The crustal remanent magnetic field of Mars remains enigmatic in many respects. Its heterogeneous surface distribution points to a complex history of formation and modification, and has been resistant to attempts at identifying magnetic paleopoles and constraining the geologic origin of crustal sources. We use a multitaper technique to quantify the spatial diversity of the field via the localized magnetic power spectrum, which allows us to isolate more weakly magnetized regions and characterize them spectrally for the first time. We find clear geographical differences in spectral properties and parameterize them in terms of source strengths and equivalent-layer decorrelation depths. These depths to the base of the magnetic layer in our model correlate with independent crustal-thickness estimates. The correspondence indicates that a significant fraction of the martian crustal column may contribute to the observed field, as would be consistent with an intrusive magmatic origin. We identify several anomalous regions, and propose geophysical mechanisms for generating their spectral signatures.