Numerical Simulation of Impact Cratering and Induced Seismic Waves in Sand Targets

TL;DR

This work presents a sand-target SPH model with a granular EOS to simulate low-velocity impact cratering and the associated seismic waves in regolith-like targets. By validating against measured sound speeds, crater radii, and π-scaling exponents, the authors demonstrate that friction, porosity, and pressure-dependent stiffness govern crater formation and seismic responses in subsonic regimes. They derive an analytical estimate for the seismic region radius and show how crater size and seismic signals scale with impact parameters, target properties, and resolution. The model provides a practical tool for predicting crater sizes on unknown small bodies and interpreting asteroid surface observations, while highlighting limitations due to the simplified EOS and absence of grain crushing at higher pressures.

Abstract

Impact cratering plays a crucial role in shaping the surfaces of small bodies, satellites, and planets, providing insights into their formation and the history of the Solar System. Small bodies are often covered with low-cohesion regolith. Using sand as a model of regolith, we constructed a numerical model for simulating impact on a sand target to investigate the mechanisms of crater formation and impact-induced seismic waves. Soda-lime glass and quartz sand targets were used for comparison. The developed sand model successfully reproduced the sound velocity measured in an experimental study. Using the new sand model, the crater formation was simulated using Smoothed Particle Hydrodynamics with a material strength parameter. The crater radius and $π$-scaling law derived from the numerical simulation were consistent with the experimental study. The vertical acceleration around the surface of the crater was consistent with the experimentally measured acceleration for the impact-induced seismic wave. The developed model can provide insight for predicting the size of craters on unknown small bodies.

Figures (13)

• Figure 1: Sound velocity as a function of confining pressure. The colors represent the materials: purple is soda-lime glass beads, and green is quartz sand. The solid and dashed lines are the longitudinal and transverse wave velocities, respectively.
• Figure 2: Snapshots of crater formation. This simulation corresponds to RUN 1 in Table \ref{['tab:sims']}. The color contour represents the pressure. Dark-blue indicates a the pressure lower than 100 Pa.
• Figure 3: Pressure (upper panel) and velocity (lower panel) distribution for Run 1 at 3 ms. The color bar shows the pressure and absolute value of the velocity, respectively.
• Figure 4: Snapshots of the crater profile for RUN 1. The red line shows the crater profile. The profile shows a cross-section between $y=-0.05$. to $y=0.05$. Particles visible at the center are residual projectile fragments.
• Figure 5: Relationship for $\pi$-scaling law. The red line shows the crater profile. Filled red and blue symbols indicate SPH simulations for soda-lime glass and quartz, respectively. Black lines with open red and blue symbols are the analytical solution calculated using Eq. \ref{['ldcrater']} multiplied by 0.1. Purple and green symbols indicate experimental results reported by Yasui2015 for soda-lime glass (Y15) and Matsue2020 for quartz (M20), respectively.