The statistical mechanics of model space shuttles

Kristopher A. Innanen

Null space shuttles are an artifice which help quantify uncertainty in seismic full waveform inversion. Recent papers have framed these shuttles in terms of artificial dynamical systems, in which high-dimensional orbits are computed in a potential produced by the objective function. Here we pursue a natural extension of this, which is to develop a barometric equation for gases of these shuttles. This paper is largely mathematical, and ends with that equation. The main effort is in developing an approach based on the eigenvalues of the shuttle mass matrix and the Hessian matrix to produce a closed-form (if yet computationally expensive) expression for the partition function.