Model Order Reduction for 3-D Inversion of Airborne Transient Electromagnetic Data

Airborne transient electromagnetic (ATEM) methods offer high resolution and efficiency but face computational challenges in three-dimensional (3D) inversion. Conventional adjoint forward method for computing sensitivity matrices require computational time several times that of forward modeling, severely limiting inversion efficiency. This paper presents a fast 3D ATEM inversion method that integrates model order reduction (MOR) based on the rational Krylov subspace with finite volume discretization for central-loop configurations. An Octree-based finite volume method (FVM) is employed to discretize the magnetic field governing equations, transforming them into time-domain transfer functions that are solved via a single-pole rational Krylov subspace. By leveraging the subspace and orthogonal basis vectors obtained from forward modeling, spectral decomposition and differential approximation are used to represent the reduced-order model’s transfer function as a superposition of exponentially decaying modes. This enables space-time decoupling and equation-free computation, significantly reducing computational complexity compared to conventional adjoint forward method. The approach also exhibits favorable parallelizability, further enhancing computational efficiency. Numerical examples validate the accuracy of the proposed method and demonstrate significant potential for computational efficiency improvement under the described model and computational environment. Field data application further confirms the practical applicability of the method for imaging complex subsurface geological structures.