Accelerating 3D Magnetotelluric Forward Modelling with Domain Decomposition and Order-Reduction Methods

Abstract. Three-dimensional (3D) magnetotelluric (MT) forward modelling is computationally demanding, limiting its use in global uncertainty quantification and sampling-based probabilistic inversion. Here, we introduce a novel forward-modelling framework that combines an iterative domain decomposition (DD) formulation with proper orthogonal decomposition (POD) reduced-order modelling to enable scalable and efficient 3D MT simulations. The DD component partitions the computational domain into subdomains, avoiding the factorization of a single global system, accelerating simulations by over 60 % compared to global solvers, and alleviating memory bottlenecks in large problems. The POD component leverages the local DD solutions to construct a reduced-order version of the problem that can deliver accurate and fast solutions to the 3D forward problem during subsequent evaluations. Using the DTM1 benchmark and a real-world conductivity model, we quantify runtime, memory, and accuracy in terms of MT quantities of interest (apparent resistivity and phase). DD–POD achieves speed-ups exceeding 90 % relative to full-order solvers and up to 70 % relative to existing ROM techniques, while maintaining acceptable accuracy. These results suggest that DD–POD can make higher-resolution 3D MT forward modelling practical within sampling-based workflows by substantially reducing both runtime and memory demands.