Abstract Global geophysical observations constrain all theories of terrestrial dynamics. We jointly interpret EGM2008 gravity, RET2014 topography and the Global Centroid Moment Tensor database from a structural point of view. We hypothesize that lateral variations of gravity and topography reflect the scale-dependent competence of rocks. We compare the spectral and spatial characteristics of the observed fields with structural predictions from the mechanics of differential grade-2 (DG-2) materials. The results indicate that these viscoelastic materials are a powerful tool for exploring dynamic processes in the Earth. We demonstrate that the known spectral range of Earth's gravity and topography can be explained by the folding, shear banding, faulting and differentiation of the crust, lithosphere and mantle. We show that the low-amplitude long-wavelength bias apparent in the disturbance field can be explained by perturbations to Earth's overall ellipsoidal shape, induced by internal slab loading of the mantle. We find by examining the directional isotropy of the data that the zonal energy in Earth's gravity disturbance is maximized about an axis coincident with the shape-perturbation minimum. The symmetry of tectonic features about this axis, extending from eastern Borneo to Brazil, and its coincidence with the equator suggest the coupling of current plate motions to true polar wander.