The nature of strong martian crustal field sources is investigated by mapping and modeling of Mars Global Surveyor magnetometer data near Apollinaris Patera, a previously proposed volcanic source, supplemented by large-scale correlative studies. Regional mapping yields evidence for positive correlations of orbital anomalies with both Apollinaris Patera and Lucus Planum, a nearby probable extrusive pyroclastic flow deposit that is mapped as part of the Medusae Fossae Formation. Iterative forward modeling of the Apollinaris Patera magnetic anomaly assuming a source model consisting of one or more uniformly magnetized near-surface disks indicates that the source is centered approximately on the construct with a scale size several times larger and comparable to that of the Apollinaris Patera free-air gravity anomaly. A significantly lower rms deviation is obtained using a two-disk model that favors a concentration of magnetization near the construct itself. Estimates for the dipole moment per unit area of the Lucus Planum source together with maximum thicknesses of ∼3km based on topographic and radar sounding data lead to an estimated minimum magnetization intensity of ∼50A/m within the pyroclastic deposits. Intensities of this magnitude are similar to those obtained experimentally for Fe-rich Mars analog basalts that cooled in an oxidizing (high fO2) environment in the presence of a strong (⩾10μT) surface field. Further evidence for the need for an oxidizing environment is provided by a broad spatial correlation of the locations of phyllosilicate exposures identified to date using Mars Express OMEGA data with areas containing strong crustal magnetic fields and valley networks in the Noachian-aged southern highlands. This indicates that the presence of liquid water, which is a major crustal oxidant, was an important factor in the formation of strong magnetic sources. The evidence discussed here for magnetic sources associated with relatively young volcanic units suggests that a martian dynamo existed during the late Noachian/early Hesperian, after the last major basin-forming impacts and the formation of the northern lowlands.