摘要
考虑脉冲源引起的2．5维弱不均匀介质波速反演问题．利用线性化方法得到了波速的二维小扰动满足的积分方程，这是一个积分几何的问题．进而由Fourier变换和脉冲函数的性质将此二维积分方程化为单交量的积分方程．最后用压缩映象理论证明了积分方程解的唯一性．本文给出了二维波速反演的一种新算法．同时，唯一性结果证明了己有的选代算法的合理性．
Consider a linearized velocity inversion in 2.5-D inhomogeneous medium. FOrpoint-sources and the correspondent responses measured on the earth's surface, we get anintegral equation satisfied by the 2-D wave velocity perturbation, which is a problem ofintegral geometry. Then we convert this 2-D equation into 1-D integral equation by POuriertransform and the properties of Delta function. Finally the uniqueness of solution to this1-D equation is proven by means of contraction mapping. The method proposed in thisarticle give a new algorithm for 2-D wave velocity inversion.
出处
《应用数学学报》
CSCD
北大核心
1998年第1期66-73,共8页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金
