Characteristics of Stress Drop and Energy Budget from Extended Slip-Weakening Model and Scaling Relationships

Abstract

The extended slip-weakening model was investigated by using a compiled set of source-spectrum-related parameters, i.e. seismic moment Mo, S-wave velocity Vs, corner-frequency fc, and source-controlled high-cut frequency fmax, for 113 shallow crustal earthquakes (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan from 1987 to 2016. The investigation was focused on the characteristics of stress drop, radiation energy-to-seismic moment ratio, radiation efficiency, and fracture energy release rate, Gc. The scaling relationships of those source parameters were also investigated and compared with those in previous studies, which were based on generally used singular models with the dimensionless numbers corresponding to fc given by Brune and Madariaga. The results showed that the stress drop from the singular model with Madariaga’s dimensionless number was equivalent to the breakdown stress drop, as well as Brune’s effective stress, rather than to static stress drop as has been usually assumed. The scale dependence of stress drop showed a different tendency in accordance with the size category of the earthquakes, which may be divided into small-moderate earthquakes and moderate-large earthquakes by comparing to Mo = 1017~1018 Nm. The scale dependence was quite similar to that shown by Kanamori and Rivera. The scale dependence was not because of a poor dynamic range of recorded signals or missing data as asserted by Ide and Beroza, but rather it was because of the scale dependent Vr-induced local similarity of spectrum as shown in a previous study by the authors. The energy release rate Gc with respect to breakdown distance Dc from the extended slip-weakening model coincided with that given by Ellsworth and Beroza in a study on the rupture nucleation phase; and the empirical relationship given by Abercrombie and Rice can represent the results from the extended slip-weakening model, the results from laboratory stick-slip experiments by Ohnaka, and the results given by Ellsworth and Beroza simultaneously. Also the energy flux into the breakdown zone was well correlated with the breakdown stress drop,   and peak slip velocity of the fault faces. Consequently, the investigation results indicate the appropriateness of the extended slip-weakening model.