海洋人工源频率域电磁法三维共轭梯度反演研究
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摘要
目前海洋电磁法的理论和方法技术已逐步趋向成熟，应用领域不断扩大，效果明显提高，在海洋深部构造地壳和上地幔的探测中已成为一种重要的手段，在石油和天然气以及金属矿床等资源的勘察中也发挥了越来越大的作用。在海上油气资源探测方面，由于海洋人工源频率域电磁法具有探测深度大、横向分辨率高、对低阻带的结构反映灵敏等优点，在国外逐渐成为油气勘测的重要手段，而国内仍然处于探索阶段。本文着重研究海洋人工源频率域电磁法三维正反演算法，建立较系统的海洋人工源频率域电磁法三维数值模拟、三维反演技术理论，为开展海洋人工源频率域电磁法的应用奠定基础。
海洋人工源频率域电磁法三维正演采用常用的交错采样有限差分算法，选用电偶源，将电磁场总场分解为一次场与二次场。使用汉克尔滤波算法，得到层状模型地下场值的分布，将其作为一次场。然后采用交错采样网格剖分模型，将麦克斯韦方程的积分形式离散化，得到线性方程组，加入特定的边界条件，采用预处理共轭梯度法求解方程组，最后得到二次场值的分布。通过与已有的算法进行对比来验证本文算法的精度。
对于海洋人工源频率域电磁法三维反演算法，本文使用共轭梯度方法进行反演。一般为了获得地下模型的物性参数，需要求取雅可比矩阵，而本文为了避免计算雅可比矩阵，采用共轭梯度方法，将雅可比矩阵计算有关的步骤转变为2次“拟正演”计算，极大地加快了反演速度，减小了所需的存储空间。通过两个模型计算验证了本文三维共轭梯度算法的可靠性。
采用多个发射源和单个发散源进行正反演计算，绘制了正演总场和二次场计算的曲线和平面等值线图，对比了不同发射情况时反演的结果。
With its gradually developed theories and techniques, marine electromagneticmethod finds expanding applications and better effects. Nowdays electronmagneticmethod has become an important tool in prospecting tectonics in oceanic crust andupper mantle, playing a greater and greater role in resources explorations likedetectings in oil, gas, solid minerals et al.When used in detecting offshare oil and gasresources, marine controled-source electromagnetic method in frequency domainshow advantanges of deep sounding, high lateral resolution and senstive response tothe low-resistance zone. While widly used abroad, this method is still pre-mature inour country. This article mainly studies the algorithms dealing with3D forward andinversion problem in marine controlled-source electriomagnetic method in frequencydomain, trying to systematically establish its3D numerical modeling and inversiontheories and techniques, which will lay foundations for its applications.
3D forward of marine controlled-source electronmagnetic method in frequencydomain relys on interlaced sampling finite difference algorithms.The totalelectromagnetic field is divided into the primary field and the sencondary field aselectric dipole source exists. Field value distributions of stratified model undergroundderived from Hankel filtering algorithm comprise the primary field. Throughinterlaced sampling grid dissection model, integral form of Maxwell equation isdiscretized to system of linear equations.This system of linear equations under certainboundary conditions are soved by preconditioned conjugate gradient method.Therecomes the secondary field.Under comparision with other algorithms, the accuracy ofthis algorithm is testified.
As to inversion of marine controlled-source electromagnetic method infrequency domain, this article adopts conjugate gradient method.Generally, Jacobimatrices need to be soved to get the parameters of models underground. Conjugategradient method transfering caculaltion procedure of Jacobi matrix into two‘quasi-forward’ caculations heps to avoid a Jacobi matrix, which significantly speeds up the inversion and decreases the storage space. Two models are used to testify thereliablity of3D conjugate gradient method involed in this article.
Forward caculations are conducted for both sigular emission source and mutipleemission sources.Moreover, this article covers the curves and plane equivalences ofthe total field and the secondary field. Comparied between inversions result underdifferent emmission conditions.
海洋人工源频率域电磁法三维正演采用常用的交错采样有限差分算法，选用电偶源，将电磁场总场分解为一次场与二次场。使用汉克尔滤波算法，得到层状模型地下场值的分布，将其作为一次场。然后采用交错采样网格剖分模型，将麦克斯韦方程的积分形式离散化，得到线性方程组，加入特定的边界条件，采用预处理共轭梯度法求解方程组，最后得到二次场值的分布。通过与已有的算法进行对比来验证本文算法的精度。
对于海洋人工源频率域电磁法三维反演算法，本文使用共轭梯度方法进行反演。一般为了获得地下模型的物性参数，需要求取雅可比矩阵，而本文为了避免计算雅可比矩阵，采用共轭梯度方法，将雅可比矩阵计算有关的步骤转变为2次“拟正演”计算，极大地加快了反演速度，减小了所需的存储空间。通过两个模型计算验证了本文三维共轭梯度算法的可靠性。
采用多个发射源和单个发散源进行正反演计算，绘制了正演总场和二次场计算的曲线和平面等值线图，对比了不同发射情况时反演的结果。
With its gradually developed theories and techniques, marine electromagneticmethod finds expanding applications and better effects. Nowdays electronmagneticmethod has become an important tool in prospecting tectonics in oceanic crust andupper mantle, playing a greater and greater role in resources explorations likedetectings in oil, gas, solid minerals et al.When used in detecting offshare oil and gasresources, marine controled-source electromagnetic method in frequency domainshow advantanges of deep sounding, high lateral resolution and senstive response tothe low-resistance zone. While widly used abroad, this method is still pre-mature inour country. This article mainly studies the algorithms dealing with3D forward andinversion problem in marine controlled-source electriomagnetic method in frequencydomain, trying to systematically establish its3D numerical modeling and inversiontheories and techniques, which will lay foundations for its applications.
3D forward of marine controlled-source electronmagnetic method in frequencydomain relys on interlaced sampling finite difference algorithms.The totalelectromagnetic field is divided into the primary field and the sencondary field aselectric dipole source exists. Field value distributions of stratified model undergroundderived from Hankel filtering algorithm comprise the primary field. Throughinterlaced sampling grid dissection model, integral form of Maxwell equation isdiscretized to system of linear equations.This system of linear equations under certainboundary conditions are soved by preconditioned conjugate gradient method.Therecomes the secondary field.Under comparision with other algorithms, the accuracy ofthis algorithm is testified.
As to inversion of marine controlled-source electromagnetic method infrequency domain, this article adopts conjugate gradient method.Generally, Jacobimatrices need to be soved to get the parameters of models underground. Conjugategradient method transfering caculaltion procedure of Jacobi matrix into two‘quasi-forward’ caculations heps to avoid a Jacobi matrix, which significantly speeds up the inversion and decreases the storage space. Two models are used to testify thereliablity of3D conjugate gradient method involed in this article.
Forward caculations are conducted for both sigular emission source and mutipleemission sources.Moreover, this article covers the curves and plane equivalences ofthe total field and the secondary field. Comparied between inversions result underdifferent emmission conditions.
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