Determination of position-gradient tensor from strain measurements and its implications for the displacement across a shear zone

A method is proposed for determination of the position-gradient tensor from conventional strain measurements. The position-gradient tensor can be multiplicatively decomposed into two components, left stretch and rotation tensors. The former is readily supplied by field strain data whereas the latter is generally unknown in nature. In order to determine the position-gradient tensor using strain data, it is assumed that structures within a shear zone are symmetric about the plane common to the transport direction and the pole to the shear zone, or alternatively, that the shear strain in the direction parallel to the pole to the shear zone on the plane normal to the transport direction in a parallel-sided shear zone is negligible. With these assumptions, the position-gradient tensor is fully determined from the attitude and principal ratios of the strain ellipsoid determined from field data. This method has been applied to the strain data from deformed fragments in a succession of Late Triassic volcanic breccias abutting a large strike-slip shear zone in north-central British Columbia. The resulting position-gradient tensor is then used to constrain the displacement across the shear zone, suggesting 39% shortening normal to, and dextral displacement of about 1700 m along, the shear zone.