An Evolutive Linear Kinematic Source Inversion

Abstract

We present a new hierarchical time kinematic source inversion method able to assimilate data traces through evolutive time windows. A linear time domain formulation relates the slip rate function and seismograms, preserving the positivity of this function and the causality when spanning the model space: taking benefit of the time‐space sparsity of the rupture model evolution is as essential as considering the causality between rupture and each record delayed by the known propagator operator different for each station. This progressive approach, both on the data space and on the model space, does require mild assumptions on prior slip rate functions or preconditioning strategies on the slip rate local gradient estimations. These assumptions are based on simple physical expected rupture models we foresee. Successful applications of this method to a well‐known benchmark (Source Inversion Validation Exercise 1) and to the recorded data of the 2016 Kumamoto mainshock (Mw=7.0) illustrate the advantages of this alternative approach of a linear kinematic source inversion. This stabilized overparameterized optimization of a linear forward problem has a potential extension to stochastic inversion in a Bayesian framework in the future to assess uncertainties on kinematic source inversions, which is more difficult to investigate under nonlinear formulations.

Early Stage and Main Ruptures of the 2015 Mw8.3 Illapel, Chile, Megathrust Earthquake: Kinematic Elliptical Inversions and Dynamic Rupture Simulations

“…The need to analyze the obtained solutions remains. It is challenging to characterize the real-time rupture process without using entire seismograms (e.g., Sánchez-Reyes et al, 2018;Uchide & Ide, 2007 The characteristics of slip patches we obtained are consistent with other studies of this earthquake in size, geometry, and timing of rupture process. The irregular rupture process of the Illapel earthquake appears in the change of rupture directivity along the dip (e.g., An et al, 2017;Meng et al, 2018;Ruiz et al, 2016;Tilmann et al, 2016) and the evolution of high-frequency generation areas (Ruiz et al, 2016;Yin et al, 2016) as reviewed in Section 1.…”

“…The need to analyze the obtained solutions remains. It is challenging to characterize the real-time rupture process without using entire seismograms (e.g., Sánchez-Reyes et al, 2018;Uchide & Ide, 2007). AOCHI AND RUIZ 10.1029/2020JB021207 12 of 20 The characteristics of slip patches we obtained are consistent with other studies of this earthquake in size, geometry, and timing of rupture process.…”

“…The need to analyze the obtained solutions remains. It is challenging to characterize the real‐time rupture process without using entire seismograms (e.g., Sánchez‐Reyes et al., 2018; Uchide & Ide, 2007).…”

Neuro‐Fuzzy Kinematic Finite‐Fault Inversion: 1. Methodology

“…Particularly this refers to the obtained phase of the source spectrum. In essential, only time-domain inversion methods, such as Progressive Inversion Strategy (PIS) (Sánchez-Reyes et al, 2018), can explicitly enforce the rupture causality. To prohibit this loss of causality, we probably need to apply a more advanced time-frequency analysis.…”