On the practical convergence of coda-based correlations: a window optimization approach

We present a novel optimization approach to improve the convergence of interstation coda correlation functions towards the medium's empirical Green's function. For two stations recording a series of impulsive events in a multiply scattering medium, we explore the impact of coda window selection through a Markov Chain Monte Carlo scheme, with the aim of generating a gather of correlation functions that is the most coherent and symmetric over events, thus recovering intuitive elements of the interstation Green's function without any nonlinear post-processing techniques. This approach is tested here for a 2-D acoustic finite difference model, where a much improved correlation function is obtained, as well as for a database of small impulsive icequakes recorded on Erebus Volcano, Antarctica, where similar robust results are shown. The average coda solutions, as deduced from the posterior probability distributions of the optimization, are further representative of the scattering strength of the medium, with stronger scattering resulting in a slightly delayed overall coda sampling. The recovery of singly scattered arrivals in the coda of correlation functions are also shown to be possible through this approach, and surface wave reflections from outer craters on Erebus volcano were mapped in this fashion. We also note that, due to the improvement of correlation functions over subsequent events, this approach can further be used to improve the resolution of passive temporal monitoring.