Normal and shear stresses acting on arbitrarily oriented faults, earthquake energy, crustal GPE change, and the coefficient of friction

Abstract

As usual, earthquake energy is defined as the total energy released from an earthquake, which is partitioned into radiated energy, friction energy, and rupture energy regardless of crustal gravitational potential energy (GPE) change. We analyze the energy and stress parameters in earthquake energy budget. For arbitrarily oriented faults, we deduce the formulas for calculating the normal and shear stresses acting on the fault under principal stresses. We show that shear stress is composed of horizontal and vertical shear stresses. Then, we provide the expressions for computing crustal GPE change and the coefficient of friction. The GPE change should be considered, except strike-slip faulting, when investigating earthquakes. Also, for various faulting types, we show that the ratio of differential stresses is related to the fault orientation and the relative magnitudes of stresses. Finally, “12 May, 2008, Wenchuan, Sichuan, China, MW 7.9 Earthquake” is cited to analyze and calculate various energy/stress parameters and the coefficient of friction. Our result of GPE change coincides with the post-event field observations.