An Evolutive Linear Kinematic Source Inversion

• Published in: Journal of geophysical research. Solid earth 2018-06, Vol.123 (6), p.4859-4885
• Main Authors: Sánchez‐Reyes, H. S., Tago, J., Métivier, L., Cruz‐Atienza, V. M., Virieux, J.
• Format: Article
• Language: English
• Subjects: Analysis; Bayesian analysis; Computer Science; Data; Earth Sciences; Earthquakes; Evolution; Formulations; Forward problem; Frameworks; Geophysics; hierarchical evolutive model parametrization; Inversions; kinematic source inversion; Kinematics; Kumamoto earthquake; linear inverse formulation; Mathematical models; Methods; Modeling and Simulation; Operators (mathematics); Physics; Preconditioning; Probability theory; Reconstruction; Rupture; Rupturing; Sciences of the Universe; Seismic activity; Seismograms; Slip; source inversion validation; Windows (intervals)
• ISSN: 2169-9313; 2169-9356
• DOI: 10.1029/2017JB015388

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. Plain Language Summary In this paper we present a new method to infer the spatial and temporal history of an earthquake through the progressive analysis of seismograms that are not completely recorded at a given moment. Nowadays, the inference of an earthquake history is a common procedure that seismologists do after some minutes of the occurrence of an earthquake. The reconstruction of this history implies explaining many physical unknowns by interpreting the available seismograms. In this work we provide evidences that a progressive reconstruction is possible through the analysis of partially recorded seismograms. Furthermore, we find that the final reconstruction of such history appears to be better through the progressive analysis of seismograms than the results obtained with a traditional analysis of completely recorded seismograms. Key Points An alternative linear inverse formulation for kinematic source reconstruction is presented Such formulation can invert progressively growing data time windows while spanning the model space Promising advantages of this method are found, thanks to the preservation of cau