Showing papers in "Geophysics in 1969"

Velocity spectra-digital computer derivation and applications of velocity functions

Abstract: Multifold ground coverage by seismic techniques such as the common reflection point method provides a multiplicity of wave travel path information which allows direct determination of root‐mean‐square velocities associated with such paths. Hyperbolic searches for semblance among appropriately gathered arrays of traces form the basis upon which velocities are estimated. Measured semblances are presented as a velocity spectral display. Interpretation of this information can give velocities with meaningful accuracy for primary as well as multiple events. In addition, the velocity data can help correctly label events. This paper outlines the fundamental principles for calculating velocity spectra displays. Examples are included which demonstrate the depth and detail of geological information which may be obtained from the interpretation of such displays.

Estimation of seismic noise structure using arrays

Abstract: A theoretical study of the use of arrays for the analysis of seismic noise fields has been completed. The frequency‐wavenumber power spectral density P(kx,ky,f) is defined and techniques for estimating it are given. The estimates require that the auto‐ and crosspower spectral densities be estimated for all elements in the array. Subject to certain asymptotic properties of these auto‐ and crosspower spectral density estimates, expressions for both the mean and variance of the estimates of P(kz,ky,f) have been obtained. It has been demonstrated that if P(kx,ky,f) is estimated by the Frequency Domain Beamforming Method, then the estimate has the same stability as the estimates of auto‐ and crosspower spectral density. P(kx,ky,f) has been estimated from both long‐ and short‐period noise recorded by the Large Aperture Seismic Array in Montana. At frequencies higher than 0.3 Hz, a compressional body‐wave component which correlates with atmospheric disturbances over distant oceans has been detected. In the frequ...

Predictive deconvolution: theory and practice

Abstract: Least-squares inverse filters have found widespread use in the deconvolution of seismograms. The least-squares prediction filter with unit prediction distance is equivalent within a scale factor to the least-squares, zero-lag inverse filter. The use of least-squares prediction filters with prediction distances greater than unity leads to the method of predictive deconvolution which represents a more generalized approach to this subject.The predictive technique allows one to control the length of the desired output wavelet, and hence to specify the desired degree of resolution. Events which are periodic within given repetition ranges can be attenuated selectively. The method is thus effective in the suppression of rather complex reverberation patterns.

The equivalent source technique

Abstract: The inherent ambiguity of potential field interpretation can be put to advantage. Bouguer anomaly measurements on an irregular grid and at a variety of elevations can be synthesized by an equivalent source of discrete point masses on a plane of arbitrary depth below the surface. By keeping the depth of the plane within certain limits relative to the station spacing, we can ensure that the synthesized field closely approximates the true gravity field in the region close to and above the terrain. Once the equivalent source is obtained, the projection of the Bouguer anomaly onto a regularly gridded horizontal plane is easily done. In addition, the equivalent source can then be economically used to carry out vertical continuation. The technique is illustrated by a hypothetical example and a case history of a local gravity survey in precipitous topography.

Contouring of vlf‐em data

Abstract: Prospecting for conductive deposits with ground VLF-EM instruments has received considerable impetus with the recent development of lightweight receivers. The large geologic noise component, which results from the relatively high‐transmitted frequency, has caused some critics to avoid use of the technique. Those who routinely perform surveys with a VLF-EM unit find that, in some areas, a 5‐degree peak‐to‐peak anomaly can be significant, whereas anomalies having amplitudes in excess of 100 degrees may occur as well. Consequently, there is a dynamic range problem when presenting the results as profiles plotted on a field map. A data manipulation procedure is described which transforms noisy noncontourable data into less noisy contourable data, thereby eliminating the dynamic range problem and reducing the noise problem. The manipulation is the result of the application of a difference operator to transform zero‐crossings into peaks, and a low‐pass smoothing operator to reduce noise. Experience has shown tha...

The use of schlumberger and equatorial soundings in groundwater investigations near el paso, texas

Abstract: Electrical soundings using the symmetric AMNB Schlumberger and the bipole‐dipole equatorial arrays were made along two profiles near El Paso, Texas, in support of a groundwater exploration program which included seismic refraction and gravity surveys. Electrode spacings (AB¯2 or R) reaching 12,000 ft allowed exploration to depths of about 7000 ft. Geoelectrical information on the subsurface materials was augmented by sounding with the bilateral equatorial configuration and by transforming Schlumberger curves into dipole‐polar sounding curves with formulas developed by Al’pin and by Tsekov. The bilateral equatorial sounding curves were found useful for detecting the direction of dip of highly resistive bedrocks whereas transformed sounding curves were used to evaluate the average longitudinal resistivity, and hence the depth, to the “electric basement.” A few of the Schlumberger sounding curves were either clearly or subtly distorted by nonhorizontal geologic structures. The interpretation of these soundin...

Bicubic Spline Interpolation as a Method for Treatment of Potential Field Data

Abstract: A method for the generation of bicubic spline functions is presented in this paper. From this method it becomes apparent that these functions derive their potential strength in accurate and reliable representation of two‐dimensional data by maintaining continuity of the variable and its slope and curvature throughout the area of observation. The results obtained by computing horizontal and vertical derivatives with model and field data illustrate the exceptional accuracy achieved with spline functions. The piecewise cubic polynomial functions expressing observed data analytically in space are used to estimate amplitude and phase spectra of magnetic anomalies. At relatively long wavelengths the amplitude spectrum thus calculated displays remarkable similarity with the true spectrum and is found to be superior to that obtained with two‐dimensional Fourier series expansion. A cubic spline method is also presented for computing values of an observed variable at equispaced points along two orthogonal direction...

Application of deep electrical soundings for groundwater exploration in Hawaii

Abstract: Forty‐five resistivity soundings, using Schlumberger and equatorial dipole electrode configurations, were made on the islands of Oahu and Hawaii to determine the applicability of direct current resistivity methods for locating freshwater aquifers in the State of Hawaii The soundings were made on the northwestern part of the island of Oahu near the town of Waialua and on the island of Hawaii on the “saddle” area near Pohakuloa and Humuula Interpretation of 32 sounding curves obtained on the island of Oahu indicates that it is possible to correlate five stratigraphic units underlain by a vesicular basalt basement and that the determination of the approximate depth to the fresh‐water‐saline‐water interface within the basalt is feasible Two of these Schlumberger soundings with electrode spacings AB¯2 reaching 6000 ft yielded sounding curves of the maximum and minimum types whose terminal branches asymptotically approach a resistivity of about 30 ohm‐m, which is believed to be the true resistivity of basalt

Ip and resistivity type curves for three‐dimensional bodies

Abstract: A new method for calculating anomaly patterns and type curves of apparent resistivity and apparent chargeability over three‐dimensional bodies imbedded in a half‐space is practicable. The solution of the boundary‐value problem for a point source of current near a body of arbitrary shape in the form of an inhomogeneous integral equation is solved numerically by the method of least squares. The solution is then used to construct the apparent resistivity and apparent chargeability functions for three and four‐electrode arrays in the vicinity of the body in a straightforward manner. Type curves show the application to an actual field example. Finally, some simple, direct aids for interpreting anomalies over mineralized zones of compact (i.e. roughly spherical) shape result. This study represents the results of the first phase of a continuing program of research into resistivity and IP interpretation theory.

The attenuation of compressional waves in marine sediments

Abstract: A number of mechanisms have been proposed to account for the attenuation of compressional waves in water‐saturated sediments. These include viscous losses between the particles and the fluid, and “solid friction” losses between the particles. The mechanisms are discussed and it is shown how the low values of attenuation observed in pure clays arise from the electrical interaction forces between the surface‐active particles. It is proposed that the attenuation in clay‐ and silt‐size sediments (up to 6 phi mean diameter) arises from viscous interaction between the clay‐water “fluid” and the non‐surface‐active particles. Both new and published experimental measurements indicate that the proposed mechanism is valid, at least in a frequency range 30 to 370 kHz. For sediments of mean particle diameter greater than 6 phi, both new and published experimental results are presented to show that, although under the circumstances of a very well sorted sediment under zero overburden pressure a viscous dissipation mech...

Seismic Attenuation of Gulf Coast Sediments

Abstract: Previous efforts to measure the attenuation of seismic energy as it propagates vertically through the earth have been restricted to thick, isotropic, homogeneous sections of material. Values have now been obtained from normally layered Gulf Coast sediments. After normalizing with respect to the shot, the spectra of many traces over a small interval in depth can be averaged to minimize reflection interference and to yield a frequency response function associated with a given depth. Except for the measurements in the low velocity layer (LVL), a cemented array of geophones 1000 ft deep was used. The LVL measurements were made using individually cemented geophones. Data were taken on a digital recorder using a 0.5 ms sampling rate, and the processing was performed on a digital computer. Attenuation was found to vary exponentially with frequency to the first power in the range from 50 to 400 Hz. The 1000‐ft section of earth, made up largely of clay and sand layers, was separated into four sections at depths of...

Optimum second‐derivative and downward‐continuation filters

Abstract: Second‐derivative and downward‐continuation filtering are often employed to enhance gravity and magnetic maps. Noise due to aliasing, measurement errors, and near‐surface sources can be greatly amplified and lead to erratic filter outputs which produce spurious anomalies. To prevent this undesirable occurrence, it is often necessary to smooth the data, or equivalently, to modify the response of the applied filter. By means of the Wiener filter theory it is possible to derive optimum second‐derivative and downward‐continuation filters in either the wavenumber or space domain. Application of the theory involves separating the power spectrum into signal and noise components. A white noise assumption is realistic if the noise is due to small random near‐surface sources, random measurement errors, and random errors in corrections for terrain and elevation. As a striking demonstration of the superiority of optimum filters, the effects of optimum and “ideal” filters on a synthetic gravity map are compared.

A least-squares method of interpreting magnetic anomalies caused by two-dimensional structures

Abstract: The equations relating the magnetic anomalies to the shape and susceptibility of a body are nonlinear with respect to the coordinates describing the shape. Therefore, iterative procedures must be used to obtain least‐squares estimates of the body coordinates. One method in general use for obtaining nonlinear least‐squares estimates is the Gauss method. This method often fails when the initial values for the structures and susceptibilities do not adequately account for the magnetic anomalies. Another method known as the steepest descent method generally converges to a solution; however, a large number of iterations are required. A method suggested by Marquardt (1963) incorporates the best features of the previous methods. In this paper the Marquardt method is applied to the interpretation of magnetic anomalies. For this purpose the two‐dimensional formulas derived by Talwani and Heirtzler (1964) are used to relate the geometry of a body to the resulting magnetic anomalies. The procedure efficiently control...

a Deep-Sea Electrical Resistivity Probe for Measuring Porosity and Density of Unconsolidated Sediments

Abstract: A study has been made of the mass physical properties and electrical resistivity of marine sediments. The well-known linear correlation of density with porosity was confirmed. A third-degree polynomial curve was found to be the best fit for the data relating porosity and the formation factor, which is the ratio of the bulk resistivity of marine sediments, to the resistivity of interstitial water. An electrical resistivity probe has been devised to obtain in place profiles of resistivity versus depth. The instrument is 13 m long and weighs 700 kg in water. About thirty rapid measurements on the sea floor can be made in one lowering. Good correlation was obtained between electrical probe measurements and direct porosity measurements made on cores taken nearby.

Quasi-Static Transient Response of a Conducting Permeable Sphere

Abstract: When a conducting body is immersed in a time-varying magnetic field, eddy currents are induced. These, in turn, produce a secondary magnetic field which may be detected by an observer external to the sphere. It has been demonstrated that a measurement of the external field can be used to estimate the conductivity of the body if certain assumptions are valid. For example, Ward (1953) has shown that the conductivity and permeability of geological core specimens from diamond drill holes may be determined by examining the frequency dependence of the time-harmonic response of the specimen. In principle, the same information should also be available from the time response of the specimen for a suddenly applied magnetic field (Wait, 1951). In this paper, we wish to discuss the transient solution when a homogeneous conducting sphere is under the influence of a transient magnetic field. Also, as suggested earlier by Wait (1951), the actual time-domain electromagnetic response of a massive sulfide body should exhibit features akin to this transient solution. Thus, the results should have application in mining geophysics. We consider both a nonpermeable and a permeable sphere, using a different approach for each. Because the former is a special case of the latter, a consistency check is obtained.

a Comparison of Terrestrial Heat Flow and Transient Geomagnetic Fluctuations in the Southwestern United States

Abstract: Magnetic time‐variations between Tucson, Arizona and Sweetwater, Texas indicate that a zone of high electrical conductivity underlies the southwestern United States. The interpretation of this zone by Schmucker as a rise of the isotherms in the upper mantle is supported by six heat flow observations along the line of the geomagnetic profile. These and other observations indicate a high but variable heat flow in the Basin and Range Province which contrasts strongly with the uniform values of 1.1μcal/cm2sec reported for the Texas Foreland. The width of this high heat flow anomaly, which may extend across the entire Basin and Range Province, suggests anomalously high temperatures in the upper mantle. This interpretation is further supported by magnetotelluric data between Phoenix, Arizona and Roswell, New Mexico and by the low seismic Pn velocity and negative gravity anomaly. It is suggested that the “anomalous mantle” may be related to the tectonic evolution of the western United States and the late Cenozoi...

Physical properties of marine sediments as related to seismic velocities

Abstract: An investigation of the dependence of seismic velocities on different physical properties of naturally occurring fresh-water sediments in Lake Erie has been conducted. Cores from one lake bottom were collected and the longitudinal seismic wave velocities as well as the physical properties (grain density, bulk density, porosity, median diameter, and phi deviation) were measured. The data were fitted with a second-order polynomial in all the physical properties to the seismic velocity. Independent variables were ranked according to their individual effect upon the sum of the squares of the regression residuals. A variance-analysis table was set up, and the coefficients were tested by a series of F ratios at certain probabilities.As porosity and bulk density are linearly related, these were not included together in the same model. There are strong indications that the porosity and its square together with the median diameter play a significant role in determining the seismic velocity at the probability of 0.90. At the higher probability of 0.99, the median diameter proved insignificant. The cubic term of porosity is insignificant at the 0.50 level.

A deep schlumberger sounding to investigate the electrical structure of the crust and upper mantle in south africa

Abstract: A deep Schlumberger electrical sounding on the Namaqualand Granite‐Gneiss Complex has been carried out. The sounding center is situated near the middle of this body which measures approximately 500 km by 150 km. Whereas in previous investigations of a similar nature, current electrode spacings have generally been limited to less than 100 km, the use of a telephone line as an emission line has made it possible to extend the maximum current electrode separation to 270 km. Factors which may have influenced the reliability of the measurements include leakage tests, measuring accuracy, lateral effects, and surface electrode effects. The interpretation of the sounding curve which shows the existence of six layers was carried out with the aid of a computer. Some comments are made about the range of the principle of equivalence in the interpretation from the computed results. In particular the results suggest that the lower crust has an extremely high resistivity of approximately 40,000 ohm‐m supposedly due to de...

The Determination of Optimum Gate Lengths for Time-Varying Wiener Filtering

Abstract: The response function of a time-varying filter changes with the output signal, or observation time. Most existing time-varying filter techniques involve the empirical division of a seismic trace into a number of gates (or time windows) of given length, and a time-invariant filter is determined for each such gate. Few treatments have dealt with analytical methods to establish the gate lengths according to some optimum criterion.This paper describes a technique for the determination of optimum gate lengths. It is based on the work of Berndt and Cooper, which is here applied to the calculation of time-varying Wiener filters. The Berndt and Cooper technique produces an upper bound for the mean-square error between the true and a given approximated time-varying correlation function. The minimization of this upper bound leads to a relation which enables one to establish gate lengths directly from the input trace. Thereafter, ordinary time-invariant Wiener filters can be computed for each gate. The overall filtered trace is obtained in the form of a suitably combined version of the individually filtered gates.Experimentally it is shown that, with the Berndt and Cooper technique to determine optimum gate lengths, time-varying Wiener filters can be better than a time-invariant filter.

Multivariate analysis used in the detection of stratigraphic anomalies from seismic data

Abstract: In attempting to interpret stratigraphic changes from seismic data, we usually try to detect quantitative changes in one or two variables: amplitude of a peak, say, or time interval between peaks. At times, we may try to detect qualitative changes in wave shape. Differentiating stratigraphic conditions from a single variable, say time interval or amplitude, is often very difficult because the observed differences within the variable may be small and within the expected range of noise. However, a linear combination of a larger number of variables can, in some cases, uniquely describe a specific stratigraphic condition. Furthermore, linear coefficients can be computed which will optimize the discrimination between stratigraphic conditions. Stratigraphic conditions such as the variation from a sand to a shale can be described by seismic measurements, say amplitudes at discrete times. For example, X11, X12, ⋯, X1n can represent the digitized amplitudes of a synthetic seismogram from one sand well; X21, X22, ⋯...

Magnetic orientation of borehole cores

Abstract: The use of natural remanent magnetization (NRM) to orient boreholes was reported at least thirty years ago (eg, Lynton, 1938) The method depends upon determining the direction of remanent magnetization of the sample and relating it to the geomagnetic field in which the rock was presumed to have been magnetized If the NRM faithfully records the relevant geomagnetic field and the field is known, the orientation of the core sample is available Unfortunately, the ancient geomagnetic pole positions are not, in general, sufficiently well known to make this method particularly successful for rocks that are older than late Tertiary Moreover, the presence of a weak, viscous component of magnetization parallel to the present geomagnetic field at a given site may produce erroneous results unless it is recognized and eliminated However, the existence of this component provides another means of orienting the core sample Isolation of this component might initially appear to be difficult, but it is actually a st

An automated ultrasonic pulse measurement system

Abstract: Many applications of ultrasonic pulse techniques for studying the elastic behavior of rock have already been disclosed by Hughes et al (1950, 1951, 1952, 1957), Birch (1960, 1961), Simmons (1964 a, b, 1965), Christensen (1965, 1966a & b), and others. Although similar ultrasonic pulse measurement systems have been described by Tocher (1957), Fairhurst (1961), and Gregory (1967), the system described in this paper is automatic and permits continuous monitoring of elastic wave traveltime. Once set up, the system can record elastic wave traveltime at a preset rate for nearly any time period without intervention by an operator. This automated system has been used to study effects of environment on longitudinal pulse velocity in several rocks (Podnieks et al, 1968) and to make other preliminary investigations of longitudinal pulse velocity variations in rock under external influences. This report notes also several applications to problems of current interest to investigators of the elastic properties of rock.

Analysis of the relationship between acoustic reflectivity and sediment porosity

Abstract: Ocean-bottom sediment porosity and acoustic reflectivity are related by a simple linear equation. The equation was derived empirically from data published by several investigations and is valid for a wide variety of sediment types and ocean conditions. The degree of validity of the relationship appears to be excellent as the correlation coefficient between the porosity and acoustic reflectivity is 0.97.

Induced polarization of synthetic high-resistivity rocks containing disseminated sulfides

Abstract: The induced polarization and resistivity of a suite of 74 synthetic, low porosity, “rock” specimens were measured by the pulse transient method. The specimens contained up to 8 percent by volume of sulfide particles in three different grain sizes. A measuring cycle of 5 sec on and 5 sec off was employed, and discharge potentials were recorded for 4 sec by oscilloscope photography. Charging current density was varied between 125μa/cm2 and 0.0125μa/cm2. Chargeability—defined as the time integral, from 15 to 415 ms after cessation of charging, of the instantaneous discharge potential divided by the charging potential—was found to vary from 1 to 30 ms. For current density less than about 0.1μa/cm2, it was independent of charge current density, but decreased about 20 percent/decade with increase in current density. A background chargeability of a few milliseconds, virtually indistinguishable from the sulfide IP, was found in nonmineralized specimens and assumed to be present in all. Chargeability due to metall...

Normal‐moveout and velocity relations for flat and dipping beds and for long offsets

Abstract: Accurate relations between NMO and velocity are needed in modern exploration seismology, especially in long‐offset CDP work, where accurate NMO corrections must be made for stacking, and where several types of velocity averages may be computed with accuracy from NMO data. The velocity average associated with NMO is the time‐rms velocity vrms. Even for long offsets the straight‐ray computation using vrms is usually adequate, but a closer approximation for horizontal reflectors is obtained by reducing the NMO calculated from vrms or reducing the value of vrms2 calculated from NMO by the factor [1-1.4(ΔT/T)(σ/vrms)2], where σ is the rms deviation of the velocity from its mean, T is zero‐offset traveltime, and ΔT the NMO. The difference between time‐average and time‐rms velocities is often several percent. For the velocity function vi=v0+az and for reflectors of arbitrary dip and strike, the NMO is shown to be ΔT≈[X2a/(2v02)]⋅[(1-cos2ψsin2α)/(eaT-1)+sin2(α/2)(sin2ψ-cos2ψcosα)] where X is offset, α is emergenc...

Electromagnetic induction in a solid conducting sphere enclosed by a thin conducting spherical shell

Abstract: By means of a straightforward boundary‐value treatment, a solution is obtained for the electromagnetic response of a homogeneous sphere enclosed by a uniform spherical shell. A quasi‐static assumption is invoked at the outset because attention is directed to slowly varying fields. Expressions are derived for the “in‐phase” and “quadrature phase” response of the induced multipoles. These are a function of the radius, conductivity, and permeability of the core, and the radius, conductivity, and thickness of the shell. Some numerical results for the nonpermeable case indicate that the dependence of the dipole response on the normalized core radius is altered significantly by the presence of the shell. On the other hand, the ability to detect the presence of the core is not greatly impaired.

Sh waves from explosive sources

Abstract: Horizontally polarized shear (SH) waves have been reported from nuclear explosions and very small explosions. This paper presents selected examples of SH waves from charges ranging up to 50 lb and detected by downhole three‐component seismometers. The examples include outgoing SH waves and SH reflections from faults and an escarpment. The SH waves usually can be identified wherever three‐component seismometers are used. The SH waves appear to be generated near the point of detonation in earth materials that have no apparent horizontal changes in lithology, but comprise layers with marked vertical velocity contrasts. The observations neither confirm theoretical explanations that require horizontal changes in material surrounding the charge nor contribute to a satisfactory theoretical explanation for the generation of SH waves from explosive sources.

A magnetotelluric study of resistivity anisotropy

Abstract: The apparent resistivity curves obtained from the magnetotelluric field measurements at the University of Alberta Geophysical Observatory, near Leduc, Alberta, reveal a strong anisotropy. The significance of the direction of the incident magnetic field in interpreting the structure from the apparent resistivity curves is examined in detail for the case of a linearly polarized incident field.The tensor impedance analysis of the data indicates that the directions of the principal axes of anisotropy are aligned parallel to the north-south and east-west measuring axis. The high coherency between the orthogonal horizontal components of the incident magnetic field is in complete agreement with this interpretation.The two apparent resistivity curves are interpreted and an anisotropic layered model is derived. The anisotropy is found to lie in the Precambrian basement down to a depth of 14 km. The isotropic upper layer has a resistivity of 8 ohm-m which is characteristic of the sedimentary section. The anisotropic resistivity structure proposed for the Precambrian basement may be attributed either to local lithological changes in the basement or to major but more distant structure.

An inverse method of magnetotelluric analysis for a multilayered earth

Abstract: In the inverse method of analysis, the model for the resistivity structure is deduced from the data. An iterative process is developed wherein the maximum residual between the measured data and the theoretically deduced values for a successively increasing number of layers is reduced to a value less than the scatter in the data. In carrying out this procedure the parameters for each successive layer are determined and the number of layers required in the interpretation is determined by both the spectral range of the data and the scatter.

Slr reconnaissance of panama

Abstract: SLR (Side‐Looking Radar) was used in lieu of optical photography for reconnaissance of the Darien Province of Panama and parts of Northwest Colombia, and for the construction of geoscience products thereof An AN/APQ‐97 side‐looking radar was used to produce high‐resolution imagery of an area containing approximately 6600 sq mi in 4 hours flying time—an area, furthermore, that is almost perpetually cloud covered The SLR imagery was used to prepare an uncontrolled mosaic and a series of geoscience overlays, including: 1 surface drainage 2 surface configuration 3 vegetation 4 engineering geology This study provides a complete overview of Darien Province and demonstrates the capability of SLR to gather geoscience data in an area that is notorious for the difficulties that its persistent cloud cover poses for the acquisition of usable, optical, aerial photography