This paper presents a 50-degree and order spherical harmonic model of the magnetic field of Mars derived at 120-km altitude using the three orthogonal components of the vector magnetic field data acquired by the Mars Global Surveyor within the 80-to 200-km-altitude range. The downward continued vector magnetic field components to the surface of Mars delineate details of the Martian magnetic field. The strong magnetic anomalies in the southern hemisphere do not show compelling evidence for magnetic lineations similar to those associated with the seafloor spreading on Earth. The anomalies are more or less equidimensional. The magnetic signatures surrounding the impact basins Hellas, Argyre, and Isidis show that the prominent magnetic anomalies are older than the impact events. An average magnetization of ~2 A/m is estimated for the upper crust surrounding Hellas basin. Four isolated magnetic anomalies are modeled by vertical prisms with circular cross sections of 170- to 190-km radius and 20- to 30-km thickness. The magnetization of the model prisms is 5 A/m more than that of the surroundings. ¿ 2001 American Geophysical Union