Gravity gradiometry and magnetometry methods are powerful noninvasive techniques for near-surface detection problems. Efficient integration of data from these techniques decreases the degree of nonuniqueness in geophysical interpretations. Deformation analysis is a powerful tool for comparison of two fields, which aids in this respect. We propose a fully quantitative approach, which uses the generalized theory of deformation for the geometric comparison of gravimetric and magnetic fields. The resulting deformation maps delineate regions where Poisson's relation is violated between the two data sets and thus discriminate between air-filled cavities and other similar low-density/susceptibility geophysical sources. We present a practical corresponding algorithm that is robust in the sense that no prior knowledge of the physical properties of the subsurface is needed.