1 Center for Energy Resources Engineering, Center, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark4 National Space Institute, Technical University of Denmark5 University of Copenhagen
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 are released in the public domain using open source and open data licenses. The code has been developed to facilitate inversion of 2D and 3D travel time tomographic data using a wide range of possible a priori models and choices of forward models.
Computers and Geosciences, 2013, Vol 52, p. 481-492
Inversion; Non-linear; Tomography; Sampling; A priori; A posteriori