电磁反演是研究地球物理电磁特性的主要方法，反演算法的优劣直接影响反演精度和应用的好坏。因此，提高电磁反演算法的精度对我国进行矿产、油气等资源的勘探具有十分重要的现实意义。

针对传统卷积神经网络在电磁反演中提取数据特征时冗余信息多，导致网络反演精度低的问题，提出一种变步长卷积神经网络（Convolutional Neural Networks，CNN）电磁反演方法。基于传统卷积神经网络，变步长卷积神经网络将输入数据拓展为一维行向量，在各层网络中交替使用不同卷积步长的卷积核进行卷积运算提取数据特征，利用变步长卷积方式替代传统卷积神经网络的池化层，完成对冗余信息的过滤和特征信息的选择，并通过小卷积核级联的方式增大网络感受野提高网络的非线性表达能力。通过二维时域有限差分法（2D-FDTD）对不同电磁参数的富水区模型进行正演计算，并根据计算得出的电场时域响应特征建立样本数据集；将变步长卷积神经网络应用于电磁反演研究，建立适用于富水区问题的变步长卷积神经网络电磁反演模型；选取二次场电场时域响应特征作为网络输入，位置及其电磁参数信息作为输出对网络进行训练，通过对卷积神经网络网络进行调参优化，确定最优的卷积神经网络结构。利用训练好的网络对反演目标进行测试，将传统卷积神经网络电磁反演方法和变步长卷积神经网络电磁反演方法的反演结果进行定量的评估，验证改进后算法的反演精度。

变步长CNN的矿井富水区电磁反演方法对坐标位置的反演平均相对误差为2.85%，对相对介电常数的反演平均相对误差为6.07%，反演结果与实际模型吻合度较高。研究结果表明，基于变步长CNN的电磁反演算法反演精度较高，理论上可应用于矿井富水区的电磁反演。

Electromagnetic inversion is the main method to study the electromagnetic properties of geophysics. The quality of the inversion algorithm directly affects the accuracy and application of the inversion. Therefore, improving the accuracy of the electromagnetic inversion algorithm has very important practical significance for the exploration of minerals, oil and gas and other resources in my country.

In order to solve the problem that the traditional convolutional neural network extracts data features in electromagnetic inversion, there is a lot of redundant information, which leads to the low accuracy of network inversion. A variable step size convolutional neural network (Convolutional Neural Networks, CNN) electromagnetic inversion method is proposed. Based on the traditional convolutional neural network, the variable-step convolutional neural network expands the input data into a one-dimensional row vector. In each layer of the network, convolution kernels with different convolution steps are used alternately to perform convolution operations to extract data features, and use variable steps The long convolution method replaces the pooling layer of the traditional convolutional neural network, completes the filtering of redundant information and the selection of feature information, and increases the network receptive field through the cascade of small convolution kernels to improve the nonlinear expression ability of the network. Forward calculation of the water-rich zone model with different electromagnetic parameters by the two-dimensional finite difference time domain method (2D-FDTD), and establish a sample data set based on the calculated electric field response characteristics in the time domain; the variable step size convolutional neural network Applied to electromagnetic inversion research, establishing a variable-step convolutional neural network electromagnetic inversion model suitable for water-rich areas; selecting the time domain response characteristics of the secondary field electric field as the network input, and the position and electromagnetic parameter information as the output to perform the network Training, by tuning and optimizing the convolutional neural network, determine the optimal convolutional neural network structure. Use the trained network to test the inversion target, quantitatively evaluate the inversion results of the traditional convolutional neural network electromagnetic inversion method and the variable-step convolutional neural network electromagnetic inversion method to verify the inversion accuracy of the improved algorithm.

The variable step size CNN electromagnetic inversion method in the rich water area of the mine has an average relative error of 2.85% for the inversion of the coordinate position and an average relative error of 6.07% for the inversion of the relative permittivity. The inversion results are in good agreement with the actual model. high. The research results show that the electromagnetic inversion algorithm based on variable step size CNN has high inversion accuracy, and can theoretically be applied to electromagnetic inversion in mine water-rich areas.

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