The effects of uncertain stochastic variations in Earth velocity structure on the inversion of seismic data for the time-domain moment tensor.

Inversions of seismic data for an effective seismic source model is routinely performed as a discriminant between underground explosions and earthquake sources. Although linear inverse theory provides the mathematical machinery to propagate data uncertainty it is often model uncertainty that is the greatest source of errors in seismic moment tensor inversions. We present a series of numerical simulations and inversions that evaluate the effects of model uncertainty on the estimates of the time-domain seismic moment tensor (TDMT), assuming noise-free data. The model uncertainty takes the form of high-wavenumber heterogeneities that would not be resolvable in, for example, tomographic inversions for seismic velocity. We first build two smooth canonical models which we then perturb them using a binary von Karman stochastic distribution of density and velocity. We find that the primary effects to synthetic data are its phase: the variance in the phase increases as time increases. However, there is no significant variation in the actual arrival time of the first-arriving seismic energy. Using a Monte Carlo method to invert for the TDMT, we find that the estimated amplitudes of the on-diagonal TDMT terms are lower than the actual amplitudes of the source model. We also observe that the amplitude of the off-diagonal terms is approximately preserved, however, they contain more energy in the high frequency portions. Based on these tests, we conclude that inverting for the TDMT using a model with stochastic heterogeneities results in the energy in the isotropic source terms being "pushed" to the higher frequency components of the off-diagonal moment tensor terms. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.