HOW BIG IS THE MARTIAN CORE? IF AS IS LIKELY THE CORE IS LIQUID WHAT QUANTITY OF LIGHT ELEMENTS MUST BE PRESENT TO HAVE INHIBITED CORE SOLIDIFICATION FOR BILLIONS OF YEARS? DOES MARS'S DEEPER MANTLE RESEMBLE EARTH'S MANTLE TRANSITION ZONE? IS THE EARTH UNIQUE AS A TERRESTRIAL PLANET OR DOES IT SHARE MUCH IN COMMON WITH OUR SMALLER PLANETARY SIBLING? EARTH-FOCUSED SEISMOLOGY HAS USED TWO COMPLEMENTARY TECHNIQUES BODY WAVES AND NORMAL MODES TO PROBE THE DEEPER INTERIOR OF OUR PLANET; EVEN WITHOUT MODERN SEISMIC PROCESSING REASONABLE MODELS OF EARTH'S STRUCTURE WERE DEVELOPED USING BODY WAVE RECORDS. LIKEWISE NOISIER LUNAR SEISMIC DATA HAVE BEEN LEVERAGED TO REVEAL THE SMALL LUNAR CORE AND PROPERTIES OF THE LUNAR DEEP MANTLE. THIS PROPOSAL HAS THE FOLLOWING AIMS: TO PREDICT BODY WAVE TRAVEL TIMES SEISMIC WAVEFORMS AND NORMAL MODE OSCILLATION CENTER FREQUENCIES FOR NEW AND EXISTING MINERALOGICALLY REASONABLE MODELS OF MARS'S INTERIOR AND COMPARE THEM TO VERY BROADBAND SEISMIC DATA FROM THE INSIGHT MISSION. IN THE EARTH WE EXPECT THAT MOST OF THE LIQUID OUTER CORE CAN BE DESCRIBED AS WELL-MIXED AND ADIABATIC. ON MARS INITIAL MODELS WILL ASSUME THAT THESE EXPECTATIONS HOLD TRUE ACROSS THE ENTIRE MARTIAN CORE WITH PARAMETERS OF AN ISENTROPIC EQUATION OF STATE (EOS) USED TO SPECIFY THE SEISMIC VELOCITY AND DENSITY. A RANGE OF EOS PARAMETERS WILL BE USED INFORMED BY PUBLISHED ESTIMATES. CORE MODELS WITH VARYING FRACTIONS OF LIGHT ELEMENTS WILL BE CONSIDERED. THUS MINERAL PHYSICS EOSS CAN PROVIDE INFORMATION TO CREATE REASONABLE MODELS OF DENSITY AND VELOCITY IN MARS'S CORE. MORE COMPLEX CORE MODELS CAN THEN BE PRESCRIBED BY ALLOWING DEVIATIONS FROM THE SIMPLER MODELS WHICH CORRESPOND TO FOR EXAMPLE THE POSSIBLE PRESENCE OF IRON "SNOW" IN THE CORE. MANTLE STRUCTURE CAN ALSO BE REPRESENTED USING REASONABLE MINERALOGY-BASED MODELS. PRELIMINARY MODELS FOR THE MANTLE CAN BE TAKEN OR ADAPTED FROM THOSE CURRENTLY IN THE LITERATURE. UPDATING MODELS OF MARS'S MANTLE MINERALOGY WILL ALSO PERMIT THE EXPLORATION OF DIFFERENT THERMAL PROFILES OR AREOTHERMS OF MARS. AS ESTIMATES OF MARS'S SHALLOWER STRUCTURE EVOLVE THEY CAN BE TAKEN INTO ACCOUNT TO BUILD MORE REASONABLE MODELS OF MARS'S DEEP INTERIOR CONSISTENT WITH BASIC GEOPHYSICAL OBSERVATIONS. BODY WAVE TRAVEL TIMES WILL BE CALCULATED USING RAY THEORY FOR A RANGE OF THESE 1D SEISMIC MODELS. WAVEFORM SIMULATIONS FOR SELECTED SEISMIC MODELS WILL BE CARRIED OUT USING AXISEM. NORMAL MODE CENTER FREQUENCY CALCULATIONS WILL BE CARRIED OUT USING AN ADAPTED VERSION OF THE MINEOS NORMAL MODE CODE. ALL THESE PREDICTIONS WILL BE COMPARED WITH OBSERVED SIGNALS FROM MARS. BODY WAVES WHICH INTERACT WITH THE DEEPER MARTIAN MANTLE WILL BE USED TO ASSESS WHICH MODELS OF THE MANTLE ARE APPROPRIATE; THIS WILL ALLOW THE REFINEMENT OF POSSIBLE THERMAL AND CORE MODELS. WAVES WHICH REFLECT FROM THE CORE OR TRAVEL THROUGH IT WILL PROVIDE STRONGER CONSTRAINTS. NORMAL MODES ARE LIKELY TO BE CHALLENGING TO OBSERVE HOWEVER MODES WITH FREQUENCIES ABOVE 5MHZ ARE MORE LIKELY TO BE OBSERVABLE THAN THOSE BELOW THAT THRESHOLD AND A NUMBER OF MODES ABOVE THIS FREQUENCY HAVE SENSITIVITY TO THE DEEP INTERIOR OF MARS. THIS PROPOSAL FITS INTO INSIGHT'S PRIMARY SCIENCE GOAL A AND WILL COMBINE TWO SEISMO-LOGICAL TECHNIQUES WITH MINERAL PHYSICS TO FURTHER OUR UNDERSTANDING OF THE CORE MANTLE AND THERMAL PROPERTIES OF MARS; IT CORRESPONDS TO THE NRA'S "SPECIAL INVESTIGATION" CRITERIA 7 AND 8.