Seismic efficiency of Martian upper crust simulant.

Introduction: Meteoroid bombardment is one of the sources of seismic activity on planetary bodies. The very first seismometer operating on the surface of another planet was successfully deployed by the NASA InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission to Mars. It gives us an opportunity to investigate the seismicity of Mars, including impact-induced seismic activity. This work investigated the seismic efficiency associated with small meteorite impacts on Mars, using numerical methods in targets analogue to the Martian surface. The Martian crust was simulated as non-porous bedrock (0% porosity) or regolith with different porosities (25%, 44% and 65%)

The seismic efficiency, k, is presented as a portion of impact energy that is transferred into seismic energy. It has been suspected that consolidated (bedrock) and non-consolidated (regolith) materials will have different values of seismic efficiency. Estimates of seismic efficiency range from k=10^-2 to 10^-6 (Schultz and Gault, 1975; Daubar et al., 2018; McGarr et al., 1969; Hoerth et al., 2014; Richardson & Kedar, 2013; Güldemeister & Wünnemann, 2017). High seismic efficiency is typical in bedrock or highly consolidated materials (k>10^-3). Low seismic efficiency is typical for sediments or unconsolidated sands and soils (k<10^-5) (e.g., Patton and Walter 1993). In this work, we used a simplified approach (e.g. Güldemeister & Wünnemann, 2017) that defines the seismic efficiency as: ; where x represents distance from the impact point, P is the amplitude of the pressure pulse, t is the duration of the pressure pulse, ρ is the density of the target, Cp is the speed of sound in the target and Ek is the kinetic energy of the impactor.

Numerical impact modelling: All simulations were performed with the iSALE-2D shock physics hydrocode (Collins, et al., 2004; Wünnemann et al., 2006). The impact conditions were modelled to replicate recent fresh meter size impact that occurred on Mars since the landing of InSight (Daubar et al., 2020). Impact crater was estimated to be ~1.5 m in diameter. Impactor radius was 4.4 cm and kinetic energy of 1.8x10⁶ J.

To simulate bedrock and fractured bedrock (25% porosity) we used the ROCK strength model (Collins et al., 2004). To simulate the regolith (44% and 65% porosity) we used Lundborg strength model (Lundborg, 1968) (Table 1). We used the Tillotsen equation of state for basalt (Tillotson, 1962; Wójcicka et al., 2020). For porous cases, we used the ε-α porosity model (Wünnemann et al., 2006;) (Table 2).

 

Table 1. Strength model parameters for targets with different porosity

Parameter	0%	25%	44%	65%
Strength model	ROCK	ROCK	LUNDD	LUNDD
Strength (damaged) (kPa)	10	0	10	0.3
Friction (damaged)	0.6	0.67	0.7	0.7
Limiting strength (damaged) (GPa)	3.5	0.17	0.25	0.25
Strength (intact) (MPa)	10	0.2
Friction (intact)	1.2	1.8
Limiting strength (intact) (GPa)	3.5	0.17

 

Table 2. ε-α porosity model parameters (Borg et al., 2005; Wünnemann et al., 2006; Wójcicka et al, 2020).

Parameter	25%	44%	65%
Initial distension, α	1.33	1.8	2.8
Elastic threshold, ε0	-4x10-4	10-4	10-5
Distension at transition αx	1.1	1.15	1.0
The rate change of distension with respect to volumetric strain, k	0.98	0.98	0.98
Ratio of speed of sound in porous over non-porous medium, χ	0.6	0.33	0.21

 

All variables in the equation for the seismic efficiency were calculated from iSALE outputs. The pressure wave was observed via gauges cells, placed at 45° equidistantly throughout the target. The pressure wave amplitude and pulse duration were calculated at full width half maximum. The sound speed was calculated from assumed bulk modulus of basalt (Wójcicka et al, 2020).

Results: Seismic efficiency was calculated for the same impact conditions in all four material models, representing the reference 1.5 m crater recently observed on Mars. There is a clear decrease in seismic efficiency with increasing porosity. It is of the order of 10^-5 for porous and highly porous regolith and 10^-4 for fractured bedrock. Estimates for the non-porous basalt bedrock are in the order of  10^-3 (Figure 1).

Porosity of the target affected pressure wave amplitudes, duration of the pressure pulse and speed of sound in the target. These are all parameters used in calculation of seismic efficiency. This implies that if impact occurs on very dusty parts of Mars with thick regolith cover, efficiency would be smaller than efficiency of the impact that occurred on the bedrock, or area with thinner regolith cover.

Figure 1. Seismic efficiency calculated in targets with different porosity

Conclusions. Impact cratering represents one of the most important geological processes in the Solar System. Defining relationship between target’s properties and seismic efficiency is of interest to the NASA InSight science, since it helps in understanding the properties of the uppermost crust on Mars. Previous approximations of seismic efficiency were of 2x10^-5 with an order of magnitude uncertainty for seismic efficiency on Mars (Teanby and Wookey, 2011) and Daubar et al. (2018) adopted the seismic efficiency of 5x10^-4 calculated from the seismic moment (Gudkova et al., 2011; 2015; Teanby 2015). In this work, we calculated the seismic efficiency in meter-size impacts on Mars to be different for bedrock (order of 10^-3) and porous materials (order of 10^-5).