No abstract

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.

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 band stop frequency rejection, and plates bounded by knife edges for low‐pass filtering. The technique is applicable to most problems encountered in seismic prospecting where spurious events obscure desired reflections. The most frequent application so far has been the removal of multiple reflections. The method has turned out to be highly useful for eliminating noise, regardless of origin, which interferes with reflections whenever the noise consists of traveling events, even though fragmental, which have different apparent velocities from the reflections. The method has also been effective in solving structural problems in tectonic areas by removing diffractions or, alternatively, by enhancing them at the expense of the reflections to delineate faults and other sources of diffraction. Ringing or reverberation can often be attenuated or eliminated in marine shooting by passing reflection frequencies that are less than the lowest observed harmonic of the fundamental reverberation frequency. Examples are shown of transforms and/or filtered sections illustrating these applications. A particularly valuable feature of this optical processing system is the ease of monitoring the results. The facility with which this can be done gives the technique distinct advantages over digital or analog methods, where the geophysicist loses contact with his results while processing is under way. Optical filtering also offers an intrinsically more economical approach to seismic data processing because hundreds of information channels can be handled n a single photographic operation.

The propagation of compressional, shear, and surface waves was studied along a 3,200 ft profile at a location where a 95‐ft‐thick surface layer of Austin chalk, with a compressional velocity of about 9,900 ft/sec, overlies a 400‐ft section of Eagle Ford shale with a speed of about 6,500 ft/sec. Woodbine sand, with a velocity of about 9,900 ft/sec, underlies the shale. Refracted first arrivals transmitted through the high speed surface layer show an increase of frequency with distance from the shot. A refracted second arrival from the Woodbine decreases in frequency and, after correction for spreading, increases in relative amplitude with distance. This would indicate that the high‐speed surface layer acts as a high‐pass filter for energy transmitted horizontally and as a low‐pass filter for energy transmitted vertically through the layer. Shear waves transmitted through the Austin chalk are also observed. Surface waves consist of two groups of arrivals; a brief train of high‐frequency waves (greater than 20 cps) propagated almost entirely in the surface layer is followed by a short train of low frequency waves. Unlike surface waves in most other localities, the two groups show almost no dispersion. The characteristics of both kinds of waves are interpreted qualitatively in terms of the layering.

A s part of a program to study ground disturbances that interfere with seismic prospecting, an experimental seismic crew of the Magnolia Petroleum Co. has been investigating Rayleigh waves from shot‐hole explosions at distances up to about 3000 ft. Waves have been recorded by vertical and horizontal geophones through a system giving flat response between 5 and 200 cycles/sec. The geophones have been disposed along surface profiles with separations that are short compared to Rayleigh wavelengths and also at various depths up to 100 ft in boreholes. Rayleigh waves from air explosions have also been recorded. Sample arrays of records are presented on which individual waves from hole and air shots can be followed for horizontal distances up to about ten wavelengths. Dispersion characteristics observed on the records are plotted in a form permitting comparison with theoretical dispersion curves for various kinds of surface layering. Effects of varying the depth of the explosion are observed and compared with theoretical predictions. Particle‐motion trajectories are plotted both at the surface and at various depths. Results all show as good agreement with classical theory as can be expected in view of the simplifying assumptions which must be made in deriving this theory. Constant‐frequency wave trains were observed immediately after the air‐wave arrival on the records made from single air explosions eight feet above the ground. These are shown to be waves of the type predicted by the Press‐Ewing theory of surface‐wave coupling to the atmosphere.