Controlled-source Electromagnetic Modelling Studies - Utility of Auxiliary Potentials for Lowfrequency Stabilization

摘要

When simulating controlled-source electromagnetic data at frequencies significantly lower than 1 Hz,standard formulations based, e.g., on the vector Helmholtz equation for the electric field, may fail toproduce faithful results, because the term in the Helmholtz equation involving conductivity decays linearlywith frequency. To stabilize low-frequency simulations, we introduce an auxiliary potential, constrained tobe zero by boundary conditions, and explicitly enforce a divergence condition. We present animplementation of our stabilization technique within a finite-difference frequency-domain algorithm. Theutility of the stabilized approach is demonstrated by showing synthetic data for frequencies as low as 0.001Hz for a 3D model roughly mimicking the geometry of the CO2 sequestration pilot site in Ketzin,Germany. In these synthetic data, we observe that instability occurring primarily in the air for nonstabilizedsimulations disappears for stabilized computations. As expected, the auxiliary potential assumesnear-zero values, but its amplitude increases with decreasing frequency due to numerical limitations. Theamplitude characteristics of the auxiliary potential, and good accuracy of our synthetic data in comparisonwith 1D simulation results, suggest that the stabilization is usable down to frequencies at whichelectromagnetic fields can effectively be considered static.