Rapid Bayesian point source inversion using pattern recognition --- bridging the gap between regional scaling relations and accurate physical modelling

Abstract:

Obtaining knowledge about source parameters in (near) real-time during or shortly after an earthquake is essential for mitigating damage and directing resources in the aftermath of the event. Therefore, a variety of real-time source-inversion algorithms have been developed over recent decades. This has been driven by the ever-growing availability of dense seismograph networks in many seismogenic areas of the world and the significant advances in real-time telemetry. By definition, these algorithms rely on short time-windows of sparse, local and regional observations, resulting in source estimates that are highly sensitive to observational errors, noise and missing data. In order to obtain estimates more rapidly, many algorithms are either entirely based on empirical scaling relations or make simplifying assumptions about the Earth's structure, which can in turn lead to biased results. It is therefore essential that realistic uncertainty bounds are estimated along with the parameters. A natural means of propagating probabilistic information on source parameters through the entire processing chain from first observations to potential end users and decision makers is provided by the Bayesian formalism.

We present a novel method based on pattern recognition allowing us to incorporate highly accurate physical modelling into an uncertainty-aware real-time inversion algorithm. The algorithm is based on a pre-computed Green's functions database, containing a large set of source-receiver paths in a highly heterogeneous crustal model. Unlike similar methods, which often employ a grid search, we use a supervised learning algorithm to relate synthetic waveforms to point source parameters. This training procedure has to be performed only once and leads to a representation of the posterior probability density function $p(m|d)$ --- the distribution of source parameters $m$ given observations $d$ --- which can be evaluated quickly for new data.

Owing to the flexibility of the pattern-recognition based approach, the algorithm can be easily extended to be used with a wide variety of input data, ranging from seismic waveform- to geodetic data. We present a way to deal with noisy observations and missing input data and show how the algorithm could be incorporated into a local earthquake early warning system.