Compressive sensing of the Tohoku-Oki Mw 9.0 earthquake: Frequency-dependent rupture modes

Abstract

[1] Compressive sensing (CS) is a technique for finding sparse signal representations to underdetermined linear measurement equations. We use CS to locate seismic sources during the rupture of the 2011 Tohoku-Oki Mw9.0 earthquake in Japan from teleseismic P waves recorded by an array of stations in the United States. The seismic sources are located by minimizing the ' 2 -norm of the difference between the observed and modeled waveforms penalized by the ' 1 -norm of the seismic source vector. The resulting minimization problem is convex and can be solved efficiently. Our results show clear frequencydependent rupture modes with high-frequency energy radiation dominant in the down-dip region and lowfrequency radiation in the updip region, which may be caused by differences in rupture behavior (more intermittent or continuous) at the slab interface due to heterogeneous frictional properties. Citation: Yao, H., P. Gerstoft, P. M. Shearer, and C. Mecklenbräuker (2011), Compressive sensing of the Tohoku-Oki Mw 9.0 earthquake: Frequencydependent rupture modes, Geophys.

A dynamic model of the frequency-dependent rupture process of the 2011 Tohoku-Oki earthquake

“…Another striking feature is the distinct location of high-frequency (HF) and low-frequency (LF) slip. Teleseismic back-projection studies find that the HF energy around 1 Hz originates from the deeper region (Kanamori and Yomogida, 2011;Meng et al, 2011;Yao et al, 2011), while other studies point to the low-frequency radiation coming from the shallower region (Simons et al, 2011;Wei et al, 2012). The present work aims to provide a dynamic interpretation of the contrasted frequency content of slip in the deeper and shallower regions of the Tohoku-Oki earthquake rupture.…”

Mitigating artifacts in back-projection source imaging with implications for frequency-dependent properties of the Tohoku-Oki earthquake

“…In contrast, the high frequency (HF) slip is distributed at the bottom of the seismogenic zone. This is inferred from teleseismic back-projection (Ishii, 2011;Koper et al, 2011b;Meng et al, 2011;Wang and Mori, 2011;Yao et al, 2011) and local strong motion studies (Asano and Iwata, 2011;Meng et al, 2011;. This frequency-dependent rupture behavior is reported by (Nakahara et al, 2008) for a number of earthquakes and has also been proposed for the 2004 Suma-tra and 2010 Maule earthquakes (Lay et al, 2012).…”

“…Hence, the reference window approach is valid in this case. The reference window approach introduces a time shift, the difference between the mean of B and B , therefore a timing correction is needed (Yao et al, 2011). This correction is readily implemented once the radiator locations have been identified in each back-projection image frame.…”

“…Therefore the correct location A is recovered and no artifact is introduced. The reference window strategy is embedded in frequency-domain back-projection techniques, such as the frequency-domain beamforming, MUSIC (Meng et al, 2011) and compressive sensing (Yao et al, 2011), in which the Fourier coefficients, or the covariance matrix, are computed based on the signals in the reference window. Because the Fourier shift implies periodic signals, the phase shift should not be too long relative to the window.…”

“…Motivated by the spatial complementarity between LF slip (<0.1 Hz) and HF slip (∼1 Hz), a number of studies (Koper et al, 2011a;Mori, 2011;Yao et al, 2011;Lay et al, 2012) attempted to probe the transition between these two frequency ranges by performing back-projection at intermediate frequencies. Their results based on the USArray recordings suggest a progressive up-dip migration of the dominant sources as a function of decreasing frequency from 1 to 0.1 Hz.…”