Exploration of the data space via trans-dimensional sampling: the case study of seismic double difference data

Abstract. Double differences (DD) seismic data are widely used to define elasticity distribution in the Earth's interior, and its variation in time. DD data are often pre-processed from earthquakes recordings through expert-opinion, where couples of earthquakes are selected based on some user-defined criteria, and DD data are computed from the selected couples. We develop a novel methodology for preparing DD seismic data based on a trans-dimensional algorithm, without imposing pre-defined criteria on the selection of couples of events. We apply it to a seismic database recorded on the flank of Katla volcano (Iceland), where elasticity variations in time has been indicated. Our approach quantitatively defines the presence of changepoints that separate the seismic events in time-windows. Within each time-window, the DD data are consistent with the hypothesis of time-invariant elasticity in the subsurface, and DD data can be safely used in subsequent analysis. Due to the parsimonious behavior of the trans-dimensional algorithm, only changepoints supported by the data are retrieved. Our results indicate that: (a) retrieved changepoints are consistent with first-order variations in the data (i.e. most striking changes in the DD data are correctly reproduced in the changepoint distribution in time); (b) changepoint locations in time do correlate neither with changes in seismicity rate, nor with changes in waveforms similarity (measured through the cross-correlation coefficients); and (c) noteworthy, the changepoint distribution in time seems to be insensitive to variations in the seismic network geometry during the experiment. Our results proofs that trans-dimensional algorithms can be positively applied to pre-processing of geophysical data before the application of standard routines (i.e. before using them to solve standard geophysical inverse problems) in the so called exploration of the data space.