Liquid water in the Martian mid-crust.

Large volumes of liquid water transiently existed on the surface of Mars more than 3 billion years ago. Much of this water is hypothesized to have been sequestered in the subsurface or lost to space. We use rock physics models and Bayesian inversion to identify combinations of lithology, liquid water saturation, porosity, and pore shape consistent with the constrained mid-crust (∼11.5 to 20 km depths) seismic velocities and gravity near the InSight lander. A mid-crust composed of fractured igneous rocks saturated with liquid water best explains the existing data. Our results have implications for understanding Mars' water cycle, determining the fates of past surface water, searching for past or extant life, and assessing in situ resource utilization for future missions.

A canonical form of the equation of motion of linear dynamical systems.

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.