We develop a methodology for systematic inversion of quantitative stratigraphic models. Quantitative stratigraphic modeling predicts stratigraphy using numerical simulations of geologic processes. Stratigraphic inversion methodically searches the parameter space in order to detect models which best represent the observed stratigraphy. Model parameters include sea-level change, tectonic subsidence, sediment input rate, and transport coefficients. We successfully performed a fully automated process based stratigraphic inversion of a geologically complex synthetic model. Several one and two parameter inversions were used to investigate the coupling of process parameters. Source location and transport coefficient below base level indicated significant coupling, while the rest of the parameters showed only minimal coupling. The influence of different observable data on the inversion was also tested. The inversion results using misfit based on sparse, but time dependent sample points proved to be better than the misfit based on the final stratigraphy only, even when sampled densely. We tested several inversion schemes on the topography dataset obtained from the eXperimental EarthScape facility simulation. The clustering of model parameters in most of the inversion experiments showed the likelihood of obtaining a reasonable number of compatible models. We also observed the need for several different diffusion-coefficient parameterizations to emulate different erosional and depositional processes. The excellent result of the piecewise inversion, which used different parameterizations for different time intervals, demonstrate the need for development or incorporation of time-variant parameterizations of the diffusion coefficients. We also present new methods for applying boundary condition on simulation of diffusion processes using the finite-difference method. It is based on the straightforward idea that solutions at the boundaries are smooth. The new scheme achieves high accuracy when the initial conditions are non vanishing at the boundaries, a case which is poorly handled by previous methods. Along with the ease in implementation, the new method does not require any additional computation or memory. / Ph. D.