  The ETAS model is widely employed to model the spatio-temporal distribution
of earthquakes, generally using spatially invariant parameters. We propose an
efficient method for the estimation of spatially varying parameters, using the
Expectation-Maximization (EM) algorithm and spatial Voronoi tessellation
ensembles. We use the Bayesian Information Criterion (BIC) to rank inverted
models given their likelihood and complexity and select the best models to
finally compute an ensemble model at any location. Using a synthetic catalog,
we also check that the proposed method correctly inverts the known parameters.
We apply the proposed method to earthquakes included in the ANSS catalog that
occurred within the time period 1981-2015 in a spatial polygon around
California. The results indicate a significant spatial variation of the ETAS
parameters. We find that the efficiency of earthquakes to trigger future ones
(quantified by the branching ratio) positively correlates with surface heat
flow. In contrast, the rate of earthquakes triggered by far-field tectonic
loading or background seismicity rate shows no such correlation, suggesting the
relevance of triggering possibly through fluid-induced activation. Furthermore,
the branching ratio and background seismicity rate are found to be uncorrelated
with hypocentral depths, indicating that the seismic coupling remains invariant
of hypocentral depths in the study region. Additionally, triggering seems to be
mostly dominated by small earthquakes. Consequently, the static stress change
studies should not only focus on the Coulomb stress changes caused by specific
moderate to large earthquakes but also account for the secondary static stress
changes caused by smaller earthquakes.
