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: 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.