The estimation of crustal structure and thickness is instrumental in
understanding the formation and evolution of terrestrial planets.
Initial planetary missions with seismic instrumentation on board face
the additional challenge of dealing with seismic activity levels that
are only poorly constrained a priori. For example, the lack of plate
tectonics on Mars leads to low seismicity which could in turn hinder the
application of many terrestrial data analysis techniques. Here we
propose using a joint inversion of receiver functions and apparent
incidence angles, which contain information on absolute S-wave
velocities of the subsurface. Since receiver function inversions suffer
from a velocity depth trade-off, we in addition exploit a simple
relation which defines apparent S-wave velocity as a function of
observed apparent P-wave incidence angles to constrain the parameter
space. We then use the Neighbourhood Algorithm for the inversion of a
suitable joint objective function. The resulting ensemble of models is
then used to derive uncertainty estimates for each model parameter. In
preparation for analysis of data from the InSight mission, we show the
application of our proposed method on Mars synthetics and sparse
terrestrial data sets from different geological settings using both
single and multiple events. We use information theoretic statistical
tests as a model selection criteria and discuss their relevance and
implications in a seismological framework.