油气电磁法勘探中的多尺度目标精确正演方法研究

The accurate forward simulation method of multicale target in inhomogeneous background has wide application in oil electromagnetic exploration. However, the present methods are not accurate and stable enough and usually only valid for the idealized model. A more accurate and stable computation method is pursued at both scientific research and engineering. The applied project focuses on the accurate electromagnetic modeling method of multiscale target in oil electromagnetic exploration. The thin dielectric structure based surface integral equation (TDS-SIE) and the current and charge integral equation (CCIE) are utilized to achieve the stable simulation, while the discontinues Galerkin (DG) is adopted to increase the modeling flexibility which is highly demanded in multiscale problem. Firstly, the higher order TDS-SIE is developed for the electromagnetic response accurate simulation of fracture in shale gas exploration. Secondly, the layered medium Green's function is integrated into CCIE for the accurate and wide band simulation of the curved and tilted borehole in inhomogeneous background. Thirdly, the hybrid spectrum integral equation (SIM) and spectrum element method (SEM) method with DG frame is developed for the layered medium application and focus on the flexible modeling and fast simulation. The developed theory and algorithms are highly valuable for scientific research and provide effective forward simulation tools for oil electromagnetic exploration.

非均匀介质中的多尺度目标精确正演技术在电磁法勘探中具有重要应用，但现有方法普遍存在模型过于理想、精度和效率较低等缺陷，学术和工程上迫切需要一种更为灵活高效的多尺度目标精确正演方法。本课题采用频率稳定的薄介质层面积分方程(TDS-SIE)和电流电荷面积分方程(CCIE)高阶矩量法，并结合建模灵活的间断伽略金法(DG)，实现油气勘探中平面分层介质环境下的结构和频率多尺度问题的精确正演分析。首先，将TDS-SIE推广到高阶算法，精确分析分层介质背景中页岩气裂缝等结构的电磁响应。其次，将CCIE与分层介质格林函数结合，实现直/曲井眼等结构的宽频带稳定分析和高精度建模。最后，结合DG，研究分层介质环境下谱域积分方程法与有限元法和/或谱元法的混合，实现复杂多尺度问题的精确灵活建模和快速求解。相关理论研究与高效算法的实现不仅具有重要的科学研究意义，还将成为电磁法勘探的重要正演分析工具。

非均匀介质中的多尺度目标精确正演技术在电磁法勘探中具有重要应用，但现有方法普遍存在模型过于理想、精度和效率较低等缺陷，学术和工程上迫切需要一种更为灵活高效的多尺度目标精确正演方法。本课题采用频率稳定的薄介质层面积分方程(TDS-SIE)和电流电荷面积分方程(CCIE)高阶矩量法，并结合建模灵活的间断伽略金法(DG)，实现油气勘探中平面分层介质环境下的结构和频率多尺度问题的精确正演分析。首先，将TDS-SIE推广到高阶算法，精确分析分层介质背景中页岩气裂缝等结构的电磁响应。其次，将CCIE与分层介质格林函数结合，实现直/曲井眼等结构的宽频带稳定分析和高精度建模。最后，结合DG，研究分层介质环境下谱域积分方程法与有限元法和/或谱元法的混合，实现复杂多尺度问题的精确灵活建模和快速求解。相关理论研究与高效算法的实现不仅具有重要的科学研究意义，还将成为电磁法勘探的重要正演分析工具。