The impact of vertical-axis rotations on shortening estimates

The total amount of deformation between two converging bodies is described by the three components of the displacement field: translation, rotation, and strain. Translations along faults and folding strain are the most common elements of the displacement field incorporated into estimates of tectonic shortening across orogenic systems. Determinations of vertical-axis rotations through paleomagnetic and structural analyses are keys for deciphering the rotational component of shortening within an orogenic system, and they can have a substantial effect on the amount of tectonic shortening in such systems. Accommodation structures observed in orogenic systems are typically noncoaxial and/or noncylindrical geometries (e.g., oblique and lateral ramps, superposed folding). These structures suggest that vertical-axis rotations have taken place, can aid in determining the relative timing of rotation with respect to translation, and may help constrain the location of the rotation axis. In this paper, we define the components of the total displacement field, describe the diagnostic and suggestive features associated with vertical-axis rotations, and apply trigonometric map-view calculations to estimate the amount of shortening contributed by such rotations. An error function relating shortening with vertical-axis rotation has been calculated and predicts values up to 50% for a 60° rotation if the rotation is not taken into account. Finally, we apply our approach to the Wyoming salient and show that previous estimates of shortening there may contain up to 14% error.