Estimating seismic velocity changes from big ambient noise databases using a Markov Chain Monte Carlo approach

The seismic velocity within the Earth is intrinsically linked to the physical properties of the constituent rock. Temporal changes in relative seismic velocity (dv/v) can be induced by a variety of tectonic, environmental and anthropogenic processes. Examples include slip events, precipitation-related changes to pore fluid pressure, tidal forces, and fluid extraction or injection. Monitoring seismic velocity changes in ambient noise correlation functions usually involves the designation of some reference seismic velocity, most commonly derived from a time-averaged (stacked) cross-correlation function that covers the entire analysis period. This definition is arbitrary, and can be prone to bias when the individual cross correlation functions and the reference function are not similar. A more recent approach involves calculating the velocity change between every unique pair of cross-correlation functions, and then performing an inversion for a continuous dv/v time series. Whilst eliminating the need for a reference velocity, the computational costs of least squares matrix inversion methods scale poorly with the amount of data involved. This restricts the temporal resolution that can be achieved using this approach, the total span of the time period that can be analysed, and the number of stations that can be used simultaneously. To address these problems, we implement a new computational method based upon a Bayesian Markov Chain Monte Carlo (MCMC) approach to calculate the dv/v time series. The inversion of a matrix is not required, and the computational memory requirements are much reduced, allow ing us to simultaneously invert big seismic data sets. Furthermore, drawing representative samples directly from the posterior distribution allows us to robustly analyse the uncertainties of the dv/v time series without imposing subjective constraints, such as the level of smoothing, upon the resulting models. To demonstrate the applicability of the MCMC approach to seismic monitoring, we apply this new method to synthetic tests and several examples using data recorded in southern California. These include the detection of transient reductions in seismic velocity following 2010 El Mayor-Cucapah earthquake, as well as the observation of hourly variations in seismic velocity at the Pinyon Flats observatory.