一维双相介质孔隙率的小波多尺度反演  

Porosity inversion of 1-D two-phase medium withwavelet multiscale method

作　　者：张新明[1] 刘家琦[2] 刘克安[2] 

机构地区：[1]哈尔滨工业大学深圳研究生院,深圳518055 [2]哈尔滨工业大学,哈尔滨150001

出　　处：《物理学报》2008年第2期654-660,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:40374046);哈尔滨工业大学跨学科交叉研究基金(批准号:HIT.MD2002·26)资助的课题.~~

摘　　要：基于多尺度的思想,将小波多分辨分析和多尺度方法结合,构造了小波多尺度反演方法,并应用于一维双相介质孔隙率的反演.利用小波变换,将原始反问题分解为不同尺度上的一系列子反问题,并按照尺度从粗到细的顺序依次求解.在每一个尺度上,都采用稳定、收敛快的正则化高斯牛顿法求解,次一级尺度上求出的"全局最优解"作为上一级的初始解,依次类推,直到求出原始问题的真正的全局最优解.将小波多尺度方法归结为三种不同算子(分解算子、求解算子、插入算子)的交替应用,给出了小波多尺度反演算法的基本流程图,并推导出当采用Daubechies紧支撑正交小波时,小波多尺度算法涉及到的分解算子矩阵和插入算子矩阵.通过与传统的正则化高斯牛顿法数值比较,显示了小波多尺度法是一个大范围收敛方法,数值模拟的结果也显示了该方法的有效性.Based on the idea of multiscale approximation, a wavelet multiscale method is proposed by combining the wavelet analysis and multiscale inversion strategy, and applied to the inversion of porosity in the two-phase medium. The inverse problem is decomposed to multiple scales with wavelet transform and hence the original inverse problem is re-formulated to a set of subinverse problem corresponding to different scales and is solved successively according to the size of scale from the smallest to the largest. On each scale, regularized Gauss-Newton method is carried out, which is stable and fast, until the optimum solution of original inverse problem is found. The wavelet multiscale method is described as the combination of three operators： the restriction operator, the relaxation operator and the prolongation operator. And then the flow of wavelet multiscale method is outlined and the restriction operator matrix and the prolongation operator matrix obtained by adapting the compactly supported orthonormal wavelet Daubechies wavelets are deduced. The inversion results obtained by wavelet multiscale method are compared with those with traditional regularized Gauss-Newton method, the results of numerical simulation demonstrated that the method is an effective and widely convergent optimization method.

关 键 词：双相介质 反演 小波多尺度方法 孔隙率 

分 类 号：O357[理学—流体力学]