基于卷积神经网络的磁异常反演

doi:10.19657/j.geoscience.1000-8527.2021.150

摘要/Abstract

摘要：

针对传统反演方法存在的初始模型依赖、计算时间较长等问题,提出一种基于卷积神经网络的磁异常反演方法。该方法首先设计大量磁异常体模型,进行正演模拟产生样本数据集;接着借鉴经典的卷积神经网络VGG-13设计了一种全新的VGG磁异常反演网络(VGGINV);然后使用样本数据集训练该网络,并优化网络参数;最后对理论模型和实测数据进行反演实验。实验结果表明,该方法可以准确地反演出磁异常体的位置和磁化强度,具有较强的学习能力和一定的泛化能力,能有效解决磁异常数据反演问题。

关键词: 深度学习, 地球物理反演, 磁异常, 卷积神经网络, VGG

Abstract:

To resolve the problems of traditional inversion methods, such as initial model dependence and long calculation time, we proposed a magnetic anomaly inversion method based on convolutional neural network. With this method, a number of magnetic anomalous body models were designed to perform forward simulation, which generated various sample data-sets. Subsequently, a new VGG magnetic anomaly inversion network (VGGINV) was designed based on the classic convolutional neural network VGG-13. After that, the sample data-set was used to train the network and optimize the network parameters. Finally, inversion experiment was performed based on this theoretical model and actual field data. The experimental results show that the proposed method can accurately invert the position and magnetization of magnetic anomaly, with strong learning ability and certain generalization ability, and can effectively solve problems in magnetic anomaly data inversion.

Key words: deep learning, geophysical inversion, magnetic anomaly, convolutional neural network, VGG

中图分类号:

P631

薛瑞洁, 熊杰, 张月, 王蓉. 基于卷积神经网络的磁异常反演[J]. 现代地质, 2023, 37(01): 173-183.

XUE Ruijie, XIONG Jie, ZHANG Yue, WANG Rong. Magnetic Anomaly Inversion Based on Convolutional Neural Network[J]. Geoscience, 2023, 37(01): 173-183.

图/表 19

图1 正反演关系示意图

Fig.1 Schematic diagram of forward and inverse relationship

图2 有限深度的垂直棱镜的几何形状 (a)剖分单元示意图;(b)棱柱体单元

Fig.2 Geometry of afinite-depth vertical prism

图3 基于CNN的磁异常反演过程

Fig.3 CNN-based magnetic anomaly inversion process

图4 VGGINV网络结构

Fig.4 VGGINV network structure

表1 模型设置

Table 1 Setting of the model

模型	形状大小
矩形模型	3×3、4×4、5×5、3×6、6×3、4×8、8×4
阶梯模型	每层2×3、每层2×5
多个矩形模型	左右:4×4,5×5;
	上下:3×3

图5 模型代表性示例 (a)矩形和阶梯模型;(b)多个矩形模型

Fig.5 Representative examples of the model

图6 训练流程图

Fig.6 Schematic flowchart of the training process

表2 不同约束系数的各项损失情况统计

Table 2 Statistics of various losses with different constraint coefficients

参数设置		cost1	cost2	cost3
a=1,b=1,c=0.01	初	70600.7	74423690	281516.1
	终	41.4994	2.826036	2791.417
a=0.3,b=1,c=0.01	初	74828.3	62532120	281406.3
	终	54.6469	2.4157293	1445.448
a=0.1,b=1,c=0.01	初	55667.2	50526652	281485.8
	终	76.7177	1.238823	1919.319
a=0.3,b=1,c=0.001	初	61337.8	53639600	281489.6
	终	30.9852	1.7518381	6934.962

图7 不同约束系数的反演结果

Fig.7 Inversion results of different constraint coefficients

表3 不同迭代次数的各项损失情况统计

Table 3 Statistics of various losses for different iteration times

迭代次数	cost1	cost2	cost3	时间/s
10000	163.3861	4.295458	184598.4	1080
20000	59.18427	3.218473	73968.87	2160
30000	38.09513	2.206896	9698.529	3240
40000	46.98742	2.305809	7262.683	4620
50000	30.98522	1.751838	6934.962	5760
60000	51.24117	3.776375	6501.225	6900

图8 不同迭代次数的总损失变化趋势

Fig.8 Total loss variation trend of different iteration times

表4 CNN网络参数设置

Table 4 CNN network parameter settings

分类	参数设置	CNN
数据样本	训练集	6737
	测试集	1685
网络设置	学习率	η=0.001
	激活函数	ReLU
	优化器	Adam
	L2正则化	λ=1
	Dropout	0.7
	目标函数	a=0.3,b=1,c=0.001
训练过程	迭代次数	30000
	批量大小	1000

图9 全部测试集样本反演结果

Fig.9 Inversion results of all samples

图10 验证集样本反演结果

Fig.10 Validation set sample inversion results

图11 上下模型分离

Fig.11 Top and bottom stacking modules

表5 VGGINV网络参数设置

Table 5 VGGINV network parameter settings

分类	参数设置	VGGINV
数据样本	训练集	7458
	测试集	1865
网络设置	学习率	η=0.001
	激活函数	ReLU
	优化器	Adam
	Dropout	0.7
	目标函数	a=0.3,b=1,c=0.001
训练过程	迭代次数	50000
	时间	2760s

图12 尕林格铁矿床磁异常等值线[23]

Fig.12 Magnetic anomaly contours of the Galinge iron deposit[23]

图13 第196行的VGGINV反演结果及钻孔结果 (a)反演结果;(b)钻孔结果

Fig.13 VGGINV inversion results of line 196

图14 第212行的VGGINV反演结果及钻孔结果 (a)反演结果;(b)钻孔结果

Fig.14 VGGINV inversion results of line 212

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