Earthquake source inversion provides an image of the spatiotemporal evolution of earthquake rupture and tsunami generation. Inferences of this kind can help us understand the geophysics of earthquake rupture and tsunami generation which is of crucial importance to improve earthquake and tsunami hazard assessments. Most inference methods currently in use are based on linear 1980s methods and make many assumptions about the rupture (plane size, orientation, discretization, regularization). It has been shown that these assumptions significantly impact the solution, but the impacts are rarely investigated. Our research develops fully nonlinear inference methods based on advanced Markov chain/sequential Monte Carlo sampling methods. The algorithms require much more computer time than linear algorithms but are ideally suited for parallel computer clusters when implemented as large groups of Markov chains that interact and exchange information to dramatically increase sampling efficiency.