bluuebunny/crossref_metadata_2025 huggingface dataset:
Evidence for recurrent faulting in the New Madrid seismic zone from Mini‐Sosie high‐resolution reflection data
Authors: Sexton John L. , Jones Paul B.
Published: October 2002

A Mini‐Sosie™ high‐resolution seismic reflection survey was conducted on Reelfoot scarp in the northwestern Tennessee portion of the New Madrid seismic zone. Interpretation of the Mini‐Sosie data revealed the need to reinterpret previously collected reflection data obtained from explosive source and Vibroseis® surveys. Interpretation and integration of the three data sets have resulted in a new model for the subsurface of Reelfoot scarp and provide evidence for recurrent movement along Reelfoot fault, the major reverse fault associated with Reelfoot scarp. Estimated displacements on Reelfoot fault vary from 60 m (60 ms) for late Paleozoic rocks to 15 m (20 ms) for late Eocene sedimentary units. No clear offsets are observed on this particular fault for units younger than late Eocene age; however, uplift, folding, and related structures are observed in younger sediments. An observed variation of offset with depth (age) and the presence of the younger structures are evidence of reactivation of Reelfoot fault. Small‐offset (10 to 20 m) faults were also detected and have been interpreted to have constant displacement with depth, and therefore, to have occurred as a single faulting event rather than as recurrent movement on a fault plane. Two of these faults are interpreted to have been formed in the middle to late Eocene. A small reverse fault located a few hundred feet east of Reelfoot fault appears to be a single faulting event which extends into sediments of Holocene age. There is a small displacement graben structure which probably extends into Holocene age sediments near the apex of the folded sediments of Reelfoot scarp. The location of the graben structure coincides with a zone of small‐offset nomal faulting with 2 to 3 m of total offset within Holocene sediments observed in a trench excavated over Reelfoot scarp. This small zone of faulting has previously been interpreted to be of tectonic origin. The close association of the faults observed in the trench and the graben structure observed on the seismic data suggests that the two features are directly related, and that both structures were formed by Holocene‐era reactivation of Reelfoot fault. Additional evidence supporting our interpretation is provided by synthetic seismograms for models derived from the various data sets and paleosections of the high‐resolution reflection data. A fault map based on all the reflection data shows that our interpretation is consistent with the data sets.
Bayesian deconvolution of gamma‐ray logs
Authors: Sheng Ping , White Benjamin , Nair Balan , Kerford Sandra
Published: October 2002

The spatial resolution of gamma‐ray logs is defined by the length 𝓁 of the gamma‐ray detector. To resolve thin beds whose thickness is less than 𝓁, it is generally desirable to deconvolve the data to reduce the averaging effect of the detector. However, inherent in the deconvolution operation is an amplification of high‐frequency noise, which can be a detriment to the intended goal of increased resolution. We propose a Bayesian statistical approach to gamma‐ray log deconvolution which is based on optimization of a probability function which takes into account the statistics of gamma‐ray log measurements as well as the empirical information derived from the data. Application of this method to simulated data and to field measurements shows that it is effective in suppressing high‐frequency noise encountered in the deconvolution of gamma‐ray logs. In particular, a comparison with the least‐squares deconvolution approach indicates that the incorporation of physical and statistical information in the Bayesian optimization process results in optimal filtering of the deconvolved results.
Test of National Uranium Resource Evaluation gamma‐ray spectral data in petroleum reconnaissance
Authors: Saunders Donald F. , Terry Stephen A. , Thompson C. Keith
Published: October 2002

Advances in interpretation techniques have made possible effective use of aerial high‐sensitivity gamma‐ray spectral data to explore for petroleum in selected environments. These data were collected by the U.S. Department of Energy during the National Uranium Resource Evaluation (NURE) program throughout the conterminous U.S. and most of Alaska between 1974 and 1981. The tests reported here were limited to portions of the following 1 degree by 2 degree National Topographic Map Series (NTMS) quadrangles: the west half of the Palestine quadrangle, the east half of the San Angelo quadrangle, and the southeast quarter of the Big Spring quadrangle, all of which are in Texas. The radiometric uranium and potassium data were normalized for surface lithology (including soil differences), as well as for variations in counting geometry and hydrologic conditions, using a new technique based on thorium measurements and geochemical relationships between thorium and potassium and between thorium and the uranium series. Uncontrolled effects of these variables have made many previous attempts at applying radiometric methods in petroleum prospecting essentially meaningless. The thorium‐based normalization approach described here resulted in anomalously low adjusted potassium values over most of the oil fields considered. Adjusted uranium analyses showed low anomalies over oil in east Texas and high anomalies in west Texas. The reasons for the different behavior of the uranium data are poorly understood, but they are attributed tentatively to the effects of the different climates on the distribution of the uranium series elements in very near‐surface soils. This application of high‐sensitivity gamma‐ray spectrometry has regional advantages and limitations, which depend on the nature, origin, moisture content, and possible shielding cover of the surface soils. If these factors are carefully considered, the NURE radiometric data offer promise as an inexpensive reconnaissance guide to help locate new onshore oil and gas prospects or possible field extensions in the East Texas Basin, the west Texas area, and similar environments.
Counting statistics in radioelement assaying with a portable spectrometer
Authors: Løvborg Leif , Mose Erik
Published: October 2002

Counting performed with a portable gamma‐ray spectrometer to assay the concentrations of potassium, uranium, and thorium in the ground normally lasts between 1 and 10 minutes. The statistical uncertainties of the count rates measured in the energy windows are taken into consideration by ascribing standard deviations to the calculated assay values. Such a standard deviation is primarily governed by the counts recorded in two neighboring energy windows. A potassium standard deviation, for example, depends not only on the counts in the potassium window, but is also affected by the mixed uranium‐thorium counts recorded in the uranium window. Counting times of 1, 2, 4, and 10 minutes are normally appropriate in assaying uranium concentrations of 10 to 13, 5 to 7, ∼3, and ∼1.5 ppm eU. By counting for 10 minutes, it may be possible to detect unusually small radioelement concentrations of 0.5 ppm eTh, 0.3 ppm eU, and 0.04 percent K. However, the smallest concentrations that can be measured with a precision of 10 percent amount to about 2 ppm eTh, 1 ppm eU, and 0.15 percent K. Low‐grade uranium ore with whole‐rock concentrations of 100 to 800 ppm eU must contain at least 20 to 100 ppm eTh before reliable thorium assay values can be provided by counting for 1 minute. The corresponding uranium determination limits on thorium mineralizations carrying from 400 to 1 600 ppm eTh are from about 100 to almost 200 ppm eU. Usable potassium assay values are generally not obtained from a ground that contains more than 200 ppm eU or 400 ppm eTh.
Suppressing the unwanted reflections of the full wave equation
Authors: Loewenthal Dan , Stoffa Paul L. , Faria Eduardo L.
Published: October 2002

In many instances in exploration geophysics we are interested in the so‐called one‐way wave equation. This equation allows the wave fields to propagate in the positive depth direction, but not in the reverse (−Z) direction. Some modeling and migration methods, such as the f-k method (Stolt, 1978) and the phase‐shift method (Gazdag, 1978), produce in a natural way the one‐way wave equation. The main advantage of the one‐way wave equation is that it does not give rise to multiples or interlayer reverberations and enables the observation of primary events only.
Investigation of a surface spectral anomaly at Table Rock gas field, Wyoming
Authors: Marrs Ronald W. , Paylor Earnest D.
Published: October 2002

Airborne spectroradiometer data reveal an unusual pattern of near‐infrared reflectance at the exposed center of Table Rock anticline, Sweetwater County, Wyoming. The feature is represented by a reflectance minimum near 2200 nm, characteristic of areas with abundant clay minerals. Smectite and mixed‐layer illite‐smectite were found associated with the anomalous spectral feature. Concentrations of iron and sulfate minerals in the soils at the center of the clay‐rich zone correspond roughly to an area of red coloring in the Wasatch formation exposed at the highest structural elevation in the center of the anticline. A photogeologic interpretation of Thematic Mapper Simulator (TMS) image data was made for the Table Rock area. Stratigraphic and structural details of the interpretation are excellent and provide greater detail than do available maps of the area. Structural analysis suggests that at least two episodes of stress affected the area. The greatest concentration of fractures occurs at the crest of the anticline and is coincident with the spectrally anomalous region. The investigation indicates that the mineralogic pattern at the surface of Table Rock anticline could result from a geochemical transformation process. Ground‐waters, with ionic concentrations in the stability field of smectite, are being drawn through fractures to the surface in the anomalous region. Evaporation and fluid replacement in the near‐surface are accelerated. Illites apparently become unstable in the near‐surface and transform into a more stable phase of smectite. Gypsum, jarosite, and carbonate cement concentrations at the surface further support this assumption and suggest a possible influence of escaping hydrocarbon reservoir gases. This process is consistent with models proposed for the formation of petroleum‐related surface anomalies. However, a cause‐and‐effect relationship between the petroleum accumulation and the surface anomaly could not be established.
Near‐infrared detection of ammonium minerals
Authors: Krohn M. Dennis , Altaner Stephen P.
Published: October 2002

Diagnostic near‐infrared spectral features have been identified for minerals with ammonium [Formula: see text] bound in the crystal structure. Spectral bands near 2.12, 2.02, and 1.56 μm are characteristic of synthetic and natural [Formula: see text] minerals. Laboratory spectra of [Formula: see text] minerals are distinct from spectra of OH‐bearing minerals and have diagnostic shifts in band position among different mineral types. [Formula: see text] minerals were detected at several mineralized hot‐spring deposits in the western U.S. by means of hand‐held and airborne instruments. Near‐infrared detection of [Formula: see text] minerals may provide useful information for prospecting for certain ore deposits and may provide a better understanding of the nitrogen cycle within geologic environments.
On the imaging of reflectors in the earth
Authors: Bleistein Norman
Published: October 2002

In this paper, I present a modification of the Beylkin inversion operator. This modification accounts for the band‐limited nature of the data and makes the role of discontinuities in the sound speed more precise. The inversion presented here partially dispenses with the small‐parameter constraint of the Born approximation. This is shown by applying the proposed inversion operator to upward scattered data represented by the Kirchhoff approximation, using the angularly dependent geometrical‐optics reflection coefficient. A fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these Kirchhoff‐approximate data for the forward problem. The inversion of these data involves integration over the source‐receiver surface, the reflecting surface, and frequency. The spatial integrals are computed by the method of stationary phase. The output is asymptotically a scaled singular function of the reflecting surface. The singular function of a surface is a Dirac delta function whose support is on the surface. Thus, knowledge of the singular functions is equivalent to mathematical imaging of the reflector. The scale factor multiplying the singular function is proportional to the geometrical‐optics reflection coefficient. In addition to its dependence on the variations in sound speed, this reflection coefficient depends on an opening angle between rays from a source and receiver pair to the reflector. I show how to determine this unknown angle. With the angle determined, the reflection coefficient contains only the sound speed below the reflector as an unknown, and it can be determined. A recursive application of the inversion formalism is possible. That is, starting from the upper surface, each time a major reflector is imaged, the background sound speed is updated to account for the new information and data are processed deeper into the section until a new major reflector is imaged. Hence, the present inversion formalism lends itself to this type of recursive implementation. The inversion proposed here takes the form of a Kirchhoff migration of filtered data traces, with the space‐domain amplitude and frequency‐domain filter deduced from the inversion theory. Thus, one could view this type of inversion and parameter estimation as a Kirchhoff migration with careful attention to amplitude.
Nonlinear integral equations for electromagnetic inverse problems
Authors: Gómez‐Treviño E.
Published: October 2002

The scaling properties of Maxwell’s equations allow the existence of simple yet general nonlinear integral equations for electrical conductivity. These equations were developed in an attempt to reduce the generality of linearization to the exclusive scope of electromagnetic problems. The reduction is achieved when the principle of similitude for quasi‐static fields is imposed on linearized forms of the field equations. The combination leads to exact integral relations which represent a unifying framework for the general electromagnetic inverse problem. The equations are of the same form in both time and frequency domains and hold for all observations that scale as electric and magnetic fields do; direct current resistivity and magnetometric resistivity methods are considered as special cases. The kernel functions of the integral equations are closely related, through a normalization factor, to the Frechét kernels of the conventional equations obtained by linearization. Accordingly, the sensitivity functions play the role of weighting functions for electrical conductivity despite the nonlinear dependence of the model and the data. In terms of the integral equations, the inverse problem consists of extracting information about a distribution of conductivity from a given set of its spatial averages. The form of the new equations leads to the consideration of their numerical solution through an approximate knowledge of their kernel functions. The integral equation for magnetotelluric soundings illustrates this approach in a simple fashion.
Multiborehole seismic imaging in steam injection heavy oil recovery projects
Authors: Macrides Costas G. , Kanasewich Ernest R. , Bharatha S.
Published: October 2002

Crosshole seismic measurements before and after steam injection were obtained for the purpose of delineating the fluid‐invaded zone. The experiment, despite its limited temporal and spatial sampling, showed significant changes in seismic signature after steam injection. A single chemical explosive seismic source was fired repeatedly at a fixed depth within the source well, for various positions of a receiver clamped within the receiver well. The seismic records of the “before” and “after” (steam flood) experiments were normalized by using the tube waves. Important results were obtained from power spectral studies which show significant changes after fluid injection. For higher resolution and increased constraints on the determination of the steam‐invaded zone, a more sophisticated cross‐hole experiment has been designed. Computer simulation of the proposed experiment has been carried out assuming an asymmetrical shape for the steam zone. Inversion via a tomographic approach by solution of an overdetermined system of linear equations produced reconstructions that were in good agreement with the assumed shape and P wave velocity of the steam zone.
Seismic velocity and Q model for the shallow structure of the Arabian shield from short‐period Rayleigh waves
Authors: Mokhtar T. A. , Herrmann R. B. , Russell D. R.
Published: October 2002

The shear velocity and [Formula: see text] structure for the upper 1 km in different tectonic regions of the Arabian shield have been investigated using high‐frequency vertical component records of Rayleigh waves (1–20 Hz), which were recorded at source‐to‐receiver separations 55–80 km during a deep seismic refraction survey. Group and phase velocities of the fundamental and first higher modes were inverted for the shear‐wave velocity structure; Rayleigh‐wave attenuation coefficients were determined from the decay of the amplitude spectrum of the fundamental mode and used to invert for the [Formula: see text] structure. Models derived from the data were tested by calculating synthetic seismograms for the fundamental and the first higher modes from surface‐wave theory with a center of compression used to represent the source; both band‐pass filtered step and Dirac delta source time functions were tested. Modeling indicates that the shear‐wave velocity of the shield increases from 2.6 km/s to 3.4 km/s in the upper 400 m of the crust. [Formula: see text] increases from 30 in the upper 50 m to 150 at 500 m depth. The underlying material has a [Formula: see text] of 400–500 for the out‐cropping igneous rocks such as granite and may reach values higher than 700 for the metamorphic green schist rock. A band‐pass filtered Dirac delta source time function produces the synthetic that is the best fit with observations.
Aspects of time‐variant filtering
Authors: Scheuer Tim , Oldenburg Douglas W.
Published: October 2002

We develop a computationally efficient time‐variant filter with idealized band‐pass characteristics, i.e., with a time‐variant boxcar‐like frequency spectrum. The filter can either be zero phase, or it can effect a time‐variant phase rotation of the input data. The instantaneous low‐frequency and high‐frequency cutoffs are independent, continuous time functions that are specified by the user. In addition, frequency‐domain rolloff characteristics of the filter can be prescribed, but the achieved spectrum depends on the length of the applied filter and the instantaneous frequency cutoffs used. The primary derivation of our theory for time‐variant filtering depends upon the properties of the complex signal and the complex delta function. This formulation is particularly insightful because of the geometrical interpretation it offers in the frequency domain. Basically, a high‐pass filter can be implemented by shifting the Fourier transform of the complex signal towards the negative frequency band, annihilating that portion of the signal that lies to the left of the origin, and then shifting the truncated spectrum back to the right. This geometrical insight permits us to infer the mathematical form of a general time‐variant band‐pass filter. In addition, we show that our time‐variant filter reduces to a Hilbert transform filter when the derivation is constrained to include real signal input.
Lithology discrimination for thin layers using wavelet signal parameters
Authors: Lange James N. , Almoghrabi H. A.
Published: October 2002

A forward modeling technique using Ricker wavelets demonstrates the need for a multiparameter approach in lithology determination using reflections from thin layers. The combination of time‐ and frequency‐domain analyses leads to a set of algorithms which define pore fluid and lithology from wavelet characteristics. The dispersive behavior of the thin layer varies considerably with the environment surrounding the layer, resulting in characteristic frequency‐domain behavior. With a limited prior knowledge of the formation environment, the pore fluid type can be determined using mode‐converted waves in the frequency domain.
Attenuation of complex water‐bottom multiples by wave‐equation‐based prediction and subtraction
Authors: Wiggins J. Wendell
Published: October 2002

Multiple reflections that are generated by the water bottom in marine seismic data can be predicted by a combination of numerical wave extrapolation through the water layer and estimation of the water‐bottom reflectivity. Attenuation of the multiples occurs when the predicted wave field is subtracted from the original record. I derive the expressions needed for prediction of the multiples, following the ideas of Morley, in a form that can be used to estimate the reflectivity of a water bottom that has a complex shape and has a reflectivity that varies with lateral position, frequency, and reflection angle. The specific form of the operations needed for prediction is implemented without assumptions about the simplicity or flatness of the water bottom. The derivation implies that the recorded wave field may be interpreted as both an upgoing and a downgoing wave. This interpretation is correct except for a simple surface ghost present in both interpretations. Application of the predictive method to data collected over a hard, complex water bottom demonstrates that it effectively attenuates water‐bottom and peg‐leg multiples even when the water bottom is complex and changes in character within the span of a shot gather. The same data were processed with various combinations of predictive attenuation, prestack automatic gain control, prestack moveout discrimination, and stacking. The multiple attenuation achieved with the predictive method alone was greater than that achieved by moveout discrimination alone; the net attenuation achieved by sequential application of all the methods was approximately additive.
Why is the Biot slow compressional wave not observed in real rocks?
Authors: Klimentos Theodoros , McCann Clive
Published: October 2002

A general theory for the propagation of elastic waves in porous, fluid‐filled media was derived by Biot (1956a, b). A fundamental prediction of this theory is the existence of three body waves: a shear wave, a fast compressional wave, and a slow compressional wave.
A theory for marine source arrays
Authors: Duren Richard E.
Published: October 2002

General mathematical expressions for a marine source array’s (1) far‐field pulse spectrum, (2) radiated energy density, and (3) directivity are developed for both a source in an infinite homogeneous medium and a source operating near the ocean surface. These results, intended to assist the analysis and design of marine source arrays, apply to any marine source array when (1) individual elements radiate isotropically, (2) their individual waveforms are specified, and (3) the array geometry is specified. Arbitrary geometry and arbitrary isotropic waveforms are allowed. The theory assumes linear superposition of the individually specified waveforms, and is consistent with the “square law effect” for identical elements. For an array of small elements, expended energy agrees with the array’s radiated energy found using far‐field methods. Also, the energy radiated from an array with large element spacing is equal to the sum of the independently radiated energies. Two closely spaced identical elements radiate four times the energy contained in a single outgoing waveform over all space. The appropriate directivity definition for marine seismic sources is the ratio of the radiated energy density per unit solid angle in a particular direction to the average radiated energy density per unit solid angle. This definition allows directivity to be expressed explicitly in terms of the individual frequency spectra and geometry.
On: “Results of a controlled‐source audiofrequency magnetotelluric survey at the Puhimau thermal area, Kilauea Volcano, Hawaii” by L. C. Bartel and R. D. Jacobson (GEOPHYSICS, 52, 665–677, May 1987).
Authors: Maurer Hans‐Martin
Published: October 2002

Bartel and Jacobson try to correct apparent resistivity values from CSAMT measurements, where the plane‐wave approximation is not valid. They want to convert CSAMT curves to passive MT curves (Cagniard curves), which can be interpreted by 2-D modeling. The measured CSAMT [Formula: see text] value is projected onto the [Formula: see text] axis in parallel with the half‐space curves of a horizontal electrical dipole in the given distance between receiver and transmitter. The example looks convincing, and it may be supposed to be a simple near‐field correction.
Shear‐wave velocity anisotropy in sedimentary rocks: A laboratory study
Authors: Rai Chandra S. , Hanson Kenneth E.
Published: October 2002

A systematic laboratory study of shear‐wave velocity anisotropy in sedimentary rocks has been carried out as a function of both hydrostatic and uniaxial stress. The presence of shear‐wave velocity anisotropy in sedimentary rocks was confirmed by transmitting a polarized shear wave in a rock sample and receiving a signal on an orthogonally polarized receiver. The magnitude of the observed velocity anisotropy is dependent upon the magnitude and nature of the applied stress and the lithology of the rock sample. Shales exhibit significant velocity anisotropy independent of both uniaxial and hydrostatic stress, which suggests the presence of preferentially aligned minerals. Sandstones also exhibit significant velocity anisotropy, but the anisotropy is strongly dependent upon the stress. Hydrostatic stress was found to diminish the velocity anisotropy and uniaxial stress was found to enhance it. This implies the presence of preferentially oriented cracks. Limestones exhibit weak velocity anisotropy. These laboratory observations may be helpful in in situ identification of lithology.
Separation of signal and noise applied to vertical seismic profiles
Authors: Harlan William S.
Published: October 2002

Inversion of the band‐limited one‐dimensional VSP response is nonunique because impedance functions with very different statistics produce equivalent responses. Least‐squares methods of inversion linearly transform noise and tend to produce impedance functions with a Gaussian distribution of amplitudes. I modify a least‐squares inversion procedure to exclude nonzero impedance derivatives that are significantly influenced by noise. The resulting earth model shows homogeneous intervals unless the data have reliable information to the contrary. The data are modeled with a one‐dimensional wave equation and three invertible functions: acoustic impedance, a source wavelet, and the traces’ amplification. First, a linearized least‐squares inverse perturbs the source function to model the downgoing wave. A relinearized inverse finds perturbations of all three modeling functions to account for first‐order reflections. Further iterations explain higher order reflections. To estimate the reliability of impedance perturbations, each linearized inversion is repeated for pure noise that equals or exceeds the noise in the data. Amplitude histograms are used to estimate probability density functions for the amplitudes of the signal and of the noise in the perturbations. Nonzero impedance derivatives are accepted as reliable if, according to the probability functions, the perturbations contain, with a high probability, only a small amount of noise. For a set of VSP data provided by L’Institut Francais du Petrole, four iterations allowed only a few nonzero impedance derivatives and modeled a recorded VSP as well as did a least‐squares inversion that accepted all proposed perturbations. Estimated probability densities for the remaining signal and noise were used to extract a tube wave that contained little signal.
Shaker tests on downhole seismic tools
Authors: de Montmollin Vincent
Published: October 2002

Shaking a downhole seismic tool in situ is a powerful test procedure able to detect abnormal acoustical behavior. It consists of feeding a swept voltage to a special geophone located inside the tool, close to the triaxial measurement geophones. The special geophone creates a swept force, which excites the tool‐formation system. The resulting motion of the tool is recorded through the triaxial geophones. In this paper, a simple model of the tool‐formation system excited by the shaker is given. Predictions from this model compare nicely with results from a field experiment conducted with a very compact seismic tool. Another field experiment, conducted with a longer tool, shows that tool intrinsic modes are clearly visible in the shaker data. Their frequencies and amplitudes depend upon the geometry of the contact between the tool and the formation. A comparison between shaker data and impulsive shot data shows that moderate modal vibrations do not significantly deteriorate the quality of VSP data, but that large modal vibrations, when present, are visible on the shot data and also correspond to an increased sensitivity to tube waves. Recording one shaker trace at each depth allows routine well‐site quality control of VSP data. Such quality control is especially important for the horizontal axes of a tool and in an open hole, where coupling conditions are not easily controlled.
Vertical seismic profile polarization method for determining reflector orientation
Authors: Spencer Terry W. , Smith Gregory A. , Cho Woon Hyun
Published: October 2002

The strike and dip of the reflecting interfaces in the vicinity of a well can be derived from VSP data recorded with a three‐component downhole seismometer. The method relies on measuring the polarizations in the direct and reflected compressional waves. The mathematical relation which is the basis of the method is exact only when the seismometer is positioned at the depth where the interface intersects the well. At that depth the polarization of the reflected wave cannot be measured because of interference with the direct wave. The orientation of the normal to the reflector can be determined to within 2° when the polarizations of the direct and reflected waves are determined within 100 m of the reflector. If the direct and reflected waves can be identified without multidepth processing, only measurements at a single depth are required to determine the reflector orientation. Error analysis and statistical refinement can be achieved by measuring the polarizations at several seismometer depths, source azimuths, or source offsets. The method is robust in the sense that the error in the interface orientation cannot exceed the error in the measurement of the polarizations. The method should be useful in structurally complex areas provided the reflections can be observed at depths above the depths of generation.
Multipole P‐wave logging in formations altered by drilling
Authors: Baker L. J. , Winbow G. A.
Published: October 2002

Wave trains produced by conventional and multipole sonic logging tools may be expected to depend upon whether the formation has been altered by the drilling process. Such alteration may include invasion by drilling fluids and/or drilling damage. We show, by theoretical modeling, that a dipole or quadrupole tool operating at conventional logging frequencies (in the range 10–20 kHz) detects P waves from the virgin formation with a much higher signal‐to‐noise ratio than does a monopole tool. This permits the multipole tool to measure formation P‐wave velocities two to three times farther away from the borehole than a conventional monopole tool. This larger radius of investigation typically extends beyond the altered zone for most situations, even for sources and receivers spaced several meters apart. Our conclusion is valid only if the velocity of the altered zone is less than the velocity of the virgin formation. If the velocity of the altered zone is larger than that of the virgin formation, no appreciable benefit is obtained by using a multipole tool. Similar results are demonstrated in measuring S‐wave velocities.
Labeling long‐period multiple reflections
Authors: Hardy R. J. J. , Warner M. R. , Hobbs R. W.
Published: October 2002

The many techniques that have been developed to remove multiple reflections from seismic data all leave remnant energy which can cause ambiguity in interpretation. The removal methods are mostly based on periodicity (e.g., Sinton et al., 1978) or the moveout difference between primary and multiple events (e.g., Schneider et al., 1965). They work on synthetic and selected field data sets but are rather unsatisfactory when applied to high‐amplitude, long‐period multiples in marine seismic reflection data acquired in moderately deep (700 m to 3 km) water. Differential moveout is often better than periodicity at discriminating between types of events because, while a multiple series may look periodic to the eye, it is only exactly so on zero‐offset reflections from horizontal layers. The technique of seismic event labeling described below works by returning offset information from CDP gathers to a stacked section by color coding, thereby discriminating between seismic reflection events by differential normal moveout. Events appear as a superposition of colors; the direction of color fringes indicates whether an event has been overcorrected or undercorrected for its hyperbolic normal moveout.
Interpretation of total wave‐field data over Lost Hills field, Kern County, California
Authors: Squires S. G. , Kim C. D. Y. , Kim D. Y.
Published: October 2002

Approximately 5 miles (8 km) of total wave‐field data were acquired by Production Geophysical Services (then Kim Tech., Inc.), using the OMNIPULSE® Multi‐mode Shear‐wave Generator source over the southern end of Lost Hills field, Kern County, California. The quality of the shear‐wave sections was excellent. They represent a significant improvement over conventional P‐wave sections from the area in that they provide better reflection continuity and imaging of the Lost Hills anticline. A multicomponent VSP, which was acquired close to the line, provided crucial P‐wave to S‐wave correlation, as well as fracture information. [Formula: see text] ratios computed from interval times ranged from 2.79 to 1.63. An anomalously low [Formula: see text] ratio of 1.65 in the zone of interest (Lower Reef Ridge to McDonald shale), confirmed by multicomponent VSP data, corresponds to the producing interval. Evidence of shear‐wave splitting due to azimuthal anisotropy was observed, so the SV‐wave and SH‐wave data sets were rotated into principal‐component axes of N45E for S1 and N45W for S2. The predominant fracture orientation changes from N45E at depth to N45W near the surface. This change in fracture orientation with depth was confirmed by multicomponent VSP data. Delay‐time ratios (used as a measure of fracture intensity) ranged from a maximum of 11.71 percent to a minimum of −5.48 percent across the structure. These ratios are interpreted to show changes in fracture intensity and orientation across the structure. Delay‐time ratios in the zone of interest were anomalously high (1.55–6.53 percent). Comparison of fracture intensity on the flanks of the structure with that on the crest indicates that the flanks have undergone greater deformation than the crest. The total wave‐field data set and associated analyses have provided significant structural and stratigraphic information on the Miocene Monterey formation over the Lost Hills field, highlighting the productive interval.
Documenting the sand/shale crossover
Authors: Neidell Norman S. , Berry Neal
Published: October 2002

All types of velocity data, i.e., surface seismic and well log or sonic log data, indicate that velocity in shallow, unconsolidated sands is lower than in associated shales, while velocity in older sands in more consolidated rock sequences is higher than in their associated shales. As the low‐velocity sands compact to become the high‐velocity member in the sand‐shale sequence, sand and shale velocities must become equal or crossover at some age and depth of burial. If the same type of velocity data is used consistently, this crossover occurs at the same depth and age of rocks in the geologic sequence as would be indicated by other types of velocity data, even though the different kinds of velocities would not agree elsewhere. If all rocks in the province are older and compacted, this crossover of sand and shale velocities may not be observed or, if observed, may be very near the surface.
The effect of geophone arrays on random noise
Authors: Levin Franklyn K.
Published: October 2002

For spatially random noise consisting of plane surface waves arriving at a geophone from all directions with equal probability, I compute the noise‐to‐signal ratio (N/S) as a function of the ratio of geophone spacing Δ to noise wavelength λ for linear arrays of 12, 24, 36, and 72 vertical and horizontal geophones. For arrays of M vertical geophones, deviation of N/S from that for pure random noise, [Formula: see text] is marked. As Δ/λ increases, N/S decreases, attaining [Formula: see text] for a value of Δ/λ that defines a coherence distance. As Δ/λ increases beyond the coherence distance, N/S continues to decrease slightly, only to increase again as Δ/λ approaches unity. For linear arrays of 12 to 72 vertical geophones, Δ/λ at the coherence distance is nearly independent of M and is about 0.32. The value of Δ/λ for which N/S = 0.5 changes with M but L/λ, L being the array length defined as MΔ, is independent of M. Introducing a random 14 percent variation into the sensitivities of the individual geophones has a small influence on the coherence distance and the N/S = 0.5 point when the N/S curves for 50 arrays are summed. Introducing a random 14 percent variation into the spatial coordinates of the geophones changes the coherence distance and 0.5 point only slightly but reduces the amount by which N/S fails below [Formula: see text] For arrays of horizontal geophones, there are two N/S curves depending upon whether the horizontal motion is in the plane of incidence of the signal (SV waves) or perpendicular to the plane of incidence (SH waves). Due to the superdirectivity of the array, N/S for SV waves incident on an SV‐wave geophone array is very small for values of Δ/λ greater than about 0.1. The N/S curves for SH waves incident on an SV‐wave array resemble those for the arrays of vertical geophones. Again there is a coherence distance, but the Δ/λ value is twice that for the vertical geophones, indicating the geophones should be separated by about two‐thirds of a wavelength.
Electromagnetic fields of electric dipoles embedded in a stratified anisotropic earth
Authors: Xiong Zonghou
Published: October 2002

The anisotropy of electrical conductivity in earth formations may be caused by crystal anisotropies of minerals, as well as by minilayers which occur frequently in sedimentary environments. The effects of anisotropy on the propagation of electromagnetic (EM) fields have been studied by many geophysicists. For instance, Kong (1972) and Wait (1981) solved the EM propagation problem for vertically anisotropic layered earths; O’Brien and Morrison (1967), for a horizontally anisotropic multilayer half‐space; Chetayev (1960), as well as Reddy and Rankin (1971), for media of dipping anisotropies; and Al’tgauzen (1969), for more complicated anisotropic media with a tensor dielectric constant of five components.
Gravity anomalies of irregularly shaped two‐dimensional bodies with constant horizontal density gradient
Authors: Pan Jeng‐Jong
Published: October 2002

An equation to compute the gravity anomalies of two‐dimensional (2-D) bodies with density contrast varying with depth (z axis) was developed by Murthy and Rao (1979). I develop an equation for computing the gravity anomalies of 2-D bodies with constant horizontal density gradient. By combining this equation with the equation of Murthy and Rao, I estimate the depth of the sedimentary basin which is adjacent to the master fault associated with the Rio Grande rift in New Mexico, where the density is assumed to decrease basinward from the fault (Cordell, 1979).
A calculus for finely layered anisotropic media
Authors: Schoenberg Michael , Muir Francis
Published: October 2002

Matrix algebra and group theory combine to offer a formalism for the simple calculation of the elastic, anisotropic, homogeneous medium which is equivalent, in the long‐wavelength limit, to a heterogeneous distribution of fine layers, each layer itself an elastic anisotropic medium. The properties of each anisotropic constituent in a set of fine layers map to an element of a commutative group. A reverse mapping returns the material properties of the constituent. Adding group elements gives the group element for the homogeneous medium equivalent to a heterogeneous set of layers. Addition of an inverse element—that is subtraction—provides the means to remove a set of layers from an anisotropic medium; then, if the remaining layer is a stable anisotropic medium, a valid decomposition of the original medium into anisotropic constituents is obtained. Within the group structure, eight subgroups corresponding to eight types of elastic symmetry systems may be identified, immediately yielding the symmetry of the equivalent medium, given the symmetry of its constituents. Sets of parallel fractures or aligned microcracks are also represented as group elements, allowing fractures and anisotropic rocks to be manipulated in a consistent and uniform manner. These group elements depend on at most six fracture parameters and are independent of the properties of the material in which the fractures are embedded. Multiple sets of fractures are easily taken into account by rotating (back in model space) a rock to a coordinate system appropriate to each fracture system, and then adding the appropriate fracture system group element.
Singularity removal: A refinement of resistivity modeling techniques
Authors: Lowry T. , Allen M. B. , Shive P. N.
Published: October 2002

Modeling techniques commonly exhibit errors of 3 to 10 percent or more in the calculation of apparent resistivities over earth models for which analytic solutions are easily available. A singularity occurs in the solution of any elliptic partial differential equation for which the forcing function is not smooth. The inability to adequately represent in discrete space a discontinuous function (in this case, the delta function describing the introduction of current at a point) commonly results in numerical error near the source of a modeled singularity. Inspection of an integrated finite‐difference method for modeling the dc resistivity geophysical technique indicates much of the error encountered is of singular origin. A procedure is herein detailed by which the singularity is mathematically removed from the modeling process and reintroduced as a last step, thus preventing it from contributing to the numerical error. Using this procedure, the average error in apparent resistivity values for a model of a polar‐dipole traverse over a nonconducting sphere is reduced by 40 percent. For a dipole‐dipole traverse of a two‐layer model the error decreases by 75 percent, and in the case of a Wenner profile of a model of a vertically faulted earth, the average error is diminished by 90 percent.
Elastic‐wave attenuation in fluid‐saturated Berea sandstone
Authors: O’Hara Stephen G.
Published: October 2002

In a previous publication (O’Hara, 1985), I presented detailed measurements on the attenuation of elastic waves in fluid‐saturated Berea sandstone. These measurements were used in a systematic empirical study of the frequency dependence of attenuation as a function of external pressure applied to the sandstone, pore fluid pressure, and the saturated sandstone temperature. Two pore fluids were used in the study: a brine solution and n-heptane. I measured the attenuation of the extensional and torsional rod modes of cylindrical specimens of the sandstone at identical conditions of pressure and temperature for each of the two fluids.
Audiomagnetotelluric study in northeast region of Paraná Basin, South America
Authors: Padilha A. L. , Trivedi N. B. , da Costa J. M. , Vitorello I. , Dupis A. , Cavoit C.
Published: October 2002

We conducted natural‐source audiomagnetotelluric (AMT) soundings at 31 stations along a 215 km profile in the Paraná Basin (South America) across the previously postulated Araxá‐Rio Grande alignment. Our objective was to study the resistive structures of the upper layers of the sedimentary sequence; our results made it possible to map the surficial layer of sediments of the Bauru group, a layer that reaches thicknesses of up to 250 m. We concluded that AMT soundings have reasonably good potential for groundwater exploration in the region. The varying thicknesses of Bauru group sediments and the irregularities of their contact surface with resistive volcanic rocks of the Serra Geral formation along the profile were not known previously. Our AMT profile crossed an important positive gravity anomaly located near the Rio Grande (a natural boundary between the states of São Paulo and Minas Gerais, in Brazil) which has not been fully interpreted. Five sites for deeper MT soundings, which may throw light on possible causes of the gravity anomaly, were selected based on the conclusions from the AMT survey.
Backprojection versus backpropagation in multidimensional linearized inversion
Authors: Esmersoy Cengiz , Miller Douglas
Published: October 2002

Seismic migration can be viewed as either backprojection (diffraction‐stack) or backpropagation (wave‐field extrapolation) (e.g., Gazdag and Sguazzero, 1984). Migration by backprojection was the view supporting the first digital methods—the diffraction and common tangent stacks of what is now called classical or statistical migration (Lindsey and Hermann, 1970; Rockwell, 1971; Schneider, 1971; Johnson and French, 1982). In this approach, each data point is associated with an isochron surface passing through the scattering object. Data values are then interpreted as projections of reflectivity over the associated isochrons. Dually, each image point is associated with a reflection‐time surface passing through the data traces. The migrated image at that point is obtained as a weighted stack of data lying on the reflection‐time surface (Rockwell, 1971; Schneider, 1971). This amounts to a weighted backprojection in which each data point contributes to image points lying on its associated isochron.
A comparison between Born inversion and frequency‐wavenumber migration
Authors: Wenzel F. , Menges D.
Published: October 2002

Employing appropriate high‐frequency approximations, we find that frequency‐wavenumber migration of spherically corrected data coincides with Born inversion for the reflectivity function. We consider zero‐offset seismic data in a 2.5-dimensional medium that consists of a homogeneous reference velocity with embedded reflectors. For marine data, where the pressure is measured, migration and inversion are identical. For land data, where vertical particle velocity is measured, modifications are required in order to match inversion and migration. The modifications become important only if dips larger than 30°are to be migrated.