基于监督下降法的短偏移距瞬变电磁快速反演研究

doi:10.11720/wtyht.2024.1005

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摘要

短偏移距瞬变电磁法(简称SOTEM)通常采用传统式基于物理建模的反演方法,反演效率较低,不易灵活融入先验信息,而基于数据驱动的反演方法能够提高反演精度与效率,泛化能力却难以保证。为了提高SOTEM数据反演的精度和效率,并兼顾可靠的泛化能力,本文探索了一种融合物理建模与数据驱动的反演方法,将机器学习中监督下降法应用于SOTEM数据反演中。基于监督下降法的SOTEM数据反演分为线下训练和线上预测,线下训练时通过合理的训练集灵活融入先验信息,获得隐含模型特征的平均下降方向,线上预测时借助物理建模函数和训练所得下降方向,在传统反演框架下完成模型参数重建。文中利用层状大地模型构建训练集和测试集,实现了基于监督下降法的SOTEM数据一维反演,并与传统Occam算法进行了对比。结果表明:基于监督下降法的SOTEM反演效率大幅提升,反演精度较高,具有良好的泛化能力。

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	饶丽婷
	武欣
	郭睿
	党博
	党瑞荣

关键词 ：瞬变电磁法, SOTEM, 快速反演, 监督下降法, 机器学习

Abstract：

The short-offset transient electromagnetic (SOTEM) data are typically processed using conventional inversion methods based on physical modeling, manifesting relatively low efficiency and difficulty in integrating priori information. In contrast, the data-driven inversion methods can enhance the inversion accuracy and efficiency but fail to ensure the generalization capability. To achieve high inversion accuracy and efficiency for SOTEM data and a reliable generalization capability, this study proposed an inversion method that integrates physical modeling with the data-driven approach, introducing the supervised descent method in machine learning into SOTEM data inversion. The proposed inversion method involves the offline training and online prediction stages. In the offline training stage, the prior information is flexibly integrated into the model training through a reasonable training dataset to obtain the average descent directions with implicit model features. In the online prediction stage, the physical modeling functions and the descent directions are employed to reconstruct the model parameters under the conventional inversion framework. In this study, the layered geodetic model was applied to design the training and test datasets for the 1D inversion of SOTEM data based on the supervised descent method. The inversion results were compared with those obtained using Occam's inversion algorithm, demonstrating that the proposed inversion method shows significantly enhanced inversion efficiency, higher inversion accuracy, and higher generalization capability.

Key words： transient electromagnetic (TEM) method short-offset transient electromagnetic (SOTEM) method fast inversion supervised descent method machine learning

收稿日期: 2023-01-03 修回日期: 2023-08-04 出版日期: 2024-10-20

ZTFLH:

P631.1

基金资助:国家自然科学基金项目(42004064);国家自然科学基金项目(42074121);河南省豫地科技集团2024年重点科研项目(JTZDKY202405);中央引导地方科技发展资金项目(2023ZY0036);广西壮族自治区重点研发计划项目(2023AB260490)

通讯作者: 武欣(1982-),男,副研究员,博士,主要从事面向地形复杂地区的矿产、地下水等资源及地下人工目标的地球物理探测理论方法研究与装备研发工作。Email:wu_xin18@163.com

作者简介: 饶丽婷(1989-),女,副教授,博士,主要从事电磁法正反演理论与数据处理方法研究工作。Email:ltrao@xsyu.edu.cn

引用本文:

饶丽婷, 武欣, 郭睿, 党博, 党瑞荣. 基于监督下降法的短偏移距瞬变电磁快速反演研究[J]. 物探与化探, 2024, 48(5): 1199-1207.
RAO Li-Ting, WU Xin, GUO Rui, DANG Bo, DANG Rui-Rong. Fast inversion of short-offset transient electromagnetic (SOTEM) data based on the supervised descent method. Geophysical and Geochemical Exploration, 2024, 48(5): 1199-1207.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2024.1005 或 https://www.wutanyuhuatan.com/CN/Y2024/V48/I5/1199

Fig.1 层状大地模型上SOTEM观测示意

线下训练

线上预测

1)生成L个先验模型

m p r i o r i

及其仿真数据

d i p r i o r

(i=1,2,…,L),重新排列
形成先验模型矩阵

M p r i o r

和先验数据矩阵

D p r i o r

;
2)设定

M 0

为初始模型;
3) for j=1,2,…,J
4)

Δ M j = M p r i o r - M j

;
5)

Δ D j = F (M J) - D p r i o r

;
6)

Δ D j = U Σ V T

;
7)

K ~ j = V (Σ 2 + α j I) - 1 Σ T U T Δ M j

;
8)

M j = M j + Δ D j · K ~ j

;
9) end

1)设定m₀为固定初始模型;
2)

Δ d = F (m 0) - d o b s

;
3) for j=1,2,…,J
4)

m j = m j + K ~ j (d o b s - F (m j))

;
5) 计算当前数据拟合差rms;
6) if rms<rms₀
7) 迭代终止;
8)

Δ d = F (m j) - d o b s

;
9) end

Table 1 算法的实施程序步骤

Fig.2 不同训练集的下降方向示意

参数	三层模型	四层模型	五层模型
ρ₁/(Ω·m)	100~300	80~120	100~400
ρ₂/(Ω·m)	20~100	300~500	20~80
ρ₃/(Ω·m)	200~500	50~150	200~400
ρ₄/(Ω·m)		300~500	20~80
ρ₅/(Ω·m)			300~500
$h 1 / m$	80~200	80~150	50~100
$h 2 / m$	100~300	80~150	50~100
$h 3 / m$	9999	150~300	100~200
$h 4 / m$		9999	150~300
$h 5 / m$			9999
个数	1024	1024	1024

Table 2 不同地电模型的训练集参数

参数	训练集	测试集
ρ₁/(Ω·m)	300~600	300~500
ρ₂/(Ω·m)	30~200	50~150
ρ₃/(Ω·m)	300~600	400~600
$h 1 / m$	100~300	100~250
$h 2 / m$	100~300	100~250
个数	1024	50

Table 3 三层模型的训练集和测试集参数设置

参数	训练集	测试集
ρ₁/(Ω·m)	300~600	300~500
ρ₂/(Ω·m)	50~150	60~140
ρ₃/(Ω·m)	200~300	200~300
ρ₄/(Ω·m)	20~100	30~90
ρ₅/(Ω·m)	300~600	300~500
$h 1 / m$	50~150	80~150
$h 2 / m$	50~100	50~100
$h 3 / m$	100~200	120~180
$h 4 / m$	100~200	100~200
个数	1024	50

Table 4 五层模型的训练集和测试集参数设置

Fig.3 部分测试样本的仿真数据

Fig.4 线下训练的残差收敛曲线

Fig.5 线上预测的预测步数与数据残差

Fig.6 三层模型3个样本的模型及其含噪正演响应与反演响应

Fig.7 五层模型3个样本的模型及其含噪正演响应与反演响应

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