Quantitative and Qualitative Seismic Imaging and Seismic Inversion

We consider seismic imaging to include seismic inversion. Imaging could use approximate operator or time instead of depth. Processing in time is an important part of seismic imaging as well as processing in depth. We can classify seismic imaging as quantitative versus qualitative methods. Quantitative method uses numerical methods to find the solution whose modeled seismic data approximates the input seismic records. Then we will progress to qualitative methods which have three aspects. The first aspect will be topology and geometry. The second aspect is semigroup method. The third aspect is to use non-differentiable solution.