Estimation of the Distribution of Ground Motion Indices Using Time-Reversal Propagation of Seismic Energy

Distribution of ground motion indices is important for characterizing earthquakes as well as early responses to earthquake disasters. We propose a method to estimate the distribution of ground motion indices using the simulation of seismic energy propagation and optimal interpolation of observed ground motions. First, we estimate the distribution and propagation direction of seismic energy by the forward calculation of the combination of optimal interpolation and energy propagation theory. At a certain time, we stop the forward calculation and calculate time-reversal energy propagation. Optimal interpolation is also applied during the time-reversal calculation to compensate for the deviation between calculated and observed seismic energies. We applied the method to the case of the 2016 Kumamoto earthquake. The result successfully retrieved the distribution of strong ground motion indices along the Futagawa and Hinagu fault zones even if some observations near the epicenter were not available.