SIPPI is a MATLAB toolbox (compatible with GNU Octave) that been been developed in order solve probabilistically formulated inverse problems (Tarantola and Valette, 1982; Tarantola, 2005) where the solution is the a posteriori probability density
where refer to the forward model, the a priori model, and the likelihood.
SIPPI allow sampling the a posteriori probability density (Mosegaard and Tarantola, 1995) in case the forward model is non-linear, and in case using a combination of a number of widely used geostatistical methods to describe a priori information (Hansen el al., 2012).
In order to make use of SIPPI one has to
Install and setup SIPPI.
Define the prior model, , in form of the
prior data structure.
Define the forward model, , in form of the
forward data structure, and the
Define the data and noise model, i.e. the likelihood , in form of the
Choose a method for sampling the a posteriori probability density (i.e. the solution to the inverse problem).
A number of forward solvers is implented: LINEAR (linear forward operator) , TRAVELTIME (ray, fat, eikonal, born), GPR_FW (full waveform modeling)
The best way to learn to use SIPPI is by going through some examples:
Lineftting example: A simple low-dimensional inverse problem.
GPR cross hole tomography: A more complexe inverse problem illustrating most uses of SIPPI.
Two manuscripts exist describing SIPPI. Part I, is a general introduction on how to setup and use SIPPI. Part II, is an example of using SIPPI to solve cross hole GPR inverse problems (see example):
Hansen, T. M., Cordua, K. S., Looms, M. C., & Mosegaard, K. (2013). SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information: Part 1 — Methodology. Computers & Geosciences, 52, 470-480.
Hansen, T. M., Cordua, K. S., Looms, M. C., & Mosegaard, K. (2013). SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information: Part 2 — Application to crosshole GPR tomography. Computers & Geosciences, 52, 481-492.
The key idea that allow using complex a priori models, referred to as 'sequential Gibbs sampling' is described in detail in
Hansen, T. M., Cordua, K. S., & Mosegaard, K. (2012). Inverse problems with non-trivial priors: Efficient solution through sequential Gibbs sampling. Computational Geosciences, 16(3), 593-611.
References to other manuscript considered/used in SIPPI is listed in the Bibliography.
SIPPI make use of other open software projects such as :
Codes and theory has been developed by the Inverse Modeling and Geostatistics Project