Energy Release in Earthquakes

TLDR

Static elasticity methods have been extended to analyze energy differences in crack propagation, with idealized strike‑slip faults modeled as elongated structures, and analogous to electrical or hydrodynamic strip problems. The study aims to adapt this technique to compute the energy released when a tear fault such as the San Andreas is introduced into a homogeneous medium under uniform shear stress. The authors model the fault as an infinite strip in a homogeneous, isotropic, elastic medium under uniform shear stress, with shear stress vanishing on the strip, allowing the problem to be solved analytically. The model yields the stress distribution and relative motion, estimating the 1906 San Francisco earthquake’s energy release at 4 × 10^23 ergs, which exceeds the elastic‑wave energy.

Abstract

The notion of applying methods of static elasticity to the study of energy differences in two states of a given structure was extended by Starr to yield the solution to problems involving the propagation of cracks in shear fields. This technique may be modified to include the solution of the problem of the energy release upon the introduction of a tear fault, such as the San Andreas fault, into an otherwise homogeneous medium subjected to a uniform shear stress. The idealized properties of such a fault are a structure elongated compared with its depth and a strike-slip motion along the fault. This configuration, by symmetry, may be imaged in the Earth's surface so that the problem is reducible to that of a strip fault of infinite length in a homogeneous, isotropic, elastic, infinite medium. The medium is subjected to a uniform shear stress at infinity and the shear stress is assumed to vanish upon the strip. This two-dimensional problem has a vector solution rather than a tensor one, and thus it has an analogue in the electrical problem of a perfectly conducting strip placed in a uniform electric field or that of a strip obstacle placed in a uniform hydrodynamic stream field. The stress distribution and the relative motion throughout the medium before and after faulting can be obtained. For the case of the 1906 San Francisco earthquake, this model yields an energy difference of the shear fields before and after faulting of 4 × 1023 ergs. This value must exceed the elastic wave energy.