基于位移逆有理Krylov子空间算法的频率域可控源电磁快速正演  

Frequency domain controlled-source electromagnetic forward modeling using the shift-and-invert rational Krylov subspace algorithm

作　　者：孙启凯 周峰 张志勇[1] 李建慧 汤文武[1] 易柯 SUN QiKai;ZHOU Feng;ZHANG ZhiYong;LI JianHui;TANG WenWu;YI Ke(School of Geophysics and Measurement Technology,East China University of Science and Technology,Nanchang 330013,China;Key Laboratory of Airborne Geophysics and Remote Sensing Geology,Ministry of Natural Resources,Beijing 100083,China;School of Geophysics and Space Information,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]东华理工大学地球物理与测控技术学院,南昌330013 [2]自然资源部航空地球物理与遥感地质重点实验室,北京100083 [3]中国地质大学(武汉)地球物理与空间信息学院,武汉430074

出　　处：《地球物理学报》2024年第10期3915-3930,共16页Chinese Journal of Geophysics

基　　金：自然资源部航空地球物理与遥感地质重点实验室(2023YFL11);国家自然科学基金(42004061,42164008);江西省自然科学基金青年基金项(20232BAB213074);江西省“水利+科技”联合计划(2023KSG01008);江西省交通运输厅科技项目(2022H0025)联合资助。

摘　　要：本文开发了一种双重复极点位移逆(SAI)有理Krylov子空间算法,实现了频率域可控源电磁法(CSEM)多频电磁场值的快速计算.在有理Krylov子空间算法中,极点选择是保障CSEM正演精度的关键,单重复极点有理Krylov子空间算法在频率域可控源电磁法应用最为广泛,但其缺点在于正演计算频段范围有限,增加极点个数能够获取更宽频段响应.为此,立足于有理Krylov子空间基本理论,推导了多重复极点位移逆算法Rayleigh商一阶秩修改公式,并利用该模型降阶算法开展了可控源电磁法正演模拟.另外,本文利用粒子群算法求解多极点收敛率函数,可以快速获取最优多极点,从而确保正演模拟精度.相比于单重复极点,多重复极点位移逆算法会增加极点计算时间,但能在更宽的频率范围内准确计算电磁场值.根据频率范围选定合适的极点后,该方法仅需要求解与极点数相同的多个线性方程组,通过场源项和系数矩阵求得有理Krylov子空间,再将正演算子投影到有理Krylov子空间中,显著降低正演算子的自由度,提高多频正演的计算效率.设计了均匀半空间和块状异常模型,并开展了算法测试,计算结果表明:在保证精度的情况下,相比于常规矢量有限元算法,单重复极点、双重复极点位移逆模型降阶算法的加速比超过10倍以上;双重复极点位移逆模型降阶算法总体计算精度要优于相应的单重复极点算法,且具有更宽的计算频带.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 cou

关 键 词：位移逆算法 有理Krylov子空间 多重复极点 频率域可控源电磁法 数值模拟 

分 类 号：P631[天文地球—地质矿产勘探]