Joint inversion of seismic traveltimes and magnetotelluric data with a directed structural constraint

We introduce a new structural constraint for joint inversion with an application to regional scale seismic traveltimes and magnetotelluric data. We call the constraint directed' as it takes into account a priori information on the sign of cross-correlation between the gradients of reconstructed parameters. With special treatment of singularities, arising from vanishing gradients and linearization, this constraint demonstrates some properties of an edge-preserving stabilizer - it provides blocky models with coincident discontinuities. We develop an algorithm for 2D pixel-based joint inversion, including the proposed structural constraint as a penalty term of the objective function; additional stabilizing terms are total variation of seismic slowness and Levenberg-Marquardt damping. The resulting regularized Gauss-Newton scheme is numerically stable and demonstrates relatively fast convergence both in data misfits and in the structural similarity measure. This is shown by a numerical study of the algorithm on a simplified regional model of the Earth's crust. The considered model has a blocky structure with a positive correlation between P-wave velocity and electrical resistivity; it represents a faulted basement overlain by sediments embedding an allochthonous salt dome. The developed joint inversion improves both velocity and resistivity reconstruction relative to separate inversions. In comparison with the cross-gradients constraint the considered structural constraint firstly fixes the sign of correlation between the gradients of the parameters, thus reducing uncertainty in the model recovery and secondly due to its stabilizing properties it limits the amount of additional regularization, which results in sharper reconstructed models.