向导点-正则化方法在水文地质参数反演中的应用

Inversion of hydrogeological parameters using pilot-points and regularization method

水文地质参数反演是地下水数值模拟中的一个重要问题.基于向导点方法,通过设定理想算例,引入SVDAssist正则化方法,反演求解向导点个数大于观测数据个数的高维不适定问题.与传统分区方法的反演结果对比结果表明:向导点-正则化法是一种有效的高维水文地质参数的反演方法,可不依赖于人为的概化分区有效地反演推估非均质渗透系数场的空间分布.还讨论了向导点个数对反演结果的影响,结果表明:向导点个数并非越多越好,随着向导点个数的逐步增加,反演结果精度逐渐提高,但达到一定数量后,向导点个数的增加不仅会增加计算工作量,同时反而会降低反演结果精度.

Inversion of hydrogeological parameters is an important issue for the groundwater numerical simulation.The pilot-points method combined with SVD-Assist regularization is adapted in this paper to solve the high-dimensional ill-posed problems by setting a number of pilot points in the study area.Base on a synthetic case,the inversion result shows that the pilot-points method combined with SVD-Assist regularization is efficient to estimate the spatial distribution of the hydraulic conductivity for the heterogeneous media,which does not rely on the artificially zone.The effect of the pilot-point number on the parameter inversion results is also discussed and the results show the accuracy improves with the increase of the pilot-point number,but deteriorates when the number exceeds the criticalnumber.The computational cost increases with the number of pilot points.The number of pilot points should be controlled within a reasonable range.