基于Hammer积分的三维地面磁共振高精度正演方法

Three-dimensional forward modeling with high precision for underground MRS based on Hammer integration

为满足三维地面磁共振正演计算的精度要求,本文提出了基于非结构不均匀四面体网格的Hammer积分算法。首先利用有限元方法实现了对地下空间的三维磁场计算,完成了地面磁共振灵敏度核函数表达式的推导。针对现有地面磁共振正演方法中常规网格尺寸大、计算精度差、细化网格尺寸小、但是数量大的问题,应用Hammer积分在常规网格中完成核函数的高精度计算。三维核函数和3个含水模型的正演仿真实验表明:基于Hammer积分的地面磁共振正演方法具有网格少、计算节点少、积分精度高的特点,能够高效解决核函数的正演计算问题。

To meet the accuracy requirement of surface three-dimensional（3D）Magnetic Resonance Spectroscopy（MRS）forward modeling.Hammer integration algorithm was proposed based on unstructured non-uniform tetrahedral mesh.First,finite element method was used to calculate the 3D magnetic field in the subsurface,and the sensitivity kernel expression was deduced.Then,to overcome the shortcoming of conventional mesh grid,that the precision becomes poor as grid size is large,while smaller grid size leads to enormous calculation task,Hammer integration was applied to calculate the kernel function with conventional grid.Synthetic results including 3Dkernel function and aquifer models show that,using Hammer integration,higher precision can be achieved with fewergrids and nodes.The forward model can be calculated efficiently.