Vertical Displacements From a Rectangular Fault in Layered Elastic-Gravitational Media

Abstract

In previous papers (rundle 1980,1981a), the techniques needed for calculation of the displacements due to various internal sources of strain embedded in layered linear elastic-gravitational continua have been developed. The method involves straightforward solution of the coupled elastic-gravitational field equations, and makes use of a matrix technique for propagating the solution from one layer to the next. As in the free oscillation problem, the six quantities propagated include two displacement kernels, two normal traction kernels and a kernel each for the gravitational potential and its gradient minus a multiple of the vertical displacement. These propagated quantities lead to 6 X 6 matrices. The method was used to numerically compute the vertical displacements arising from a 30° dipping point double-couple thrust source in an elastic-gravitational layer over an elastic-gravitational half-space (rundle 1981a). A result from this work is that most of the gravitational effect for dislocations arises from terms associated with the surface acceleration g, as opposed to the terms involved with the gravitational constant G0which represents self-gravitation effects. The present paper exploits this result by noting that for fault dislocation sources, the equations can be decoupled, reducing the matrices in the problem to 4 X 4 rather than 6 X 6. The advantage gained is significant reduction in computation time. After derivation of the reduced propagator matrices from the more general ones given in rundle (1980, 1981a), vertical displacements due to a rectangular, dipping fault in an elastic-gravitational layer over an elastic-gravitational half space are computed and compared with corresponding elastic solutions. The character of the elastic-gravitational displacements differs substantially from the elastic displacements when moduli contrasts become large. © 1981, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.