多先验信息约束的三维电阻率反演方法

3Dresistivity inversion with multiple priori-information constraint

先验约束信息可以有效提高直流电阻率三维反演精度,多数约束信息的施加是通过修改目标函数实现的,具有约束信息单一、施加约束信息繁琐的不足。为了改进上述问题,修改迭代重加权最小二乘法反演方程,将数据加权矩阵中的重加权函数修改为误差函数和互补误差函数的形式,增加结构度量、权重均值和标准偏差等参数,通过修改地下空间不同区域的重加权函数参数,达到施加不同先验约束信息目的;反演方程计算采用并行共轭梯度最小二乘法,以提高反演速度。在合成数据算例中,分别施加了平滑约束、块状约束和多信息混合约束,反演结果表明多信息约束的成像精度远大于单一信息约束。工程项目中可根据地质结构状况合理选择权函数参数,达到提高三维电阻率反演精度和计算速度的目的。

The use of prior-information constraint can improve the inversion accuracy of 3D DC electrical resistivity.However,in most cases,single prior-in- formation is used to modify the objective function and the results are inaccurate.In order to solving the problems,the inversion equation of iterative reweighted least-squares is modified;parameters such as the structural metric,weight mean,and standard deviation are added;and the weight function of the model parameters is replaced by the error function and complementary error function. Then different prior-information can constrain the inversion with modifying parameters of weightfunction in different zones.The parallel conjugate gradient least-square method is used to effectively improve the inversion calculation.In synthetic data inversions,smoothness constraint,block constraint,and resistivity extreme-constraint are used. The results show that the inversion constrained with multiple priori-information is more accurate than that with single prior-information.In practice,parameters of weight functions can be selected based on geological structures to improve the accuracy of 3D resistivity inversion and the calculation efficiency.