黏弹性双相介质参数反演的同伦方法  

Inversing physical parameter of two-phase viscoelastic media by homotopy method

作　　者：田迎春[1] 章梓茂[2] 马坚伟[1] 杨慧珠[1] 

机构地区：[1]清华大学航天航空学院地震波勘探开发研究所,北京100084 [2]北京交通大学土建学院力学所,北京100044

出　　处：《地球物理学报》2009年第9期2328-2334,共7页Chinese Journal of Geophysics

基　　金：国家重点基础研究发展计划(973)项目(2007CB209505);国家自然科学基金(10572072)联合资助

摘　　要：本文以介质的动态时域响应(位移、速度、加速度)作为反演的依据,对黏弹性双相介质的材料参数进行了反分析研究.根据附加条件,并考虑到由于测量误差和测量数据的不充分造成的反演问题的不适定性,将黏弹性双相介质的参数反演问题转化为非线性泛函的极小值问题,然后应用大范围收敛的同伦方法求出使泛函极小的根作为反问题的解.最后,以二维半空间黏弹性双相介质模型为例进行了数值反演分析,数值结果表明本文方法在参数的反演过程中目标函数稳定收敛,且具有一定的抗"噪声"干扰性能;与利用速度和加速度信息反演的结果相比,利用位移信息反演的结果具有较高的精度和抗噪声能力.In this paper, we inverse the physical parameters of saturated porous viscoelastic media from observed dynamic responses of displacement, velocity, or acceleration in time domain. This inverse problem is ill-posed due to the measurement error and the high insufficient measured data. In this paper, the ill-posed parameter inverse problem in the two-phase viscoelastic media is solved by computing a minimization problem of nonlinear functional by homotopy method, which has good convergent property for given initial values. Numerical results show our algorithm convergences well even with measurement noises or errors. We also observe that the inversed results based on observed response of displacement are better than the results based on responses of velocity and acceleration.

关 键 词：黏弹性双相介质 参数反演 同伦法 时域 动力响应 

分 类 号：P631[天文地球—地质矿产勘探]