Evidence for non-self-similarity in the M w 7.7 2001 Bhuj earthquake sequence

Abstract

Scaled energy, apparent stress, seismic moments, stress drops and corner frequencies are measured through the Levenberg–Marquardt nonlinear inversion modeling of S-wave displacement spectra for 489 selected earthquakes (M w 2.05–5.52) from the 2001 M w 7.7 Bhuj earthquake sequence. The iterative inversion scheme is formulated based on the ω-square source spectral model, which enabled us to estimate stable source parameters. The estimated seismic moment (M o ) and source radius (r) vary from 1.5 × 1012 to 2.4 × 1017 to N m and 139.1–933.9 m, respectively, while estimated stress drops (Δσ) and the multiplicative factor (E mo) values range from 0.1 to 14.4 MPa and 1.0–4.1, respectively. The corner frequencies (f c) are found to be ranging from 1.4 to 9.3 Hz. The mean standard deviation for f c, r and Δσ are estimated to be 0.7 Hz, 91.4 m and 2.9 MPa, respectively. The radiated seismic energy and apparent stresses range from 2.1 × 105 to 4.1 × 1013 Joule and 0.005–8.0 MPa, respectively. Our estimated corner frequencies and seismic moments satisfy the relation M o ∞ f c −(3+) , where e (measure for a deviation from self-similarity) is found to be 1.33 for the larger earthquakes (M o ≥ 2 × 1015 N m), while the parameter e is estimated to be 6.74 for smaller earthquakes (M o < 2 × 1015 N m). We feel that the larger value of e may require to satisfy the increasing trend of scaled energy with moment for smaller earthquakes. We also notice that stress drops increase with seismic moment, approximately as Mo3 (Δσ∝M o 3) for smaller events (M o < 1015.3 N m), while for larger earthquakes (M o ≥ 2 × 1015 N m) stress drop increases approximately with M 1 (Δσ∝M 1 ). Adding credence to this non-self-similar theory, our estimated seismic moments and source radii (r) also reveal a break in the linear self-similar source scaling at M o = 2 × 1015 N m and r = 300 m, which is attributed to constant source radius for smaller earthquakes. Further, a comparative study between apparent stresses and static stress drops suggests a probable frictional overshoot mechanism for larger earthquakes, while smaller shocks are showing both partial stress drop and frictional overshoot mechanisms. We hypothesize that larger events are probably subject to the regional state-of-stress and fluid flow in the fault zone, whereas smaller earthquakes are sensitive to the local state-of-stress associated with material heterogeneities and fluid flows within the fault zone. We also propose that the relations developed in this study could be useful for accessing proper seismic hazard in the region.