The terracing operator works iteratively on gravity or magnetic data, using the sense of the measured field's local curvature, to produce a field comprised of uniform domains separated by abrupt domain boundaries. The result is crudely proportional to a physical-property function defined in one (profile case) or two (map case) horizontal dimensions. This result can be extended to a physical-property model if its behavior in the third (vertical) dimension is defined, either arbitrarily or on the basis of the local geologic situation. The terracing algorithm is computationally fast and appropriate to use with very large digital data sets. Where gravity and magnetic data are both available, terracing provides an effective means by which the two data sets can be compared directly. Results of the terracing operation somewhat resemble those of conventional susceptibility (or density) mapping. In contrast with conventional susceptibility mapping, however, the terraced function is a true step function, which cannot be depicted by means of contour lines. Magnetic or gravity fields calculated from the physical-property model do not, in general, produce an exact fit to the observed data. By intent, the terraced map is more closely analogous to a geologic map in that domains are separated by hard-edged domain boundaries and minor within-domain variation is neglected. The terracing operator was applied separately to aeromagnetic and gravity data from a 136 km X 123 km area in eastern Kansas. Results provide a reasonably good physical representation of both the gravity and the aeromagnetic data. Superposition of the results from the two data sets shows many areas of agreement that can be referenced to geologic features within the buried Precambrian crystalline basement. The emerging picture of basement geology is much better resolved than that obtained either from the scanty available drill data or from interpretation of the geophysical data by inspection.