SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information: Part 2 - Application to crosshole GPR tomography

We present an application of the SIPPI Matlab toolbox, to obtain a sample from the a posteriori probability density function for the classical tomographic inversion problem. We consider a number of different forward models, linear and non-linear, such as ray based forward models that rely on the high frequency approximation of the wave-equation and ’fat’ ray based forward models relying on finite frequency theory. In order to sample the a posteriori probability density function we make use of both least squares based inversion, for linear Gaussian inverse problems, and the extended Metropolis sampler, for non-linear non-Gaussian inverse problems. To illustrate the applicability of the SIPPI toolbox to a tomographic field data set we use a cross-borehole traveltime data set from Arrenæs, Denmark. Both the computer code and the data is released in the public domain using open source and open data licenses. The code has been developed to fascilitate inversion of 2D and 3D travel time tomographic data using a wide range of possible a priori models and choices of forward models.