Three-dimensional magnetotelluric inversion using non-linear conjugate gradients

We have formulated a 3-D inverse solution for the magnetotelluric (MT) problem using the non-linear conjugate gradient method. Finite difference methods are used to compute predicted data efficiently and objective functional gradients. Only six forward modelling applications per frequency are typically required to produce the model update at each iteration. This efficiency is achieved by incorporating a simple line search procedure that calls for a sufficient reduction in the objective functional, instead of an exact determination of its minimum along a given descent direction. Additional efficiencies in the scheme are sought by incorporating preconditioning to accelerate solution convergence. Even with these efficiencies, the solution’s realism and complexity are still limited by the speed and memory of serial processors. To overcome this barrier, the scheme has been implemented on a parallel computing platform where tens to thousands of processors operate on the problem simultaneously. The inversion scheme is tested by inverting data produced with a forward modelling code algorithmically different from that employed in the inversion algorithm. This check provides independent verification of the scheme since the two forward modelling algorithms are prone to different types of numerical error.