Programming an Ising computer for seismic tomography

Kristopher A. Innanen

The computational cost of our modern seismic methodologies continues to grow, motivating research into programming seismic procedures in the languages of other computing paradigms. Ising computation is one of these. Programming an Ising computer involves mapping between the problem of interest and the binary ``up/down'' variables of Ising systems, as well as the energetics that specify a system's behaviour as it seeks equilibrium. We set up a specialized discretization of the slowness and ray objects of seismic tomography, map them to Ising variables, and then equip a notional Ising computer with both coupling constraints and background field quantities. We hypothesize that in such a system, when equilibrium is found, the resulting states can be meaningfully queried for slowness and raypath estimates. Monte Carlo simulations of such a computer are promising. But, we identify several conceptual issues which will require more consideration, especially in the ray determinations, including the need to relax our standard definition of rays, and practical issues, including the need for quite narrow weighting of the system to force it towards acceptable equilibrium states. All that said, the primary aims of the project have been successful: it is possible to ``program'' an Ising computer to do seismic tomography, and it may be of interest to expand this to other kinds of inversion in anticipation of Ising hardware being available in the not-too-distant future.