Method for estimating the stress field from seismic moment tensor data based on the flow rule in plasticity theory

• Published in: Geophysical research letters 2016-09, Vol.43 (17), p.8928-8935
• Main Author: Matsumoto, S.
• Format: Article
• Language: English
• Subjects: Crystallization; Earthquakes; Estimating; Inversions; Mathematical analysis; Nonlinear programming; Plastic deformation; Plasticity; Plastics; Seismic activity; seismic moment tensor; stress field; Stress tensors; Stresses; Tensors
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1002/2016GL070129

The stress field is a key factor controlling earthquake occurrence and crustal evolution. In this study, we propose an approach for determining the stress field in a region using seismic moment tensors, based on the classical equation in plasticity theory. Seismic activity is a phenomenon that relaxes crustal stress and creates plastic strain in a medium because of faulting, which suggests that the medium could behave as a plastic body. Using the constitutive relation in plastic theory, the increment of the plastic strain tensor is proportional to the deviatoric stress tensor. Simple mathematical manipulation enables the development of an inversion method for estimating the stress field in a region. The method is tested on shallow earthquakes occurring on Kyushu Island, Japan. Key Points Estimation of stress field using sum of seismic moment tensors based on classical equation in plasticity theory Simple summation of seismic moment tensors provides stress tensor without instability due to nonlinearity in the ordinary stress inversion The results of the estimated stress tensor in this study mostly coincide with those obtained by ordinal stress tensor inversion