Showing papers in "Geophysics in 1979"

Complex seismic trace analysis

Abstract: The conventional seismic trace can be viewed as the real component of a complex trace which can be uniquely calculated under usual conditions. The complex trace permits the unique separation of envelope amplitude and phase information and the calculation of instantaneous frequency. These and other quantities can be displayed in a color-encoded manner which helps an interpreter see their interrelationship and spatial changes. The significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas.

Magnetotellurics with a remote magnetic reference

Abstract: Magnetotelluric measurements were performed simultaneously at two sites 4.8 km apart near Hollister, California. SQUID magnetometers were used to measure fluctuations in two orthogonal horizontal components of the magnetic field. The data obtained at each site were analyzed using the magnetic fields at the other site as a remote reference. In this technique, one mUltiplies the equations relating the Fourier components of the electric and magnetic fields by a component of magnetic field from the remote reference. By averaging the various crossproducts, one can obtain estimates of the impedance tensor that are unbiased by noise, provided there are no correlations between the noises in the remote channels and the noises in the local channels. Even for data for which the E-E predicted coherencies were as low as 0.1, the apparent resistivities obtained from this technique were consistent with apparent resistivities calculated from high coherency data at adjacent periods. Apparent resistivities calculated by conventional analysis of the same data were biased by as much as two orders of magnitude. The estimated standard deviation for periods shorter than 3 s was less than 5%, and, for 87% of the data, was less than 2%. Where data bands overlapped between periods of 0.33more » s and 1 s,the average discrepancy between the apparent resistivities was 1.8%.« less

Attenuation of seismic waves in dry and saturated rocks; I, Laboratory measurements

Abstract: The attenuation of compressional (P) and shear (S) waves in dry, saturated, and frozen rocks is measured in the laboratory at ultrasonic frequencies. A pulse transmission technique and spectral ratios are used to determine attenuation coefficients and quality factor (Q) values relative to a reference sample with very low attenuation. In the frequency range of about 0.1–1.0 MHz, the attenuation coefficient is linearly proportional to frequency (constant Q) both for P‐ and S‐waves. In dry rocks, Qp of compressional waves is slightly smaller than Qs of shear waves. In brine and water‐saturated rocks, Qp is larger than Qs. Attenuation decreases substantially (Q values increase) with increasing differential pressure for both P‐ and S‐waves.

Attenuation of seismic waves in dry and saturated rocks: II. Mechanisms

Abstract: Theoretical models based on several hypothesized attenuation mechanisms are discussed in relation to published data on the effects of pressure and fluid saturation on attenuation. These mechanisms include friction, fluid flow, viscous relaxation, and scattering. The application of these models to the ultrasonic data of Toksoz et al (1979, this issue) indicates that friction on thin cracks and grain boundaries is the dominant attenuation mechanism for consolidated rocks under most conditions in the earth’s upper crust. Increasing pressure decreases the number of cracks contributing to attenuation by friction, thus decreasing the attenuation. Water wetting of cracks and pores reduces the friction coefficient, facilitating sliding and thus increasing the attenuation. In saturated rocks, fluid flow plays a secondary role relative to friction. At ultrasonic frequencies in porous and permeable rocks, however, Biot‐type flow may be important at moderately high pressures. “Squirting” type flow of pore fluids from...

Wave attenuation in partially saturated rocks

Abstract: A model is presented to describe the attenuation of seismic waves in rocks with partially liquid‐saturated flat cracks or pores. The presence of at least a small fraction of a free gaseous phase permits the fluid to flow freely when the pore is compressed under wave excitation. The resulting attenuation is much higher than with complete saturation as treated by Biot. In general, the attenuation increases with increasing liquid concentration, but is much more sensitive to the aspect ratios of the pores and the liquid droplets occupying the pores, with flatter pores resulting in higher attenuation. Details of pore shape other than aspect ratio appear to have little effect on the general behavior provided the crack width is slowly varying over the length of the liquid drop.

The self-potential method in geothermal exploration

Abstract: Laboratory measurements and field data indicate that self-potential anomalies comparable to those observed in many areas of geothermal activity may be generated by thermoelectric or electrokinetic coupling processes. A study using an analytical technique based on concepts of irreversible thermodynamics indicates that, for a simple spherical source model, potentials generated by electrokinetic coupling may be of greater amplitude than those developed by thermoelectric coupling. Before more quantitative interpretations of potentials generated by geothermal activity can be made, analytical solutions for more realistic geometries must be developed, and values of in-situ coupling coefficients must be obtained.If the measuring electrodes are not watered, and if telluric currents and changes in electrode polarization are monitored and corrections made for their effects, most self-potential measurements are reproducible within about + or -5 mV. Reproducible short-wavelength geologic noise of as much as + or -10 mV, primarily caused by variation in soil properties, is common in arid areas, with lower values in areas of uniform, moist soil. Because self-potential variations may be produced by conductive mineral deposits, stray currents from cultural activity, and changes in geologic or geochemical conditions, self-potential data must be analyzed carefully before a geothermal origin is assigned to observed anomalies.Self-potential surveys conducted in a variety of geothermal areas show anomalies ranging from about 50 mV to over 2 V in amplitude over distances of about 100 m to 10 km. The polarity and waveform of the observed anomalies vary, with positive, negative, bipolar, and multipolar anomalies having been reported from different areas. Steep potential gradients often are seen over faults which are thought to act as conduits for thermal fluids. In some areas, anomalies several kilometers wide correlate with regions of known elevated thermal gradient or heat flow.

Deconvolution with the l 1 norm

Abstract: Given a wavelet w and a noisy trace t = s * w + n, an approximation s of the spike train s can be obtained using the l 1 norm. This extraction has the advantage of preserving isolated spikes in s. On some types of data the spike train s can represent s as a sparse series of spikes, which may be sampled at a rate higher than the sample rate of the data trace t. The extracted spike train s may be qualitatively much different than those commonly extracted using the l 2 norm.The l 1 norm can also be used to extract a wavelet w from a trace t when a spike train s is known. This wavelet extraction can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends.Given a trace t and an initial approximation for either s or w, it is possible to alternately extract spike trains and wavelets to improve the representation of trace t.Although special algorithms have been developed to solve l 1 problems, all of the calculations can be performed using a general linear programming system. Proper weighting procedures allow these methods to be used on ungained data.

Resistivity modeling for arbitrarily shaped three-dimensional structures

Abstract: A numerical technique has been developed to solve the three‐dimensional (3-D) potential distribution about a point source of current located in or on the surface of a half‐space containing an arbitrary 3-D conductivity distribution. Self‐adjoint difference equations are obtained for Poisson’s equation using finite‐difference approximations in conjunction with an elemental volume discretization of the lower half‐space. Potential distribution at all points in the set defining the subsurface are simultaneously solved for multiple point sources of current. Accurate and stable solutions are obtained using full, banded, Cholesky decomposition of the capacitance matrix as well as the recently developed incomplete Cholesky‐conjugate gradient iterative method. A comparison of the 2-D and 3-D simple block‐shaped models, for the collinear dipole‐dipole array, indicates substantially lower anomaly indices for inhomogeneities of finite strike‐extent. In general, the strike‐extents of inhomogeneities have to be approxi...

Synthetic sonic logs—a process for stratigraphic interpretation

Abstract: Modern seismic reflection data may be processed to approximate closely the reflection coefficient series of a sedimentary section. Inversion of the series will produce a low‐cut filtered impedance log. Extension of the technique to include density correction and replacement of missing low‐frequency components leads to generation of a synthetic sonic log having dimensions and characteristics similar to a conventional borehole sonic log. A synthetic sonic log section provides several advantages over conventional seismic sections, particularly for stratigraphic exploration. Direct depth display largely eliminates the vertical scale distortion inherent in time sections and simplifies integration with other subsurface data. Resolution is generally improved. The process is well adapted to automated generation of stratigraphic sections. Individual rock units are mapped by contours of constant transit‐time, to show facies changes and depositional sequences in detail. The detailed measurements of velocity may be u...

Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model); Part I, Biot theory

Abstract: An exact theory of attenuation and dispersion of seismic waves in porous rocks containing spherical gas pockets (White model) is presented using the coupled equations of motion given by Biot. Assumptions made are (1) the acoustic wavelength is long with respect to the distance between gas pockets and their size, and (2) the gas pockets do not interact. Thus, the present theory essentially is quite similar to that proposed by White (1975), but the problem of the radially oscillating gas pocket is solved in a more rigorous manner by means of Biot’s theory (1962). The solid‐fluid coupling is automatically included, and the model is solved as a boundary value problem requiring all radial stresses and displacements to be continuous at the gas‐brine interface. Thus, we do not require any assumed fluid‐pressure discontinuity at the gas‐water contact, such as the one employed by White (1975). We have also presented an analysis of all of the field variables in terms of Biot’s type I (the classical compressional) w...

Computer program; numerical integration of related Hankel transforms of orders O and 1 by adaptive digital filtering

Abstract: A linear digital filtering algorithm is presented for rapid and accurate numerical evaluation of Hankel transform integrals of orders 0 and 1 containing related complex kernel functions. The kernel for Hankel transforms is defined as the non‐Bessel function factor of the integrand. Related transforms are defined as transforms, of either order 0 or 1, whose kernel functions are related to one another by simple algebraic relationships. Previously saved kernel evaluations are used in the algorithm to obtain rapidly either order transform following an initial convolution operation. Each order filter is designed with identical abscissas over a large range so that an adaptive convolution procedure can be applied to a large class of kernels. Different order Hankel transforms with related kernels are often found in electromagnetic (EM) applications. Because of the general nature of this algorithm, the need to design new filters should not be necessary for most applications. Accuracy of the filters is comparable t...

Quasi-static transient response of a conducting half-space; an approximate representation

Abstract: For a step‐function excitation, it is shown that, to a first‐order approximation, the quasi‐static transient response in the air due to an arbitrary loop situated at the earth’s surface can be represented by a downward and outward moving current filament, of diminishing amplitude and having the same shape as the transmitter loop.

Wave-equation datuming

Abstract: Wave-equation datuming is the name given to upward or downward continuation of seismic time data when the purpose is to redefine the reference surface on which the sources and receivers appear to be located. This technique differs from conventional datuming methods in the repositioning of seismic reflections laterally as well as vertically in response to observed time dips. The most interesting applications of the technique are those in which the redefined reference surface is an actual geologic interface having an irregular topography and a large velocity contrast. Wave-equation datuming can remove the deleterious effect such an interface has on seismic reflections originating below it. Wave-equation datuming also is applicable in seismic modeling.The computations required in wave-equation datuming are related to those of migration. The Kirchhoff integral formulation of the wave equation can provide a basis for computation to deal with the irregular surfaces and variable velocities that are central to the problem. The numerical implementation of the Kirchhoff approach can be reduced to an efficient procedure involving summations and convolutions of seismic traces with short shaping and weighting operators.

Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies

Abstract: Complete analytical expressions for the first and second derivatives of the gravitational potential in arbitrary directions due to a homogeneous polyhedral body composed of polygonal facets are developed, by applying the divergence theorem definitively. Not only finite but also infinite rectangular prisms then are treated. The gravity anomalies due to a uniform polygon are similarly described in two dimensions.The magnetic potential due to a uniformly magnetized body is directly derived from the first derivative of the gravitational potential in a given direction. The rule for translating the second derivative of the gravitational potential into the magnetic field component is also described.The necessary procedures for practical computer programming are discussed in detail, in order to avoid singularities and to save computing time.

An electrochemical model of the induced‐polarization phenomenon in disseminated sulfide ores

Abstract: A disseminated sulfide ore is idealized by a system of electronically conducting metallic spheres randomly dispersed in an electrolytically conducting host medium. When an external electric field is applied, the transport of cations and anions in the interphase region near the metal‐electrolyte interface will involve both drift and diffusion flux densities. The flow of ions to or from the metal‐electrolyte interface causes an excess or deficit of inactive ions to accumulate there, since the metal is neither a source nor sink for these ions. These inactive ions are loosely held to the metallic particles by image forces, and concentration gradients build up which oppose the migration of these ions due to electric fields. In addition to the inactive anions and cations, a minor concentration of active cations is assumed to exist in the electrolytic medium, and the electric fields at the electrolyte‐metal interface cause these to engage in electrochemical reactions making possible charge transfer across the in...

Numerical evaluation of the transient acoustic waveform due to a point source in a fluid-filled borehole

Abstract: A key measurement employed in oil well wireline logging is the acoustic wave traveltime over a specified formation interval, typically 1 ft. In the traditional measurement, only the compressional head wave is monitored, but for some time it has been obvious that there is significant additional information, such as the shear head wave arrival, in the received waveform. We describe two numerical methods for computing the profile and parameter dependence of the transient waveform based on a model of the acoustic logging problem consisting of a point source on the axis of a fluid-filled cylindrical borehole. The response to this excitation is determined at a distance from the source, generally on the borehole axis. In the first of the two numerical methods, called 'real axis integration', the complete acoustic waveform is obtained. The second method, called 'branch-cut integration', evaluates the first compressional and shear-pseudo-Rayleigh arrivals individually with much less computation time than the first method. The validity and accuracy of the two methods are demonstrated by their close agreement within appropriate time windows. It is also shown that the results from the ordinary asymptotic method that exist in the literature predict different behavior. The dependence of the transient arrivals on formation parameters is illustrated by various numerical results in both time and frequency domains.

Long-wave elastic anisotropy in transversely isotropic media

Abstract: Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality (c11-c44)(c33-c44)⩾(c13+c44)2 derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limesto...

Velocity inversion procedure for acoustic waves

Abstract: An approximate solution is presented to the seismic inverse problem for two‐dimensional (2-D) velocity variations. The solution is given as a multiple integral over the reflection data observed at the upper surface. An acoustic model is used, and the reflections are assumed to be sufficiently weak to allow a “linearization” procedure in the otherwise nonlinear inverse problem. Synthetic examples are presented demonstrating the accuracy of the method with dipping planes at angles up to 45 degrees and with velocity variations up to 20 percent. The method was also tested under automatic gain control, in which case velocity estimates were lost but the method nonetheless successfully migrated the data.

Near-infrared (1.3-2.4 mu m) spectra of alteration minerals; potential for use in remote sensing

Abstract: Reflection spectra of particulate samples of minerals that commonly occur in hydrothermally altered rocks and soils were recorded to display their features at their natural spectral bandwidths in the near-infrared from 1.3 to 2.4 mu m. Atmospheric transmission spectra were recorded over limited wavelength segments in the same region to demonstrate the availability of some of the diagnostic mineral bands that occur close to regions of intense absorption. Changes occur in the appearance of all these spectra caused by instrumental factors such as less than adequate spectral resolution and response time. The features in the mineral spectra are sufficiently characteristic to be used for analytical purposes, especially including those near 1.4 mu m which are unavailable for remote-sensing activities because of atmospheric obscuration. For remote-sensing purposes, the features in the 2.2-mu m region are emphasized as particularly valuable because they are common to alteration minerals and allow discrimination from nonalteration minerals which provide features only as close as 2.4 mu m. Detection of unique features near 1.76 mu m that occur only in alunite and gypsum is possible through the atmosphere and so provides diagnostic potential. The location and shape of mineral spectral features are retained unaltered in the spectra of rocks, and intensity with which they appear is governed by the accessibility of the particular mineral in the rock to the interacting radiation. For remote-sensing purposes, it appears that at least two 0.1-mu m wide filters in the 2.2-mu m region would be necessary to unambiguously identify the presence or absence of alteration minerals, and that judicious selection of the exact location of filters could provide finer discrimination.

Error analysis for remote reference magnetotellurics

Abstract: Remote reference magnetotellurics (MT) yields estimates ZR of the true impedance tensor Z in terms of average crosspowers between a reference field measured at a distant site and the electric and magnetic fields at the sounding location. In contrast to conventional estimates of Z, ZR is unbiased by the noise power in any field, provided the reference is uncorrelated with the noise in the electric and magnetic channels. When bias errors are eliminated, the accuracy of an estimate of Z is determined by random errors. The variance in each element of ZR can be expressed in terms of known average powers, if it is assumed the noises are independent of the signals, and that the noises are stationary. The variances decrease as the number of measurements N contained in the average powers increases. Hence, they can be made arbitrarily small. For small errors, the variance in any function of Z (for example, apparent resistivity, the phase of Z and the skewness), can be obtained from a Taylor expansion of the functio...

Effects of formation anisotropy on resistivity‐logging measurements

Abstract: Some developments in the mathematical analysis of resistivity well-logging measurements in anisotropic beds are presented. Treatment of the no-borehole case in which two thick, anisotropic beds meet at a plane interface for bedding planes parallel to the interface is extended to include arbitrary orientation of the bedding planes. Relations are derived for finding the potential distributions in the two media produced by a point current source in one of them. Numerically evaluated apparent-resistivity profiles across the boundary between two anisotropic beds are shown for a normal resistivity-logging device for various conditions of anisotropy and dip. For electrode devices using alternating current, solutions are derived in terms of the vector potential for the case of a borehole penetrating a thick anisotropic bed normal to the bedding planes and for the no-borehole case where the sonde axis is perpendicular to a sequence of beds with all bedding planes parallel to the bed boundaries. For induction-logging devices, the transmitter-coil sources of the electromagnetic (EM) field are treated as (alternating) magnetic dipoles. When the source- and receiver-coil axes both are oriented perpendicularly to the bedding planes, only the component of resistivity parallel to the bedding planes affects the responses. With the addition of coilsmore » oriented parallel to the bedding planes, it is theoreticallypossible to determine formation dip from the out-of-phase (reactive) voltages in the receiver coils. Analyses are outlined for a homogeneous medium, for a thin bed, and for borehole cases usually considered. Values of the horizontal and vertical conductivities (and coefficient of anisotropy) can, in principle, be derived from the measured values of the induction-logging conductivity signal and the out-of-phase signal from the formation. 21 figures, 4 tables.« less

Interpretation of depositional facies from seismic data

Abstract: Depositional environments can be predicted from seismic data through an orderly approach to the interpretation of seismic reflections. One keystone to this approach is an understanding of the effects of lithology and bed spacing on reflection parameters. Amplitude, frequency, and continuity are some of the parameters most useful for interpreting environments. Reflection amplitude contains information on the velocity and density contrasts at individual interfaces and on the extent of interbedding. Frequency is primarily a characteristic of the nature of the seismic pulse, but it is also related to such geologic factors as the spacing of reflectors or lateral changes in interval velocity. Continuity of reflections is closely associated with continuity of bedding (e.g., continuous reflections suggest widespread, layered deposits).A second keystone to this interpretive approach is the parallelism of reflection cycles to gross bedding and, therefore, to physical surfaces that separate older from younger sediments. Exceptions to this concept include (1) fluid contact reflections, (2) limitations imposed by seismic resolution, and (3) various non-geologic coherent events. In spite of these exceptions, this concept provides a powerful tool for the analysis of reflection patterns.Reflection cycle patterns include the configuration of reflections (i.e., layered, chaotic, and reflection-free) and the nature of cycle terminations at the depositional unit boundaries. The external form of the depositional unit can be analyzed from a grid of seismic lines and is valuable in interpreting the depositional processes responsible for the unit. Sheet, sheet drape, wedge, lens, fan, and other forms are described. The areal associations of these forms are often critical to environmental interpretation. Examples of facies interpretation from seismic sections are shown for depositional environments ranging from shelf to basin floor.

On White’s model of attenuation in rocks with partial gas saturation

Abstract: In two important papers, J.E. White and coauthors (White, 1975; White et al, 1976) have given an approximate theory for the calculation of attenuation and dispersion of compressional seismic waves in porous rocks filled mostly with brine but containing gas-filled regions. Modifications of White's formulas for k/sub E/ and Q in the case of gas-filled spheres brings the results into good agreement with the more exact calculations of Dutta and Ode' (1979 a, b, this issue), who used Biot's theory for porous solids. In particular, the modified formulas give the expected Gassman-Wood velocity at very low frequencies. Inclusion of the finite gas compressibility in numerical calculations for gas-filled spheres shows an interesting maximum of the attenuation at low gas saturations which is not seen if the gas is ignored. A comparison of the attenuation calculated for the same rock and fluids but for three different geometries of the gas-filled regions suggests that the configuration of the gas-filled zones does not have an important effect on the magnitude of the attenuation.

Seismic velocities in transversely isotropic media

Abstract: When a sedimentary earth section is layered on a scale much finer than the wavelength of seismic waves, the waves average the physical properties of the layers; a seismic wave acts as if it were traveling in a single, transversely isotropic solid. We compute the velocities with which P‐waves, SV‐waves, and SH‐waves travel in transversely isotropic solids formed from two‐component solids and find the corresponding moveout velocities from t2-x2 plots. The combinations studied are sandstone and shale, shale and limestone, water sand and gas sand, and gypsum and unconsolidated material, one set of typical physical properties being selected for each component of a combination. A reflector at 1524 m and a geophone spread of 0–3048 m are assumed. The moveout velocity for an SH‐wave is always the velocity for a wave traveling in the horizontal direction. The P‐wave moveout velocity found from surface seismic data can be anywhere from the vertical P‐wave velocity to values between those for vertical and horizontal...

Seismological investigations at The Geysers geothermal field

Abstract: Two short (4 and 6 day) recording periods at The Geysers geothermal field provided useful data on two large refraction explosions and numerous microearthquakes. The vapor-dominated reservoir appears to be characterized by regionally anomalous high P- and S-wave velocities and low attenuation, but the anomaly seems to decrease, possibly reversing, with depth. Microearthquakes occur in a diffuse pattern, with no indication of dominant throughgoing faults and an absence of activity in the main production zone. Mechanisms are generally consistent with northeast-southwest compression. Occurrence rates indicate a slightly high incidence of smaller magnitude shocks. It is possible that the microearthquake activity is related to an expanding steam zone. While the present anomalies appear to delineate the reservoir, it is not certain that they would have been detectable during exploration prior to large-scale exploitation of the field.

Calculations of self‐potential anomalies near vertical contacts

Abstract: The self‐potential anomalies due to streaming potential effects in the vicinity of a vertical contact are analyzed. This approach is different from most previous studies in that the source is tied to a specific physical mechanism instead of arbitrarily selected charge distributions or current sources. The analysis is valid for any source mechanism that can be thought of in terms of crosscoupled flows, e.g., the thermoelectric effect or chemical potential gradients. The anomalies tend to be antisymmetric across the contact with the magnitude of the anomaly being larger on the more resistive side of the contact. An analytic expression for the case of a constant intensity, rectangular source is derived from the general solution. The anomalies for this simple case are computable with a handheld calculator and can be used to estimate the location, extent, and magnitude of the anomaly source region. With this information it is possible to determine the most probable crosscoupling source mechanism.

One-dimensional inversion of natural source magnetotelluric observations

Abstract: Natural source magnetotelluric (MT) data are inverted to find a subsurface resistivity which is isotropic and a continuous function of depth. The inversion consists of two parts. In the first, our concern is to construct a resistivity structure whose responses are acceptably close to the observations, that is, the measured amplitudes and/or phases. This construction proceeds iteratively and is realized through an automated algorithm which is characterized by numerical stability and rapid convergence. In the second part, we attempt to investigate the degree of nonuniqueness inherent in the problem. This is accomplished by considering only spatial averages of the resistivity because all models linearly close to the constructed model will have the same average resistivity. The predictions of this statement are examined quantitatively in an example where the averages from five different models which reproduce the observations are compared. In an example using data from a moderately complex layered model, we h...

Cross-borehole electromagnetic probing to locate high-contrast anomalies

Abstract: Electromagnetic (EM) probing between boreholes is useful for locating high-contrast geophysical anomalies such as a tunnel. Theoretical and experimental studies of EM field interaction with a tunnel show that minima in the received signal can be used for locating the tunnel. The theoretical studies show that as a transmitter and receiver are lowered in separate boreholes, the minima can be interpreted easily to yield both the lateral and vertical positions of the tunnel. The main mechanism of EM field interaction with the tunnel appears to be diffraction, and the spatial variation of the field strength is affected by the tunnel shape. Frequencies from 10 to 70 MHz were studied to assess the usable frequencies. The field in the receiver borehole was an effective diagnostic when a half-wavelength in the surrounding medium was less than or equal to the diameter of the tunnel. EM probing at two test sites gave the locations of tunnels within 1 ft of the surveyed locations.

A signal processing method for circular arrays

Abstract: The theory of spectral representations of stationary random processes can be a useful tool in signal processing. Using this theory, it is possible to derive simple methods of estimating the phase velocity of surface waves from observations made with a circular array. The methods are totally nondirectional, thus allowing the use of microseisms for exploration seismology. Furthermore, the methods can be extended to yield directional information about both correlated and uncorrelated signals.