AN INVERSE SOURCE PROBLEM FOR THE ELASTIC WAVE IN THE LOWER HALF-SPACE

作者：Tittelfitz Justin^*

来源：SIAM Journal on Applied Mathematics, 2015, 75(4): 1599-1619.

DOI：10.1137/140971671

• inverse problems
• elastic wave equation
• geophysical imaging
• microlocal analysis
• thermoacoustic tomography

We consider an inverse source problem for the wave equation in a heterogeneous, isotropic, elastic media (i.e., the dynamical Lame system). We assume our data are of the form Lambda f := u vertical bar([0,T]x Gamma), where u is the solution of the elastic wave equation with initial displacement f and Gamma subset of {x(n) = 0}, and show that the singularities (wavefront set) of f can be recovered in a unique and stable way. This follows the work of Stefanov and Uhlmann [Inverse Problems, 25 (2009), 075011] (partial data for an acoustic wave equation) and, more recently, of this author [Inverse Problems, 28 (2012), 055004] (full data for the same elastic system).

• 出版日期2015