Abstract: The gravitational instability of a simple two‐layered medium resting on a rigid base has been treated in terms of the analog model of Biot. In order to avoid complications of purely mathematical nature which are unrelated to the physics of the process of instability and do not affect the results significantly, the analysis is presented for the two‐dimensional case. It is shown that such a system is unstable if the density contrast Δρ between the top layer (overburden) and the bottom layer (salt) is positive. The physically important parameters of the instability are the viscosity ratio and the thickness ratio between overburden and salt and the relative density contrast Δρ/ρ1. These parameters determine the amplification rate of a given initial sinusoidal perturbation of wavelength L of the overburden‐salt interface. For the purpose of isolating the role of each parameter and to provide an understanding of the underlying mechanics, several tables are presented which show the influence of each of these par...

Abstract: Z. F. Danes’s mathematical formulation of salt dome dynamics was modified to the extent that explicit solutions can be obtained. For both the two‐dimensional and three‐dimensional model, a formula is derived relating the rate of growth and the wavenumber of a fundamental mode with the physical and geometrical parameters. It is shown that there exists one wavenumber for which the rate of growth reaches a maximum. In time this component will dominate and control the final pattern.

Abstract: Self‐potential anomalies caused by inclined sheets of infinite horizontal extension may be interpreted in terms of two infinite line poles situated on the body at positions nearest and furthest from the free surface, respectively. The direct interpretation of such pairs of line poles in terms of their positions and strength is possible from the observed anomaly profile. The solution is unique in its own family, i.e., no pair of line poles other than that arrived at by the present method can give rise to the observed anomaly.

Abstract: Body‐wave dispersion is documented for a three‐dimensional case using the pulse propagation experiment in the Pierre Shale conducted by McDonal et al. (1958) and for a two‐dimensional case using ultrasonic pulse propagation in a Plexiglas plate. The magnitude of the dispersion for a five‐octave frequency band was only about two to three percent but easily observable by using Fourier‐analysis techniques. Body‐wave dispersion is shown to be predictable from the attenuation coefficient by following the causal transform technique of Futterman (1962). The principle of superposition is shown to be applicable for the prediction of the pulse anywhere in a medium if the complex propagation constant is known and if the pulse is known at one location. Pulse‐form prediction based on the attenuation coefficient alone is inadequate, while prediction based on attenuation and dispersion is in good agreement with observed results.

Abstract: Underground cavities (and similar marked lateral changes in seismic impedance) having dimensions of tens to hundreds of meters should markedly reflect artificial seismic waves and locally obstruct reflections from deeper horizons. This should be especially true for liquid‐filled cavities if shear waves are employed. Attempts have been made to apply these principles in delineating solution‐mined cavities in bedded salt. In one seismically reverberant area, results from a brine‐filled cavity 300 m below the surface were unclear. Strong seismic “shadows” were found, however, in a seismic reflection survey of solution cavities 500 m below the surface, in a seismically favorable area. At present, the method requires good reflecting horizons both above and below the stratum to be explored. The amplitude ratio of the two reflections is used to represent the seismic “opacity” of the stratum between, normalized for the effect of varying seismic efficiencies at the shots and detectors. Among other applications, the...

Abstract: Recordings to depths of 5 km have been made on the Pacific Ocean bottom with self-rising internally recording seismometers. Simultaneous recordings have been made at land stations. The ocean-bottom noise spectrum is between one and five orders of magnitude higher power than the land spectrum in the region from 0.1 to 9.0 cps. Coherence between two simultaneous instruments separated one-quarter kilometer is above the 95 percent confidence level from 0.1 cps to 0.6 cps. Attempts to associate narrow-beam Love and Rayleigh peaks with large storm-generating areas or with heavy swell striking shore have not produced consistent results. Although some records show the bulk of the microseism peak energy in well-defined modes, the energy is carried in different modes at different times and locations. Some of our data fit a model of microseism generation in a 100-mile strip, by a statistical superposition of incident waves and waves reflected from shore; and the subsequent conversion of the energy to Rayleigh and Love modes propagating away from the generation zone. However, the shapes of the mid-ocean spectra strongly imply additional sources far from shorelines or recognized storms, unless microseisms attenuate far less in the ocean than on land.

Abstract: Change in shear‐wave velocity for four dry sedimentary rocks has been studied as a function of the variation of both external hydrostatic pressure and internal pore pressure in the range 0 to 2,500 psi. The experimental method employs a beam of ultrasonic energy passing through a liquid in which a copper‐jacketed parallel‐sided slab of rock is rotated. The shear‐wave velocity is calculated from the laws of refraction and reflection of waves at a liquid‐solid boundary applied to the angle at which minimum energy is transmitted. The variation of shear‐wave velocity with pressure has been found to be a function of net overburden pressure, Pe-nPi, where Pe=external hydrostatic pressure on the jacketed sample, Pi=internal pore pressure and n = a pressure‐dependent factor less than unity. The values of n at several differential pressures were chosen to yield a smooth curve passing through the displaced data points when the shear‐wave velocities were plotted as a function of net overburden pressure. Using the n ...

Abstract: A procedure suitable for use on high‐speed digital computers is presented for interpreting two‐dimensional gravity anomalies. In order to determine the shape of a disturbing mass with known density contrast, an initial model is assumed and gravity anomalies are calculated and compared with observed values at n points, where n is greater than the number of unknown variables (e.g. depths) of the model. Adjustments are then made to the model by a least‐squares approximation which uses the partial derivatives of the anomalies so that the residuals are reduced to a minimum. In comparison with other iterative techniques, convergence is very rapid. A convenient method to use for both the calculation of the anomalies and the adjustments is the two‐dimensional method of Talwani, Worzel, and Landisman, (1959) in which the outline of the body is polygonized and the anomalies and the partial derivatives of the anomaly with respect to the depth of a vertex on the body can be expressed as functions of the coordinates o...

Abstract: In a horizontally stratified absorptive earth with vertically traveling plane compressional waves, denote the Fourier transforms of the reflectivity, delayed transmissivity, and the acoustic impedance by R, T, and Z, respectively. It is shown that both Z and 1±R are positive real (p‐r) functions. Although R, in general, is neither p‐r nor minimum phase, |R|<1 for real frequencies. T (the transmission function referred to a time origin t1—the one‐way traveltime through the section) is not, in general, p‐r. If the absorption law is a minimum‐phase function, however, then T is minimum phase. If absorption is absent, then the inverse filter for T is not only minimum phase, but is also of a finite duration equal to 2t1.

Abstract: When coherent light from a laser beam is passed through a transparent reduction of a variable‐density or variable‐area record section, the seismic signals act as an optical grating to produce a diffraction pattern which is the two‐dimensional Fourier transform of the section itself. With suitable lenses the diffraction pattern can be converted back into an image of the original section. By obstructing portions of the pattern corresponding to particular frequencies or dips on the section one can remove such frequencies or dips from the reconstructed image. The equipment developed for this processing incorporates special design features to combine high optical resolution, precise discrimination of moveouts and frequencies, limitation in the length of the overall optical path to permit the use of a short optical bench, and visual monitoring by use of a microscope or a closed‐circuit TV system. Filter elements consist of wedges mounted on a rotary stand for velocity rejection, wires of various diameters for b...

Abstract: It is shown that in dry sedimentary rock the velocity of elastic waves depends not only on the present values of the internal and external pressures but also on the past pressure history of the sample. The internal and external pressures are shown to be equally effective in changing velocities, provided the pressure differential follows a pressure cycle previously impressed upon the sample.

Abstract: A new data‐processing technique is presented which utilizes optimum multichannel digital filtering in conjunction with common subsurface horizontal stacking for the efficient rejection of multiple reflections. The method exploits the differential normal moveout between primary and multiple reflections that results from an increase in average velocity with depth. Triple subsurface coverage is obtained in the field; the common subsurface traces are individually prefiltered with different filters and stacked. The digital filters are designed on the least‐mean‐square‐error criteria to preserve primaries (signal) in the presence of multiples (noise) of predictable normal moveout, and random noise. The method achieves wide‐band separation of primary and multiple energy with only a three‐point stack; it can work effectively with small normal moveout differences eliminating the need for long offsets and the attendant signal degradation due to wide‐angle reflections; it does not require equal multiple moveout on t...

Abstract: Accurate laboratory measurements of dry bulk densities of 79 samples of Paleozoic sedimentary rocks from a 2,851‐ft deep core hole near Barberton, Ohio, are the basis of a vertical profile of “natural” density which differs on the average 0.013gm/cm3 or less from a profile of in‐situ density calculated from gravity variations observed using a LaCoste and Romberg gravimeter in an adjacent 2,247‐ft‐deep vertical mine shaft. Both profiles agree well with the most meaningful Barberton core sample densities reported by Hammer (1950, Fig. 3), but are significantly lower than in‐situ interval densities calculated by Hammer from gravity variations observed in the shaft using a Gulf gravimeter. The 0.13gm/cm3 average discrepancy between the old and new in‐situ density profiles is probably attributable to a 12‐percent error in calibration of the Gulf gravimeter. The close agreement between the new profiles of “natural” and in‐situ density suggests that changes in bulk volume of compact sedimentary rocks that occur ...

Abstract: Sediment samples from the Guadalupe Site Mohole drilling program of 1961 have been tested for sound speed and related physical properties. Laboratory measurements of sound speed have been corrected to in‐situ values by making corrections for the temperature gradient within the sediment body, for hydrostatic water pressures within sediment pore spaces, and for a small reduction in porosity. Resulting in‐situ sound speeds vary from 1,484 m/sec at the sediment surface to 1,584 m/sec at a depth in the sediment of 136 m. The resulting sound‐velocity gradient is approximately 1.0sec-1; the interval velocity is about 1,565 m/sec. Sound speed in the surficial sediments is about 2.2 percent less than in the water just above the sea floor.

Abstract: It is shown that care should be taken in using the term "velocity" in connection with wave propagation in inhomogeneous media. An expression is derived for phase velocity which depends on frequency and depth. Exact solutions are found for normal and oblique incidence, for plane-wave propagation in a liquid medium. It is shown that the geometrical optics approximation solution, valid for high frequencies, is the first term in an asymptotic expansion of the exact solution.The reflection coefficients are obtained for a linear transition layer between two homogeneous half-spaces. Both first-order and second-order discontinuities in density and bulk modulus are considered at the boundaries of the transition layer.

Abstract: The use of normal modes to represent the propagation of elastic waves at large horizontal offset is well known. By addition of the relevant leaky modes, the mode theory is shown to be useful for representation of the seismograms at shorter range. A theoretical model consisting of a 2‐cm brass layer over a steel half‐space is considered. Dispersion curves and excitation functions are computed for the first four normal modes and the first three PL modes. Attenuation as a function of frequency also is computed for the PL modes. A suite of seismograms is computed for the distance range 50–70 cm, showing each mode individually and their sum (the total seismogram). It is found that, for the distances used, the individual modes do not approximate transients with a definite “arrival” time. Only their sum is required to exhibit this physical behavior. In addition, at short distances, the dispersion of a single mode is not visually obvious although the dispersion curve may be recovered by use of Fourier transform m...

Abstract: Recordings taken in a region having a very thin sedimentary section (less than 100 m thick) with normal reflection prospecting equipment, using 100 to 300 kg of explosive in holes less than 10 m deep, with geophone spreads 580 m long set from two to 15 km from the shot, show events most easily interpretable as reflections. If the reflection interpretation is accepted and multiple reflections are too weak to be observed, then there are many reflectors of low dip between 8‐ and 35‐km depth in this region. The strongest and most consistent group of events in the 22 recordings arrives at about 8 sec and corresponds to a depth agreeing approximately with the crustal depth obtained by refraction methods across this region. It is emphasized that the reflection view and the refraction view may be essentially different; the latter being insensitive to low‐velocity layers and to thin, high‐velocity layers such as sills might present, whereas the former is insensitive to a gradual transition over a kilometer of dept...

Abstract: This paper reports an investigation by the scale‐model method of how the response of a horizontal‐loop electromagnetic system to a vertical, sheetlike conductor is modified by the presence of a conducting overburden. It was found that the overburden makes the vertical conductor seem more conductive and more deeply buried than it really is, and that the vertical conductor’s in‐phase anomaly may become reversed in sign.

Abstract: During 1962 and 1963, the Dominion Observatory conducted refraction seismic surveys in the islands north of the Canadian mainland. These surveys are part of a project of the Government of Canada to explore the Polar Continental Shelf. The operation consisted of three stationary recording units and a shooting party which traversed the frozen sea in a tractor train. Three refraction‐seismic profiles form a continous section from the Canadian Shield through the Franklinian Geosyncline and the Sverdrup Basin to the Arctic Ocean. Post Devonian sediments in the Sverdrup Basin were found to be 10 km thick. The lower, basic portion of the crust is indicated by a velocity of 7.3 km/sec at a depth of 24 km and the base of the crust at 38 km.

Abstract: The weak dependence of the results of pulsed neutron logging on the presence of the oil well borehole suggests that thermal neutron die‐away measurements in an open hole may be capable of “seeing” beyond a limited amount of borehole fluid invasion. In order to obtain an estimate for the depth of investigation which can be expected from pulsed neutron logging when some invasion has occurred, multigroup neutron diffusion theory was used to calculate thermal neutron lifetimes for the open‐hole logging geometry. The transient, three‐group equations were solved with the aid of an IBM 7090 computer. Two cases of open‐hole fluid invasion were investigated: Fresh‐water filtrate invading a salt‐water‐saturated formation, and salt‐water filtrate invading a formation saturated with fresh water (or oil). In both cases the formation is assumed to be a 20 percent porosity sandstone and the fluid‐filled borehole is taken to be 20 cm in diameter. It is shown that for any given depth of borehole fluid invasion, up to the ...

Abstract: Variable‐density seismograms were originally developed in exploration work to aid in the visualization of strata formations. They can also be directly analyzed by means of optical diffraction. When a plane wave of spatially coherent monochromatic light passes through a variable‐density seismogram, a diffraction pattern can be formed which defines the seismic frequencies. The seismogram is placed so that it affects the incident light in the same manner as a diffraction grating in a conventional spectroscopic apparatus. Resulting diffraction patterns reveal continuous energy‐density spectra over a range of about nine octaves. The spectra are normally two‐dimensional. When variable‐density profiles are used, the second dimension of the spectra is wavenumber, which is expressed as the diffraction caused by density variations across the data channels. The spectra can be made one‐dimensional by inserting a cylindrical lens so that an image of the seismograms is formed in one direction in the same plane that Fra...

Abstract: As part of a continuing program, Texas A. and M. University has been making a surface‐ship gravity survey of the Gulf of Mexico. The 1963 free‐air anomaly map of the Gulf is the second in a series of maps resulting from these investigations; it includes not only a larger area than the first map, but also measurements having considerably higher accuracies. The present map indicates, as the first one suggested, that the Gulf of Mexico is essentially in isostatic equilibrium but contains local mass anomalies. Two cross sections of crustal layers were constructed which are consistent with the gravity observations and published seismic‐refraction results. One section extends from Galveston, Texas, to the Yucatan Peninsula, and the other from the Sigsbee Deep to Florida. Both sections consist of four to six layers, in which layer densities were assumed to be uniform laterally and the density below the Mohorovicic discontinuity constant. Densities of the layers were converted from seismic velocities using the Dr...

Abstract: High‐frequency geometric ray theory is used to investigate the refracted arrival from a high‐speed layer embedded in an infinite medium. The effect of changing the layer thickness to dominant wavelength ratio (E/λd) and the range to depth ratio (ρ/H) is analyzed for a point compressional source. The results approximate the exact solution when E/λd⩾1. The theory predicts shingling and shows that it is range‐limited. Factors which improve the resolution between reflected arrivals increase the range over which shingling occurs. As the range increases, the traveltime curves for all the multiply reflected rays which cross the layer the same number of times in the shear mode approach the same asymptote (regardless of the number of crossings in the compressional mode). When the layer is thick compared to the dominant wavelength, the refracted arrival may consist of a series of events separated by equal time intervals. Each event is produced by the superposition of reflected waves which cross the layer the same n...

Abstract: Six examples of relationships between aeromagnetic anomalies and producing areas are presented by maps of subsurface structure, observed aeromagnetics, second vertical derivatives of the aeromagnetic fields, and maps of the magnetic basement computed from the aeromagnetic data whenever all these are available. In addition, a copy of an original aeromagnetic traverse is included. The examples embrace Puckett in the Delaware Basin of West Texas, Grieve in the Wind River Basin of Wyoming, Tioga and Onstad in the Williston Basin of North Dakota, Swanson River in the Cook Inlet Basin of Alaska, and Zelten in the Sirte Basin of Libya. These include both “before and after” examples with basement maps prepared in some cases before discoveries, and in other cases afterwards. The paper purports to demonstrate that correlative magnetic anomalies exist in either event. Moreover, these anomalies would be disclosed by any competent technique, so techniques of interpretation are not a part of the argument. It is well kn...

Abstract: Large differences in group velocities of short‐period Rayleigh waves from stripmine blasts for different propagation paths in the Ozark Uplift‐Illinois Basin area have been observed. Good well control in the area makes possible the construction of structural models of the sediments‐basement system for these paths. Theoretical group velocities computed for these models agree well with observations, thus explaining the large variations in velocities in terms of basement‐depth differences. This sensitivity of short‐period surface waves to sedimentary thickness suggests an inexpensive, single‐station technique of basin reconnaissance where commercial blasting is available.

Abstract: This note discusses some applications of convolution filter theory to gravity and magnetic maps. Sampling of the field is equivalent to a multiplication, and the corresponding convolution determines the sampling spectrum. If aliasing is acceptably small a specific filtering multiplication in the wavenumber domain corresponds to a convolution of a set of grid coefficients with gridded map values. The application of this theory to single-ring residuals, certain vertical derivatives, downward continuation, and low-pass filtering is discussed.

Abstract: Deep seismic sounding of the earth’s crust was conducted along a line of seven recording sites running from Flin Flon to Mafeking, Manitoba. Two interfaces, the Conrad and the Mohorovicic discontinuities, were distinguished. The following head‐wave types were observed: P*, SPP, SPS, S*, Pn, PSPSP, SSPSS, SPPPS, SSPPS, and PSPSS. Even though only a single shotpoint was used, it was found possible to determine velocities, layer thicknesses, and structure, using the interpretational possibilities of converted head waves. Discontinuities were determined as follows: Conrad—rises from 15.5±1‐km depth near Flin Flon to something just under 10‐km depth near Mafeking; Mohorovicic—rises from 34±1‐km depth near Flin Flon to 31±1‐km depth near Mafeking. Velocities are as follows upper layer—V1=6.15±0.05km/sec, v1=3.65±0.05km/sec; intermediate layer—V2=6.65±0.10km/sec, v2=3.90±0.010km/sec; lower layer—V3=7.90±0.10km/sec. Ratio of vertical to horizontal radial displacement was experimented with as a method of identifyi...

Abstract: During the last three years the discovery of the world’s second largest natural gas field at Groningen in the Netherlands has touched off in the North Sea one of the greatest competitive offshore geophysical operations in history. Before 1962, only minor amounts of geophysical work had been done there. Severe weather conditions were expected, but seismic operations have not been as much affected by weather as was originally anticipated. However, strong currents, making cable location uncertain, hampered reflection stacking and refraction operations. Location by radio was also a serious problem due to lack of sufficient available frequencies for a lane identification system. Seismic work was carried out safely in areas mapped as mine fields. Few problems with the fishing industry have so far been encountered. As a preliminary, the geophysics of the Groningen area are discussed. A gravity compilation of the North Sea shows that there are three major basins—the Northwest German Zechstein Basin, the British N...

Abstract: Since its invention and first use, the fluxgate magnetometer has had sensitivity, stability, speed of response, and other characteristics which were entirely suitable to the needs of both mineral and petroleum exploration, and which were compatible with the limitations and error functions of simple airborne surveying systems. The introduction of nuclear‐precession magnetometers employing the principle of quantum electronics has permitted and forced a revision of surveying systems and techniques to take advantage of the hundred‐fold increase in resolution they afforded. It appears that the new magnetometers have resolution capabilities beyond conventional survey needs, and measurement accuracy better than the accompanying survey positional accuracy.