基于PARDISO直接求解器的三维自然电位正反演

doi:10.11720/wtyht.2024.1150

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摘要

近年来自然电位法在海底硫化物资源的勘探和评价中发挥了重要作用。本文开展的是基于PARDISO直接求解器的3D自然电位正反演算法研究。首先,利用有限体积法离散自然电位控制方程,采用PARDISO直接求解器提高正演计算的效率,通过数值解与解析解对比,验证了正演算法的可靠性。其次,在3D反演算法中考虑了地形因素,同时将最小支撑约束与深度加权加入目标泛函中,理论模型数据的反演结果很好地恢复了矿体的结构。最后,利用该算法对室内沙箱实验获得的自然电位数据进行反演,结果显示得出的电流密度异常与金属棒的位置基本一致。因此,本文提出的反演算法在未来大规模自然电位数据反演中具有重要作用。

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	苏朝阳
	沈金松
	罗辉

关键词 ：自然电位法, 3D聚焦反演, PARDISO直接求解器

Abstract：

In recent years, the self-potential method has played a significant role in the exploration and evaluation of seafloor massive sulfide resources. This study explored the 3D forward and inverse modeling algorithms for self-potential based on the PARDISO direct solver. First, the finite volume method was employed to discretize the self-potential control equation, and the PARDISO direct solver was utilized to improve the forward modeling efficiency. The reliability of the forward modeling algorithm was verified by comparing the numerical solution with the analytical solution. The 3D inverse modeling algorithm considered the topographic factor and incorporated the minimum support constraint and depth weighting into the objective function. The inversion results of theoretical model data effectively reconstructed the ore body structure. Finally, the self-potential data obtained from indoor sandbox experiments were inverted using the inverse modeling algorithm, obtaining that the current density anomaly was roughly consistent with the position of the metal bar. Therefore, the inverse modeling algorithm proposed in this study holds critical significance for subsequent inversion of large-scale spontaneous potential data.

Key words： self-potential method 3D focusing inversion PARDISO direct solver

收稿日期: 2023-04-10 修回日期: 2023-05-22 出版日期: 2024-04-20

ZTFLH:

P631

基金资助:国家自然科学基金项目(42074217)

通讯作者: 沈金松

作者简介: 苏朝阳(1995-),男,博士研究生,主要从事海洋瞬变电磁和自然电位方法及应用研究工作。Email:2019310419@student.cup.edu.cn

引用本文:

苏朝阳, 沈金松, 罗辉. 基于PARDISO直接求解器的三维自然电位正反演[J]. 物探与化探, 2024, 48(2): 451-460.
SU Zhao-Yang, SHEN Jin-Song, LUO Hui. 3D forward and inverse modeling of self-potential data based on the PARDISO direct solver. Geophysical and Geochemical Exploration, 2024, 48(2): 451-460.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2024.1150 或 https://www.wutanyuhuatan.com/CN/Y2024/V48/I2/451

Table 1 直接求解器与迭代求解器运行速度对比

Fig.1 有限体积法的正演响应与解析解对比
a—网格剖分示意;b—y=0 m切片(2D网格);c—数值解与解析解;d—相对误差

Fig.2 3D正演模型及自然电位响应结果
a—模型及切片位置;b—接收器采集到的平面电场分布;c—剖面AA’是位于x = 0 m的切片;d—剖面BB’是位于y = -75 m的切片;e—测线AA’上的自然电位分布;f—测线BB’上的自然电位分布

Fig.3 3D自然电位反演结果及切片
a—反演结果及切片位置;b—位于z=0 m处的切面;c—剖面AA’的反演结果;d—剖面BB’的反演结果

Fig.4 3D自然电位模型及反演结果
a—模型;b—反演结果;c—模型切片(深度z=-65 m的切片);d—反演结果(深度z=-65 m处的切片);e—模型剖面(y=-65 m);f—反演结果(y=-65 m)

Fig.5 起伏地形条件下的3D自然电位模型及反演结果
a—3D模型;b—反演结果;c—模型水平切片(z=-30m);d—反演结果水平切片(z=-30 m);e—模型垂直剖面(x = 0 m);f—反演结果剖面(x =0 m处)

Fig.6 正演的观测数据与预测数据
a—正演数据;b—反演得到的预测数据;c—正演数据与观测数据之间的误差

Fig.7 沙箱实验示意图

Fig.8 氧化还原反应发生后的自然电位分布等值线

Fig.9 沙箱实验数据的3D反演结果

Fig.10 沙箱试验的自然电位数据与反演的预测数据
a—沙箱试验数据;b—反演得到的预测数据;c—沙箱试验数据与观测数据之间的误差

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