Showing papers in "Geophysics in 1975"

Computed seismic speeds and attenuation in rocks with partial gas saturation

Abstract: Calculations for an unconsolidated sand with partial gas saturation show a 20 percent increase in compressional wave velocity between 1 and 100 hz and attenuation of 27 db/1000 ft at 31 hz and 82 db/1000 ft at 123 hz. Shear velocity and attenuation are not affected. Fluid‐flow waves are shown to be responsible for the dispersion and attenuation at low frequencies; relations are derived by extending Gassmann’s viewpoint to include coupling between fluid‐flow waves and seismic body waves. This appears to be an important loss mechanism for heterogeneous porous rocks.

On the Dependence of the Elastic Properties of a Porous Rock on the Compressibility of the Pore Fluid

Abstract: An equation is derived for the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. More generally, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling a cavity in the container. If the pore system or cavity under consideration is filled with a fluid of compressibility κF, the compressibility κ* of the closed container is given by (κ*-κM)-1=(κA-κM)-1+[(κF-κϕ)ϕ]-1. Here κA is the compressibility of the container with the fluid pressure held constant in the interconnected pore system or cavity. Fluids in other pores or cavities not connected with the one in question contribute to the value of κA. ϕ is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, κM and κϕ, of the material exclusive of the pore fluid. When this material is homogeneous, one has κM=κϕ, and the equation reduces to a well‐know...

Three-Dimensional Induced Polarization and Electromagnetic Modeling

Abstract: The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response va...

Resistivity inversion with ridge regression

Abstract: The problem of direct interpretation of apparent resistivity curves from horizontally layered earth models is solved by using the ridge regression estimator. This ridge regression estimator is more stable than the generalized linear inverse estimator that was advocated in a previous paper. The generalized linear inverse method is unstable if the problem is nearly singular. The problem of estimating the standard deviations of the estimated parameters is analyzed. In some layered models the covariance matrix is an accurate estimate of the standard deviations. However, in problems where there is high correlation between parameters, the covariance matrix is not always an accurate estimate. Confidence regions can be contoured in selected parameter spaces to give an accurate estimate of the range of possible layered models that fit the data. Five soundings were chosen to test the inversion scheme. Two of the soundings were theoretical, and the remaining three were field cases. The method works well since it is ...

Audio-frequency magnetotellurics with a grounded electric dipole source

Abstract: The conventional audio‐frequency magnetotelluric method has been useful in problems of shallow exploration to depths of a few kilometers. Because the natural sources are unpredictable in strength and direction, we have examined the possibility of doing magnetotelluric sounding utilizing the ratio of horizontal electric field to horizontal magnetic field from a controlled source. The source chosen for this study was a grounded electric dipole. The equations for the electric and magnetic fields around this antenna as a function of range and azimuth have been calculated for a half‐space and for a one‐layered earth. These calculations were checked for the half‐space case with an analog model and in the field at the Bonneville Salt Flats. In addition, layered cases were calculated, and a field example near Timmins, Ont., studied. Provided the distance of the observation point from the source is three skin depths (relative to the greatest resistivity in the section) or more, the conventional magnetotelluric int...

Spectral Analysis of Gravity and Magnetic Anomalies due to Two-Dimensional Structures

Abstract: The expressions for the spectra of both gravity and magnetic anomalies due to a two-dimensional structure consist of (except for a factor) sums of exponentials. The exponents of these exponentials are functions of frequency and the locations of the corners of the polygonal cross-section of the structure. Two computationally feasible methods for determining the exponents from a given spectrum are described in this paper; they are essentially based on the generation of a system of linear equations. The unknown coefficients in this system of equations are functions of the corner locations.The first method requires expansion of the exponentials in the expressions for the spectra in the form of a series and works reliably when the amplitudes of low frequencies are analyzed. The unknown parameters are determined fairly accurately with this method by suitable combinations of the spectra of the observed anomaly and its moments.The second method utilizes an exponential approximation technique for producing the system of linear equations. If only the spectrum of the anomaly is used, the system of equations becomes ill-conditioned in most cases resulting in grossly inaccurate solutions. However, particular combinations of the spectra of the anomaly and its first and second order moments are found to improve significantly the behavior of the system of equations and thus the quality of results.It has also been found that the mean values of corner locations can be calculated fairly accurately by taking the ratios of the spectra of the anomaly and its moments. Once the corner locations are found, computation of the density contrast in the case of a gravity anomaly and the magnetization contrast for a magnetic anomaly is straightforward.

Recommended standards for digital tape formats

Abstract: Recently a new demand for demultiplexed formats has arisen in the seismic industry due to the utilization of minicomputers in digital field recording systems and because of a growing need to standardize an acceptable data exchange format.

Radar transparencies of mine and tunnel rocks

Abstract: Laboratory measurements of RF complex permittivity have been made on a variety of 'rocks' encountered in mining, tunneling, and engineering works. An RF impedance bridge and a parallel-plate capacitance test cell were employed at frequencies of 1, 5, 25, and 100 Mhz. The results predict that low-loss propagation will be possible in certain granites, limestones, coals, and dry concretes. Existing VHF mining radar equipment should be capable of exploring into such rocks to distances of up to hundreds of feet.Useful but shorter probing distances are predicted for other coals, gypsums, oil shales, dry sandstones, high-grade tar sands, and schists. Radar probing distances of less than 10 ft are predicted for most shales, clays, and fine-grained soils. Uncombined moisture content is evidently the governing factor. Efforts were made throughout the experiments to preserve or simulate the original moisture content of the 'rocks' in place.

The electromagnetic response of a low‐loss, 2‐layer, dielectric earth for horizontal electric dipole excitation

Abstract: The use of the radio interferometry method requires a detailed understanding of the nature of electromagnetic wave propagation in structures composed of materials with low electrical loss. This paper contains the results of a detailed experimental and theoretical study into the response of a 2-layer, plane-stratified, low-loss dielectric earth. The technique used to construct a scale model with microwave equipment to experimentally simulate the 2-layer structure response is discussed. The wave nature of the response derived from the theoretical investigations is used to interpret the features of the experimental results. The experimental results are useful in turn in demonstrating the reliability of approximate theoretical solutions for the electromagnetic fields about the dipole obtained by normal mode and geometrical optics methods. Such features as (1) the modification of the dipole radiation pattern seen when the antenna is placed at the interface between media of differing electrical properties, and (2) the development of guided and leaky modes in the layered structure are examined in detail.

Amplitudes of seismic waves; a quick look

Abstract: A form of Kirchhoff’s wave equation is presented which is useful to the geophysicist doing an amplitude interpretation of seismic reflection data. A simple rearrangement of Kirchhoff’s retarded potential equation allows the reflection process to be evaluated as a convolution of the derivative of the source wavelet with a term called the “wavefront sweep velocity”. The wavefront sweep velocity is a measure of the rate at which the incident wavefront covers the reflecting boundary. By comparing wavefront sweep velocities for geologic models with different curvature, one obtains an intuitive feeling for the relation of diffraction and reflection amplitudes to boundary curvature. Also, from this convolutional form of the wave equation, the geometrical optics solution for the reflection amplitude is easily obtained. But more important, from the wavefront sweep velocity approach, a graphical method evolves which allows the geophysicist to use compass and ruler to estimate the effects of curvature and diffractio...

Computer migration of oblique seismic reflection profiles

Abstract: A reflecting interface with irregular shape is overlain by a material of constant velocity VT. Multifold reflection data are collected on a plane above the reflector and the reflector is imaged by first stacking then migrating the reflection data. There are three velocity functions encountered in this process: the measured stacking velocity VNMO; the true overburden velocity VT; and a profile migration velocity VM, which is required by present point‐imaging migration programs. Methods of determining VNMO and, subsequently, VT are well‐known. The determination of VM from VT, on the other hand, has not been previously discussed. By considering a line‐imaging migration process we find that VM depends not only on the true section velocity but also on certain geometrical factors which relate the profile direction to the structure. The relation between VM and VT is similar to, but should not be confused with, the known relation between VNMO and VT. The correct profile migration velocity is always equal to or gr...

Recent advances and applications in complex resistivity measurements

Abstract: Several years of accumulating complex resistivity spectral measurements have indicated that there are still many unexplored areas in induced polarization surveying that need to be investigated for a more complete understanding of the polarization process. In addition to providing mineral discrimination capabilities, complex resistivity spectra can be used to differentiate between various barren host rock responses, to facilitate the complete removal of electromagnetic coupling, and to identify pipeline, fence, and various other cultural coupling effects. Results of field measurements are presented in an effort to demonstrate the utility of and necessity for making complete spectral measurements for serious geophysical interpretation. Correlation of field measurements with laboratory measurements on core samples from the same area demonstrates that strong electromagnetic coupling can be accurately removed from complete spectra without removing the important rock response. Recent field and laboratory measur...

Ground and airborne resistivity surveys of permafrost near fairbanks, alaska

Abstract: In permafrost regions investigations for such geotechnical endeavors as route selection for roads and pipelines and site investigations for buildings and dam construction often require that a careful assessment be made of the presence or absence of frozen ground, of the ice content of frozen ground, and of the depth of frozen ground. In the vicinity of Fairbanks, Alaska, where the permafrost is discontinuous, ground and airborne methods of mapping electrical resistivity using radiowaves were tested as means of delineating permafrost. When the resistivity maps are compared with surficial geological data, the following conclusions are reached: (1) In areas of fine‐grained sediments, where the near surface sediments are relatively uniform, VLF resistivity delineates permafrost. (2) In areas where surface sediments vary widely (flood plains), VLF resistivity shows little information on permafrost conditions but can provide other important geotechnical information, such as, depth to bedrock, surface soil type,...

Inversion of Gravity Profiles by Use of a Backus-Gilbert Approach

Abstract: Geophysical inversion methods are most effective when applied to linear functionals: it is therefore advantageous to employ linear models for geophysical data. A two‐dimensional linear model consisting of many horizontal prisms has been developed for interpretation of gravity profiles. A Backus‐Gilbert inversion which finds the acceptable model “nearest” to an initial estimate can be rapidly computed; iterative application of the technique allows a single‐density model to be developed at a modest expense in computer time. Gravity data from the Guichon Creek batholith were inverted as a test of the method, with results comparable to those from a standard polygon model.

Magnetotelluric response of laterally inhomogeneous and anisotropic media

Abstract: The lack of agreement between magnetotelluric field measurements and the calculations based on essentially two‐dimensional models with either anisotropy or lateral inhomogeneity necessitates a more complex model of the earth than has been previously considered. The Galerkin finite‐element method is applied to a two‐dimensional structure with a tensor conductivity. The importance of considering conductivity as a tensor is illustrated by a model consisting of an anisotropic, conducting dike embedded in an anisotropic half‐space. This model can be distinguished from an isotropic model by the nonvanishing diagonal elements of the impedance tensor, the ellipticity indices, and the skew.

The block move sum normal moveout correction

Abstract: A new normal moveout technique designated Block Move Sum (BMS) is described. In theory it better approximates the ideal inverse NMO process than do currently utilized techniques. Data blocks are corrected as units thus eliminating trace stretching and reducing trace distortion. The proposed correction and two common production methods are applied to both synthetic and real data and compared. Crosscorrelations calculated from synthetic seismogram data suggest the BMS method creates the least signal distortion. For field CDP data, the BMS does improve signal resolution for events at early times.

EM coupling, its intrinsic value, its removal and the cultural coupling problem

Abstract: The induced polarization method of geophysical prospecting has been in use for more than 25 years with varying degrees of success. Until recently, its two principle drawbacks were (1) the inability to distinguish between anomalous rock responses and, (2) inability to distinguish between these rock responses and inductive coupling. The first problem was solved by K. L. Zonge in 1972. Solutions to the coupling problem go back to 1932, and have been expanded and elaborated upon by successive authors since then. In most of these papers, electromagnetic coupling was separated into two functions, here designated as P, a purely inductive term, and Q, a grounding or purely resistive term. This paper extends this work into a study of the reflective coupling contribution and the effects of anisotropy. Two immediate results are: (a) the development of an ultra‐low‐frequency deep sounding technique for highly conductive overburden environments, and (b) a successful iterative technique for the removal of coupling from...

Migration velocity determination; Part 1, Philosophy

Abstract: Classical stacking velocity determination consists of applying NMO corrections, with a number of constant velocities, to the traces of a CDP gather; computing coherent energy for the NMO‐corrected traces; and mapping the coherency obtained as a function of traveltime and velocity in a form suitable for interpretation. Migration Velocity Determination may be performed by generating migrated traces with a number of constant velocities; computing coherency of the energy migrating into identical positions of the migrated traces; and mapping the coherency as a function of (in this case) vertical traveltime and velocity in a form suitable for interpretation. A typical result of Migration Velocity Determination is a contoured display of coherency as a function of time and velocity. Because of the migration process, the velocities obtained are velocities to points situated along vertical column of the subsurface and are suited to provide an optimum migrated section (migration before stack).

Deep crustal reflections in europe

Abstract: Deep crustal reflected arrivals in the near-vertical and the wide-angle range have been recorded in various parts of Europe. A high resolution of deep crustal structures can be obtained by special seismic investigations. Reconnaissance surveys may be performed during routine prospecting work by using recording lengths up to 15 sec. Several profiles with multiple coverage and digital processing of the data demonstrate the possibility of obtaining seismic cross-sections down to the Moho.In addition to near-vertical reflection work, studies of wide-angle arrivals at distances up to 150 km and more are most favorable for a calculation of seismic velocities in the deeper crust. Ray-tracing programs have revealed low-velocity zones at depths below 10 km in many continental crusts. From a comparison of reflected amplitudes in the near-angle and the wide-angle ranges and from other observations, a lamellar structure in the deeper crust is often detected. Regional differences of various traveltime branches show characteristic crustal structures. It is shown that deep seismic sounding is useful for estimating the shape and development of sedimentary troughs and their connection to oil-bearing structures, heat energy, and possible ore deposits.

Compressional velocities of partially saturated, unconsolidated sands

Abstract: The possibilities inherent in reflection amplitude anomalies or “bright spots” on seismic cross‐sections as indications of gaseous hydrocarbons have stimulated widespread interest. To help evaluate these possibilities, laboratory measurements were made on specimens of compacted Ottawa sand of approximately 30 percent porosity. The measurements were made at five different water saturations (0 percent and 100 percent, and approximately 9 percent, 45 percent, and 85 percent) and net confining pressures to 10,000 psi. The gas was air. Measurements were made with acoustic pulses with a peak frequency of about 700 khz.

Field measurement of the electroseismic response

Abstract: The electroseismic response is a change in apparent resistivity induced by seismic excitation. It can be measured under field conditions with a conventional Wenner array and an explosive seismic source. In coastal plain sedimentary rocks near Gordon, Georgia, a Wenner array with 9-m electrode spacing measured a change in voltage of 100 to 300 μv per mm/sec of 15 hz vertical particle velocity at the surface. The response correlates best with the Rayleigh surface waves and compressional body waves. By assuming a layered medium which is excited uniformly by a seismic disturbance, we can use a Taylor series expansion of the voltage expression for a Wenner array in terms of layer resistivities to obtain estimates of the perturbations of the resistivities in the layers.

The telluric‐magnetotelluric method

Abstract: The telluric-magnetotelluric method uses magnetotelluric measurements at the base site, but only telluric measurements at remote sites. It thus combines the economy, simplicity, and speed of the traditional telluric method with the quantitative advantages of the traditional magnetotelluric method. The dominant features of the combined method are the following: First, the time required to set up a telluric site is less by a factor of at least 5 than the time for a complete magnetotelluric site. Second, one does not need to record magnetic field data at the base site simultaneously with the electric field recorded at each remote site. One needs only enough magnetic data to adequately determine the base tensor. A telluric transfer tensor coupling electric field measurements at the base site and each remote site can be used to transfer the base impedance tensor to an impedance tensor at each remote site. By being much more selective of the magnetic data used in the analysis, one can significantly improve the signal-to-noise ratio. Third, the data are analyzed to determine each element of the complex impedance tensor so that important phase information as well as amplitude information is available for interpretations which are more sophisticated than those currently attempted in conventional telluric surveys. Finally, in making the ultimate interpretation in terms of the impedance tensor rather than the telluric tensor used in conventional telluric surveys, one essentially refers the interpretation of remote electric field observations to the magnetic field at the base site rather than to the electric field. Both experience and model studies demonstrate that the magnetic field is much more homogeneous than the electric field in the vicinity of lateral heterogeneities; thus the selection of a proper base site is not as critical in the combined method as it is in the conventional telluric method.

Automatic three-dimensional modeling for the interpretation of gravity or magnetic anomalies

Abstract: Transformation of gravity or magnetic anomaly maps into isodepth maps of a surface separating two homogeneous media may be accomplished by (1) systematically estimating an average depth and density or magnetization contrast for the surface and (2) using an iterative method to adjust local depths compared to the average depth of the surface. Average depth, density or magnetization contrast, and iterative adjustment of local depths are determined using the Fourier transform of the field to be interpreted and that of the field generated by an equivalent surface. This leads us to propose a method of estimating the average depth of the sources and a distribution function for the depths and then a complete and very economical algorithm for the calculation of the corresponding equivalent surface.

The tokyo surface ship gravity meter: recent developments and results of comparison measurements

Abstract: The Tokyo Surface Ship Gravity Meter (TSSG) employs a single vibrating string accelerometer which is inherently nonlinear. This leads to errors unless its frequency is essentially constant over the sampling intervals. A new processor incorporating pulse train logic and employing a rapid sampling rate of about 50/sec has been designed to replace the digital computer which used about 2/sec.

Elastic‐wave velocity measurements in rocks and other materials by phase‐delay methods

Abstract: The phase delay of a continuous sinusoidal elastic wave after transmission through a medium may be used to determine the velocity of propagation of the wave in the medium. The change in path length for a given frequency, or the change in frequency for a given path length, required to change the phase delay by integral multiples of 360 degrees is measured in the laboratory by the use of source and receiver piezoelectric transducers whose signals are applied to the horizontal and vertical deflection circuits of an oscilloscope. The accuracy of the method depends upon the accuracy with which the frequency of the transmitted wave and its path length through the medium (or change in path length) can be determined, provided the effect of extraneous signals (e.g., boundary reflections, multiple reflections, alternate modes of propagation, etc.) is negligible. The phase‐delay methods are illustrated and compared with conventional pulse methods by using both to make compressional‐velocity measurements in water and...

Digital Convolution for Computing Gravity and Magnetic Anomalies due to Arbitrary Bodies

Abstract: The magnetic and gravitational potentials and fields due to arbitrarily shaped bodies with homogeneous magnetization and uniform density distribution are expressed as a convolution of the source geometry and the Green’s function. The Green’s function depends on the location of the observation point and on either the magnetization vector (in the case of the magnetic field) or the density (in the case of the gravitational attraction). A fast digital convolution algorithm is used for efficiently and accurately calculating anomalies caused by irregular bodies. The shapes of the calculated anomalies faithfully reproduce the exact shapes when the sampling interval selected for digitizing the source geometry and the Green’s function is less than one‐tenth of the depth of the source. In the digital convolution method for computing anomalies, it is unnecessary, for any given structure, to perform analytical integration of the dipolar magnetic field or the gravitational field of a point mass. One of the examples gi...

Deconvolution and spectral estimation using final prediction error

Abstract: Least‐squares, zero‐lag inverse filters may be used for predictive deconvolution of stationary time series and for obtaining autoregressive or maximum entropy spectral estimates. The greatest problem in finding such an inverse filter is determining the optimum operator length for a given finite length of data. The identical problem of determining the correct order of an autoregressive model for the data has been solved by Akaike, whose final prediction error (FPE) statistic is a minimum for the optimum length model. This minimum FPE criterion may be applied to both single and multiple time series. The FPE procedure has been used successfully on simultaneous three‐component seismometer and hydrophone data for the detection of refracted arrivals from explosions up to 1350 km away and for estimation of spectra of microseismic noise observed at the time of each shot. The data were recorded with an ocean bottom seismometer.

Exploring for stratigraphic traps with gravity gradients

Abstract: The vast and growing literature on the search for stratigraphic traps for petroleum ignores gravity gradients, for which the theory has been available since the heyday of the Eotvos torsion balance decades ago. These are discussed in this paper. The horizontal and vertical gradients can be measured with available gravimeters and (to a limited extent) with the Eotvos torsion balance. A major advantage of the gradient method is that surveying to determine position and elevation of the station is not required. Both theory and practice have been reported in the geophysical literature, but the important application to stratigraphic traps has not been mentioned. We evaluate here the method for locating “pinchouts”, a term which embraces “stratigraphic” and “unconformity” traps in Halbouty’s (1972) classification. Both position and depth of the assumed pinchout are determined by the gradient anomaly. The magnitudes of anomalies of horizontal and vertical gradients are about equal. However, pending new instrument...

Special report of the subcommittee on polarity standards

Abstract: This is a report of the SEG Subcommittee on Polarity Standards in exploration seismic recording. A Polarity Standard is recommended for analog and digital representations of seismic impulse signals. A four-bit polarity code is proposed to define: (1) the polarity convention for impulse-source systems; and (2) the relative polarity between a swept-frequency pilot signal and the recorded seismic data for vibratory-source systems. Polarity conventions are to be demonstrated by field tests and confirmed by computer analysis.

The dipole mapping method

Abstract: In the bipole-dipole mapping method, a current field is set up by the use of a bipole current source The current field is then studied by making measurements of electric field intensity with dipole receivers at many locations around the bipole source The values for electric field intensity may be used to compute apparent resistivities if we assume that the earth is uniform or to compute apparent conductance if we assume that the earth resembles a conducting sheet Maps of apparent resistivity values or apparent conductance values may be interpreted by comparing them with similar maps computed analytically for various simplified earth models The bipole-dipole mapping method is useful mainly in locating areas where ground resistivity varies rapidly in the horizontal direction It has found application mainly in exploration for geothermal reservoirs but also has been used for mining exploration and engineering studies, and an example of each is described