Simulating the Speed of Seismic Waves Through a Granular Medium

Many small asteroids are believed to be collections of discrete particles held together by cohesive forces and self-gravity. The propagation speed of a seismic impulse due to an impact or other perturbation depends on the internal pressure of the body, which increases towards its center. We aim to characterize the velocity of a seismic wave through an environment of thousands to millions of granular particles as a function of the confining pressure of the medium. We will compare our numerical results with the laboratory experiments of Tancredi et al. (2019, EPSC-DPS2019-1017), in which high-speed projectiles were shot at containers of millimeter-sized sand and glass granules compressed up to pressures of 40 MPa. We use ‘pkdgrav’, a parallel N-body gravity code that uses the soft-sphere discrete element method to model particle contact interactions. Particle collisions are modeled by a Hooke’s law spring, where the restoring force between particles in contact is mediated by an adjustable spring constant, Kn. Kn is related to the Young’s modulus or the stiffness of individual particles. The Kn we use corresponds to a Young’s modulus on the order of 10 GPa, to prevent excessive overlaps at the most extreme confining pressures. In our simulations, we fill a 0.5 m length square container with spherical particles and pressurize the container from above with a confining wall of massive particles under Earth gravity. Confining pressures range from 7–40 MPa. We shoot a projectile with speeds ranging from 60–320 m/s towards the top of the container and measure the resulting wave speed in the medium as a function of confining pressure. We expect to find that the wave speed increases with pressure, as found in the laboratory experiments of Tancredi et al. With this validation of the numerical method, we can apply it to low-gravity environments such as small-asteroid surfaces to quantify the propagation efficiency of seismic waves in regolith.