流体饱和多孔隙介质波动方程多尺度反演

Multiscale Inversion of Wave Equation in Fluid-Saturated Porous Media

基于多尺度的思想,将小波多分辨分析和多尺度方法相结合,应用于流体饱和多孔隙介质孔隙率的反演。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,依此类推,直到求出原始问题的真正的全局最优解。通过与传统的正则化高斯牛顿法相比较,显示了小波多尺度法是一个大范围收敛、能够有效节省计算量的方法,数值模拟的结果也表明了方法的有效性。

The wavelet multiscale method is applied to the inversion of porosity in the fluid-saturated porous media.The inverse problem is decomposed into multiple scales with wavelet transform and hence the original inverse problem is re-formulated as a set of sub-inverse problem corresponding to different scales and solved successively according to the size of scale from the smallest to the largest.On each scale,Regularization Gauss-Newton method is carried out until the optimum solution of original inverse problem is found.The numerical simulations demonstrate the convergency within a wide region of this method to outperform the conventional Regularization Gauss-Newton method.