监督下降的直流电阻率法二维反演

Two-dimensional inversion of DC resistivity based on supervised descent method

为了解决拟线性反演中先验信息利用不充分及大批量数据计算效率低的问题,本文将监督下降法(Supervised Descent Method,SDM)应用到直流电阻率法二维反演中.SDM包括离线训练和在线预测两个阶段.训练集由根据先验信息生成的模型和正演模拟数据组成.在训练过程中,学习从初始模型到训练模型的下降方向.在预测过程中,同时考虑了训练过程中获取的下降方向和计算出的数据残差.通过合成数据算例,讨论了SDM的反演精度、收敛速度、抗噪能力与泛化能力.在线预测结果显示,块状体和分层结构的混合模型,反演数据误差为0.0037,表明块状模型与层状模型的模块化训练集能有效增强SDM的泛化能力.在对实测数据反演中,通过实测数据视电阻率结果构建训练集,可以优化训练集的模型数据质量及完整性.通过与高斯牛顿法对比,讨论了SDM针对批量实测数据的反演精度及效率.结果表明,针对单一数据,SDM反演耗时(训练时长与预测时长总和)较高斯牛顿法长,但当训练阶段完成后,预测阶段耗时不超过0.5 s,针对同类型、同维度、大批量数据,SDM具有进行批量处理的能力,反演效率更高.

To address the issues of inadequate prior information utilization and low computational efficiency for quasi-linear inversion with large amounts of data,this paper utilizes supervised descent method(SDM)for two-dimensional inversion of DC resistivity.SDM involves two stages:offline training and online prediction,with the training set consisting of models generated from prior information and simulation data.In the training process,the direction of descent(from the initial model to the trained model)was learned,and in the prediction process,both the learned direction of descent and the calculated residuals were taken into account.Through synthesis data tests,we present a discussion on the inversion accuracy,convergence speed,anti-noise robustness,and generalization performance of the proposed SDM.Online prediction results show that,with an inversion data error of 0.0037,using the modular training set of mixed models(i.e.,block and hierarchical structure)can significantly improve the generalization performance of SDM.For field-data inversion cases,the training set is constructed using the resistivity results of the measured data,and the quality and integrity of the model data in the training set can be optimized.Comparing with the Gaussian Newton method,we also discussed the inversion accuracy and efficiency of SDM for batch measured data.The results demonstrate that the inversion time for a single data is longer than the Newton method,yet the prediction process takes less than 0.5 s after the training process is completed,indicating that the proposed SDM has higher inversion efficiency for large batches of data with the same type,dimension,and size.