Uncertainty of Green Functions for Waveform-based Earthquake Source Inversions

Abstract:

Green functions (GFs) are an essential ingredient in waveform-based earthquake source inversions. Hence, their error due to imprecise knowledge of a crustal model is the major source of uncertainty of the inferred earthquake source parameters. Strategies how to incorporate the modeling error (uncertainty) of the GFs in waveform inversions have been recently introduced (Yagi and Fukahata, 2011; Duputel et al., 2014). They rely on statistical description of the GFs uncertainty by means of the covariance matrix.

This study is devoted to estimation of covariance matrix of full wavefield GFs, describing the effect of velocity model uncertainty. By means of Monte Carlo simulations in randomly perturbed 1D velocity models we analyze the dependence of the covariances on the strength of the perturbations, receiver-source distances, and frequency ranges. Since the covariance matrix estimation is numerically very expensive and thus hardly applicable in practice, we propose simplified approaches. The first simplification uses the „Approximate covariance function“ based on GFs in the mean velocity model. The second possible simplification „Stacionarized covariance function“ (i.e. averaged over time) leads to a simple analytical formula for covariance function. The both simplifications exhibit very good agreement with the Monte Carlo simulations, and may be easily implemented in currently existing inversion techniques.

References:

Duputel, Z., Agram, P.S., Simons, M., Minson, S.E. Beck, J.L., 2014. Accounting for prediction uncertainty when inferring subsurface fault slipl, Geophys. J. Int., 197 (1), 464-482.

Yagi, Y. Fukahata, Y., 2011. Introduction of uncertainty of Green's function into waveform inversion for seismic source processes, Geophys. J. Int., 186 (2), 711-720.