Controlled-source Electromagnetic Modelling Studies – Utility of Auxiliary Potentials for Low-frequency Stabilization
Controlled-source Electromagnetic Modelling Studies – Utility of Auxiliary Potentials for Low-frequency Stabilization
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受控源电磁建模研究 - 低频稳定辅助电位的实用性
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
K. Spitzer
中科院分区：
文献类型：
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作者：
R. Streich;C. Schwarzbach;M. Becken;K. Spitzer
当模拟频率明显低于1hz的受控源电磁数据时，基于（例如电场的矢量亥姆霍兹方程）的标准公式可能无法产生忠实的结果，因为亥姆霍兹方程中涉及电导率的项随频率线性衰减。为了稳定低频模拟，我们引入了一个被边界条件约束为零的辅助势，并显式地强制执行散度条件。我们提出了在有限差分频域算法中实现我们的稳定技术。在德国Ketzin的二氧化碳封存试点基地中，3D模型模拟了低至0.001 Hz的频率合成数据，证明了稳定方法的实用性。在这些合成数据中，我们观察到非稳定模拟中主要发生在空气中的不稳定性在稳定计算中消失。正如预期的那样，辅助电位的值接近于零，但由于数值限制，其幅度随着频率的降低而增加。辅助电位的幅度特性，以及与一维仿真结果相比，我们的合成数据具有良好的准确性，表明在电磁场可以有效地视为静态的频率下，这种稳定是可用的。
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 to produce faithful results, because the term in the Helmholtz equation involving conductivity decays linearly with frequency. To stabilize low-frequency simulations, we introduce an auxiliary potential, constrained to be zero by boundary conditions, and explicitly enforce a divergence condition. We present an implementation of our stabilization technique within a finite-difference frequency-domain algorithm. The utility of the stabilized approach is demonstrated by showing synthetic data for frequencies as low as 0.001 Hz 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 non-stabilized simulations disappears for stabilized computations. As expected, the auxiliary potential assumes near-zero values, but its amplitude increases with decreasing frequency due to numerical limitations. The amplitude characteristics of the auxiliary potential, and good accuracy of our synthetic data in comparison with 1D simulation results, suggest that the stabilization is usable down to frequencies at which electromagnetic fields can effectively be considered static.