A consistent full waveform inversion scheme for imaging heterogeneous isotropic elastic media

Multi-parameter teleseismic full-waveform inversion (FWI) can provide key insights on the composition and thermal state of the lithosphere. In the isotropic version of such inversions, one classically inverts for a set of independent model parameters,  for example (density, Vp, Vs). In this study, we demonstrate that by introducing model covariance matrices with non-diagonal terms to FWI, i.e. accounting for the existing correlations between density, Vp, and Vs, has a dramatic impact on the quality of the reconstructed models. We perform synthetic tests using with a simple subduction model. The teleseismic and regional wavefields are computed with our FK-SEM hybrid method. We invert vertical and radial component P waveforms from four teleseismic events coming from different epicentral distances and azimuths. We use a hierarchical iterative l-BFGS inversion, starting at long period (T > 10 s) to obtain a long wavelength model, and then progressively decreasing the spatial smoothing and cut-off period to 5 s and then 2.5 s. We also demonstrate that a complete non-diagonal model covariance matrix allows us to make the inversion results consistent, i.e. independent of the model parameterization. The inversions which account for the correlations between model parameters provide better models especially for density and Vs, less numerical artifacts, and are characterized by a faster convergence rate compared to inversions performed by assuming that model parameters are independent.