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The InSight mission collected four years of seismic data from Mars, providing unprecedented data on the planets interior. Two seismic events one marsquake and one meteorite impact took place on the opposite side of Mars to InSights broadband seismometer 1. These two far-side events were initially located using mantle-transiting PP and SS waves, but we demonstrate that their waveforms contain additional seismic arrivals which are sensitive to the properties of the Martian core. Using multiple seismic methods, we obtain SKS differential travel times for S0976a, a distant marsquake, and S1000a, a distant impact. SKS travels through Mars core as compressional waves and is therefore sensitive to its elastic properties. We use these differential travel times to build the first seismically informed models of Mars core 2. The core velocity of Mars is low: 4.9-5.0 km/s at the CMB. We use our seismic results to estimate the fraction of light elements in Mars core, finding a high fraction of sulphur is needed, together with lesser amounts of oxygen, carbon and hydrogen. In addition to the SKS signals observed, the waveforms from S1000a contain evidence for a seismic wave which diffracts along a molten silicate layer at the base of the Martian mantle and also reflects from the core-mantle boundary. The presence of a basal silicate molten layer has implications for the areotherm, and could reduce both estimates of metallic cores radius and its fraction of light elements 3. The SKS detections reported provide information about the physical properties of the liquid core of Mars. A solid inner core at the centre of Mars is unlikely; we assess what structures inside the Martian core can be excluded based on existing data and models. 1 Horleston et al., 2022. Seism. Rec., 2(2), 88-99 2 Irving et al., 2023. PNAS, 120, e2217090120 3 Samuel et al., 2023, Nature, 622, 712717
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