Estimating temporal changes in seismic velocity using a Markov chain Monte Carlo approach

Abstract

SUMMARY We present a new method for estimating time-series of relative seismic velocity changes (dv/v) within the Earth. Our approach is a Markov chain Monte Carlo (MCMC) technique that seeks to construct the full posterior probability distribution of the dv/v variations. Our method provides a robust, computationally efficient way to compute dv/v time-series that can incorporate information about measurement uncertainty, and any prior constraints that may be available. We demonstrate the method with a synthetic experiment, and then apply the MCMC algorithm to three data examples. In the first two examples we reproduce dv/v time-series associated with the response to the 2010 M 7.2 El Mayor-Cucapah earthquake at two sites in southern California, that have been studied in previous literature. In the San Jacinto fault zone environment we reproduce the dv/v signature of a deep creep slip sequence triggered by the El Mayor-Cucapah event, that is superimposed on a strong seasonal signal. At the Salton Sea Geothermal Field we corroborate the previously observed drop-and-recovery in seismic velocity caused by ground shaking related to the El Mayor-Cucapah event. In a third, new example we compute a month long velocity change time-series at hourly resolution at Piñon Flat, California. We observe a low amplitude variation in seismic velocity with a dominant frequency of 1 cycle per day, as well as a second transient signal with a frequency of 1.93 cycles per day. We attribute the 1-d periodicity in the dv/v variation to the combined effects of the diurnal tide and solar heating. The frequency of the signal at 1.93 cycles per day matches that of the lunar (semi-diurnal) tide. Analysis of the uncertainties in the Piñon Flat time-series shows that the error contains a signal with a frequency of 1 cycle per day. We attribute this variation to seismic noise produced by freight trains operating within the Coachella Valley. By demonstrating the applicability of the MCMC method in these examples, we show that it is well suited to tackle problems involving large data volumes that are typically associated with modern seismic experiments.