Seismic surveys on land are frequently conducted along nonlinear survey lines. Familiar examples include crooked lines controlled by existing road networks or by surface typography, lines that are otherwise linear but along which shotpoints occasionally must be offset laterally, and intentionally designed three‐dimensional (3-D) or broad‐line surveys. Departures from linear profiles introduce an element of complexity—crossdip—into the problem of estimating residual near‐surface reflection static time corrections (statics). Crossdip is the component of dip normal to the local profile direction. We have incorporated the effect of crossdip into the system of simultaneous equations that model residual static anomalies. The observed traveltimes of all reflections selected for analysis are represented as linear combinations of source and receiver static anomalies, structural shapes, residual normal moveouts, and crossdip terms. The static time components are taken to be surface‐consistent and independent of reflecting horizon, whereas the other solution parameters are subsurface‐consistent and pertain to specific horizons. Unfortunately, the inclusion of crossdip in the equations increases the degree of nonuniqueness of residual statics solutions. Its inclusion, however, is a necessity wherever horizons having differing crossdips are analyzed simultaneously. Such simultaneous analysis often is the best means for upgrading the reliability of the crosscorrelation estimates (i.e., the traveltime observations) upon which all statics are based. Synthetic‐data examples demonstrate the degree to which crossdip estimates and statics estimates can be separated from one another. Although estimates of crossdips are a useful by‐product, the accuracy of the static corrections is considered of prime importance. When critical crossdip terms are ignored in a statics solution, the quality of the common‐depthpoint (CDP) stacks suffer, as shown in comparison processings of field sections. Moreover, crossdip estimates from 3-D or broad‐line surveys are questionable if crossdip and static corrections are not considered in a unified solution.
Kimberlites and exploration geophysics
Authors: Macnae James C.
Published: October 2002

This paper discusses geophysical prospecting techniques for kimberlite pipes, a major source of diamonds. A simple geologic model based on descriptions by Hawthorne (1975) and Nixon (1973) is given, and the varied geophysical responses obtained over kimberlite pipes are interpreted in terms of this model. The three main factors controlling these responses are the original size and inhomogeneity of the pipe, the depth of erosion, and the degree of weathering. Kimberlite pipes are roughly elliptical in surface exposure in most cases, with a “carrot shaped” extension at depth. The unweathered portion of the pipe generally contains a few percent magnetite, and this in most cases produces a clearly detectable magnetic anomaly. The presence of deep weathering may alter the magnetite in the top of the pipe to nonmagnetic oxides of iron, thus resulting in an increased depth to the magnetic source. If this depth is large, the magnetic response may not be large enough to detect the kimberlite in the presence of noise and the effect of other structures. In addition, if little erosion has taken place since emplacement, kimberlitic sediments known as epiclastic kimberlite will be present to considerable depths in the pipe, and this may also lead to the absence of a clear magnetic anomaly. In one large survey in South Africa, electromagnetic (EM) techniques have proven to be remarkably effective in detecting the presence of weathered clays or epiclastic kimberlite contained within the pipes. All pipes discovered during this survey had unmistakable EM signatures, while five out of eight had very small magnetic anomalies which would not likely have been selected as potential targets on the basis of magnetic data alone. These examples would indicate that in any area where deep weathering is expected, an EM survey is essential in combination with a magnetic survey if reconnaissance is to be based on airborne geophysical techniques. Due to the emplacement mechanism of kimberlite, considerable inhomogeneity within a pipe may be present, leading to significant variation in the response of any geophysical technique to one pipe, with resultant interpretation difficulties. Although this is not a limitation in the discovery of new pipes, it does make their geophysical delimitation difficult.
Quantitative analysis of a mud volcano gravity anomaly
Authors: Nettleton L. L. , Herring A. T.
Published: October 2002

A gravity survey made some 30 years ago on the Island of Trinidad shows a negative anomaly of about 8 mgal over the Maruga Bouff mud volcano. An analysis of this anomaly is made, using an iterative three‐dimensional (3-D) modeling technique. The resulting model shows low‐density material superimposed on an underlying diapiric uplift. By comparison with other mud volcanoes which have been drilled, the model is considered reasonable.
Gravity terrain corrections for stations on a uniform slope—A power law approximation
Authors: Campbell David L.
Published: October 2002

A hand calculator program for gravity terrain corrections should include functions to (1) calculate the standard terrain correction due to topography of constant elevation throughout a given sector of a terrain correction graticule, and (2) calculate the terrain correction due to topography that slopes uniformly throughout the graticule sector. Equations for function (1) and for a special case of function (2) were given by Hammer (1939). Hammer’s equation covers the useful case where the uniform slope extends in azimuth a full 360 degrees around the gravity station. Using this equation, Sandburg (1958) published tables of gravity terrain corrections for stations on complete (360 degree) uniform slopes of slope angles 0 degrees to 30 degrees. This note points out that Hammer’s equation, as well as the corresponding equation for the incomplete uniform slope (one extending under a single graticule sector only), may both be approximated by a square‐power law. The resulting forms are particularly convenient for hand calculator use. A particular application gives a new rule of thumb for estimating Hammer inner‐zone terrain corrections.
Search area analysis of exploration drilling for hydrocarbons
Authors: Rangarajan S. , Mehta C. H.
Published: October 2002

In an exploratory search for oil and gas in any basin, it is desirable to evaluate from time to time the remaining hydrocarbon potential of the basin. From a statistical point of view, the productivity of the search area and the efficiency (or skill) of exploration are the parameters which are embodied in the actual history of exploration. A careful analysis of the past history can enable us to (1) extract an index for the efficiency of the past exploration, (2) obtain objective estimates of remaining reserves, and (3) predict the probability of success in the next few drillings. Here, we propose a model for which the input is the past chronological record of exploration in the search area. Efficiency is quantified by comparing the observed history with that which would have resulted had the search been random, other parameters remaining the same. In this respect, our method is qualitatively akin to that proposed recently by Cozzolino (1977). However, there are major conceptual differences between the two models resulting in different quantitative predictions for the same data. These are discussed and illustrated by applying the two methods to exploration in the southwestern portion of the Williston basin in the United States. It is shown that our approach yields parameters which are more stable with respect to variation in the length of the input history; in this sense our model is more reliable.
Borehole resistivity curves near spheroidal masses
Authors: Dobecki T. L.
Published: October 2002

Modeling of in situ energy extraction processes (e.g., coal gasification and oil shale retorting) has been examined by assuming the affected zones may be described by oblate or prolate spheroids of lowered electrical resistivity. The purpose of the model study is to determine if such subsurface bodies may be monitored and defined by electrical resistivity measurements made in boreholes away from the reaction zone. Solutions of the Laplace equation in (1) oblate and (2) prolate spheroidal coordinate systems enable theoretical determination of the electrical potential distribution as would be measured in a borehole near an anomalous body of oblate or prolate shape. The body is assumed to be enclosed within an infinite, homogeneous mass. Normal (pole‐pole) type curves of (1) electrical resistivity for various electrode spacings (sounding curves) and (2) electrical resistivity for various positions in the borehole (vertical profiling) are developed for both oblate and prolate spheroidal models using spheroids of increasing size as a sensitivity parameter. Modeling results verify that an oblate body of the same cross‐sectional shape as a prolate body produces the larger anomaly. For the various size and resistivity parameters specified in this study, deviations from the homogeneous case (i.e., no spheroid) range from 3 percent for the smallest oblate and prolate bodies up to 60 percent for the largest modeled oblate body. If a ±5 percent uncertainty because of instrumentation, field technique, or random noise may be assumed, this implies a lower limit to the size of a detectable body. On this basis, the smaller spheroids of this study would not be detectable. However, both sounding and profiling type measurements offer promise as effective monitoring tools, and, if repeated over the period of process time, may enable process growth estimates. Further, because the oblate case is independent of azimuth while the prolate is not, measurements made in a series of borings surrounding the process center may describe the shape tendency (oblate versus prolate) of the process and determine directivity (azimuth of prolate major axis) of the process if existent.
Well‐logging method
Authors: Segesman F. F.
Published: October 2002

By 1930, the resistivity log was recorded commercially in several countries, and in 1931 the self‐potential (SP) measurement was added. An electromagnetic (EM) teleclinometer was introduced in 1932, a continuous temperature log in 1933, and an anisotropy dipmeter ca. 1935. The significance of the SP was an ongoing study until about 1962. The bases for the quantitative interpretation of resistivity for saturation were formulated by 1941. The years from about 1940 into the 1960s saw the development of other basic logs—dipmeter, gamma ray, neutron, induction, microresistivity, focused resistivity, density, and acoustic velocity—as well as other miscellaneous logs. Suites of resistivity logs were evolved to provide more accurate analysis. Much effort was expended on the interpretation of shaly sands. Neutron, density, and acoustic logs yielded information on porosity, lithology, gas saturation, and/or shaliness. Availability of porosity from these logs facilitated resistivity‐log interpretation. In the late 1950s, interest developed in the use of computers for log interpretation. By about 1961, dipmeter logs were being recorded on digital magnetic tape suitable for computer input, and other logs were available by about 1965. Digital recording has also facilitated transmission of logs via radio and telephone. Recently, digital systems for wellsite computations have been introduced.
High‐sensitivity aeromagnetic survey of the U.S. Atlantic continental margin
Authors: Behrendt John C. , Klitgord Kim D.
Published: October 2002

The U.S. Geological Survey contracted a high‐sensitivity, digital aeromagnetic survey that was flown over the U.S. Atlantic continental margin over a period of 15 months between 1974 and 1976. The 185,000 km of profile data have a relative accuracy approaching a few tenths of a nanotesla, which allowed compilation into maps at a scale of 1:250,000, with a contour interval of 2 nT. Automatic data processing using the Werner method allowed calculations of apparent depth to sources of the magnetic anomalies on all of the profiles, assuming a dike or interface as a source. Comparison of the computed depths to magnetic basement with multichannel seismic profiles across the survey area helped to reduce ambiguities in magnetic depth estimates and enabled interpolation of basement structures between seismic profiles. The resulting map showing depth to basement of the Atlantic continental margin is compatible with available multichannel seismic data, and we consider it a reasonable representation of the base of the sedimentary column.
Interpretation of total gamma logs in thin and dipping beds
Authors: Moore Donald C.
Published: October 2002

The proportional relationship between the grade‐thickness product and the area under a gross gamma‐ray log is well known and generally accepted as correct. A set of conditions for its correctness is derived. It is shown that the proportionality factor (K factor) is independent of the dip angle of the bed, because both the thickness of the bed (measured along the borehole) and the area under the gross gamma‐ray log increase in the ratio of the secant of the dip angle. Experimental data supporting this conclusion are presented. It is also shown that the dip angle of a relatively thick bed can be estimated by deconvolving the log near the edge of the bed. Finally, the comparison parameters between a formation and a calibration model are shown to be grade, gamma‐ray mass attenuation coefficient, moisture content, and an integral function of the build‐up factor and the gamma‐ray linear absorption coefficient.
On: “A technique for the continuous representation of dispersion in seismic data” by J. C. Robinson (GEOPHYSICS, August 1979, p. 1345–1351).
Authors: Warren G. L.
Published: October 2002

Robinson’s paper concerns a topic of discussion in which geophysicists often find interest in attempting to describe the effect of the propagating medium on pulse wave shape and subsequently removing anelastic distortion. The present theory of linear anelastic wave propagation associates a dispersive mechanism and an absorptive mechanism with the change in pulse shape during propagation (Futterman, 1962; Ginzburg, 1955). In deference to causal considerations, these two mechanisms have been related to one another through the approximation of the Kramers‐Kronig relation.
Discrete inverse methods for elastic waves in layered media
Authors: Berryman James G. , Greene Robert R.
Published: October 2002

The seismic inverse problem for waves at normal incidence on horizontally layered media is discussed. The emphasis is theoretical rather than practical, but some long‐standing questions concerning the general applicability of the often taught Goupillaud inverse method are answered. The main purpose is to demonstrate in detail the equivalence between the Goupillaud method of inversion for the wave equation and the Marchenko integral equation (inverse scattering) method for the Schroedinger equation. We show that the very simple method of solution due to Goupillaud for a specialized model (layers of equal traveltime) actually has a much wider significance. If seismic data are smoothed before sampling using a type of antialiasing filter, the Goupillaud method gives a valid approximate inversion for models with arbitrary layer thicknesses (or continuous impedance variation) when the “reflection coefficients” are appropriately reinterpreted. In all, three inverse methods are considered: (1) the Goupillaud method for the wave equation and both (2) continuous and (3) discrete inverse scattering methods for the Schroedinger equation. A computationally fast algorithm for solving the inverse scattering formulas is deduced from the equivalent Goupillaud method. By comparing the continuous and discrete formalisms in the continuum limit, a preferred form is found within the class of symmetric tridiagonal discretizations of the Schroedinger equation. For the elastic wave inverse problem, two cases are distinguished: (1) If the impedance is continuous, we show that both the Goupillaud method and the discrete inverse scattering method converge to the impedance when the equal‐traveltime layer thickness goes to zero; and (2) if the impedance has a finite number of discontinuities, we show that the inverse scattering method assigns the arithmetic average across the discontinuity at the point of discontinuity, while the Goupillaud method assigns the value of the right‐hand (spatially deeper) limit. Thus, in the continuum limit, both methods will reconstruct the same impedance except (possibly) for the values at a finite number of jump points in any finite span of traveltime.
A generalized multibody model for inversion of magnetic anomalies
Authors: Bhattacharyya B. K.
Published: October 2002

The height of the observation surface above a magnetized region primarily determines the critical dimension of the smallest inhomogeneity in magnetization that can be resolved from magnetic survey data. When a rectangular block is smaller in size than this critical dimension, it appears homogeneously magnetized in the observed magnetic field. This consideration leads to the selection of a unit rectangular block of suitable dimensions with homogeneous magnetization. The magnetized region creating the anomalous field values in the area of observation can, therefore, be broken up into several blocks having different magnetizations, each block being equal in size and uniformly magnetized. The iterative method described here assumes initially that the anomalous field values are caused by a three‐dimensional (3-D) distribution of magnetized rectangular blocks. The optimum orientation of these blocks with respect to geographic north is then determined. This orientation is particularly insensitive to adjustments in the dimensions of the blocks. The top and bottom surfaces of each of the blocks in one or more layers are adjusted in a least‐squares sense to minimize the difference between observed and calculated field values. A method is also described for constraining the magnetization vector of each block to lie within a specified angle of the normal or reversed direction of the geomagnetic field vector. The procedure for analysis of data can also be extended to the case of anomalies over a draped surface. At the conclusion of the iterations, a 3-D distribution of magnetization is generated to delineate the magnetized region responsible for the observed anomalous magnetic field. Examples including model and aeromagnetic data are provided to demonstrate the usefulness of a generalized multibody model for inversion of magnetic anomalies.
Transient time‐domain electromagnetics
Authors: Kuo John T. , Cho Dong‐heng
Published: October 2002

For externally imposed electric and magnetic sources, the electromagnetic (EM) field equations may be derived from the symmetrical Maxwell’s equations. Two variational principles for the initial boundary‐value problem of electromagnetics are derived. The first one of the Gurtin type is deduced from the integro‐differential equations equivalent to the EM field equations, while the second one is a simplified version of the first variational principle. The variational field equations are placed in a form suitable for a finite‐element formulation in space. An explicit central‐differences scheme is then applied to the finite‐element variational equation to yield a recursive relation for time integration. The results from. Newmont electromagnetic pulse (EMP) survey done in the Mutooroo prospect in Australia are verified numerically. The finite‐element model which simulates the Mutooroo survey assumes a thin vertical dike embedded in conductive host rock that is overlain by a thick layer of conductive over‐burden. The effect of overburden on the time‐domain EM response appears first at the transmitter, continues to build up, eventually splits into two parts, and migrates away from the transmitter. As such, the effect of overburden is being migrated away, the effect of the deep‐seated dike and the host rock on the response emerges and decays. The calculated EMP anomalies due to the dike agree with the corresponding field survey results in their shapes and magnitudes. The zero crossover point of the antisymmetrical vertical magnetic component and the anomaly peak of the symmetrical horizontal magnetic component are located immediately above the dike on the surface, the magnitudes of which are quantitatively comparable. The electric field decays more slowly than the magnetic field and could provide additional information in the exploration of mineral deposits. The agreement between the finite‐element solution and the field results thus provides a means of interpreting time‐domain EM survey data.
Optimization of gamma‐ray logging techniques for uranium
Authors: Conaway John G. , Bristow Quentin , Killeen Patrick G.
Published: October 2002

In gamma‐ray logging for uranium exploration and evaluation, many factors affect the accuracy of the final processed log. This paper presents the results of a study of various logging and data processing parameters over which the logger can exercise control. These include probe velocity, sampling interval, detector length, and, in the case of analog recording, ratemeter time constant and chart paper depth scale. Numerous replications of gamma‐ray logs past the same sequence of radioactive zones varying one logging parameter at a time, combined with theoretical considerations, lead to some useful conclusions regarding the effects of those parameters on the accuracy and resolution of the logs, and the efficacy of deconvolution techniques under various conditions. In general, digital recording is preferable to analog recording because, with the latter, the accuracy of the computed grade‐thickness product can suffer as a result of the extra steps of converting count rate to an analog chart record and back again to digital form for processing. In the case of digital gamma‐ray logging for uranium, it appears that it is less important to log slowly for good statistical accuracy than it is to use a small sampling or digitization interval. Under the high count‐rate conditions encountered in uranium logging, the factors limiting the accuracy of the log are likely to be detector length (which limits spatial resolution) and geologic noise (e.g., inhomogeneities in the rock); logging more slowly does not remedy these problems. In cases where the recorded gamma‐ray flux is low, such as in lithologic correlation, it may still be necessary to log very slowly to achieve acceptable statistical reliability.
Depth migration before stack
Authors: Schultz Philip S. , Sherwood John W. C.
Published: October 2002

When seismic data are migrated using operators derived from the scalar wave equation, an assumption is normally made that the seismic velocity in the propagating medium is locally laterally invariant. This simplifying assumption causes reflectors to be imaged incorrectly when lateral velocity gradients exist, irrespective of the degree of accuracy to which the subsurface velocity structure is known. A finite‐difference method has been implemented for migration of unstacked data in the presence of lateral velocity gradients, where the operation of wave field extrapolation is done in increments of depth rather than time. Performing this depth migration on unstacked data results in the imaging of reflectors on the zero‐offset trace, whereupon a zero‐offset section becomes a fully imaged‐in‐depth seismic section. Such a section, in addition to being a correctly migrated depth section, shows the same order of signal amplitude enhancement as in a normal stacking process.
Algorithms for least‐squares linear prediction and maximum entropy spectral analysis—Part II: Fortran program
Authors: Barrodale I. , Erickson R. E.
Published: October 2002

We present a set of Fortran subroutines which implement the least‐squares algorithm described in Part I (Barrodale and Erickson, 1980, this issue) for solving three variants of the linear prediction problem. When combined with a suitable driver program, these subroutines can be used to calculate maximum entropy spectra without imposing a Toeplitz structure on the model.
A wide‐band electromagnetic exploration method—Some theoretical and experimental results
Authors: Won I. J.
Published: October 2002

Theoretical electromagnetic (EM) responses of a conductive circular cylinder in a conductive half‐space are obtained for a frequency range between 10 Hz and 30 kHz. The results show that the spectral characteristics can be used to determine the subsurface configuration of a target body, particularly in terms of its depth. Laboratory experiments using a wide‐band sweep‐frequency source provide support for the theoretical prediction of the spectral behavior. The experiment employed a harmonic EM source continuously sweeping logarithmically from 4 kHz to 4 MHz over a graphite slab submerged in a conductive solution. The results suggest that a wide‐band EM spectral profile displayed in a frequency‐distance space may provide many intuitive interpretation schemes which may not be possible with a single or discrete frequency profile.
Movement of radon in overburden
Authors: Soonawala N. M. , Telford W. M.
Published: October 2002

An analytical solution for simple one‐dimensional geometry establishes the basic theory of the movement of [Formula: see text] (radon) in overburden, involving diffusion and convection. The computer‐adapted finite‐difference method is then used to determine radon concentrations for the following more complex configurations: a two‐dimensional source, a vertical fault, a three‐dimensional source, and multilayered overburden. The key parameters are the radon concentration at the source, the diffusion coefficient of the overburden, and the geometry. This analysis indicates that if diffusion is the only transport process considered, the maximum depth at which uranium mineralization can be detected by the usual types of field equipment is limited to a few tens of meters. However, if convective transfer is also considered, radon attenuation is significantly decreased, e.g., by as much as a factor of 800 for a one‐dimensional configuration considered. It appears that an upward velocity component for the movement of radon, or geochemical dispersion of uranium and radium, are needed for long‐distance detection of uranium mineralization.
On: “A technique for the continuous representation of dispersion in seismic data (J. C. Robinson, GEOPHYSICS, August 1979, p. 1345–1351).
Authors: McNaughton Neal C.
Published: October 2002

At the risk of seeming pedantic, I would like to take issue with Robinson (1979) on his use of the word dispersion. From the Futterman (1962) relationship, Robinson shows that pulse broadening due to absorption must be accompanied by dispersion of the velocities of the component wavelengths. While this is certainly true, there is a tendency using this approach to regard dispersion as a by‐product of absorption. This is not the case in geometrical optics, where the dispersion of light passing through a prism, for instance, is not produced by absorption, as glass is virtually a loss free medium at optical frequencies.
COCORP South Carolina and Central Michigan data
Authors: Kaufman S.
Published: October 2002

The Consortium for Continental Reflection Profiling (COCORP) announces the availability of data packages for two areas, the Charleston, SC area and the Central Michigan area, for the cost of reproduction. These data were obtained by COCORP who are applying sophisticated, continuous seismic reflection techniques to the solution of geologic problems of the earth’s crust and upper mantle. The operation is part of the U.S. Geodynamics Project sponsored by the National Academy of Sciences and funded by the National Science Foundation. The executive committee of the consortium consists of members from Cornell University, University of Houston, Princeton University, the University of Texas at Austin, and the U.S. Geological Survey. Cornell University is the operating institution.
Modeling seismic impedance with Markov chains
Authors: Godfrey Robert , Muir Francis , Rocca Fabio
Published: October 2002

Acoustic impedance is modeled as a special type of Markov chain, one which is constrained to have a purely exponential correlation function. The stochastic model is parsimoniously described by M parameters, where M is the number of states or rocks composing an impedance well log. The probability mass function of the states provides M-1 parameters, and the “blockiness” of the log determines the remaining degree of freedom. Synthetic impedance and reflectivity logs constructed using the Markov model mimic the blockiness of the original logs. Both synthetic impedance and reflectivity are shown to be Bussgang, i.e., if the sequence is input into an instantaneous nonlinear device, then the correlation of input and output is proportional to the autocorrelation of the input. The final part of the paper uses the stochastic model in formulating an algorithm that transforms a deconvolved seismogram into acoustic impedance. The resulting function is blocky and free of random walks or sags. Low‐frequency information, as provided by moveout velocities, can be easily incorporated into the algorithm.
A borehole induction procedure for investigating electrical conductivity structure within the broad vicinity of a hole
Authors: Worthington M. H. , Kuckes A. , Oristaglio M.
Published: October 2002

A field test was carried out of a controlled‐source induction procedure in which a source loop was positioned on the surface of the ground encircling a borehole, and the horizontal component of the magnetic field was measured within the hole. The problem of measuring the component of an alternating magnetic field at right angles to a small diameter hole was overcome by the construction of a μ‐metal frame for the induction coil that greatly increased the effective cross‐section of the coil. Data obtained with this configuration of source and receiver are dependent upon the electrical conductivity of the ground within a broad region around the hole. The method is effective in providing constraints on the location and distribution of regions of anomalous electrical conductivity which are not revealed by the drilling operation. These conclusions are supported by theoretical estimates of the magnetic field that would result from known conductivity distributions obtained using finite element techniques.
In situ determination of heat flow in unconsolidated sediments
Authors: Sass J. H. , Kennelly J. P. , Wendt W. E. , Moses T. H. , Ziagos J. P.
Published: October 2002

Subsurface thermal measurements are the most effective, least ambiguous tools for locating geothermal resources. Measurements of thermal gradient in the upper few tens of meters can delineate the major anomalies, but it is also desirable to combine these gradients with reliable estimates of thermal conductivity, to provide data on the energy flux and to constrain models of the heat sources responsible for the anomalies. Problems associated with such heat flow measurements include the economics of casing or grouting holes, the long waits and repeated visits necessary to obtain equilibrium temperature values, the possible legal liability arising from disturbance of aquifers, the hazards presented by pipes protruding from the ground, and the security problems associated with leaving cased holes open for periods of weeks to months.
Estimating acoustic attenuation from a quantitative seismic profiler
Authors: Tyce Robert C.
Published: October 2002

Recent work has indicated that acoustic attenuation in marine sediments can be estimated from thin wedges of sediment by means of a quantitative seismic profiler. A capability for near‐bottom seismic profiling at 4 kHz has been developed at the Scripps Institution of Oceanography Marine Physical Laboratory and utilized to determine effective attenuation for several areas of the sea floor. As part of the deep‐tow instrumentation system of the Marine Physical Laboratory, this profiler provides very high lateral resolution. Real time computer displays of equivalent plane‐wave pressure and intensity for seismic profiles have been developed as part of this system. These displays are produced on a standard graphic recorder and can be employed directly to determine effective attenuation by plotting displayed equivalent intensity as a function of depth of burial for a reflector covered by a wedge of sediment. For pelagic sediments, values of about 0.25 dB/m at 4 kHz appear to be common. For the Southern California borderland, a wide range of sediment types is observed, with measured values of effective attenuation ranging from 0.21 to 0.63 dB/m. Highly calcareous (85 percent carbonate) sediments of the Carnegie ridge give quite low values, from 0.1 to 0.2 dB/m, with a suggestion of a rapid decrease in attenuation with depth. For nonbiogenous sediments, values of effective attenuation appear useful for predicting other physical properties such as grain size and porosity, as well as general sediment type, from established interrelations.
A novel approach to seismic signal processing and modeling
Authors: Mendel Jerry M. , Kormylo John , Aminzadeh Fereydoun , Lee Ja Sung , Habibi‐Ashrafi Farroukh
Published: October 2002

This paper demonstrates some results obtained using state‐variable models and techniques on problems for which solutions either cannot be or are not easily obtained via more conventional input‐output techniques. After a brief introduction to state‐variable notions, the following seven problem areas are discussed: modeling seismic source wavelets, simultaneous deconvolution and correction for spherical divergence, simultaneous wavelet estimation and deconvolution, well log processing, design of recursive Wiener filters, Bremmer series decomposition of a seismogram (including suppression of multiples and vertical seismic profiling), and estimating reflection coefficients and traveltimes.
Wavelet estimation and deconvolution
Authors: Oldenburg D. W. , Levy S. , Whittall K. P.
Published: October 2002

Three methods have been presented for constructing a smooth wavelet from either a (possibly poor) estimate of the reflectivity sequence or an approximate inverse filter for the source wavelet. An approximate reflectivity sequence might be derived from a velocity log at, or near, the site where the normal incidence seismogram was recorded, or it might be equated to the averages obtained from minimum entropy deconvolution (MED). The approximate inverse filter for the source wavelet is provided by MED. All methods performed well when tested on data generated from wavelets of different character, and this provides optimism that these methods will work satisfactorily in a variety of geophysical problems where the data are the convolution of a smooth wavelet and a “spikey” model. The deconvolution problem discussed here is nonunique, and satisfactory wavelet constructions require that some subjectivity be introduced by the investigator. Even so, we present one example where the computed wavelet and reflectivity sequence, both of which appear geophysically reasonable, differed significantly from the “true” functions. This example illustrates the nonuniqueness inherent in this problem and shows the importance of additional constraints on the deconvolution results.
Maximum uncertainty of interval velocity estimates
Authors: Hajnal Z. , Sereda I. T.
Published: October 2002

The Dix equation (Dix, 1955) is commonly used to estimate interval velocities from stacking velocity and travel‐time information. The errors in these estimates can result from a number of factors, including indiscriminate substitution of stacking velocities for root‐mean‐square (rms] velocities without compensating for the effects of spread‐length or dipping reflectors. A first‐order error equation has been developed which estimates the maximum uncertainty for Dix‐derived interval velocities when the accuracy of the input rms velocity and normal incidence time information is considered. Some simple numerical experiments using this equation indicate that the uncertainty in the calculated interval velocity increases with depth and is inversely proportional to layer thickness, even when the errors in the input velocity and time variables remain constant.
Seismic data display and reflection perceptibility
Authors: Feagin Frank J.
Published: October 2002

Relatively little attention has been paid to the final output of today’s sophisticated seismic data processing procedures—the seismic section display. We first examine significant factors relating to those displays and then describe a series of experiments that, by varying those factors, let us specify displays that maximize interpreters’ abilities to detect reflections buried in random noise. The study.—From psychology of perception and image enhancement literature and from our own research, these conclusions were reached: (1) Seismic reflection perceptibility is best for time scales in the neighborhood of 1.875 inches/sec because, for common seismic frequencies, the eye‐brain spatial frequency response is a maximum near that value. (2) An optimized gray scale for variable density sections is nonlinearly related to digital data values on a plot tape. The nonlinearity is composed to two parts (a) that which compensates for nonlinearity inherent in human perception, and (b) the nonlinearity required to produce histogram equalization, a modern image enhancement technique. The experiments.—The experiments involved 37 synthetic seismic sections composed of simple reflections embedded in filtered random noise. Reflection signal‐to‐noise (S/N) ratio was varied over a wide range, as were other display parameters, such as scale, plot mode, photographic density contrast, gray scale, and reflection dip angle. Twenty‐nine interpreters took part in the experiments. The sections were presented, one at a time, to each interpreter; the interpreter then proceeded to mark all recognizable events. Marked events were checked against known data and errors recorded. Detectability thresholds in terms of S/N ratios were measured as a function of the various display parameters. Some of the more important conclusions are: (1) With our usual types of displays, interpreters can pick reflections about 6 or 7 dB below noise with a 50 percent probability. (2) Perceptibility varies from one person to another by 2.5 to 3.0 dB. (3) For displays with a 3.75 inch/sec scale and low contrast photographic paper (a common situation), variable density (VD) and variable area‐wiggly trace (VA‐WT) sections are about equally effective from a perceptibility standpoint. (4) However, for displays with small scales and for displays with higher contrast, variable density is significantly superior. A VD section with all parameters optimized shows about 8 dB perceptibility advantage over an optimized VA‐WT section. (5) Detectability drops as dip angle increases. VD is slightly superior to VA‐WT, even at large scales, for steep dip angles. (6) An interpreter gains typically about 2 dB by foreshortening, although there is a wide variation from one individual to another.
Deepwater vibrator operations—Beaufort Sea, Alaska, 1979, winter season
Authors: Mertz R. W. , Brooks Lonnie D. , Lansley Malcolm
Published: October 2002

During the four‐month period January—April, 1979, a relatively extensive seismic survey was undertaken by Sohio Petroleum Co. in the offshore Beaufort Sea area. This discussion is simply a case history of the project from the planning stage through its conclusion. Example data and production statistics are given.
COCORP Oklahoma Area, Part I
Authors: Kaufman S.
Published: October 2002

The Consortium for Continental Reflection Profiling (COCORP) announces the availability of the data package and tapes for the Oklahoma area, part I, for the cost of reproduction. These data were obtained by COCORP who are applying sophisticated, continuous seismic reflection techniques to the solution of geologic problems of the earth's crust and upper mantle. The operation is part of the U.S. Geodynamics Project sponsored by the National Academy of Sciences and funded by the National Science Foundation. The executive committee of the consortium consists of members from Cornell University, University of Houston, Princeton University, the University of Texas at Austin, and the U.S. Geological Survey. Cornell University is the operating institution.
Ultrasonic velocities in Cretaceous shales from the Williston basin
Authors: Jones Leonie E. A. , Wang Herbert F.
Published: October 2002

Compressional and shear‐wave velocities were measured in the laboratory from 1 bar to 4 kbar confining pressure for wet, undrained samples of Cretaceous shales from depths of 3200 and 5000 ft in the Williston basin, North Dakota. These shales behave as transversely isotropic elastic media, the plane of circular symmetry coinciding with the bedding plane. For compressional waves, the velocity is higher for propagation in the bedding plane than at right angles to it, and the anisotropy is greater for the 5000-ft shale. For shear waves, the SH‐wave perpendicular to bedding and the SV‐wave parallel to bedding propagate with the same speed, which is about 25 percent lower than that for the SH‐wave parallel to bedding. In general, compressional and shear velocities are higher for the indurated 5000-ft shale than for the friable 3200-ft shale. All velocities increase with in‐increasing confining pressure to 4 kbar. The 3200-ft shale exhibits velocity hysteresis as a function of pressure, whereas this effect is almost nonexistent for the 5000-ft shale. Many features of the dependence of velocity on pressure can be explained by consideration of effective pressure and the degree of water saturation. For both shales, laboratory compressional wave velocities are on average 10 percent higher than log‐derived velocities. The discrepancy cannot be explained completely, but likely contributing factors are sampling bias, velocity dispersion, and formation damage in situ.
Time‐depth and velocity‐depth relations in sedimentary basins—A study based on current investigation in the Arctic Islands and an interpretation of experience elsewhere
Authors: Acheson C. H.
Published: October 2002

Velocities of P‐waves in the Arctic Islands obey the same power‐law equations (1) [Formula: see text], (2) [Formula: see text] that apply to Western Canada (Acheson, 1963). They appear to be closely related to the theoretical one‐sixth power law (n = 5/6) derived by Gassmann (1950), Brandt (1955), and others. Equations (1) and (2) are piece‐wise continuous at any given location and consist of a number of discrete segments corresponding to geologic units, each characterized by a distinct set of values for a, b, c, and n. Except for a limited number of velocity anomalies such as permafrost, these units relate to formations or groups of formations. Velocity changes in a, c, and n correspond to major changes in lithology, pressure, or compaction. Velocity fluctuations within the formations caused by variation in grain size, porosity, fluid‐to‐matrix coupling, and so on are not indicated in this analysis, and the velocity‐depth relation refers to secular velocity variation only. Correlation of reported velocity findings from many parts of the world through a common relationship to the one‐sixth power law suggests this system of equations has widespread, possibly global, application to important geophysical problems of many kinds.
The theoretical seismic reflection response of sedimentary sequences
Authors: Velzeboer C. J.
Published: October 2002

A sedimentary sequence can quite often be considered very fruitfully as a discrete Markov chain, and thus can be described by a stochastic matrix. Knowing this matrix and the thickness probability distributions of the layers of the various participating lithologies, while assuming that their densities and velocities are normally distributed, an expression is derived for the autocorrelation (or power spectrum) of the seismic reflection response. This expression can bring out essential characteristics of the power spectra, i.e., the low‐frequency droop and its slope. This then leads to the possible estimation of some physical and sedimentary parameters of the sequence such as the scatter of the reflection coefficients and the sand‐shale ratio or sedimentary cycle thickness. The case of a binary sequence, as the predominant sequence of the sediments of the Gulf Coast area and Nigeria, is analyzed in detail. The theoretical results conform well with field data and lead to the interesting conclusion that indeed the estimation of the above mentioned parameters is possible.
Modeling of the acoustic wave equation with transform methods
Authors: Gazdag Jenö
Published: October 2002

Numerical methods are described for the simulation of wave phenomena with application to the modeling of seismic data. Two separate topics are studied. The first deals with the solution of the acoustic wave equation. The second topic treats wave phenomena whose direction of propagation is restricted within ±90 degrees from a given axis. In the numerical methods developed here, the wave field is advanced in time by using standard time differencing schemes. On the other hand, expressions including space derivative terms are computed by Fourier transform methods. This approach to computing derivatives minimizes truncation errors. Another benefit of transform methods becomes evident when attempting to restrict propagation to upward moving waves, e.g., to avoid multiple reflections. Constraints imposed on the direction of the wave propagation are accomplished most precisely in the wavenumber domain. The error analysis of the algorithms shows that truncation errors are due mainly to time discretization. Such errors can be limited by the choice of the time step. Perhaps the most significant error phenomenon is related to aliasing. This becomes noticeable when a narrow pulse traverses a region with strong velocity variations. It is shown that aliasing errors can be limited by the choice of the pulse width. The feasibility of these modeling methods is demonstrated on numerical examples.
Synthetic vertical seismic profile
Authors: Wyatt K. Dautenhahn
Published: October 2002

A time‐domain model has been developed for calculation of a synthetic vertical seismic profile (SVSP) from a sonic log recorded in a borehole. The SVSP has proven to be extremely useful in the interpretation of seismic data since it allows the interpreter to analyze the propagation of the source pulse through the earth in depth as well as time. Previously, the synthetic seismogram technique allowed analysis of the earth’s response to the source pulse at the surface only. However, the development of the SVSP allows insight into the entire wave propagation problem since the calculation shows the response of the earth to the source pulse at any depth point in the subsurface. For example, the synthetic seismogram can be used to identify an event on the seismic section as a multiple, whereas, the SVSP cannot only identify a multiple, but can also show which path the source pulse took through the earth layers to create the multiple. The SVSP can also be used to analyze the change in character of the source pulse due to the layering effect of the earth, for example, effects of a thin bed sequence; to study amplitude variations due to transmission losses; and to examine the effects of different source pulse bandwidths on the final surface seismogram, etc. As interpreters gain experience in analyzing the SVSP, many more applications are expected to appear.