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.
The study of resistivity surveys over buried spheres is facilitated by the use of a bipolar coordinate system. Without solving the incident potential problem exactly, the author obtains an exact solution for the apparent resistivity as measured by the Wenner configuration of electrodes situated directly over a buried conducting sphere. From a study of depth profiles over a set of spheres buried at different depths, it is concluded that one cannot expect to find by direct current methods a sphere buried to a depth greater than the radius of the sphere. This result is generalized to include bodies of more arbitrary shape.
Solutions of Laplace’s equation in prolate and oblate spheroidal coordinates are applied to problems that arise in resistivity surveys over filled hemispheroidal sinks. Comprehensive sets of theoretical curves are presented for both horizontal and vertical profiles in the vicinity of filled sinks. The effectiveness of these theoretical curves is demonstrated not only for the interpretation of resistivity data but also for the planning of proper field techniques in resistivity surveying over such sinks. Excellent correlation between theoretical and observed field resistivity curves is shown over a shale sink in the Tri‐State lead‐zinc mining district, near Joplin, Missouri. It is shown that a filled sink can be approximated in its resistivity edge effects by 1) a vertical dike if the width of the sink is small in comparison with its length and its depth; and 2) a vertical fault if the sink is large in comparison with the electrode separation. A study of the Lee and Wenner configurations indicates that the former gives additional information that more than justifies the extra time and expense involved.
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