AZ&act: A linear filter model of the complicated seismic process can be formulated by assuming that (1) the layering of the earth is described by the continuous velocity log, (2) the shot pulse is time-invariant and propagates as a plane wave with normal incidence, and (3) all multiples, ghosts, and other noise are negligible. Then, the model earth with discrete layers can be considered a filter whose impulse response is the set of reflection coefficients. The set of reflection coefficients becomes the reflectivity function when the model earth has a continuously varying velocity. By definition, the reflectivity function is the derivative of the logarithm of velocity, where both are functions of two-way travel time The input to this filter is the time-invariant shot pulse. The output is a synthetic seismogram that contains the reflectivity function filtered by the shot pulse; in other words, it consists of primary reflections only. Since the filter is linear, the input and the filter may be Interchanged, the reflectivity function becoming the input and the shot pulse becoming the filter.A non-mathematical discussion of the reflecttons from simple, ideal velocity layering shows that: (1) The reflection from a step velocity function is the shot pulse itself. (2) Thin beds produce a differentiated shot pulse.(3) Beds which approximate a square pulse in velocity produce a pair of shot pulses, with the second delayed in time and reversed in phase with respect to the first. The composite reflection has its greatest amplitude when the layer thickness (in two-way travel time) is one-half the basic period of the shot pulse. This situation is called "tuning." The strongest reflections on field records result when the shot pulse is tuned to the velocity layering. (4) Ramp-transition zones (linear increase in the logarithm of velocity) produce integrated shot pulses at the changes in slope of the velocity function. A correspondence can be established between the velocity function and the synthetic seismogram by shifting the velocity function later in time The shift is required because of "filter delay." The amount of filter delay is related to the impulse response waveform, which, in the case of the synthetic seismogram, is given by the reflection from a step velocity function. IN-TRODUCTION-This paper presents a treatment of the fundamentals of synthetic seismograms from the view of linear filter theory. It gives a detailed description of a linear filter model of the seismic process in the earth, and discusses reflections from simple velocity layering. The paper also contains a discussion of depth-time correspondence between the earth and the related seismogram, and some examples comparing field records and synthetic seismograms.The paper is written for the benefit of seismic interpreters. We want it to be of practical value to them, as we believe a thorough understanding of synthetic seismograms will contribute to a better interpretation of field records. For this reason, we have chosen a descriptive rather than a mathemat...
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.
As part of a program of fundamental research on seismic waves, a generator was built for applying a transient horizontal force at the surface of the ground and the resulting seismic waves were observed in some detail. The force is applied when a mass swinging through an arc strikes a target anchored to the earth. Surface geophones along a line in the direction of the force register vertically polarized shear waves refracted back up to the surface, whereas geophones on a line perpendicular to the force register horizontally polarized shear waves. The speeds of the two types of shear waves are often different, indicating anisotropy. Geophones buried below the target show a down‐going shear wave. Variation of amplitude with angle, and other features, are in qualitative agreement with the results given by Rayleigh and others for the waves due to a force at a point in an infinite solid. Love waves and other surface waves were observed, which of course would not be expected from an nterior force.
Seismic propagation studies made in the Delaware Basin of West Texas by the Field Research Laboratories of the Magnolia Petroleum Company have disclosed several unusual kinds of traveling waves. The near‐surface zone in this area is characterized by alternating high‐ and low‐velocity layers, with a thin high‐velocity cap. Physical characteristics of the recorded waves have been correlated with this layering. Five types of waves have been identified: 1) Waves refracted along the tops of high‐speed near‐surface markers which have been multiply reflected, at the critical angle, between the marker beds and interfaces nearer the surface. 2) Shear waves refracted at shear velocity along a competent bed several hundred feet deep. 3) Compressional waves propagated by normal‐mode transmission in the wave guide formed by a low‐speed layer situated between two high‐speed layers. 4) A single‐cycle, apparently non‐dispersive Rayleigh wave propagated in a thin limestone surface layer and in an underlying low‐speed layer of sand and gravel. 5) An inversely dispersive Rayleigh wave train in which the group velocity appears to decrease with increasing wave length; this type of dispersion, just the opposite of the kind ordinarily recorded, is attributed to the fact that the low‐speed surface layer is unusually thick compared with the wave length corresponding to the cut‐off frequency of the instrumental system.
As part of a program of fundamental research on seismic waves, a generator was built for applying a transient horizontal force at the surface of the ground, and the resulting seismic waves were observed in some detail. The force is applied when a mass swinging through an arc strikes a target anchored to the earth. Surface geophones along a line in the direction of the force register vertically polarized shear waves refracted back up to the surface, whereas geophones on a line perpendicular to the force register horizontally polarized shear waves. The speeds of the two types of shear waves are often different, indicating anisotropy. Buried geophones below the force show a down-going shear wave. Variation of amplitude with angle and other features are in qualitative agreement with the results given by Rayleigh and others for the waves caused by a force at a point in an infinite solid. Love waves and other surface waves were observed, which of course would not be expected from an interior force.
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