1. A computer-implemented method for ensuring stability of iterative inversion of seismic data to infer a model of at least one physical property of a subsurface region, wherein a model update is computed, using a programmed computer, for a next iteration by optimizing an objective function measuring misfit between the seismic data and model-simulated seismic data, said method comprising: using the computer, determining when a model update will cause an unstable simulation, and in response to such a determination, using a Projection Onto Convex Sets to find a nearest stable model; and using a final model from the iterative inversion for geophysical prospecting, wherein the optimizing of the objective function comprises performing a line search in model space in a direction indicated by a gradient of the objective function, and wherein the stability projection operator P is applied before beginning the line search, the line search determining an update for each model parameter m from the i th iteration to the i+1 iteration using a relationship that can be expressed as 
 m n+1 =m n +β( P[m n +αs n ]−m n ) with the search being on β, 0<β<1, with α fixed.