Determining the Principal Azimuths of Valles Marineris: A Comparative Analysis of Bezier Spline and Geographic Information System Techniques

Valles Marineris (VM), the most prominent example of a Martian Valley Network, has been extensively studied for over 50 years, yet no detailed examination of the principal azimuths of the system exists. To address this, two methods are presented to precisely calculate the principal azimuths, a Bezier Spline analysis and a Geographic Information System (GIS) technique. The medial axis of the main canyon of VM was determined analytically from cubic polynomial splines fitted to 93 coordinate points along both north and south edges of the canyon. These splines were optimized and medial axis points were calculated through numerical techniques that ensured orthogonality between the tangents of each spline and their connecting normal lines. 1,000 medial axis points were extracted and various regression models constructed, including fitting to sinusoidal and cubic polynomial curves, achieving accuracies with R2 values of 0.98 and 0.99, respectively. Principal azimuths were obtained using the sinusoidal equation with the slope of the tangent at any point x simply determined by the derivative of the curve’s equation. This analytic approach was cross-validated by a GIS method (using QGIS software), where a vector medial axis was obtained which produced principal azimuths that agreed with values from the analytic study with a correlation coefficient of 1.00 and a p value of 6.43e-65. The findings demonstrate that an azimuthal framework can be rigorously constructed as a potential standard reference in VM geoscience, replacing less precise and ambiguous compass bearings with the accurate azimuths necessary for high-resolution spatial analysis for future investigations.