基于监督下降法的直流电测深曲线反演

Inversion of Direct Current Sounding Curve Based on Supervised Descent Method

摘要: 电阻率反演是直流电测深资料最重要的定量解释方法之一，但常规基于梯度信息的反演算法中灵活实现层厚和电阻率的区间约束比较困难。为此，本文将监督下降法引入电测深曲线反演以实现灵活的先验信息引入，进而重构地下模型参数。利用正演合成的数据，论证了训练集中不同初始模型的选择对SDM反演可行性的影响。此外，开展了两组数值实验进一步探讨SDM的泛化能力。结果表明，采用SDM融入先验信息具有可行性。该方法反演过程中不涉及偏导数的计算，不仅可以克服对初始模型的依赖达到快速收敛的目的，并且具有一定的泛化能力。

Abstract: Resistivity inversion is one of the most important quantitative interpretation methods for DC sounding data, but it is difficult to flexibly implement interval constraints of layer thickness and resistivity in conventional gradient information-based inversion algorithms. To this end, this pa-per introduces the supervised descent method into the inversion of electrical sounding curves to achieve flexible introduction of prior information, and then reconstruct the parameters of the underground model. Using the data synthesized by forward modeling, the influence of the selection of different initial models in the training set on the feasibility of SDM inversion is demonstrated. In addition, two sets of numerical experiments were carried out to further explore the generalization ability of SDM. The results show that it is feasible to use SDM to incorporate prior information. The inversion process of this method does not involve the calculation of partial derivatives, which can not only overcome the dependence on the initial model to achieve fast convergence, but also has certain generalization ability.