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Abstract:
The problem of solving nonlinear inverse problems and related uncertainty quantification can be addressed by employing sampling strategies, i.e., Monte Carlo methods. Such approach can avoid linearizations and strives to explore regions of the model space where plausible models are located. Recent interest in such strategy has brought to attention the Hamiltonian Monte Carlo (HMC) method, thanks to its peculiar properties which permit tackling high-dimensional problems exploiting information from the gradient of the posterior probability density function. In this work we show how different geophysical problems can be solved with sampling strategies under a common framework, which facilitates experimenting with algorithms, tuning, forward models, etc.. This has been implemented in a software package named "HMCLab", a numerical laboratory which provides: 1) a set of sampling algorithms, particularly focusing on the HMC method, which can be combined with the 2) set of geophysical forward problems such as wave propagation, gravity and magnetic anomalies modelling, seismic traveltimes, etc. Each of the geophysical problems consists of routines to solve the forward problem and to compute the gradient of a misfit functional with respect to the model parameters. The sampling algorithms can thus be used to solve one of the implemented geophysical problems or combined with a user-provided problem. We show examples of the inverse problems that can be addressed with HMCLab and the kind of information that can be retrieved with a probabilistic (or Bayesian) approach.
