Attenuationin the earth appreciably affects the usefulness of seismic waves in geological studies. It limits the distance over which the waves can be transmitted and it is the major factor in determining the frequency band of the useful energy. Variation of attenuation with frequency is assumed to be responsible for wave form distortion, thus complicating the interpretation of seismic data. Attenuation has also been suspected of influencing propogation velocities. For these reasons, we have undertaken a series of experiments to verify the reports of others as well as to investigate questions which have not been touched by others. The approach has been wholly experimental -that is to say, we have tried only to describe the phenomenon in question. The region of cretaceous shale outcrops in eastern Colorado was chosen for the site of the experiments. This region also served Dr. Ricker in a similar work which he has previously reported. In this area, the outcropping Pierre shale is approximately 4000 feet thick and exceptionally uniform. The largest variation in the 7oo-foot section used represents a reflection coefficient of only 4/100. For vertical travel, the average compressional velocity was measured to be 7100 feet/second and the average shear velocity 2630 feet/second. For horizontal travel at a depth of 500 feet, the corresponding velocities were 7360 and 2680 feet/second, respectively.The most consistent and dependable results were obtained with compressional waves from dynamite explosions. Charges were fired in shot holes and consisted of boosters, one pound of dynamite, or ten pounds. In order to obtain vertically travelling shear waves, we used a horizontally swinging mass of 2000 pounds that was caused to strike a concrete block anchored into the earth. Satisfactory wave forms were not obtained however. On the other hand, satisfactory horizontally travelling waves were produced by the impact of a zoo-pound mass on the bottom of a shot hole.

Attenuation measurements were made near Limon, Colorado, where the Pierre shale is unusually uniform from depths of less than 100 ft to approximately 4,000 ft. Particle velocity wave forms were measured at distances up to 750 ft from explosive and mechanical sources. Explosives gave a well‐defined compressional pulse which was observed along vertical and horizontal travel paths. A weight dropped on the bottom of a borehole gave a horizontally‐traveling shear wave with vertical particle motion. In each case, signals from three‐component clusters of geophones rigidly clamped in boreholes were amplified by a calibrated, wide‐band system and recorded oscillographically. The frequency content of each wave form was obtained by Fourier analysis, and attenuation as a function of frequency was computed from these spectra. For vertically‐traveling compressional waves, an average of 6 determinations over the frequency range of 50–450 cps gives α=0.12 f. For horizontally‐traveling shear waves with vertical motion in the frequency range 20–125 cps, the results are expressed by α=1.0 f. In each case attenuation is expressed in decibels per 1,000 ft of travel and f is frequency in cps. These measurements indicate, therefore, that the Pierre shale does not behave as a visco‐elastic material.

This experimental study of the generation of shear waves hy explosive sources stemmed from Heelan' s theoretical result that pressure acting on the wall of a cylindrical hole in a solid should radiate shear waves quite as effectiveI> as compressional waves. The measurements confirm this expectation. but good overall agreement was not achieved until expressions were derived which take into account radiation from strong water-pulse waves in the shothole.Our results show that the ratio of shear-to-compressional amplitudes generated 1)~ an explosive source increases as the charge size decreases. .it an angle of 4.5 degrees, the ratio is approximately unity for a charge consisting of 10 It of Primacord. \Ve found that the shot-generated water pulse (tube wave) is a strong shear source, continuouslv generating shear energy in the formation as it travels in the borehole. This drastically affects the directivity of Siwaves and in Pierre shale gives a pattern whose maximum is near-vertical. This suggests the possibility of prospectivg with shear waves, using a distributed charge detonated at shear velocity to generate substantial downwardthrection shear energy in the earth. However, the substantially larger attenuation of shear waves compared to compressional waves has discouraged us from I' ursuing this further. Stonelcy has concluded that the .TfI and SV velocities will he different in this type of material and that IThen a shear wave is traveling vertically its velocity will he the .S1-velocity. Several authors have discussed velocities in laminated media, where the media arc made of two materials, each homogeneous and isotropic, with the laminae of irregular thickness. They show that when the laminae are horizontal, the compressional velocity is greater horizontally than vertically and, for horizontally traveling shear waves, the SH lrelocity is greater than the SI' velocity. Background ior this work \vas a theory for the radiation of elastic waves, from a cylindrical source of finite length in an infinite medium, developed by Heelan (1953). His development sho\ved that \vhen a uniform, lateral pressure acts upon the lvalls of a cylindrical cavity, both compressional and shear \\-aves ate generated. The shear waves are polarized in the plane that includes the direction of propagation and the axis

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...

No abstract