Abstract：Three-dimensional (3D) magnetotelluric (MT) forward modeling requires solutions to electromagnetic field distribution of two polarization sources at several frequencies, thus leading to enormous computational costs. This paper accele-rates 3D MT forward modeling by order reduction based on block rational Krylov method. The novelty of this algorithm lies in the following aspects. First, the source-term explicit expression of MT is represented as planar current source, and the frequency-dependent electric field response is a produ-ct of a transfer function and a constant vector of the current source. As a result, the rapid solution of electric field response at all frequencies is reali-zed through the construction of a rational Krylov subspace, which avoids repeated solutions of large sparse linear equations with different frequencies. Second, the paper adopts the block Krylov technique to express polarizations of TE and TM as block source vectors and simplifies forward mode-ling response of the two polarizations into the construction of a block rational Krylov subspace. Additionally, an asymptotic convergence formula is introduced to obtain the optimal single repeated polarization of the Krylov method. Combined with direct solver, the forward modeling computational cost of 3D MT is reduced to a coefficient matrix decomposition and dozens of matrix back substitutions. This algorithm ensures the forward mode-ling accuracy and significantly improves the forward modeling speed. Numerical results of forward modeling in half space model and 3D DTM1 model show that compared with the conventional frequency-dependent forward modeling solutions, block rational Krylov can notably increase the modeling speed.
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