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| 3D forward and inverse modeling of self-potential data based on the PARDISO direct solver |
SU Zhao-Yang1( ), SHEN Jin-Song1(), LUO Hui2 |
1.College of Geophysics, China University of Petroleum (Beijing), Beijing 102249, China
2. Production Operation Management Department,SINOPEC Northwest Oil Field Company, Urumqi 842100, China |
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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.
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Received: 10 April 2023
Published: 16 April 2024
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Corresponding Authors:
SHEN Jin-Song
E-mail: 2019310419@student.cup.edu.cn;shenjinsongcup@163.com
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| 模型尺寸 | 运算时间/s | 最小二乘
迭代求解器 | 共轭梯度
迭代求解器 | PARDISO
直接求解器 | | 20 × 20 × 20 | 0.15 | 0.04 | 0.005 | | 40 × 40 × 40 | 1.23 | 0.15 | 0.04 | | 60 × 60 × 60 | 5.80 | 0.89 | 0.25 |
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Comparison between direct solver and iterative solver
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Comparison of forward response of finite volume method and analytic solutions
a—schematic diagram of mesh; b—the slice at y = 0 m (2D mesh); c—numerical and analytical solutions; d—relative error
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3D model and forward response results
a—model and slice position; b—plane electric field distribution collected by receiver; c—section AA' is the slice at x = 0 m; d—BB' Slices are slices located at y = -75 m; e—spontaneous potential distribution on line AA'; f—spontaneous potential distribution on line BB'
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3D self-potential inversion results and slices
a—inversion result and slice position; b—slice at z=0 m; c—inversion results of profile AA'; d—inversion of profile BB' performance result
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3D self-potential model and inversion results
a—inversion result and slice position; b—inversion result; c—model slice(at z=-65 m);d—inversion results of profile (slice at z = -65 m); e—model (y=-65 m); f—inversion result(y=-65 m)
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3D self-potential model and inversion results
a—3D model; b—inversion result; c—horizontal slice of model (z=-30 m);d—horizontal slice was recovered by inversion (z=-30 m); e—vertical slice of model (x=0 m); f—vertical slice was recovered by inversion (slice at x=0 m)
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Observed data and predicted data obtained by inversion
a—observed data obtained by forward modeling; b—predicted data obtained from inversion; c—error between observed data and predicted data
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Schematic diagram of sandbox experiment
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Contour diagram of self-potential distribution after the occurrence of redox reactions
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3D inversion results of sandbox experimental data
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self-potential data from sandbox experiment and predicted data obtained by inversion
a—sandbox experiment; b—predicted data obtained from inversion; c—error between experiment data and predicted data
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