一维波动方程联合反演的分步正则化法

Step Regularization Method of Simultaneous Inverse Problem in One-Dimensional Wave Equation

本文只用一个纵波信息,对一维波动方程的速度和震源函数进行联合反演.并考虑到波动方程的反问题是一不适定问题,对震源函数和波速分别用正则化法分步迭代求解,大大减少了反问题的计算工作量,改善了该反问题的计算稳定性.为计算实际一维地震数据提供了一种方法.文中给出了只用一个反问题补充条件同时进行多参数反演的详细公式,并对相应的数值算例进行了分析和比较.

A simultaneous numerical inverse method of seismic function and lithology parameter in one dimensional wave equation with oidy one complementary condition of P wave is presented. Because multi-parameters inverse problem is ill-posed this paper use a step regularization iterative method to solve lithology parameter and seismic function sepcrately. By using this method the computational work is decreased and the stability of the step regularization method is improved. Theoretical analysis and numerical examples demonstrate the existence of solution, stability and accuracy of the method. The numerical results show that the method of this paper is not only a theoretical method but also a practical way to solve seismic exploration problem when both seismic function and lithology parameter arc unknown at the same time.