We use numerical modeling with a full-system Stokes solver to elucidate the effects of nonlinear rheology and strain-induced anisotropy on ice flow at ice divides. We find that anisotropic rheology profoundly affects the shape of both isochrone layering and surface topography. Anisotropic effects cause the formation of a downward curving fold, i.e., a syncline, in isochrones in the lower central area beneath the ice divide. When the resulting syncline is superimposed on the well-known Raymond anticline, a double-peaked Raymond bump is formed. Furthermore, to each side of the Raymond bump, flanking synclines are formed. In addition, anisotropic effects are found to give rise to a subtle concavity in the surface profile to both sides of the summit. The lower center syncline, the flanking synclines, and the near-summit surface concavity have all previously been observed in nature, but hitherto no explanation for the genesis of these features has been given. We compare modeling results with radiograms collected from Fuchs Ice Piedmont and Kealey Ice Rise, Antarctica. Good overall agreement is found. In particular, we are able to reproduce all observed qualitative features of surface geometry and internal layering by including, and only by including, the effects of induced nonlinear rheological anisotropy on flow. Rheological anisotropy has the potential to profoundly affect the age distribution with depth, and caution must be exercised when estimating age of ice from ice cores with an isotropic model. The occurrence of linear features parallel to the ridge of ice divides, often seen in satellite imagery, is indicative of long-term stability rather than signs of ongoing ice divide migration as previously suggested. Such ice divides are ideal locations for extracting ice cores.