Object-Based High Contrast Traveltime Tomography
We consider a traveltime tomography problem that involves detection of high-velocity structures in a homogeneous medium. If we only have limited measurements, this problem becomes an under-determined inverse problem and a common approach would be using prior information to guide the reconstruction process. We restrict the possible velocity into discrete values and model it as a discrete nonlinear inverse problem. However, typical iterative linearized reconstruction algorithms on grid-spacing model usually have very poor reconstruction results in the presence of high-contrast boundaries. The reason is that the travel path bends significantly near the boundary, making it very difficult to infer the travel path and velocity value from measured traveltime. To handle this scenario, we propose an object-based approach to model high-velocity structures by predefined convex objects. Compared to the typical grid-spacing model, which has variables that are proportional to the number of cells, our approach has an advantage that the number of unknown variables in the system is proportional to the number of objects, which greatly decreases the problem dimension. We have developed a fast algorithm to provide an estimate of the appearance probability of high-velocity structures in the region of interest. Simulations show that our method can efficiently sample the model parameter space, and provide more robust reconstruction results for the scenario where the number of measurements is limited.