The response of two half spaces to point dislocations at the material interface

Abstract

The exact solution to the problem of a general point dislocation situated at an interface between two half spaces of different elastic moduli is derived using a vector function expansion and the Cagniardde Hoop technique. For source functions that are nonsingular in either time or space the solution is given in terms of finite range integrals suitable for numerical integration. The integration ranges can be divided into two intervals: the first corresponds to a time‐space response carried by head wave disturbances, the second to a time‐space response carried by direct geometrical waves. Additional interface waves (Stoneley waves, leaky modes) enter the solution when the integration contours pass near their corresponding poles in the complex ray parameter domain. The head waves and other interface waves strongly distort the near field waveforms from corresponding waveforms in a homogeneous full space. It is shown that the distribution of travel times, amplitudes and motion polarities due to slip between two dissimilar media is different from what is predicted for slip in a homogeneous full space. It is therefore suggested that the interpretation of observed seismic data, especially those recorded in the near field of faults, be undertaken with consideration given to effects arising from material heterogeneity in the source region. The solution presented in this paper may be used as an integration kernel to give the response of two dissimilar half spaces to a finite propagating rupture at the material interface. Using the early parts of borehole seismograms to avoid free surface phases, such a response may be utilized to obtain source and fault parameters. Copyright © 1990, Wiley Blackwell. All rights reserved