We present a kinetic model for the interaction of electrons precipitating along magnetic field lines into Mars' atmosphere and develop a technique for detecting crustal magnetic fields, which act as magnetic mirrors, reflecting some of the incident electrons back to spacecraft altitudes. We present an initial map covering 20% of the planet, which shows the topology of magnetic sources along the dichotomy boundary and reveals new magnetic sources in the northern lowlands, implying the existence of preserved Noachian crust beneath at least some regions of the apparently young plains.