A BAYESIAN APPROACH TO MODELING GRAVITY DATA: APPLICATION TO SYNTHETIC DATA AND NATURAL DATA FROM THE RIO GRANDE GORGE BRIDGE

We present a new 2D gravity inversion method based on Bayesian statistics. Unlike many standard methods for gravity inversion, our approach does not use rectangular subsurface blocks. Nor do we solve for a single best-fit model that matches the gravity data. Instead, we use Markov chain Monte Carlo (MCMC) methods to construct an approximate probability distribution on a set of possible subsurface polygons. By incorporating parallel tempering (i.e., replica-exchange MCMC sampling), we avoid trapping that can occur in certain model geometries. We can also compare probabilities among models with different parameters (e.g., different n). Statistics of interest, such as area, center of area, and occupancy probability (the probability that a spatial point belongs to the subsurface object), are easily computable from such a distribution. Our Bayesian approach allows us to incorporate uncertainty in both the data and model results. Geologically plausible geometries, as well as polygon parameters (i.e. the number of vertices n and the ratio of the perimeter squared to the area, denoted α), can be explored in a forward model before the inversion.

Although prior studies have applied Bayesian approaches to synthetic gravity data, we know of no applications to natural systems. After illustrating our approach with several synthetic datasets, we analyze gravity data from the Rio Grande Gorge Bridge in New Mexico. This setting is ideal because the subsurface object—the air below the bridge—is well determined. In addition, there is a large density contrast between air and rock, and the canyon can be approximated as two-dimensional. In our model, we examine polygons where α is less than 3.0 and n varies between 3 and 10, and determine the corresponding model probabilities. While the model with n = 7 is found to be most probable within computational uncertainties, all of our models for n > 5 make similar predictions and are consistent with the known canyon geometry.