  It was recently shown that certain subsurface hydrological inverse problems
-- here framed as determining the composition of an aquifer from pressure
readings -- can be solved on a quantum annealer. However, the quantum annealer
performance suffered when solving problems where the aquifer was composed of
materials with vastly different permeability, which is often encountered in
practice. In this paper, we study why this regime is difficult and use several
pre- and post-processing tools to address these issues. This study has three
benefits: it improves quantum annealing performance for real-world problems in
hydrology, it studies the scaling behavior for these problems (which were
previously studied at a fixed size), and it elucidates a challenging class of
problems that are amenable to quantum annealers.
