初至波走时层析成像中的正则化方法

Normalized approach in tomographic imaging of first breaks travel time

波场的等效性、观测数据的有限性和观测误差等因素导致地球物理反演本身具有严重的多解性,降低这种多解性的一种重要途径就是对反演过程进行约束。传统的初至波走时层析成像方法,通常是在外部对模型空间施加显式的约束和平滑处理,这样就会破坏模型参数与传播算子之间的相关性,难以达到有效利用先验信息的目的,甚至会影响反演的稳定性。针对这一问题,本文将先验信息分为三类,在此基础上阐述了通过正则化手段将各种先验信息纳入到反演方程当中,替代传统的外部约束模式。理论试验结果表明,正则化方法比外部约束方法有效地提高了反演的精度和分辨率;将该正则化方法应用于实际二维资料处理,也得到了比较好的反演结果。

Because of equivalence of wave field,and the limitation and errors of surveyed data,the geophysical inversion has serious multi-solution and an important way reducing the multi-solution is to carry out constraint for the inversion process.The traditional first breaks travel-time tomographic imaging is usually to add apparent constraint to model space from outside and carry out slipping process,which can destroy the correlation between model parameters and propagation operator,and is difficult to reach the goal effectively using prior information,even affects the stability of inversion.In view of the difficulty,the paper divided the prior information into three categories and expounded how to add various kinds of prior information into inversion equations by normalized way on that basis,replacing traditional outside constrained mode.The theoretical tests showed the normalized approach can effectively improve the precision and resolution of inversion than that in outside constrained method; using normalized approach for 2-D practical data processing can also gain better inversion results.