基于改进的和声搜索算法的地面核磁共振反演*

地面核磁共振反演能抽象为一个求解矩阵方程An=E的问题,A为与背景电阻率空间分布有关的核函数矩阵,E为测量信号的初始振幅值,n为带求解的含水量分布值,由于A和E都存在误差,为了提高n的求解精度和稳定性,构造了正则化-总体最小二乘模型,并将该模型转化为受条件约束的非线性优化问题,设计了改进的和声搜索算法以求解该问题,在含水层数大于激发脉冲矩数的欠定方程或者病态方程的求解中,该算法仍然适用。野外实测数据反演中,导电层电阻率分布情况来自垂向电测深勘探结果,观测信号的信噪比为6.9 d B,算法的反演结果含水量值的方均根为3.12%,法国Samovar v6.2反演软件反演结果含水量值的方均根为3.65%,两种反演结果均与钻探结果接近,但本文算法略显优势。

Research on Inversion of Surface Nuclear Magnetic Resonance Data by Improved Harmony Search Algorithm

The inversion of surface nuclear magnetic resonance (SNMR) data can be abstracted as the solution of the matrix equation , where is a kernel function matrix, is a initial amplitude sequence of the measured data, is the water content distributions sequence as unknowns. The precision of mainly depends on estimating of resistivity distributions. Because of the intrinsic error existing in both and and the high condition number of , a regularization - total least square (R-TLS) model of the SNMR inversion is proposed to improve the stability and accuracy of the inversion result in this paper. Then it is transformed into a constrained nonlinear optimization problem, the solution is found by an improved harmony search algorithm (IHS). Even though being a highly underdetermined equation, the algorithm still works effectively in the simulation. SNMR has been used in combination with Vertical Electrical Sounding (VES) in the field example. The results of the field example agree well the information from an in-site borehole under poor SNR (SNR=6.9dB) at the root mean square (RMS) 3.12%, which has slightly higher precision than the result of the inversion software Samovar v6.2 (RMS=3.65%).