Simple Models in the Mechanics of Earthquake Rupture
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Starting from Navier’s equations of motion in elastodynamics, it is shown that the slip on an earthquake fault can be written as a convolution of the stress changes on the fault with the half-space Green’s function. An alternate representation relation in which the fault slip is a convolution of the fault slip on other parts of the fault at previous times with a different kernel is also derived. Using either of these (equivalent) expressions, the behavior of the fault slip as a function of space and time as a fault grows at a constant speed from a point to a finite circular shape (the “interior” crack problem) is obtained. Spontaneous faults, in which the fault speed is not assumed a priori but determined from some fracture criterion, are considered, and the limiting rupture speeds in different cases obtained. The growth of a pre-existing circular crack is determined. Finally, the rupture of a zone surrounded by already ruptured zones (the “exterior” crack problem) is studied. In the last two cases, it is shown that the rupture process is so complex that the terms “rupture front” and “rupture velocity” are no longer meaningful.
KeywordsFault Plane Rayleigh Wave Shear Crack Stress Drop Crack Edge
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