Consider an inverse problem of reconstructing the coefficient in a linearwave equation on an inhomogeneous slab with density ρ(z) and wave velocity c(z). The inversioninput information is the reflection and transmiss...Consider an inverse problem of reconstructing the coefficient in a linearwave equation on an inhomogeneous slab with density ρ(z) and wave velocity c(z). The inversioninput information is the reflection and transmission data corresponding to a point source. Byapplying the characteristic theory for hyperbolic equations, we establish an integral system fromwhich ρ(z) and c(z) can be recovered simultaneously. In contrast to some known results, our inverseapproach is carried out for depth variable, rather than for travel-time variable. Thereforeinversion results in this paper are more appropriate for the physical interpretation of a mediumslab.展开更多
文摘Consider an inverse problem of reconstructing the coefficient in a linearwave equation on an inhomogeneous slab with density ρ(z) and wave velocity c(z). The inversioninput information is the reflection and transmission data corresponding to a point source. Byapplying the characteristic theory for hyperbolic equations, we establish an integral system fromwhich ρ(z) and c(z) can be recovered simultaneously. In contrast to some known results, our inverseapproach is carried out for depth variable, rather than for travel-time variable. Thereforeinversion results in this paper are more appropriate for the physical interpretation of a mediumslab.
