Simulating the Seismic Signal from Impacts on Asteroids
Authors: Luther Robert , Wünnemann Kai 
Published: September 2022

&lt;p&gt;&lt;strong&gt;1. Introduction&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Seismic waves can be applied to study the interior of a body, as was done during the Apollo missions on the Moon [e.g. 1] or during the InSight mission on Mars [e.g. 2]. Recent numerical simulations using the iSALE shock physics code have been applied to study seismic signals in the frame of both missions, and for signals in samples from laboratory experiments [3-6].&lt;/p&gt;
&lt;p&gt;In the NEO-MAPP project (Near Earth Object Modelling and Payloads for Protection) by the EC, Horizon 2020, a potential lander with a seismometer is discussed to study the characteristics of the interior of an asteroid (i.e. layering, mechanical properties, size of heterogeneities in the subsurface). Although possible natural sources for seismic waves on an asteroids exist (e.g. tidal forces, meteoroid impacts), we focus on studying an artificial impact of a spacecraft, which is better constrained and plannable.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;2. Method&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;We use the iSALE shock physics code [7-9] to conduct a systematic parameter study by simulating different impact scenarios. iSALE enables to describe the resistance of rocks against deformation and the thermodynamic response to compression by different material models. We use a Lundborg rheology with a coefficient of friction of 0.77 and a cohesion of 1.4 kPa. We vary target porosities between 10 - 50%. We use the ANEOS for basalt. These material properties reflect the strength of regolith simulant, which was used for laboratory impact experiments [e.g. 10]. iSALE was validated against these experiments recently [11].&lt;/p&gt;
&lt;p&gt;Our study on impact-induced seismicity on asteroids focuses on DART-scale kinetic impactor scenarios and we analyse the seismic signal generated by a 600 kg impactor at 6 km/s.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;3. Results&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;We observe a decay of the peak pressure (i.e. P-wave in the elastic regime) with distance for targets with increasing porosity from 10 &amp;#8211; 50% (Figure 1). Due to the energy consumption by pore compaction, the decay of pressure occurs closer to the impact point for a more porous target. We quantify the attenuation of the signal with distance &lt;em&gt;r&lt;/em&gt; as shown by [3] with the help of the quality factor &lt;em&gt;Q&lt;/em&gt;, which describes the decay of the amplitude &lt;em&gt;A&lt;/em&gt; of the seismic wave as:&lt;/p&gt;
&lt;p&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; A(r) = A&lt;sub&gt;0&lt;/sub&gt; e&lt;sup&gt; -b r&lt;/sup&gt;&amp;#160; ,&lt;/p&gt;
&lt;p&gt;where &lt;em&gt;b&lt;/em&gt; is a material parameter, which relates the quality factor to the length &lt;em&gt;&amp;#955;&lt;/em&gt; of the pressure pulse as:&lt;/p&gt;
&lt;p&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; &amp;#160; b = &amp;#960; / ( Q &amp;#955; ).&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Figure 1:&lt;/strong&gt; Peak pressure decay with distance for targets with a cohesion of 1.4 kPa.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;We observe a slight increase of the quality factor from 1.8 &amp;#8211; 3.8 with increasing porosity (Figure 2).&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Figure 2:&lt;/strong&gt; Quality factors for granular homogeneous targets, and for competent rocks [3,12].&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;4. Discussion&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Our results are in line with expectations that seismic waves on asteroidal targets, like the granular regolith materials that we simulated in this study, attenuate faster than more consolidated materials. Comparing our results with simulations assuming competent rock as target [3,12] shows that our determined quality factors are smaller by an order of magnitude than the numerically and experimentally derived values for quartzite, sandstone and tuff, which vary in porosity from 0 &amp;#8211; 42%. The dampening of the seismic signal in a granular target is more efficient. However, this also implies that the seismic behaviour on monolithic asteroids is different to the one on rubble pile asteroids.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;5. Outlook&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;We aim at analysing further materials. More specifically, we plan to expand our study to heterogeneous targets, where we resolve boulders explicitly. We expect that the presence of boulders causes more complex wave patterns in the interior, depending on the presence or absence of large scale voids and boulders.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Acknowledgements&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;We gratefully acknowledge the developers of iSALE (www.isale-code.de). We acknowledge the funding from the European Union&amp;#8217;s Horizon 2020 research and innovation program under grant agreement No. 870377 (NEO-MAPP).&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;
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