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Diffraction of point-source signals by a circular crack

THE TECHNOLOGICAL INSTITUTE NORTHWESTERN UNIVERSITY, EVANSTON, ILLINOIS 60201

Abstract

An analysis is presented of the diffraction by a hydraulically induced crack of time-harmonic signals emitted by a point source. Both diffraction by an empty crack and diffraction by a fluid-filled crack are considered. It is assumed that the crack is plane and of circular shape. The analysis is based on elastodynamic ray theory, which yields relatively simple approximations to the diffracted fields if a/c_L is sufficiently larger than unity, where is the circular frequency of the incident waves, a is the radius of the crack, and c_L is the velocity of longitudinal waves. The diffracted fields include direct diffractions from the crack edges as well as diffractions of signals which travel via the crack faces. The relative magnitudes of these various contributions have been plotted. For three positions of the point of observation, numerical results for the three displacement components have been displayed in graphs.

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				J. D. ACHENBACH, A. NORRIS, and K. VISWANATHAN Mapping of crack edges by seismic methods Bulletin of the Seismological Society of America, June 1, 1982; 72(3): 779 - 792. [Abstract] [PDF]