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A two-dimensional model study of the directivity function

DEPARTMENT OF GEOLOGY AND GEOPHYSICS UNIVERSITY OF MINNESOTA, MINNEAPOLIS, MINNESOTA
DEPARTMENT OF GEOPHYSICS UNIVERSITY OF BRITISH COLUMBIA, VANCOUVER, B.C., Canada

Abstract

The directivity method of Ben-Menahem has been applied to the study of Rayleigh waves generated by an internally induced tensile fracture in a glass plate. Independent studies show that velocity of fracture propagation in glass initially increases over a short distance before a terminal rupture velocity is attained. The directivity function has been calculated for such a fracture in terms of four parameters: the length a and duration T₁ of the accelerated phase of fracture, the terminal rupture velocity v, and the total length of the fracture b. Theoretical directivity functions have been chosen to fit observed directivity functions in five cases. Although the theoretical functions do not furnish a detailed fit to the observed directivity functions, they do reproduce most of the essential features. Independent measurements of b and v indicate that those parameters may be determined by the directivity method to within about 15 per cent. Values of a and T₁ obtained by the directivity method cannot be checked directly but appear to be reasonable. It is suggested that the discrepancy between the lengths obtained from the phase and from the modulus of the directivity function for the Chilean earthquake of May, 1960, may be associated with an increase of velocity of rupture over perhaps the first 100 km of the total fault length.

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