Moment–Area Scaling Relationship Assuming Constant Stress Drop for Crustal Earthquakes

Abstract

For crustal earthquakes, the scaling relationship between the seismic moment M0 and rupture area S varies with the size of the earthquake, due to the limited thickness of the seismogenic layer. In those M0–S scaling relations, in most cases, the calculated static stress drop is altered with the size of earthquake, although the change depends on the assumed fault model. However, it is not clear whether the dependence of the stress drop on M0 is physically reasonable. In this study, the scaling relation between M0 and S, which assumes a constant stress drop over a wide M0 range, is discussed based on the analytical stress drop formula of a rectangular strike-slip fault. In the proposed relation, M0 is proportional to S3/2 for small and medium faults and to S1 for long faults. In addition, the relation between M0 and S varies in the intermediate range, depending on the aspect ratio. The scaling relation showed good agreement with past event data when the saturated rupture width was set to around 15–20 km and the stress drop was set to about 3 MPa.

A Proposal of the Scaling Relation for the Short-Period Level Associated With the Three-Stage Model of Inland Crustal Earthquakes

“…As a result, the average stress drops Δσ in each stage are 3.07 MPa, 3.20 MPa, and 3.20 MPa, respectively. These Δσs are similar to 3 MPa reported by Hikima and Shimmura 15) , corresponding to the earthquake data from the first to third stages, and 3.1 MPa reported by Fujii and Matsu'ura 22) and 3.4 MPa reported by Dan et al 7) corresponding to the earthquake data of the second and third stages.…”

“…Nagashima et al 9) found that from a study using the source inversion results of a number of overseas inland crustal earthquakes in the range of 7.96×10 15 Nm ≤ M0 ≤ 9.42×10 20 Nm, the asperity area scaled with respect to the seismic moment is consistent with the area obtained by multiplying the fault area from Eq. (2) by 0.22 times.…”

“…There are studies by Dan et al 7), 14) and Hikima and Shimmura 15), 16) on scaling, in which the average stress drop of the entire fault Δσ and the stress drop of asperity Δσasp are constant over a wide range of earthquake magnitude scales, and as a result, the asperity area ratio, Sasp/S becomes constant. In these studies, they first set an equation to evaluate Δσ from M0 and S. Thereafter, based on the equation, they constructed the scaling law of M0-S by giving a certain Δσ that matches the earthquake data of M0 and S. Then, the stress drop on asperity, Δσasp was provided to match the short-period level of earthquake data.…”