Spectral factorization of partial differential equations

In the second part, I use multidimensional spectral factorization to facilitate solving multidimensional partial differential equations (PDEs) with application to exploration seismology. As an illustration of the methodology, in Chapter , I show how the Helmholtz operator can be factored into two filters, which then can used to propagate waves. With more practical interests in mind, in Chapter , I apply the methodology to the problem of implicit finite-difference modeling and migration by wavefield extrapolation. Chapter  describes how the method can be applied in areas where the velocity varies laterally.