Multiscale waveform tomography with two‐step model parameterization

[1] In geophysical tomography, a proper model parameterization scheme for forward modeling is not necessarily a suitable one for the inversion stage, and vice versa. To take full advantage of the merits of parameterization in both stages, we propose a two-step model parameterization approach, in which different model bases for forward computation and inversion are adopted and the basis change is achieved by applying a spatial projection directly to the sensitivity matrix. We demonstrate this approach through an experimental study of waveform tomography for the Pacific upper mantle shear wave structure using first-orbit long-period Rayleigh waves. In the forward modeling, a normal-mode-based nonlinear asymptotic coupling theory is used for the computation of the synthetics and sensitivity matrix, and the model is parameterized in terms of spherical harmonics which provide efficient analytical solutions for path integrals in the forward modeling. Prior to the inversion, the model basis of the sensitivity matrix is transformed to local functions within the study region. After mapping, only local bases around the data sampling path receive effective sensitivities. Accordingly, the computation cost in the inversion is significantly reduced. Furthermore, the two-step model parameterization also adds flexibility to the inversion schemes. In particular, a wavelet-based multiscale inversion is implemented, and its results are compared to simple damping solutions. The general concept and applications of the two-step model parameterization are not restricted to the forwarding modeling technique or model parameterization schemes employed in this experimental study. This approach benefits any inverse problems wherever transformation of model bases helps to better constrain the results.

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