Quantitative comparison between the radiation-corrected EGF and the conventional EGF

Abstract:

It is important to investigate earthquake source processes for understanding the underlying physics of earthquake ruptures and the background stress field. Slip inversion is a useful method to estimate earthquake source processes, in which spatial and temporal slip distribution is estimated so that the source time functions are convoluted with Green’s function to reproduce observed waveforms. Usually, the slip inversion is formulated as a least-square linear inversion problem to solve for slip amount at each subfault at each time-step to minimize the waveform misfit. While the ordinary slip inversion uses theoretical Green’s functions calculated from a given velocity structure (e.g. Bouchon, 1981; Takeo, 1985), it is also popular to use real waveforms of a smaller earthquake with a similar mechanism in the vicinity as empirical Green’s functions (EGF) (e.g. Hartzell, 1978). Although EGF has an advantage in accounting for the effect of the real complex velocity structure, the method requires a nearby earthquake with a similar mechanism whose waveforms can be used as EGF.

However, as far as the ray paths from two earthquakes mostly share the common ray path near each station, where most of the waveform complexity is determined, the waveform from one event with known mechanism can be potentially used as an EGF to analyze the other event with a slightly different mechanism at a slightly different location by correcting the effects of the radiation patterns. Thus, in this study, we develop a waveform inversion with the radiation-corrected EGF to extend the potential of slip inversion with EGF. Specifically, based on the ray theory, we can calculate the theoretical radiation patterns of the EGF event and those at each subfault of the target earthquake. Then, using the ratio of the radiation patterns at each station, we correct the amplitude of the EGF for each of P, SV, and SH waves.

We apply this new method to synthetic waveforms and compare the results with and without radiation correction under the same settings of source locations, source mechanisms, and station distribution. We repeat this application 200 times for each case of the 20 cases; four different conditions of distance between epicenters of a target and a reference event (Δ), Δ = 0 km, Δ < 5 km, Δ = 10 km, Δ = 20 km, and five different conditions of Kagan angle (θ), θ = 0 degrees, θ < 15 degrees, θ < 30 degrees, θ < 60 degrees, θ < 120 degrees. We used the velocity structure of JMA2001 (Ueno et al., 2002) and source depths of target events and reference events are set to 9.99km. The theoretical waveforms are calculated using fk application (Zhu and Rivera, 2002). And the moment magnitude of reference events and target events are set to 5.0, therefore, the moment ratio estimated by inversion should be 1.

The following figure shows the distribution of moment ratios for 200 samples for each abovementioned 20 cases. The samples are generated so that Δ and θ are within given range for each case, which is written on the top of each panel. The white and blue bars represent the distribution of the results by the conventional method and our method of radiation correction, respectively. The black and blue dot lines express their median value for the conventional method and the new method, respectively.

As a result, the correction of the radiation pattern improved the moment ratio. However, the moment ratios are not exactly 1 for many samples due to the existence of relatively large converted or reflected waves at the surface, which have different radiations from the direct waves. Therefore, we discuss about the reasonable range for the EGF selection using the results of inversions.