Theory of time‐dependent rupture in the Earth

Using the concepts of fracture mechanics, we develop a theory of the earthquake mechanism which includes the phenomenon of subcritical crack growth. The theory specifically predicts the following phenomena: slow earthquakes, multiple events, delayed multiple events (doublets), postseismic rupture growth and afterslip, foreshocks, and aftershocks. The theory also predicts that there must be a nucleation stage prior to an earthquake and suggests a physical mechanism by which one earthquake may ‘trigger’ another. These predictions are obtained by combining two fundamental concepts. The first is that , and the second that , where k is the stress intensity factor, Δτ is stress drop, X is rupture length, is rupture velocity, C is a geometrical factor, and K 0 , V 0 , and n are material constants. The first is a fundamental result of fracture mechanics; the second describes stress corrosion cracking, a well‐established physical process that results in subcritical crack growth. We investigate in detail two phenomena of special interest and which are not predicted by ordinary fracture mechanics: nucleation and delayed multiple events. In the first case we find that all earthquakes must be preceded by quasi‐static slip over a portion of their rupture surfaces, but it may be difficult to detect in practice. In the second case we studied two pairs of delayed multiple events that were separated by the same ‘barrier’ in order to calculate n . We find that the stress corrosion index n is ∼24.