  Earthquakes cause lasting changes in static equilibrium, resulting in global
deformation fields that can be observed. Consequently, deformation measurements
such as those provided by satellite based InSAR monitoring can be used to infer
an earthquake's faulting mechanism. This inverse problem requires a numerical
forward model that is both accurate and fast, as typical inverse procedures
require many evaluations. The Weakly-enforced Slip Method (WSM) was developed
to meet these needs, but it was not before applied in an inverse problem
setting. Consequently, it was unknown what effect particular properties of the
WSM, notably its inherent continuity, have on the inversion process. Here we
show that the WSM is able to accurately recover slip distributions in a
Bayesian-inference setting, provided that data points in the vicinity of the
fault are removed. In a representative scenario, an element size of 2 km was
found to be sufficiently fine to generate a posterior probability distribution
that is close to the theoretical optimum. For rupturing faults a masking zone
of 20 km sufficed to avoid numerical disturbances that would otherwise be
induced by the discretization error. These results demonstrate that the WSM is
a viable forward method for earthquake inversion problems. While our
synthesized scenario is basic for reasons of validation, our results are
expected to generalize to the wider gamut of scenarios that finite element
methods are able to capture. This has the potential to bring modeling
flexibility to a field that if often forced to impose model restrictions in a
concession to computability.
