基于交叉梯度约束的时间域激发极化法二维同步反演

Two-dimensional synchronous inversion of TDIP with cross-gradient constraint

时间域激发极化法(Time-domain induced polarization method,简称为TDIP)已有的反演算法采用的是分步反演的思路,即先由视电阻率资料反演电阻率,固定电阻率再由视极化率资料反演极化率,这样就存在极化率结果严重依赖于电阻率反演结果的问题.为了有效解决这一问题,本文实现了TDIP二维数据空间分步反演算法,提出了基于交叉梯度约束的TDIP二维同步反演策略,实现了交叉梯度约束的电阻率和极化率二维同步反演算法.分别用电阻率和极化率结构一致和不一致的二维模型合成数据进行了分步和同步反演试算,对不同模型试算结果进行了对比分析.结果表明:对于电阻率和极化率结构一致和不一致模型,同步反演结果比分步反演结果能更好地确定异常体的空间分布范围,反演得到的电阻率和极化率值更接近真值.理论模型算例表明本文提出的同步反演算法有效解决了分步反演的问题,优于分步反演算法,具有更好的实用性.

The existing inversion algorithm of time-domain induced polarization（TDIP）data is a step-wise one,in which the polarizability value is gained after the calculation of the resistivity value is completed with the resistivity value fixed,which results in that the polarizability value depends on the resistivity value.To solve this problem,we study a two-dimensional synchronous inversion algorithm of TDIP data with cross-gradient constraint.Based on well-developed twodimensional forward and inversion algorithms for DC resistivity,we propose two-dimensional forward and inversion algorithms for induced polarization and synchronous inversion algorithm with common inversion grids and cross-gradient as the structural constraint.Both resistivity and polarizability models are able to be synchronously updated.Trial computation of synchronous inversion has been carried out on the synthetic data from a model with the same physical structure and different physical structures.Results indicate that compared with step-wise inversion,synchronous inversion is better in recovering both the various models′numerical values and spatial morphology.The resistivity and polarizability values of the conductive-high polarizabilitymodels are much closer to the true model in synchronous inversion,while by the resistive-high polarizability model,synchronous inversion not only can improve the values of TDIP data to some extent,but also has large improvement in increasing the accuracy of spatial distribution.Moreover,synchronous inversion can improve the result of the model with different physical structures and thus has wide applicability.