各向异性地层中套管井间电磁响应的三维耦合势GPU并行正演研究

3D parallel forwading simulation method based on the coupled potentials will established in the project，to solve the fast simulation problem of cross-well EM responses in the anisotropic formation.Firstly，By introducing the vector-scalar potential’s functions, Maxwell’s equation is reformulated into Helmholtz equations， which has fast convergence speed in the low frequency domain.And then, according to the Coulomb gauge, stabilization is introduced to avoid the problem of numerical iterative non-convergence caused by high contrast permittivity between metal casing pipe and formation.Applying the finite volume integral averaging technique, the Helmholtz equations are discreted successfully. The compressed sparse row(CSR)format matrix storage scheme is applied to store the coeifficient matrix of discrete equations. By means of ILU preconditioning technique and BICGSTAB method based on GPU parallel computing， the large linear equations are solved efficiently.Fast finite volume parallel method is finally established to simulate the crosswell EM logging’s response.his project is expected to develop a fast simulation software that could be used to solve milions unknowns in several GPU computing nodes .And then the characteristics of effects in the different cases such as formation anisotropy , dipping angle, conductivity and peremitivity of casing pipe are investigated, in order to provide a theoretical basis on instrument optimal design and development of cross-well imaging technique.technique.

本项目拟建立一套基于耦合势的三维并行正演模拟算法，用于解决三维各向异性地层中井间的电磁响应快速模拟问题。首先，通过引入矢势-标势函数将Maxwell方程组优化为在低频条件下更易收敛的耦合势Helmholtz方程组。然后，根据库仑规范引入稳定项，解决由于金属套管与地层磁导率大反差而产生的方程组数值迭代不收敛问题，并利用有限体积平均技术实现对Helmholtz方程组的离散。利用行格式压缩存储离散方程组的大型稀疏矩阵，借助于GPU并行的ILU分解预处理技术和稳定双共轭梯度法实现对方程组的快速求解。最终，建立一套模拟低频井间电磁测井响应的快速有限体积并行算法。项目预期研制出能在多个GPU计算节点上实现求解数百万个未知数的快速模拟软件，进而重点考察地层电阻率各向异性、井斜角度、套管电导率和磁导率等对测井响应的影响规律，为新型仪器的优化设计以及推动井间成像技术的发展提供理论依据。

本项目针对电导率各向异性地层中三轴发射-接收线圈系的井间电磁响应，开展三维正演算法及模拟研究工作。将发射线圈简化为三轴正交磁偶极子源，利用低感应数预处理方法建立基于矢势与标势的Helmholtz方程。实现了非等间距的Yee氏交错网格的建立、单元内多介质的参数的体积加权平均，以及积分形式的有限差分格式推导，最终得到基于离散耦合势的超大规模线性方程组。通过使用不完全LU分解预处理的稳定双共轭梯度法实现对超大稀疏线性方程组的数值计算，并利用OPENMP并行技术对算法进行了优化。通过与有限元软件COMSOL和解析解的数值结果对比验证本项目所建模型与算法的有效性。.项目中重点考察了垂直三轴井间电磁各分量响应特征以及各向异性系数等参数对井间电磁响应的影响。大量的数值结果表明：在横向同性地层的垂直井间模型中，井间电磁的横向分量xx和yy能反映出地层电导率各向异性信息，但横向探测能力较差。而轴向分量zz虽只反映地层水平电阻率信息，但具有较好的横向探测能力，且对地层中异常体非常敏感，而交叉分量xz、zx则具备较强的层边界识别能力。数值结果证实了将多分量发射接收系统应用在各向异性地层或异常体的探测的可行性，并为进一步研究井间电磁反演与成像奠定正演算法基础。此外针对存在金属套管或裂缝环境下的单井电磁响应也进行数值仿真来验证其在复杂地层模型下的算法有效性。项目资助待发表SCI文章一篇，在审SCI文章一篇。培养、硕士生3名，其中3名已经取得硕士学位