基于改进的和声搜索算法的地面核磁共振反演

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

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。

The inversion of surface nuclear magnetic resonance （SIX/MR） data can be abstracted as the solution of the matrix equation An = E, where A is a kernel function matrix, E is a initial amplitude sequence of the meas- ured data, n is the water content distributions sequence as unknowns. The precision of A mainly depends on esti- mating of resistivity distributions. Because of the intrinsic error existing in both A and E and the high condition number of A, a regularization-total least square （R-TLS） model of the SNMR inversion is proposed to improve the stability and accuracy of the inversion result. Then it is transformed into a constrained nonlinear optimization problem, the solution is found by an improved harmony search algorithm （IHS）. Even though An = E being a highly underdetermined equation, the algorithm still works effectively in the simulation. SNMR has been used in combina- tion 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. 9 dB） 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 % ）.