Journal of Geophysical Research: Solid Earth New perspectives on self-similarity for shallow thrust earthquakes

Scaling of dynamic rupture processes from small to large earthquakes is critical to seismic hazard assessment. Large subduction earthquakes are typically remote, and we mostly rely on teleseismic body waves to extract information on their slip rate functions. We estimate the P wave source spectra of 942 thrust earthquakes of magnitude M w 5.5 and above by carefully removing wave propagation eﬀects (geometrical spreading, attenuation, and free surface eﬀects). The conventional spectral model of a single-corner frequency and high-frequency falloﬀ rate does not explain our data, and we instead introduce a double-corner-frequency model, modiﬁed from the Haskell propagating source model, with an intermediate falloﬀ of f − 1 . The ﬁrst corner frequency f 1 relates closely to the source duration T 1 , its scaling follows M 0 ∝ T 31 for M w < 7 . 5 , and changes to M 0 ∝ T 21 for larger earthquakes. An elliptical rupture geometry better explains the observed scaling than circular crack models. The second time scale T 2 varies more weakly with moment, M 0 ∝ T 52 , varies weakly with depth, and can be interpreted either as expressions of starting and stopping phases, as a pulse-like rupture, or a dynamic weakening process. Estimated stress drops and scaled energy (ratio of radiated energy over seismic moment) are both invariant with seismic moment. However, the observed earthquakes are not self-similar because their source geometry and spectral shapes vary with earthquake size. We ﬁnd and map global variations of these source parameters. frequency dependence of the interference between the direct and depth phases. Other studies [ 1986; Boatwright and Choy , 1989, 1992] used the amplitude spectrum of the P wave train to construct the P source spectrum, without discussing the impact on radiated energy. For most thrust earthquakes, the interference is destructive, with the energy of the P + pP + sP phase smaller than the sum of the individual energies. This study aims to provide a self-consistent approach to measuring static and dynamic properties of earthquakes for a wide range of magnitudes. We adopt a two-step approach to removing path eﬀects: (1) a simpliﬁed Earth model that we combine with a depth-phase transfer function for the smaller earthquakes and (2) the use of nearby small earthquakes to calibrate 3-D paths for the larger earthquakes. Most commonly used source spectral shape models adopt a single time scale, manifested in a single-corner frequency f c with a ﬂat asymptote for frequencies lower that f c and a high-frequency falloﬀ varying from f − 1 . 6 to f − 3 [ Aki , 1967; Brune , 1970; Boatwright , 1980; Ye et al. , 2016a], f − 1 . 6 being chosen to bound the seismic energy. In contrast, the presence of a low falloﬀ rate at intermediate frequencies in the spectra reﬂects two dominant time scales. Madariaga [1979] suggested that the source P pulse of thrust earthquakes recorded at steep takeoﬀ angles could exhibit a clear distinction between the starting/stopping phase pulse time scale and the total source duration time scale. BoatwrightandChoy [1989] and BoatwrightandChoy [1992] reconstructed source acceleration spectra from moderate and large earthquakes and found that source spectra of the larger ones exhibited an intermediate falloﬀ slope of about f − 1 . 25 . Our study conﬁrms that a double-corner-frequency model (i.e., two time scales) better explains our observations than a single-corner frequency. Inspired by the Haskell source model of unilateral ruptures [ Haskell , 1964], we construct a two-corner-frequency model with an intermediate falloﬀ of f − 1 and a high-frequency