This report is motivated by the need to understand the possible applications of two-dimensional (2-D) modeling of stochastic processes and related techniques in signal processing to problems of inversion of geophysical data. Here we first provide a brief overview of 2-D modeling and signal processing techniques. We then address the problem of passing from free air gravity anomaly data (FAG) to bathymetry. We present an approach to this fundamental inversion problem, based on a systematic spatial segmentation of the 2-D data followed by statistical modeling within the segments. We also suggest possible improvements on current approaches based on transfer function methods.