Large earthquakes are usually modeled with simple planar fault surfaces
or a combination of several planar fault segments. However, in general,
earthquakes occur on faults that are non-planar and exhibit significant
geometrical variations in both the along-strike and down-dip directions
at all spatial scales. Mapping of surface fault ruptures and
high-resolution geodetic observations are increasingly revealing complex
fault geometries near the surface and accurate locations of aftershocks
often indicate geometrical complexities at depth. With better geodetic
data and observations of fault ruptures, more details of complex fault
geometries can be estimated resulting in more realistic fault models of
large earthquakes. To address this topic, we here parametrize non-planar
fault geometries with a set of polynomial parameters that allow for both
along-strike and down-dip variations in the fault geometry. Our
methodology uses Bayesian inference to estimate the non-planar fault
parameters from geodetic data, yielding an ensemble of plausible models
that characterize the uncertainties of the non-planar fault geometry and
the fault slip. The method is demonstrated using synthetic tests
considering checkerboard fault-slip patterns on non-planar fault
surfaces with spatially-variable dip and strike angles both in the
down-dip and in the along-strike directions. The results show that
fault-slip estimations can be biased when a simple planar fault geometry
is assumed in presence of significant non-planar geometrical variations.
Our method can help to model earthquake fault sources in a more
realistic way and may be extended to include multiple non-planar fault
segments or other geometrical fault complexities.