Frequency domain controlled-source electromagnetic forward modeling using the shift-and-invert rational Krylov subspace algorithm
This paper presents a double-repeated-pole shift-and-invert(SAI)rational Krylov subspace algorithm,which enables rapid computation of multi-frequency responses for frequency domain controlled-source electromagnetic(CSEM)method.In the rational Krylov subspace algorithm,poles selection is crucial for ensuring the accuracy of CSEM forward modeling.The single-repeated-pole rational Krylov subspace algorithm is widely used in frequency domain controlled-source electromagnetic method,but it has the limitation of computation frequency range.Therefore,based on the fundamental theory of rational Krylov subspace,we derive the algorithm for multiple-repeated-pole shift-and-invert method using Rayleigh quotient one-order rank modification formula and implement forward modeling using this model reduction method.The particle swarm algorithm is used to solve the multi-pole convergence rate function,which can quickly obtain the optimal multiple poles.Compared to single-repeated-pole method,the multiple-repeated-pole shift-and-invert method increases poles'computational memory but allows for accurate electromagnetic field calculation over a broader frequency range.The method requires solving linear equation systems the same number times of poles.After selecting appropriate poles by the frequency range and obtaining the rational Krylov subspace through source term and coefficient matrix,the forward operator is projected into rational Krylov subspace,reducing the degrees of freedom and improving efficiency for multi-frequency forward modeling.Tests on uniform half-space and block anomaly models are conducted to evaluate the algorithms'performance.The results demonstrate that,under certain tolerance,the model reduction algorithms of single-repeated-pole and double-repeated-pole shift-and-invert approximation outperform ordinary vector finite element method,achieving an acceleration of over 10 times.The double-repeated-pole shift-and-invert model reduction algorithm outperforms the single-repeated-pole counterpart in computation accuracy on average and has a broader computation frequency range.
万方数据
维普
