Morphometric Analysis of Granular Impact Craters through Time-of-Flight Cameras. Depth Prediction Model and Lateral Opening Mechanisms

Abstract

Laboratory made granular-granular impact craters have been used as model analogues of planetary impact craters. These kind of craters have been observed and studied using profilometry techniques that allow to retrieve important morphologic features from the impacted surface. In this thesis, we propose to use a Time-of-Flight camera (Microsoft Kinect One) for the acquisition of depth data. We show comparisons between the typically used technique and the analysis derived from the Time-of-Flight data. We also release craterslab, a Python library developed to automate most of the tasks from the process of studying impact craters produced by granular projectiles hitting on the surface of granular targets. The library is able to acquire, identify, and measure morphological features of impacted surfaces through the reconstruction of 3D topographic maps. Our results show that using a Time-of-Flight camera and automating the data processing with a software library for the systematic study of impact craters can produce very accurate results while reducing the time spent on different stages of the process.

This study investigates granular impact craters on both loosely and more tightly packed sand targets. We observe significant deviations in the depth vs. energy power-law predicted by previous models. To address this discrepancy, we introduce a physical model of uniaxial compression that explains how depth saturates in granular collisions.

Furthermore, our results reveal a greater transfer of vertical to horizontal momentum on compacted surfaces compared to loosely packed sandbox targets, and we present an energy balance that describes it.

Central peak formation also appears to play an essential role in better transferring vertical momentum to horizontal degrees of freedom, resulting in shallow craters on compacted sandbox targets. However, this is an open topic for further investigation.

On the other hand, we report granular vs. granular experiments that consistently adhere to power-law scaling laws for diameter as a function of impacting energy, similar to those reported by other groups for their experiments utilizing both solid and granular projectiles. However, this result deviates significantly on compacted impact surfaces. To address this, we developed a radial model of lateral opening mechanism where a logarithmic dependence of the diameter on energy is obtained. This is experimentally confirmed.

Our findings indicate that the depth-to-diameter aspect ratio results are consistent with prior and novel observational data from planetary bodies, providing significant insights into the physical processes governing natural crater formation and allowing us to interpret the shallowness of planetary craters in light of the uniaxial compression mechanism proposed in this work. Finally, counterintuitively, we found that the rim height abruptly saturates concerning the impact energy, creating a new paradox for the scientific community.