Nonlinear inversion for magnetotelluric sounding based on deep belief network

Abstract

To improve magnetotelluric (MT) nonlinear inversion accuracy and stabilitythis work introduces the deep belief network (DBN) algorithm. Firstlya network frame is set up for training in different 2D MT models. The network inputs are the apparent resistivities of known modelsand the outputs are the model parameters. The optimal network structure is achieved by determining the numbers of hidden layers and network nodes. Secondlythe learning process of the DBN is implemented to obtain the optimal solution of network connection weights for known geoelectric models. Finallythe trained DBN is verified through inversion testsin which the network inputs are the apparent resistivities of unknown modelsand the outputs are the corresponding model parameters. The experiment results show that the DBN can make full use of the global searching capability of the restricted Boltzmann machine (RBM) unsupervised learning and the local optimization of the back propagation (BP) neural network supervised learning. Comparing to the traditional neural network inversionthe calculation accuracy and stability of the DBN for MT data inversion are improved significantly. And the tests on synthetic data reveal that this method can be applied to MT data inversion and achieve good results compared with the least-square regularization inversion.

摘要

为进一步提高大地电磁非线性反演的准确度和稳定性, 本文将深度置信网络引入大地电磁反演。 首先, 针对建立的大地电磁二维地电模型数据库设计深度置信网络结构, 对网络隐含层数和各层节点 数进行优选, 网络输入为已知地电模型的视电阻率参数, 输出为该地电模型参数; 然后, 根据优选的 网络参数进行深度置信网络学习训练, 计算出多种地电模型网络连接权值和阈值的最优解; 最后, 将 网络最优连接权值和阈值对未知模型进行反演测试, 网络输入为测试地电模型的视电阻率参数, 输出 为该地电模型电阻率参数。模型实验表明: 相比传统的 BP 神经网络算法, 深度置信网络算法具有全 局寻优的能力, 在保证较快收敛效率的同时, 明显提高了网络收敛成功率和稳定性, 在反演测试中能 够更加准确地逼近真实模型; 相比经典的最小二乘正则化反演法, 深度置信网络算法具有较好的泛化 性能和自学习能力, 反演效率更高, 反演效果更精确。