Global 3-D imaging of mantle electrical conductivity based on inversion of observatory C-responses-I. An approach and its verification

We present a novel frequency-domain inverse solution to recover the 3-D electrical conductivity distribution in the mantle. The solution is based on analysis of local C-responses. It exploits an iterative gradient-type methodlimited-memory quasi-Newton methodfor minimizing the penalty function consisting of data misfit and regularization terms. The integral equation code is used as a forward engine to calculate responses and data misfit gradients during inversion. An adjoint approach is implemented to compute misfit gradients efficiently. Further improvements in computational load come from parallelizing the scheme with respect to frequencies, and from setting the most time-consuming part of the forward calculationscalculation of Greens tensorsapart from the inversion loop. Convergence, performance, and accuracy of our 3-D inverse solution are demonstrated with a synthetic numerical example. A companion paper applies the strategy set forth here to real data.