Seismic observations

1. Combination of Backprojection (BP) and Spectral analysis (SP) to infer the spatial and temporal evolution of earthquake rupture

We develop a methodology that combines the backprojection (BP) and source spectral analysis (SP) of teleseismic P waves to provide metrics relevant to earthquake dynamics of large events. We improve the compressive sensing backprojection (CS-BP) method (Yao et al., 2011; Yin & Yao, 2016) by an auto-adaptive source grid refinement as well as a reference source adjustment technique to increase spatial and temporal resolution of the locations of the radiated bursts. We also use a two-step source spectral analysis based on (i) simple theoretical Green’s functions that include depth phases and water reverberations and on (ii) empirical P-wave Green’s functions. Furthermore, we propose a source spectrogram methodology that provides the temporal evolution of dynamic parameters such as radiated energy and falloff rates. Combination of BP and SP analysis provides a spatial and temporal evolution of these dynamic source parameters and is an attempt to bridge kinematic observations with earthquake dynamics. For more details, please see Yin et al. (2018 JGR).

Illapel observations
Observations on the 2015 Illapel earthquake: (a) low frequency data (0.08-0.5Hz) BP results. (b) high frequency (0.5-1Hz) BP results. Size and color of circles corresponds to the relative amplitude and source time, respectively. (c) Recovered source spectra in the time-frequency space. (d) and (e) Temporal variations of radiated energy and spectral falloff rate in both low and high frequency bands, respectively. Published in Yin et al. (2018)

 

2. Backprojection resolution from the theoretical formulation

Based on the theoreitcal formulation of linear back projection (see here), the resolution matrix \(\mathbf{F}(\omega)\) only depends on source mechanism and source-receiver geometry, we can further calculate the resolvability, which is defined as the 2D correlation coefficient between the resolution matrix and an identity matrix, and use it to evaluate the BP resolutions for real seismic array-source configurations. For more details, please see Yin and Denolle (2019 GJI).

global resolvability
BP resolvability for most of the seismic arrays in the world. The higher resolvability implies better BP resolution for a specific seismic array towards a seismic region.