Assessing the Optimal Solution Roughness of Earthquake Fault Slip
Distributions Using Synthetic Aperture Radar Interferometry

S.C. Put, G.J. van Zwieten, and R.F. Hanssen

With Synthetic Aperture Radar Interferometry (InSAR), it has been
proved possible to determine the fault plane geometry and slip
distribution of earthquakes. Given a fault plane geometry and slip
distribution, surface displacements can be calculated by assuming a
homogeneous elastic half-space. For the inverse case there is an
ambiguity problem, i.e. there are more combinations of fault plane
geometry and slip distribution that cause the same surface
displacement (which is observed with InSAR). This implies that the
inverse model needs constraints to yield a unique solution.
  
One possible constraint for the inverse model is the roughness of the
slip distribution. In general, a solution with a rough slip
distribution will fit best to the data, but represents a fault plane
geometry and slip distribution that is physically impossible. However,
a smooth solution will have a larger misfit with the data. Somewhere
in-between is the 'optimal' slip distribution roughness. Nevertheless,
choosing the optimal value for this constraint is not trivial.
  
In this study, methods for determining the optimal slip distribution
roughness are compared. Furthermore, it is examined whether using this
roughness as a constraint is the best choice, since other quantities
can also be constrained to yield a unique solution.