Bayesian inference in seismic inversion
This year (2014) Shell has funded a Research Studentship in the University of Cambridge to investigate how Bayesian inference and machine-learing methods developed in the Cavendish Astrophysics Group may be used to in probabilistic seismic inversion problems.б In particular, the project will focus on the use of nested sampling methods, embodied in the MultiNest software package, to estimate the Bayesian evidence for different physical models and explore the posterior probability distribution of their parameters.б These algorithms will first be applied to single-trace based inversions (with 100-500 dimensions), but the study will also include high-dimensional (multi-trace laterally continuous) model representations, with possibly 1000s of dimensions and possessing multiple modes and/or long degeneracies. Such problems are extremely challenging and may require furtherб development of the state-of-the-art methods, such Galilean nested sampling. The key aspects of interest are: efficiency; accuracy
of the estimate of the posterior and evidence; capability to sample multi-modal distributions; and capability to sample a combination of continuous and categorical variables.
In Bayesian analysis, the evaluation of the likelihood function of the data for a given set of model parameter values can be very computationally expensive. To this end, the Cavendish Astrophysics Group has combined MultiNest with an in-house generic neural network training software package, called SkyNet, to produce the BAMBI (Blind Accelerated Multimodal Bayesian Inference) package. In this approach a neural network is trained as a proxy/surrogate model for the likelihood function as the sampling process progresses. The process accelerates as the net becomes a better approximation, and the sampling progresses faster. This approach will be compared with the present MCMC, ED, linear-proxy and adjoint-based approaches. In particular, Shell wishes to apply this methodology to the assisted history matching problem in reservoir simulation.б Low (100s) and high dimensional (1000s) models of the reservoir will be tested. Galilean nested sampling and/or Guided Hamiltonian sampling will be investigated as a replacement for the MultiNest component for high-dimensional space representations where gradients are needed. The project also has the scope to explore new sampling algorithms, or combinations of Shell and Cambridge approaches.
The student will be based in the Cavendish Astrophysics Group, under the supervision of Professor Michael Hobson, but will be expected to spend significant time (several weeks per year) at Shell Rijswijk to receive proper support and maintain the connection with the Shell researchers.