Hierarchical Bayesian Inversion for the Centroid Moment Tensor

Abstract:

Kinematic point source inversions using data from complex tectonic settings (e.g. geothermal or volcanic areas and mines) often result in large non-double-couple components. Examining events with mechanisms more complex than shear motion on a planar fault requires a sophisticated inversion method. We have developed a technique within the probabilistic Bayesian framework that combines previous knowledge about the mechanism with the information from the data and results in a posterior probability distribution for the model parameters. It is capable of yielding parameter uncertainties, which cannot be analytically calculated for a non-linear inversion that includes the source location. The code uses time-series of displacements of regional earthquakes and explosions with moderate magnitudes to compute the centroid location and the seismic moment tensor.

The noise is also treated as an unknown in the inversion, in order to determine the level of data fit. As a result, the model complexity (i.e. the contribution of isotropic and compensated linear vector dipole components) is determined by the data themself. Furthermore, the noise weights the contribution of each waveform and the noise covariance matrix accounts for both observational and theoretical errors.

The code has been extensively tested in synthetic experiments with a variety of focal mechanisms and different types of noise added to synthetic waveforms. It showed fast convergence of the centroid location, accompanied with thorough sampling of the moment tensor parameters leading to narrow posterior distributions. Subsequently, it is being applied to waveforms from earthquakes that occurred in various tectonic environments.