A matrix-free Gauss-Newton inversion of realistic CSEM data

Abstract In hydrocarbon exploration, frontier areas and the increasing demand for realistic geoelectrical models constitute significant challenges to the industry. In this context, the marine controlled-source electromagnetic (CSEM) method has emerged as an important complementary tool for subsurface imaging and characterization. In this study, we evaluate the effectiveness of the second-order Gauss–Newton method for the inversion of realistic CSEM data. Second-order methods can incorporate curvature information into the inversion, potentially improving parameter estimation in deeper and poorly constrained regions and enhancing the recovery of structural and resistivity variations in the subsurface. The Gauss–Newton inversion is implemented using the second-order adjoint-state method, such that the Hessian matrix is neither explicitly constructed, stored, nor inverted. Instead, the action of the Hessian operator on a vector in the model-parameter space is computed directly through Hessian–vector products. This matrix-free formulation is mathematically well defined and avoids the memory requirements associated with the explicit construction and storage of the Hessian matrix. To stabilize the linear system associated with the Gauss–Newton step, we employ a damping parameter scaled by the trace of the Hessian matrix, which is approximated using a stochastic trace estimator. The forward, perturbed, and adjoint electromagnetic fields required by the inversion are modeled in the fictitious time domain by applying the correspondence principle. We compare the performance of Gauss–Newton and L-BFGS-B inversions using two gradient-preconditioning strategies: illumination compensation and an adaptive gradient approach. The results show that the Gauss–Newton method, with Hessian-trace-based damping and adaptive gradient preconditioning, provides the best overall performance among the tested configurations. The numerical experiments recover geologically representative models of realistic subsurface environments with fewer artifacts and improved reconstruction of deeper and poorly constrained regions, while maintaining a favorable balance between memory requirements and computational performance.