What do faults feel? A Bayesian framework for the estimation of tectonic stress parameters at seismogenic depths

Earthquakes provide a key means of estimating tectonic stress at seismogenic depths, and thereby of investigating directly the mechanisms by which faults slip during earthquakes and interact. To date, however, stress estimation algorithms have not provided sufficiently reliable uncertainty estimates to enable the detection of fine temporal or spatial variations in stress. We have developed a probabilistic (Bayesian) technique for estimating tectonic stress directions from routine seismological observations. The Bayesian approach combines a geologically motivated prior model of the state of stress with an observation model that implements the physical relationships between the stresses acting on a fault, slip during an earthquake, and the observed seismic waves. We first quantify the constraints on the four determinable stress tensor parameters imposed by a single focal mechanism in terms of a joint probability density function. Next, we formalise the process of estimating stress tensor parameters from a number of such mechanisms by combining the corresponding probability density functions. We explicitly include the limitation that, in general, the two nodal planes of a given focal mechanism cannot be unambiguously distinguished and are invariably subject to measurement error. Our formulation is equivalent to a well-known analytical solution for a single, errorless focal mechanism observation (McKenzie, BSSA, 59, 1969). The new approach has the distinct advantage, however, that including (1) multiple earthquakes, (2) fault plane ambiguities, (3) observational errors, and (4) prior knowledge of the stress field is mathematically tractable, albeit computationally intensive. Our approach is intended to yield reliable tectonic stress estimates that can be confidently compared with other tectonic parameters, including seismic anisotropy and geodetic strain rate observations, and used to investigate spatial and temporal variations in stress associated with major faults and coseismic stress perturbations.