How Do Geologic Data Constrain Shear Zone Models, Really?
Joshua Davis, Carleton College
Sarah Titus, Carleton College
Vasileios Chatzaras, University of Wisconsin - Madison
,
,
Suppose that a geologist wishes to understand the kinematics or dynamics of a shear zone: its geometry, boundary conditions, material properties, etc. Her study can be informed by various kinds of data, such as directions (paleomagnetic directions, dike poles), orientations (foliation-lineation pairs, faults with slip), and ellipsoids (anisotropy of magnetic susceptibility, X-ray computed tomography of grains). In principle, the data constrain the kinematics/dynamics. But how tight are those constraints? When do they refute a model outright? Rigorously addressing such questions requires a degree of statistical analysis rarely found in geologic studies.
We describe a conceptual framework for quantifying the uncertainty in shear zone models. Three key elements are a velocity field, a predictor for how each data type arises from that field, and a way of comparing predictions to data quantitatively. These elements are controlled by parameters, whose values we wish to know. A fourth element is a set of prior probability distributions for the parameters, reflecting our geologic knowledge of the system (or lack thereof). In a Bayesian Markov chain Monte Carlo simulation, the four elements cooperate to produce a posterior probability distribution, which gives a best answer for the parameter values while also providing detailed information about the uncertainty in that answer.
We demonstrate this framework using several velocity field styles, synthetic and natural data sets, and geologic data types. In some cases, the predictors exhibit certain kinds of asymptotic or periodic behavior, which can produce large uncertainties in the modeling results. The conclusions of any modeling study should account for these uncertainties.