The impact of grid partitioning on the convergence efficiency of tree-based Bayesian inversion

Abstract Bayesian inversion commonly employs the rj-MCMC sampling algorithm for global search, but it is known for its low efficiency. To enhance sampling efficiency in multidimensional subspaces, advanced model parameterization methods are required. Hawkins proposed a tree-based model parameterization using wavelet basis functions, which leverages the tree structure to subdivide the subsurface model. This paper examines the impact of logarithmic interval subdivision of the subsurface and a combination of shallow uniform subdivision with deep logarithmic interval subdivision on sampling efficiency. The results indicate that the combined approach of shallow uniform subdivision and deep logarithmic interval subdivision leads to faster convergence in the inversion process.