Quantitative Sensitivity Assessment of Martian Geodetic Parameters to Interior Model: Implications for Joint Inversion

Abstract Geodetic parameters are widely used in joint inversion to infer the interior structure of planets. However, joint inversion often involves complex parameterizations that may be computationally costly. In this study, we quantitatively evaluated the local and global sensitivities of key Martian geodetic parameters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">M</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>I</mml:mi> <mml:mo stretchy="true">/</mml:mo> <mml:mrow> <mml:mi>M</mml:mi> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Q</mml:mi> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> </mml:math> ) to structural parameters, with the aim of providing parameter trade-off references for joint inversion parameterizations. We constructed a five-layer interior model of Mars and introduced derivative-based local sensitivity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mi>l</mml:mi> </mml:math> ) as well as Soboĺ’s global sensitivity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mi>g</mml:mi> </mml:math> ) to study quantitative sensitivities. Our results show that geodetic parameters are sensitive to the outer core, basal molten layer (BML), and mantle of Mars, but relatively insensitive to an inner core and crust. The total mass and mean moment of inertia are primarily dominated by radius and density of the outer core and mantle, whereas tidal-related geodetic parameters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Q</mml:mi> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> </mml:math> ) are mainly influenced by outer radius, S-wave velocity, and viscosity of the BML and mantle. We conclude that highly sensitive structural parameters should adopt smaller iterative steps and refine their prior ranges, while insensitive parameters may be fixed as constants based on the research objective. Our parameter trade-off strategy can accelerate computation and improve the robustness of interior models.