Spectral-Element Method with Divergence-Free Constraint for 2.5-D Marine CSEM Hydrocarbon Exploration

Rapid simulations of large-scale low-frequency subsurface electromagnetic measurements are still a challenge because of the low-frequency breakdown phenomenon that makes the system matrix extremely poor-conditioned. Hence, significant attention has been paid to accelerate the numerical algorithms for Maxwell's equations in both integral and partial differential forms. In this letter, we develop a novel 2.5-D method to overcome the low-frequency breakdown problem by using the mixed spectral element method with the divergence-free constraint and apply it to solve the marine-controlled-source electromagnetic systems. By imposing the divergence-free constraint, the proposed method considers the law of conservation of charges, unlike the conventional governing equation for these problems. Therefore, at low frequencies, the Gauss law guarantees the stability of the solution, and we can obtain a well-conditioned system matrix even as the frequency approaches zero. Several numerical experiments show that the proposed method is well suited for solving low-frequency electromagnetic problems.