Springer Online Journal Archives 1860-2000
Abstract The scale invariant inclusion theory of failure is applied to the problem of aftershock sequences. In the inclusion theory, a macrocrack, or void of low aspect ratio, the length of which depends upon the magnitude of the impending mainshock, forms within the inclusion zone of the impending earthquake. The fault zone that precedes the inclusion zone represents that part of the macrocrack that has closed. It is shown that bifurcation (branching) of the macrocrack and its associated fault must occur within the focal region of the inclusion during the growth phase of the earthquake. The bifurcation process produces extensive faulting of the material that comprises the focal region. A prediction of the inclusion theory is that each fault within the focal region will terminate within a zone of concentrated dilatancy that may or may not be in an unstable state. When the zone is unstable, an aftershock will occur. It is shown that these inclusion zones will, on the average, occur near the boundaries of the focal region. Failure of these unstable zones leads to additional failures within the interior portions of the focal region. These failures represent ‘lock point’ failures along the fault(s) and will, in general, exhibit few or no additional aftershocks. The bifurcation model of aftershock sequences leads to five results: (1) The aftershock sequence will exhibit an inverse hyperbolic time decay law when the stresses that are applied at distances far removed from the hypocenter remain constant during the sequence and when there isno interaction between the brittle lithosphere (where aftershocks occur) and the underlying asthenosphere. (2) The mean magnitude of any group of aftershocks within the sequence will be approximately constant in time. (3) The aftershocks will, in general, have focal mechanisms identical to that of the mainshock. (4) Large seismic events that occur throughout the aftershock zone will be independent of one another when the aftershocks are sufficiently far apart (∼two-three ‘fault’ lengths) and when the applied tectonic stresses remain constant during the sequence. (5) The bifurcation model predicts that theb-value of the aftershock sequence will be 1.0 when both the Utsu relationship between aftershock area and mainshock magnitude and the Gutenburg Richter frequency-magnitude relationship are satisfied.
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