bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparison of maximum entropy spectral analysis (MESA) and least‐squares linear prediction (LSLP) methods for some artificial samples
Authors: Kane R. P. , Trivedi N. B.
Published: October 2002

Spectral analysis is a very useful technique for studying geophysical problems. In earlier days, the only methods available were those of Fourier analysis or the method of Blackman and Tukey (1959) based on autocorrelation function. Recently, Burg (1967, 1968) introduced maximum entropy spectral analysis (MESA) which gives good resolution even for periods comparable to the data length. Ulrych and Bishop (1975) gave a critical appraisal of Burg’s algorithm. Several workers noticed and reported some inherent shortcomings. Thus, Chen and Stegan (1974) showed that, for truncated sinusoids, the spectral maxima showed frequency shifts sometimes as large as 20 percent, depending upon the initial phase and the length of the sample. Also, under certain conditions, the Burg spectra display line‐splitting in the presence of low noise, and as the noise is increased, the multiple peaks coalesce into a single peak shifted substantially away from the correct value (Fougere et al, 1976; Fougere, 1977). These defects can be rectified by the elaborate computer program given by Fougere (1977). Another difficulty is in selection of the appropriate length of the prediction error filter (LPEF). Whereas low LPEF is generally inadequate to resolve all the peaks, high LPEF, while resolving all peaks, produces instability in the spectra and gives spurious peaks. For determining the optimum LPEF, Ulrych and Bishop (1975) suggested the use of the Akaike’s (1969) final prediction error (FPE) criterion. And if this failed, an LPEF of about 50 percent of the data length was suggested to be generally adequate. Gutowski et al (1978) suggested the use of partial correlation coefficient. Berryman (1978) suggested an empirical solution [Formula: see text] where N = number of data points. Our experience (Kane 1977, 1979) indicated that for samples containing peaks in a wide range of frequency LPEF of about 50 percent of data length was adequate to resolve frequencies exceeding the fifth harmonic, while for lower harmonics, LPEF even as high as 90 percent was sometimes needed, with the danger of peak‐splitting ever present.
Linear inverse theory and deconvolution
Authors: Treitel Sven , Lines L. R.
Published: October 2002

Seismic source wavelet deconvolution can be treated within the framework of the Backus‐Gilbert (BG) inverse theory. A time shift‐invariant version of this theory leads to the Wiener shaping filter, which has enjoyed widespread use for source wavelet deconvolution in exploration seismology. The model of the BG theory is the ground impulse response, the BG mapping kernel is the source wavelet, and the BG resolving kernel is the convolution between the source wavelet and the Wiener shaping filter. BG inversion involves the minimization of an optimality criterion under a set of constraints. The application of the BG “filter energy” or “noise output power” constraint to Wiener filter design leads to the familiar prewhitening parameter that stabilizes the filter on the one hand, but degrades resolution on the other. The BG “unimodular” constraint produces an unbiased estimate of the model, or ground impulse response. These constraints provide novel insights into the performance of deconvolution filters.
The problem of hollow space correction in subsurface gravity surveys
Authors: Murty B. V. Satyanarayana , Reddy P. Chandra
Published: October 2002

In spite of the extensive computational work involved in the reduction of data especially in estimating the effects of terrain, the gravity method has earned its own esteemed place in mineral exploration. Measurement of gravity in subsurface openings such as mine shafts, drives, and adits is much more valuable in mineral exploration and also useful in the planning, design, and maintenance of mines. However, because the anomalies being sought in this context are usually of very small magnitudes, accuracy at every stage of the gravity investigation is essential. Besides those corrections which are known for the surface gravity measurements, an additional correction for the subsurface gravity data is the result of hollow spaces.
A vertical borehole geophone array
Authors: Bergh Sven , Ekström Ulf , Gustafsson Matts , Israelson Hans , Morén Per , Pihl Jörgen
Published: October 2002

This note describes a vertical borehole geophone array which can be used in slim boreholes. The array was designed as part of a research program in Sweden to study the potential of seismic crosshole techniques for mapping cracks and fracture zones in crystalline rock. The design meets not only the constraints imposed by the slim boreholes (diameter 56 mm) available in Sweden for crosshole surveys, but also the desire to make array recordings with three component locked geophones. The use of vertical arrays in boreholes has been discussed by Galperin (1974).
Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data
Authors: Bednar J. Bee
Published: October 2002

Seismic exploration problems frequently require analysis of noisy data. Traditional processing removes or reduces noise effects by linear statistical filtering. This filtering process can be viewed as a weighted averaging with coefficients chosen to enhance the data information content. When the signal and noise components occupy separate spectral windows, or when the statistical properties of the noise are sufficiently understood, linear statistical filtering is an effective tool for data enhancement. When the noise properties are not well understood, or when the noise and signal occupy the same spectral window, linear or weighted averaging performs poorly as a signal enhancement process. One must look for alternative procedures to extract the desired information. As a nonlinear operation which is statistically similar to averaging, median filtering represents one potential alternative. This paper investigates the application of median filtering to several seismic data enhancement problems. A methodology for using median filtering as one step in cepstral deconvolution or seismic signature estimation is presented. The median filtering process is applied to statistical editing of acoustic impedance data and the removal of noise bursts from reflection data. The most surprising conclusion obtained from the empirical studies on synthetic data is that, in high‐noise situations, cepstral‐based median filtering appears to perform exceptionally well as a deconvolver but poorly as a signature estimator. For real data, the process is stable and, to the extent that the data follow the convolutional model, does a reasonable job at both pulse estimation and deconvolution.
Inverse scattering for a layered acoustic medium using the first‐order equations of motion
Authors: Howard M. S.
Published: October 2002

The inverse scattering problem for a layered acoustic medium is considered from the first‐order differential equations of motion, resulting in a vector formulation of the problem, and using a vector form of the Schrödinger inverse scattering methods. The result is a vector Marchenko equation. The differentiability constraints on the acoustic impedance are somewhat relaxed compared to the more standard approach of beginning with the wave equation. The solution for plane waves at normal incidence is given along with a good approximate solution which is easily obtainable and takes into account transmission losses not included in the normal WKBJ‐Born approximation. A new solution for extracting separately the velocity and density of the medium using the reflection response for two different angles of incidence is given, which involves a nonlinear integral equation to relate the apparent traveltimes to depth.
On: Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms (GEOPHYSICS, v. 47, p. 376–387).
Authors: Roth J.
Published: October 2002

The above‐cited paper usefully examines and extends the application of the Hilbert transform to potential field interpretation. However, the authors’ terse mention of Nabighian’s paper (Geophysics, 1972) fails to characterize adequately and acknowledge his original insights and contributions to the Hilbert transform presented in that paper. It is surprising as well that none of the reviewers and/or editors saw fit to rectify this undeserved omission.
Thermal hydrology and heat flow of Beowawe geothermal area, Nevada
Authors: Smith Christian
Published: October 2002

Inflections in temperature‐depth profiles from forty 150 m thermal gradient holes define a shallow thermal flow system in the Whirlwind Valley near the Beowawe Geysers. U.S. Geological Survey hydrologic data reveal the vertical and west‐to‐east components of cold water flow at the water table above the thermal flow system. The temperature inflections break most abruptly in areas with a downward component of flow at the water table. The inflections are thought to indicate the level where the buoyant thermal water maintains a dynamic equilibrium with the overlying cold water. Combining these geophysical and hydrologic data suggests areas away from The Geysers where thermal water may rise from the deep reservoir into the alluvium. These leakage areas may be viable geothermal exploration targets. Even if the temperatures of the leakage were subeconomic, knowledge of where upwelling occurs could be helpful in assessing the potential for energy production. The systematic acquisition of hydrologic data is recommended as a standard component of hydrothermal resource exploration programs. Measurements of thermal conductivity from chip samples from the shallow holes and from Chevron Resources Company’s Ginn 1–13 geothermal exploration hole (2917 m T.D.) enable inferences based on heat flow. The average heat flow east of the Dunphy Pass fault zone, [Formula: see text], may be representative of background in this portion of the Battle Mountain high heat flow province. Thermal gradient and conductivity data from the deep well have a wide range of values (65–144°C/km, [Formula: see text]) but produce a relatively constant heat flow of [Formula: see text] above a depth of 1600 m. The shallow data indicate that the area with similarly high surficial heat flow extends as far east as the Dunphy Pass fault zone, suggesting that this Miocene rift boundary may form the eastern margin of the Beowawe hydrothermal system.
Migration with the full acoustic wave equation
Authors: Kosloff Dan D. , Baysal Edip
Published: October 2002

Conventional finite‐difference migration has relied on one‐way wave equations which allow energy to propagate only downward. Although generally reliable, such equations may not give accurate migration when the structures have strong lateral velocity variations or steep dips. The present study examined an alternative approach based on the full acoustic wave equation. The migration algorithm which developed from this equation was tested against synthetic data and against physical model data. The results indicated that such a scheme gives accurate migration for complicated structures.
Experience with the EM-60 electromagnetic system for geothermal exploration in Nevada
Authors: Wilt M. , Goldstein N. E. , Stark M. , Haught J. R. , Morrison H. F.
Published: October 2002

Lawrence Berkeley Laboratory (LBL) conducted controlled‐source electromagnetic (EM) surveys at three geothermal prospects in northern Nevada to test and demonstrate the applicability of LBL’s EM-60 system to geothermal exploration. During the late summer and early fall of 1979, over 40 soundings were made in Panther Canyon (Grass Valley), near Winnemucca; Soda Lakes, near Fallon; and McCoy, west of Austin. The EM-60 is a frequency‐domain system using three‐component magnetic detection. For the surveys reported here, we applied ±65 A to a 100-m diameter four‐turn horizontal loop, generating a dipole moment [Formula: see text] over the frequency range [Formula: see text] to [Formula: see text]. With such a source loop and a remote magnetic reference for noise cancellation, we made soundings at transmitter‐receiver separations of up to 4 km over the frequency range of 0.05 to 500 Hz. This has yielded a maximum depth of exploration to 2 km or more, adequate for the purposes of the geothermal investigations. Recorded spectra are interpreted by means of simple apparent‐resistivity calculations made in the field and by layered‐model inversions computed in the laboratory. The EM interpretations are then compared with other available geologic/geophysical data sets for the purpose of combined interpretation and method evaluation. Experience with the EM-60 system in Nevada has shown it to be an efficient and possibly more cost‐effective alternative to dc resistivity and magnetotellurics for geothermal exploration. An average of two soundings per field day for depths of exploration up to 2 km was obtained routinely. Results from EM-60 work at Panther Canyon compare very favorably with earlier dipole‐dipole resistivity surveys. Both methods outlined an irregularly shaped, buried conductive body associated with a region of high heat flow, but the feature was delineated by means of the EM-60 in just over half the field time required for the dipole‐dipole resistivity survey. At Soda Lakes, 13 high‐quality EM soundings were obtained from two transmitters in six field days under ideal field conditions. With the EM-60 data, we were able to map the depth to and inclination of a buried conductive body associated with an area of high subsurface temperatures. In this case, the EM results confirmed an earlier MT survey interpretation and gave additional detailed near‐surface information. At the remote and mountainous McCoy site, data interpretation was complicated because of the rugged terrain. By modifying existing interpretive software, we were able to calculate the effects of tilted‐source dipoles and elevation differences on soundings and thus interpret data. The EM soundings detected a conductive zone at a depth of 200 m at the south end of the prospect, where a nearby drillhole had encountered water at 100°C at the same depth. In addition, EM soundings at McCoy provided information on a deep conductor below 2 km which has yet to be drilled.
Localized heat flow and Tertiary mineralization in southern New Mexico
Authors: Zielinski Gary W. , DeCoursey Gail Moritz
Published: October 2002

Eight shallow (<100 m deep) relative heat flow determinations from southern New Mexico reveal a systematic 3 HFU [Formula: see text] increase occurring within a distance of 2 km. The maximum surface heat flow appears roughly to overlie a Tertiary granitic body at a depth of about 600 m within an area of known hydrothermal mineralization. The presence of the anomaly, believed to be of subsurface origin, implies an active heat source centered at a depth of 1140 m, perhaps associated with hydrothermal circulation. Higher radioactive heat production in granites may contribute to convective instability and explain the apparent lateral coincidence between the anomaly and the body. This situation appears, on a local scale, analogous to coinciding zones of high present‐day heat flow and mineralization in England and Wales (Brown et al, 1980). In both cases, mineralization is associated with granitic intrusion that has occurred at a previous time which is much greater than the thermal time constant for cooling bodies. Shallow heat flow determinations may be useful in locating other similar areas and investigating possible associations of mineralization and thermal history.
Modeling the effect of static errors in areal seismic data caused by glacial erosion over carbonate reefs
Authors: Kotcher Janet S. , Gardner G. H. F. , McDonald John A.
Published: October 2002

An effective way of exploring for structural features is by areal seismic methods. In addition to finding depth and location, the area of a structure may be determined at a reasonable cost. However, the efficacy of the areal method can be rapidly destroyed by static shifts in the seismic traces. In this paper we investigate the effect of statics on the crossed array method of areal data collection. Seismic data were collected in the northern Michigan reef trend, an area containing numerous small pinnacle reefs. The surface topography is flat, but it contains deep erosional valleys filled with glacial drift which produce time shifts in the data. The data were processed without static corrections. To predict the effect of static errors, a model was designed to produce data resembling those taken over a pinnacle reef. Seismic data were collected over this model by a method simulating the crossed array technique. Horizontal displays of the power envelope and the instantaneous phase of the migrated data were generated at a specified one‐way time, when various source and receiver dependent statics had been introduced into the raw data. The statics were designed to simulate the effect of glacial drift. If the diameter of the migration aperture is significantly larger than the distance along the source and receiver lines affected by statics, the effect on the migrated output is minimal. However, if the distance affected by statics approaches the diameter of the migration aperture, the effects are significant.
The relationship between “direct, discrete” and “iterative, continuous” one‐dimensional inverse methods
Authors: Gray Samuel H.
Published: October 2002

Two distinct approaches to solving the one‐dimensional seismic inverse problem are compared. These are (1) the “direct” method of Goupillaud (1961), applied to discretely varying media, and (2) the “iterative” methods of Gjevik et al (1976), or Gray and Hagin (1982), applied to discretely or continuously varying media. These two approaches are shown to be equivalent in two important respects. First, each method can be recovered from the other [e.g., the discretized version of the iterative methods yields the same set of equations as the direct method]. Second, because of the first equivalence, each method uses the same amount of information in reconstructing a profile to a certain depth z or traveltime τ into the medium. This information is the reflection data received for times less than 2τ. In particular, neither approach uses the “redundant data” received after time 2T in an inversion for a profile which is known to vary only for depths which correspond to traveltime T. In this sense the methods are as economical as possible, using the minimum amount of information required to solve the idealized problem. The key to relating the discrete, direct inversion to the continuous, iterative inversion is the Bremmer (1951) series for the reflected wave field. By using this series, it is possible to show that the equivalent inversion methods invert the same equation for the unknown acoustic impedance variations. The difference in the approaches used to solve this equation is analogous to the difference between solving a system of linear equations “directly” or “iteratively.”
Electromagnetic modeling of three‐dimensional bodies in layered earths using integral equations
Authors: Wannamaker Philip E. , Hohmann Gerald W. , SanFilipo William A.
Published: October 2002

We have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three‐dimensional bodies in layered earths. The inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions. A matrix equation is constructed using the electric tensor Green’s function appropriate to a layered earth, and it is solved for the vector current in each cell. Subsequently, scattered fields are found by integrating electric and magnetic tensor Green’s functions over the scattering currents. Efficient evaluation of the tensor Green’s functions is a major consideration in reducing computation time. We find that tabulation and interpolation of the six electric and five magnetic Hankel transforms defining the secondary Green’s functions is preferable to any direct Hankel transform calculation using linear filters. A comparison of responses over elongate three‐dimensional (3-D) bodies with responses over two‐dimensional (2-D) bodies of identical cross‐section using plane wave incident fields is the only check available on our solution. Agreement is excellent; however, the length that a 3-D body must have before departures between 2-D transverse electric and corresponding 3-D signatures are insignificant depends strongly on the layering. The 2-D transverse magnetic and corresponding 3-D calculations agree closely regardless of the layered host.
Three‐dimensional terrain corrections for mise‐à‐la‐masse and magnetometric resistivity surveys
Authors: Oppliger G. L.
Published: October 2002

Three‐dimensional modeling of topographic effects in mise‐à‐la‐masse and magnetometric resistivity surveys is accomplished using the surface integral equation method. The technique provides a means for (1) analyzing these effects on earth models of homogeneous conductivity; and (2) removing terrain effects from field data. A new method combining current source images with surface charge is developed to treat the electric field boundary conditions at the air‐earth interface. The method uses an image of each subsurface current source positioned above the surface, so as to induce a surface charge distribution which approximately cancels the charge distribution induced by the subsurface current source. The resulting residual surface charge distribution varies spatially more gradually than either of the original charge distributions, and hence may be represented accurately on a coarsely segmented model surface with simple basis functions. The topographic surface is modeled by a finite number of facets, each with constant slope and surface charge density. Charge values are obtained with an iterative solution technique. Surface electric fields are calculated from the surface charge distribution, current sources, and images. The magnetic field is found by evaluating a surface integral involving surface slopes and electric fields. The numerical solution is verified by comparisons with dipole‐dipole resistivity results from a two‐dimensional finite‐element model of a valley, and with analytic solutions for the magnetic fields over a dipping interface. Methods for terrain correcting mise‐à‐la‐masse and magnetometric resistivity data are demonstrated with examples using actual field measurements. The results of this study show that (1) rugged topography can significantly distort measurements in mise‐à‐la‐masse and magnetometric resistivity surveys; and (2) the described modeling technique provides an effective means of calculating terrain corrections for both the mise‐à‐la‐masse and magnetometric resistivity methods over complex three‐dimensional topography.
On: “Effect of surface polarization on resistivity modeling” by D. Guptasarma (GEOPHYSICS, v. 48, p. 98–106, January, 1983).
Authors: Apparao A.
Published: October 2002

I read the above paper by Guptasarma (1983) with great interest since it concerns the work done jointly by a group that includes me (Apparao et al., 1980). While I agree with some of his conclusions, I disagree with the others. The article reports an interesting result that, in physical modeling for resistivity and IP, an excitation current frequency of at least twenty times the maximum characteristic frequency [Formula: see text] must be used along the length of the profile, when one employs either a solid metallic conductor as a target or electronic conducting material in the target. He also reports that the value of [Formula: see text] is as low as 4.5 Hz with some models. For many others (not measured by Guptasarma), [Formula: see text] may turn out to be much less than 1 Hz. He hastened to conclude that all the laboratory measurements carried out at 50 or 60 Hz (referring to our papers) are likely to be grossly erroneous and should be viewed with “suspicion.” That his conclusion is incorrect can be seen from the following five‐point discussion.
Linear inversion of body‐wave data—Part III: Model parameterization
Authors: Bée M. , Jacobson R. S.
Published: October 2002

A velocity gradient model parameterized with the tau‐zeta inversion for seismic refraction data is examined with respect to a synthetic traveltime data set. The velocity‐depth model consists of a stack of laterally homogeneous layers, each with a constant velocity gradient. The free model parameters are the velocities of the layer bounds and the number of layers. The best velocity gradient solutions, i.e., with the least deviation from the true model, were obtained from “constrained” models in which the velocities of the layer bounds are the velocities of the observed refracted waves. An arbitrary selection of layer bound velocities was found to be a suboptimal choice of model parameterization for the tau‐zeta inversion. A trade‐off curve between model resolution and solution variance was constructed with the constrained model parameterization from examination of numerous solutions with a diverse number of layers. A constrained model with as many layers as observed data points represents a satisfactory compromise between model resolution and solution variance. Constrained models with more layers than observed data points, however, can increase the resolution of the velocity gradient model. If model resolution is favored over solution variance, a constrained model with many more layers than observed data points is therefore the best model parameterization with the tau‐zeta inversion technique.
The inverse problem of resistivity sounding
Authors: Parker Robert L.
Published: October 2002

The electric potential due to a single point electrode at the surface of a layered conducting medium is calculated by means of a linear combination of the potentials associated with a set of two‐layer systems. This new representation is called the bilayer expansion for the Green’s function. It enables the forward problem of resistivity sounding to be solved very efficiently, even for complicated profiles. Also, the bilayer expansion facilitates the solution of the resistivity inverse problem: the coefficients in the expansion are linearly related to apparent resistivity as it is measured and they are readily mapped into parameters for a model. Specifically, I consider models comprising uniformly conducting layers of equal thickness; for a given finite data set a quadratic program can be used to find the best‐fitting model in this class for any specified thickness. As the thickness is reduced, models of this kind can approximate arbitrary profiles with unlimited accuracy. If there is a model that satisfies the data well, there are other models equally good or better whose variation takes place in an infinitesimally thin zone near the surface, below which there is a perfectly conducting region. This extraordinary class of solutions underscores the serious ambiguity in the interpretation of apparent resistivity data. It is evident that strong constraints from outside the electrical data set must be applied if reliable solutions are to be discovered. Previous work seems to have given a somewhat overly optimistic impression of the resolving abilities of this kind of data. I consider briefly a regularization technique designed to maximize the smoothness of models found with the bilayer inversion.
Inversion of horizontal loop electromagnetic frequency soundings
Authors: Fullagar P. K. , Oldenburg D. W.
Published: October 2002

A procedure has been developed to perform automatic inversion of HLEM frequency soundings by the method of Backus and Gilbert (BG). Using a linearized iterative scheme, a layered conductivity is constructed satisfying the available soundings to an accuracy consistent with the observational uncertainties. Subsequently, in order to investigate the resolving power of the data and hence (hopefully) to determine the broad scale features which are common to all conductivity models which satisfy the data, BG average conductivities are computed for the constructed model at a number of depths. In examples with both synthetic data and field data these averages proved to be identical (except for random error) to the corresponding average conductivities computed for a number of different models satisfying the same data. The additional models for this analysis were generated by maximizing or minimizing the conductivities of individual layers in the original constructed model using linear programming techniques. On the basis of these empirical results, in conjunction with the uniqueness theorem for HLEM soundings, it is concluded that BG average conductivities computed for a particular constructed model will often provide a valid characterization of the true ground conductivity over a depth range governed by survey parameters.
Semblance processing of borehole acoustic array data
Authors: Kimball Christopher V. , Marzetta Thomas L.
Published: October 2002

A new method of processing borehole acoustic array data is described. The method detects arrivals by computing the scalar semblance for a large number of possible arrival times and slownesses. Maxima of semblance are interpreted as arrivals, and their associated slownesses are plotted on a graph whose axes are slowness and depth. The processing makes few prior assumptions about the data and the algorithm is uncomplicated. Results of the processing applied to data from a 12-receiver device are presented for both open and cased holes.
On: “Effect of surface polarization on resistivity modeling” by D. Guptasarma (GEOPHYSICS, v. 48, January 1983, p. 98–106).
Authors: Duckworth K.
Published: October 2002

I am glad to see that this paper confirms the resistive behavior of metallic models when immersed in electrolyte and subject to low‐frequency currents, which my coauthor and I reported in 1978 (Saydam and Duckworth, 1978). It is also gratifying that this paper confirms the transition from resistive to conductive behavior with increase of frequency which we reported in that same paper. However, I must call into question the validity of the conclusions reached by the author of this paper. I do so for several reasons, the first of which is that the author is not entitled to display complex resistivity spectra derived in a model tank environment unless evidence is provided that those spectra are invariant for a range of primary currents extending over at least two decades from an upper limit of 1 mA. I say this because a current of 1 mA, as apparently used by the author, causes severe nonlinearity in tank modeling as my coauthor and I showed in 1978 (Saydam and Duckworth, ibid). In tests of stainless steel which we performed and in tests on pyrite performed by Anderson and Keller (1964) the maximum permissible current density for linear conditions to exist was [Formula: see text]. Current densities at the surface of the aluminum cylinder of 3 cm diameter used by the authors would have been as high as [Formula: see text] when it was located at a depth of 7 mm (as quoted) directly under one of the current electrodes if the delivered current was 1 mA. It seems unlikely that aluminum would behave linearly at current densities 32 times greater than the maximum permissible for either stainless steel or pyrite, but we have no way of knowing because this paper fails to provide any experimental evidence in this regard. However, in the case of the results for a vertical stainless steel cylinder shown by the author in Figure 6 we can readily compute that if a 1 mA input current was used, the current density at the surface of the cylinder closest to the [Formula: see text] electrode would have been [Formula: see text]. Thus, in this case, linearity could only have been ensured by using an input current at least an order of magnitude lower than the 1 mA quoted by the author.
A preliminary analysis of the NRL airborne gravimetry system
Authors: Brozena John M.
Published: October 2002

The Naval Research Laboratory has developed an airborne gravimetry system for marine use. The system utilizes global positioning system navigation and high‐resolution radar altimetry to overcome the major difficulties of Eötvös correction and vertical acceleration determination. Precise measurements of aircraft motions permit system operation in the noisy low‐altitude environment and allow averaging data over fairly short periods. This results in good system response to short‐wavelength gravity anomalies. Preliminary analysis indicates average errors of 4 mGals or less on three aircraft profiles over a gravity equipment evaluation range for a flight altitude of 150 m and air speed of 400 km/hr.
Noise processing techniques for time‐domain EM systems
Authors: Macnae James C. , Lamontagne Y. , West G. F.
Published: October 2002

A variety of signal processing techniques can be used to minimize the effects of noise on linear, wideband, electromagnetic (EM) systems operating in the time‐domain. All systems use repetitive waveforms with polarity reversal in alternate half‐cycles. Exponential averaging or digital integration (stacking) is employed to increase signal‐to‐noise (S/N) ratios by limiting the noise acceptance to narrow frequency bands centered on odd harmonics of the repetition frequency, the width of the acceptance bands being inversely proportional to stacking time. For certain types of nonstationary noise (e.g., occasional transients) or coherent noise (e.g., powerlines) it is possible to increase S/N ratios above those obtained by simple stacking for an equal time by use of techniques such as pruning, tapered stacking or randomized stacking. With some system waveforms and when the noise spectrum is not “white”, use of preemphasis filtering in the transmitter and a corresponding de‐emphasis filter in the receiver may significantly improve the input S/N ratio before stacking. Specific applications of the various techniques are discussed with reference to one particular time‐domain EM system, the UTEM 3 system. By their use, improvements in S/N ratio of as much as 6 to 1 have been regularly achieved without any increase in transmitter power, depending on the nature of the local noise.
Kirchhoff elastic wave migration for the case of noncoincident source and receiver
Authors: Kuo John T. , Dai Ting‐fan
Published: October 2002

In taking into account both compressional (P) and shear (S) waves, more geologic information can likely be extracted from the seismic data. The presence of shear and converted shear waves in both land and marine seismic data recordings calls for the development of elastic wave‐migration methods. The migration method presently developed consists of simultaneous migration of P- and S-waves for offset seismic data based on the Kirchhoff‐Helmholtz type integrals for elastic waves. A new principle of simultaneously migrating both P- and S-waves is introduced. The present method, named the Kirchhoff elastic wave migration, has been tested using the 2-D synthetic surface data calculated from several elastic models of a dipping layer (including a horizontal layer), a composite dipping and horizontal layer, and two layers over a half‐space. The results of these tests not only assure the feasibility of this migration scheme, but also demonstrate that enhanced images in the migrated sections are well formed. Moreover, the signal‐to‐noise ratio increases in the migrated seismic section by this elastic wave migration, as compared with that using the Kirchhoff acoustic (P-) wave migration alone. This migration scheme has about the same order of sensitivity of migration velocity variations, if [Formula: see text] and [Formula: see text] vary concordantly, to the recovery of the reflector as that of the Kirchhoff acoustic (P-) wave migration. In addition, the sensitivity of image quality to the perturbation of [Formula: see text] has also been tested by varying either [Formula: see text] or [Formula: see text]. For varying [Formula: see text] (with [Formula: see text] fixed), the migrated images are virtually unaffected on the [Formula: see text] depth section while they are affected on the [Formula: see text] depth section. For varying [Formula: see text] (with [Formula: see text] fixed), the migrated images are affected on both the [Formula: see text] and [Formula: see text] depth sections.
The effect of binning on data from a feathered streamer
Authors: Levin Franklyn K.
Published: October 2002

In a recent paper (Levin, 1983), I derived the common midpoint (CMP) time‐distance relations for reflection from a plane of arbitrary orientation when the streamer carrying the hydrophones was feathered by currents. The streamer was assumed to be straight but deviated at a constant angle γ. This assumption corresponds well to what is observed during marine exploration. I considered two cases: first, the CMP points chosen to be what they would have been in the absence of feathering and second, the CMP points selected to lie along a line perpendicular to the profile direction. The second choice is the one normally made and the only one I’ll consider in this short note. In the paper, I assumed the CMP points were allowed to extend from the origin, which was the point of coincident source and detector, to whatever distance from the line corresponded to the maximum source‐to‐detector separation. While this is a possible choice, it is not the choice of many of those who must process marine 3-D data. Instead they demand that all CMP points fall within a bin centered on the profile line. I shall call this choice “binning.”
The behavior of the apparent resistivity phase spectrum in the case of a polarizable prism in an unpolarizable half‐space
Authors: Soininen Heikki
Published: October 2002

In the application of the broadband induced polarization method, it is necessary to know how a petrophysical resistivity spectrum is transformed into an apparent spectrum measured in the field. Investigated in the present work was the forming of an apparent spectrum in the case of a polarizable three‐dimensional prism embedded in an unpolarizable half‐space for gradient and dipole‐dipole arrays. The computations were done numerically using the integral equation technique. The frequency dependence of the resistivity of the prism was depicted by means of the Cole‐Cole dispersion model. With this simple model geometry, the phase spectra of apparent resistivity resemble quite closely in functional form the original petrophysical phase spectrum of the Cole‐Cole dispersion model. The apparent spectra have shifted on the log‐log scale downward, owing to geometric attenuation, and toward lower frequencies. The apparent Cole‐Cole parameters have been inverted from the apparent spectra. The apparent chargeability is generally noticeably smaller, owing to the geometric attenuation, than the chargeability of the original petrophysical spectrum. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The shift of the apparent phase spectrum toward lower frequencies partly compensates for the decrease in the apparent time constant caused by attenuation of the spectrum. The apparent time constant is thus close to the true time constant of the petrophysical spectrum. It is therefore possible in principle to obtain by direct inversion from an apparent spectrum measured in the field a reasonable estimate of the frequency dependence and time constant of the true spectrum of a polarizable body.
On: “Homomorphic deconvolution” by D. J. Jin and J. R. Rogers (GEOPHYSICS, 48, 1014–1016).
Authors: Lane Mark , Ulrych Tad
Published: October 2002

The recent note by Jin and Rogers (1983) presented examples of the failure of the homomorphic transform to invert properly. Since this transform is not only of interest in geophysics, but has also found applications in other fields (Oppenheim and Schafer, 1975), these results are of concern. We consequently attempted to reproduce Jin and Rogers’ results. We failed to do so. In fact, in our experience, the transform has always inverted successfully. Our results using the first example of Jin and Rogers are shown in Figure 1. We used the algorithm of Tribolet (1977) with a modified Goertzel algorithm (Bonzanigo, 1978) for phase unwrapping. The figure is arranged as in Jin and Rogers’ paper. Figure 1a shows the input: impulses separated by 20 samples, of magnitude 2000 and 1999. Figure 1b shows its complex cepstrum. We have set the zero‐quefrency point to zero since this represents a scale factor and can dominate the plotting. Note the minimum delay cepstrum with a small amount of aliasing. The sequence returned by the inverse transform is shown in Figure 1c, demonstrating a successful inversion. The effect of noise is also shown. Noise with a standard deviation of 5 was added to the sequence of Figure 1a. This is shown in Figure 1d. Note that our noise realization is undoubtedly different from that of Jin and Rogers. The noise has changed the relative magnitude of the original spikes such that they are maximum delay. This is reflected in the cepstrum (Figure 1e). Figure 1f shows the returned sequence, again demonstrating the successful inversion.
GEOPHYSICS EDUCATION AT AN ENGINEERING INSTITUTION
Authors: Wantland Dart
Published: October 2002

The background and development of the courses of instruction in Exploration Geophysics at the Colorado School of Mines as well as the limiting factors in shaping a geophysics curriculum and the time devoted to various phases of the graduate courses in applied Geophysics offered are discussed. The present positions occupied by geophysics graduates of the institution after 12 years of operation of the Geophysics Department are shown, and a summary is given of the replies of these men to an inquiry as to their opinion of the instruction they received.
THE FORM AND NATURE OF SEISMIC WAVES AND THE STRUCTURE OF SEISMOGRAMS
Authors: Ricker Norman
Published: October 2002

A theory is presented to account for the structure of seismograms. It is demonstrated mathematically that a sharp seismic disturbance gives rise to a traveling wavelet, of shape determined by the nature of the earth’s absorption spectrum for elastic waves, and that a seismogram is composed of a succession of these wavelets, generally overlapping but sometimes in the clear. It is further brought out that it is the center of the wavelet which travels with a velocity characteristic of the medium, and that the wavelet broadens as it moves along in accord with a definite law. Experimental support of the theory also is presented.
On: S. Hammer’s replies to N. C. Steenland, A. T. Herring, and W. C. Pearson’s discussions of “Airborne gravity is here” (GEOPHYSICS, 49, 310–311, March 1984; and 49, 470–477, April 1984).
Authors: Hall M. J.
Published: October 2002

Hammer’s replies to Steenland’s, Herring’s and Pearson’s discussions of his paper, “Airborne gravity is here!,” are nothing short of incredulous. Both his paper and his replies would suggest that he did not expect those with experience in dynamic gravity to read them. Hammer accuses his critics of ignoring “…the low‐pass filter which was applied for realistic comparison with the airborne data.” I shall call this “Hammer’s Rule:” you filter the very standard against which you will compare any new method without concern for the truth. Hammer’s Rule frees us from annoyingly difficult rigor. If the airborne filter eliminates the anomaly, then so must the ground truth anomaly be eliminated. Fair is fair, and Hammer’s Rule gives a “realistic comparison” between something which is wrong and something which is wrong.
The magnetotelluric impedance tensor properties with respect to rotations
Authors: Spitz Simon
Published: October 2002

A serious limitation to conventional data analysis is that the data refer mainly to elongated bodies. When three‐dimensional distortions are present, quantitative interpretation based only on the off‐diagonal elements of the conventionally rotated impedance tensor is inadequate, because these off‐diagonal elements are insensitive to the tensor trace. The impedance tensor eigenstate formulation proposed in the literature defines a complete set of parameters suitable for recognition of three‐dimensionality. Generally, though, the eigenvalues do not stand for the off‐diagonal elements of an impedance tensor measured in a physical coordinate system. It is shown how the eigenvalues are modified when the relationship between coordinate system rotations and the eigenstate formulation is clarified. A generalization of the conventional analysis results, but the rotation angle obtained is neither unique nor complete To improve the situation, two new analytical rotation angles are proposed. These angles define two complete intrinsic coordinate systems suitable for magnetotelluric data analysis when a general three‐dimensional structure is involved.
Reply by the author to discussion on Tooley et al. (GEOPHYSICS, 49, 2195–2196).
Authors: Spencer Terry W.
Published: October 2002

Denham and Palmeira recently pointed out in December 1984 Geophysics that the energy flux at normal incidence in Figure 11 of Tooley et al. (1965, 30, 552) is not correct for a compressional velocity ratio [Formula: see text] less than unity. The problem is that there is a discrepancy between the curves and the parameters cited. The curves correctly represent the angular dependence of energy flux ratios but for density ratios significantly less than the value of unity cited in Figure 11. Because both the density and velocity ratios vary, Figure 11 cannot be used to isolate the effect of changing the velocity ratio as was originally intended.
Direct phase determination of S‐wave velocities from acoustic waveform logs
Authors: Ingram J. D. , Morris C. F. , MacKnight E. E. , Parks T. W.
Published: October 2002

A new technique for producing S-wave logs from borehole acoustic waves has been developed. The procedure is based on direct phase calculations for time‐windowed waveforms obtained with an acoustic logging tool. A window is positioned over the S-wave portion of the signals, and window moveout is chosen to give zero‐phase differences in a band of frequencies across the array of receivers. A major issue in application of this method is the error introduced by windowing and by interfering signals such as casing arrivals, residual P-waves, and modes propagating in the borehole. Examples using synthetic data are presented illustrating these errors and the means of reducing them. A capture effect, characteristic of phase methods, may be exploited to reduce the effect of interference. Examples are presented showing logs made in different lithologies using a conventional two‐receiver long‐spacing tool. A pulsed transmitter was used with energy in a frequency range 10 to 20 kHz. In hard formations there is little difficulty in obtaining good shear logs. In softer formations, with reduced shear amplitudes, the problems caused by interfering waves become more severe. Careful choice of frequency bands used in the analysis can reduce interference problems and may improve logs in soft formations.