Traveltime Tomography And Nonlinear Constrained Optimization

Fermat's principle of least traveltime states that first arrivals follow ray paths with the smallest overall traveltime from the point of transmission to the point of reception. This principle determines a definite convex set of feasible slowness models - depending only on the traveltime data - for the fully nonlinear traveltime inversion problem. The existence of such a convex set allows us to transform the inversion problem into a nonlinear constrained optimization problem. Fermat's principle also shows that the standard undamped least-squares solution to the inversion problem always produces a slowness model with many ray paths having traveltime shorter than the measured traveltirne (an impossibility even if the trial ray paths are not the true ray paths). In a damped least-squares inversion, the damping parameter may be varied to allow efficient location of a slowness model on the feasibility boundary.