Realistic uncertainties for Surface Wave dispersion curves and their influences on 1D S-wave profiles

Surface wave (SW) dispersion curves are widely used to retrieve 1D S-wave profiles of the Earth at different depth-scale, from local to global models. However, such models are generally constructed with a number of assumptions which could bias the final results. One of the most critical issue is the assumption of a diagonal error covariance matrix as representative of the data uncertainties. Such first-order approximation is obviously wrong for any SW practitioner, given the smoothness of dispersion curves, and could lead to overestimate the information content of the dispersion curves themselves.

In this study, we compute realistic errors (i.e. represented by a non-diagonal error covariance matrix) for Surface Wave dispersion curves, computed from earthquakes data. Given the huge amount of data available worldwide, realistic errors can be easily estimated using empirical formulations (i.e. repeated measurements of the same quantity). Such approach leads to the computation of a full-rank empirical covariance matrix which can be used as input in standard Likelihood computation (e.g. to drive a Markov chain Monte Carlo, McMC, sampling of a Posterior Probability Distribution, PPD, in case of a Bayesian workflow).

We apply our approach to field measurements recorded along one decade in the British Islands. We first compute the empirical error covariance matrices for 12 two-stations dispersion curves, under different assumptions, and, then, we invert the curves using a standard trans-dimensional McMC algorithm, to find relevant 1D S-wave profiles for each curve. We perform both an inversion considering the full-rank error covariance matrix, and one inversion using a diagonal version of the same matrix. We compare the retrieved profiles with published results. Our main finding is that 1D profiles obtained using a full-rank error covariance matrix are often similar to profiles obtained with a diagonal matrix and published profiles obtained with different approaches. However, relevant differences occur in a number of cases, which leads to potentially question some details in 1D models. Given the extreme easiness of computing the full-rank error covariance matrix, we strongly suggest to include realistic error computation in SW studies.