On forward and inverse modelling in seismology: Raytracing in inhomogeneous media

The first part of this thesis deals with forward modelling. We present a raytracing method based on the concept of simulated annealing: a computational tool based on physical principles used for obtaining optimal solutions of problems in areas ranging from combinatorics to condensed matter physics. Our method solves for rays that render signal traveltime stationary, in accordance with Fermat's principle of stationary traveltime. We test this method for two types of media: layered inhomogeneous media and linearly inhomogeneous media. We show that rays and traveltimes generated from this algorithm for these models quantitatively agree with predicted results.; The second part of the thesis deals with inverse modelling. In this part, we introduce the generalized form of Radon's transform and its adjoint operator. We show that by treating traveltime as Radon's transform acting on the slowness function along a ray, we can use the adjoint operator to recover qualitative information about a medium from collected traveltimes. This method of back-projection is presented as an application of our raytracing method. We calculate rays and their associated traveltimes between sources and receivers on a square lattice for layered- and linearly-inhomogeneous media and use the back-projection method to construct slowness functions for each set of data. We show that although the back-projection method does not retain the quantitative properties of the original medium, results indicate that qualitative properties of the medium can be resolved by this method.