Accelerating the Frequency Domain Controlled-Source Electromagnetic Data Inversion Using Rational Krylov Subspace Algorithm

Controlled-source electromagnetic (CSEM) method is crucial for detecting and locating underground anomalies and structures. However, it is challenging to interpret the field data with multifrequency via 3-D CSEM inversion. To fully excavate and utilize the valuable information of CSEM data at different frequencies, we propose an efficient algorithm for 3-D multifrequency CSEM (MFCSEM) inversion based on rational Krylov (RK) subspace. Within the framework of our algorithm, we first use the three-term Lanczos recursion to construct the RK basis matrix quickly; thus, the fast MFCSEM forward modeling can be realized via the RK approximation. Subsequently, we present a novel cyclic projection and correction (CPC) algorithm to solve the MFCSEM adjoint forward problems. Finally, the nonlinear conjugate gradient (NLCG) method is adopted to seek a solution to this nonlinear inverse problem. We demonstrate the excellent performance of our algorithm by synthetic and field datasets. The inversion results show that our algorithm is computationally efficient, resulting in considerable speedup compared with the conventional method. Our algorithm provides a new idea that would significantly improve the efficiency of MFCSEM inversion.