A hybrid inverse method for hydraulic tomography in fractured and karstic media

摘要

We apply a stochastic Newton (SN) approach to solve a high-dimensional hydraulic inverse problem in highly heterogeneous geological media. By recognizing the connection between the cost function of deterministic optimizations and the posterior probability density of stochastic inversions, the Markov chain Monte Carlo (MCMC) sampler of SN is constructed by two parts: a deterministic part, which corresponds to a Newton step of deterministic optimization, and a stochastic part, which is a Gaussian distribution with the inverse of the local Hessian as the covariance matrix. The hybrid inverse method exploits the efficient tools for fast solution of deterministic inversions to improve the efficiency of the MCMC sampler. To address the ill-posedness of the inverse problem, a priori models, generated by a transition probability geostatistical method, and conditioned to inter-well connection data, are used as regularization constraints.