Pulsating oblate and prolate three-dimensional strains

The progressive ductile deformation of competent spherical inclusions is modeled analytically. Results of this study may help to understand better the limitations connected to geological field methods using competent inclusions for strain analyses. Parameters studied and quantified here are the strain magnitude, the progressive change in inclusion shape, the orientation of the finite strain axes, the frequency of pulsation, and the coupling between the strain ellipticity and viscosity contrast. Competent inclusions develop pulsating apparent strains if the host material is subjected to a component of simple shear and provided time or strain rate is sufficient to complete the strain cycle. The disparity between the strain magnitude inferred from competent viscous inclusions and that undergone by the host rock, increases for larger viscosity between them. The pulsation of the inclusion may suggest zero strain after a strain cycle has been completed, even though strain in the host rock is extremely large. The inclusion will develop pulsating oblate strains if a shortening rate is superposed normal to the plane of pulsation. Conversely, pulsating prolate strains occur if an extension rate is superposed instead of shortening. Stretching lineations outlined by deformed competent inclusions within shear zones beneath collapsing nappe sheets may even point perpendicular to the direction of nappe transport. This finding offers an explanation for the occurrence of mutually perpendicular pebble elongations in nearby locations within the Bygdin conglomerate beneath the Jotun nappe, Norwegian Caledonides.