Inversion of Geodetic data using least-square method in a non-Gaussian framework

C.‭ ‬Marchica,‭ ‬B.‭ ‬Valette,‭ ‬M.‭ ‬Radiguet


Modeling‭ ‬surface deformation is an important problem in geophysics.‭ ‬The‭ ‬deformation‭ ‬field‭ ‬can have various origins:‭ ‬volcanoes,‭ ‬earthquakes,‭ ‬aseismic fault slip...‭ ‬In this study,‭ ‬we focus on non-volumetric sources,‭ ‬such as dislocations along faults segments.‭ ‬We propose an original method to invert static surface displacement for slip on a known fault interface,‭ ‬based on a least-square approach in a Bayesian framework.‭ ‬The originality of the approach consists in considering non-Gaussian probability functions for the model parameters while keeping the least-square method related to the Gaussian framework.‭ ‬This is achieved by defining a change of variable in the model parameters in such a way that the new variables are Gaussian,‭ ‬while the initial physical parameters present the desired non-Gaussian distribution.‭ ‬More precisely,‭ ‬to allow a precise control of the slip direction over the fault we assign a decreasing power law to the probability function for the slip amplitudes that imposes positivity and values as small as possible.‭
We apply the method to‭ ‬the inversion of the interseismic GPS displacement field along the Northern Andes subduction zone‭ (‬from Peru to Columbia‭)‬.‭ ‬The data consist of‭ ‬100‭ ‬horizontal GPS vectors‭ (‬Nocquet et al.‭ ‬2014‭)‬.‭ ‬The slab geometry is extracted from the Slab‭ ‬1.0‭ ‬model‭ (‬Hayes‭ ‬2012‭)‬.‭ ‬We‭ ‬have‭ ‬tested several model‭ ‬parameterizations to assess the robustness of our results.‭ ‬The‭ ‬optimal model is‭ ‬globally‭ ‬in good agreement with previous studies,‭ ‬presenting two highly coupled zones,‭ ‬the first‭ ‬one in Northern Ecuador,‭ ‬and the second one in‭ ‬Central‭ ‬Peru.‭ ‬But in contrast with‭ ‬Nocquet et al.‭'‬s study,‭ ‬we directly‭ ‬invert‭ ‬the GPS data without previously removing a two-block solid rotation,‭ ‬related to coastal slivers.‭ ‬This yields models that correctly fit the GPS vectors in Northern‭ ‬Ecuador and in central and Southern Peru.‭ ‬At the Golf of Guayaquil latitude,‭ ‬the fit is‭ ‬less‭ ‬accurate,‭ ‬probably due to complexities both in the slab geometry and in the continental deformation‭ ‬that are not taken into account.‭
We thus validate‭ ‬this approach in the case‭ ‬of the Northern Andes subduction zone,‭ ‬but it can be applied to any kind of surface deformations data‭ (‬GPS,‭ ‬InSAR‭)‬,‭ ‬and‭ ‬various‭ ‬model‭ ‬parameterizations‭ ‬can be developed for other applications‭ ‬via specific probability density functions.


References:‭

Nocquet,‭ ‬J.‭ ‬M.,‭ ‬Villegas-Lanza,‭ ‬J.‭ ‬C.,‭ ‬Chlieh,‭ ‬M.,‭ ‬Mothes,‭ ‬P.‭ ‬A.,‭ ‬Rolandone,‭ ‬F.,‭ ‬Jarrin,‭ ‬P.,...‭& ‬Martin,‭ ‬X.‭ (‬2014‭)‬.‭ ‬Motion of continental slivers and creeping subduction in the northern Andes.‭ ‬Nature Geoscience,‭ ‬7‭(‬4‭)‬,‭ ‬287.

Hayes,‭ ‬G.‭ ‬P.,‭ ‬D.‭ ‬J.‭ ‬Wald,‭ ‬and R.‭ ‬L.‭ ‬Johnson‭ (‬2012‭)‬,‭ ‬Slab1.0:‭ ‬A three-dimensional model of global subduction zone geometries,‭ ‬J.‭ ‬Geophys.‭ ‬Res.,‭ ‬117,‭ ‬B01302,‭ ‬doi:10.1029/2011JB008524.