Theory of earthquakes. Part III: Inclusion collapse theory of deep earthquakes

A theory of deep earthquakes, termed the inclusion collapse theory, is proposed in this paper. In the inclusion theory of crustal (or shallow) earthquakes, faults were shown to terminate within an inclusion zone. This zone represents a region within the brittle portion of the lithospheric plate that contains open cracks (voids) of varying sizes that, to a first order approximation, are uniformly distributed throughout the inclusion zone. When the lithospheric plate containing these faults and their associated inclusions is subducted into the mantle, the stress normal to the fault planes must increase. A depth is eventually reached where slippage along the fault planes is no longer possible. Earthquakes are postulated to occur at a specified depth within the mantle as a result of processes leading to collapse of these voids.When the long-term modulus of the plate is much greater than the long-term modulus of the mantle, large pressures are shown to develop within the plate during periods of active subduction. These pressures are shown to be sufficient to initiate partial collapse of voids of similar geometry throughout the inclusion zone.The inclusion collapse theory and the concentration of pressure within the plate lead to four results. (1) Earthquakes that are produced by a void collapse mechanism will not occur below a subduction depth calculated to be between 350 and 1000 km (2) The physical process most likely responsible for producing void collapse is the formation of shear, melt zones whose thicknesses are on the order of 1 to 10 cm in the immediate vicinity of the voids. This mechanism, is shown to produce a precursor time on the order of a few hundred seconds during which there is a release of shear strain prior to the earthquake. (3) The maximum energy released by void collapse is independent of the source depth. (4) The number of earthquakes produced by this process will decrease hyperbolically with source depth. Source depth, in the context used in this article, refers to the depth in the mantle to the inclusion zone where voids of similar geometry are undergoing partial collapse. The maximum source depth refers to the depth where all voids have closed.