Article,
Total energy and energy spectral density of elastic wave radiation from propagating faults
Bulletin of the Seismological Society of America, 54 (6A): 1811--1841 (Dec 1, 1964)
Abstract
Starting with a Green's function representation of the solution of
the elastic field equations for the case of a prescribed displacement
discontinuity on a fault surface, it is shown that a shear fault
(relative displacement parallel to the fault plane) is rigorously
equivalent to a distribution of double-couple point sources over
the fault plane. In the case of a tensile fault (relative displacement
normal to the fault plane) the equivalent point source distribution
is composed of force dipoles normal to the fault plane with a superimposed
purely compressional component. Assuming that the fault break propagates
in one direction along the long axis of the fault plane and that
the relative displacement at a given point has the form of a ramp
time function of finite duration, T, the total radiated P and S wave
energies and the total energy spectral densities are evaluated in
closed form in terms of the fault plane dimensions, final fault displacement,
the time constant T, and the fault propagation velocity. Using fault
parameters derived principally from the work of Ben-Menahem and Toksöz
on the Kamchatka earthquake of November 4, 1952, the calculated total
energy appears to be somewhat low and the calculated energy spectrum
appears to be deficient at short periods. It is suggested that these
discrepancies are due to over-simplification of the assumed model,
and that they may be corrected by (1) assuming a somewhat roughened
ramp for the fault displacement time function to correspond to a
stick-slip type of motion, and (2) assuming that the short period
components of the fault displacement wave are coherent only over
distances considerably smaller than the total fault length.
