Exploring viable geologic interpretations of gravity models using distance-based global sensitivity analysis and kernel methods

We have explored ways to integrate alternative geologic interpretations into the modeling of gravity data. These methods are applied to the Vaca Fault east of Fairfield, California, USA, where the structure across the fault is in question, and the Vaca Fault is used as a case study to demonstrate the method. The Vaca Fault is modeled using gravity data collected along a 10 km line perpendicular to the strike of the fault. Of particular interest is how the gravity data might inform on the dip of the Vaca Fault and thickness of the nonmarine section and whether spatial autocorrelation of density internal to the geologic units significantly influences the resulting gravity anomaly. We approach these questions by creating a suite of structural geologic models, which we then populate with geostatistically generated densities and from which the respective synthetic gravity anomalies are calculated. We perform distance-based generalized sensitivity analysis to identify which model inputs most leverage the calculated gravity anomaly. We then use multidimensional scaling to transform the gravity anomalies into a metric space and estimate the posterior probabilities of each structural geologic model using a Bayesian approach. We find that the gravity anomalies are particularly sensitive to zones of autocorrelated density values generated from geostatistical modeling. The structural geologic models most likely to produce gravity anomalies that match the observed data are the moderately dipping normal faults, 45° and 60°, although the probability that the fault dips more steeply, including in a strike slip or reverse fault orientation, is approximately 30%. The probability of a thicker nonmarine unit is 67%, more probable than a thinner nonmarine unit. This suggests that the Vaca Fault dips moderately to the east and truncates a thicker nonmarine unit, but that any further process modeling should include alternatives of the geologic structures.