Data error covariance in matched-field geoacoustic inversion

Abstract

Many approaches to geoacoustic inversion are based implicitly on the assumptions that data errors are Gaussian-distributed and spatially uncorrelated (i.e., have a diagonal covariance matrix). However, the latter assumption is often not valid due to theory errors, and can lead to reduced accuracy for geoacoustic parameter estimates and underestimation of parameter uncertainties. This paper examines the effects of data error (residual) covariance in matched-field geoacoustic inversion. An inversion approach is developed based on a nonparametric method of estimating the full covariance matrix (including off-diagonal terms) from the data residuals and explicitly including this covariance in the misfit function. Qualitative and quantitative statistical tests for Gaussianity and for correlations in complex residuals are considered to validate the inversion results. The approach is illustrated for Bayesian geoacoustic inversion of broadband, vertical-array acoustic data measured in the Mediterranean Sea.

Bayesian inversion of marine controlled source electromagnetic data offshore Vancouver Island, Canada

“…These assumptions are verified a posteriori by applying statistical tests (Dosso et al 2006). The joint likelihood function for a number of independent data sets with different covariance matrices (in this study, data sets for each receiver), becomes…”

“…which provides a closed form expression for the maximumlikelihood a estimate in terms of the model parameters m which are sampled explicitly (Dosso et al 2006). The inversion approach estimates both the optimal number of layers, using the BIC, and the data covariance matrices from residual analysis.…”

“…Parameter inter-relationships are examined in terms of joint marginal densities (see e.g. Dosso et al 2006).…”

“…The final estimate for the most probable number of layers is determined by minimizing the BIC. MHS is then carried out starting at the optimal model after the second inversion with ASSA and BIC, and uses the non-Toeplitz covariance matrix (Dosso et al 2006) to calculate the misfit with eq. (6).…”

“…The non-Toeplitz data covariance matrix is estimated by computing the autocorrelation of the residuals for each receiver, analogously to Dosso et al (2006), with (i is dropped for readability)…”