A Multiresolution Approach to the Waveform Tomography Inverse Problem

Full waveform tomography refers to a technique that can used in imaging internal structures of a target object without altering or damaging it in anyway. The term full waveform means that the wave is utilized in its full form. The imaging can be done using either acoustic waves or electromagnetic waves. The goal of this thesis is to explore the concept of waveform inversion, the physical theory behind it and possible applications in real life. In the computational part of this thesis a multiresolution approach to solve a mathematical waveform inversion problem is introduced. The numerical test setup was based on a minimal configuration of three sources. A single resolution approach was used as a reference method. Numerical experiments were conducted in a 2D domain and the results of the multi and single resolution were compared to each other. Based on the results of the numerical experiments the multiresolution approach turned out to be a feasible method to solve our inversion problem. In addition to the memory savings gained compared to the single resolution method, the multiresolution also proved to be more accurate with suitably chosen regularization parameters