Ripple arrays are formed under certain growth conditions upon the surface of epitaxial Si1-xGex on Si, and their nature is examined in detail using transmission electron microscopy, atomic force microscopy, and x-ray diffraction measurements. The driving force for ripple formation on the strained layers is the lowering of the system free energy by partial elastic strain relief due to oscillatory lattice plane distortion. We present the first direct measurement of the lattice distortion and demonstrate that this corresponds to near-complete relaxation in the ripple peaks in a direction normal to the ripple rows. The additional compressive lattice plane distortion present at ripple troughs is also estimated and is likely to promote misfit dislocation nucleation. Surface faceting can reduce the energy of the configuration, allowing troughs to deepen and minimize the dislocation nucleation barrier. The way in which the ripple strain fluctuations couple to already formed underlying misfit dislocations (often pinned bunches) is also demonstrated.