用脉冲谱法确定承压含水层非均值导水系数

An Algorithm for Determining Inhomogeneous Transmissivities of Confined Aquifer by Pulse Spectrum Technique

本文将确定二维承压含水层非均值导水系数的问题提为Poisson方程的参数控制反问题;利用脉冲谱法(PST)将该反问题的求解过程转化为求解正问题和第一类Fredholm积分方程的迭代过程,并采用?正则化方法处理积分方程的不适定性问题,从而提出并实现了确定非均值导水系数的解算程式.数值计算结果表明,本文提出的解算程式比较适应尺度大、非均值性强的情况;求解所需的附加信息仅为透水边界上的水头和单宽流量,可明显减少获取附加信息所需的钻孔工作量,因而能满足地下水、渗流等工程问题确定非均值导水系数或渗透系数的需要.

The problem of determining inhomogeneous transmissivities of two-dimensional confined aquifer is presented as a parameter-control inverse problem for Poisson Equation in this paper. By virtue of PST, the solution of the inverse problem is converted into an interation procedure of solving a direct problem and solving a Fredholm integral equation of the first kind. Besides, ? normalization method is introduced to treat the uncertainty caused by the integral equation. Thus an algorithm for determining inhomogeneous transmissivities has been formulated and implemented. Numerical results show: (a) the algorithm presented in the paper is suitable to strongly inhomogeneous aquifer with large scale; (b) the additional information needed for solution is merely the water head and discharge per width on the permeable boundary, so that drill works, otherwise needed for gaining additional information, can be reduced remarkably; and (c) the algorithm is applicable to determining inhomogeneous transmissivities or transmission coefficients in groundwater engineering or other engineering.