A graphical–algebraic method for analysing shear zone displacements from observations on arbitrarily oriented outcrop surfaces

We present a practical graphical–algebraic method that enables one to achieve the true displacement and shape of deformed geological markers in fault or shear zones as observed on arbitrarily oriented outcrop surfaces. We use as our natural example deformed quartz veins that have been sheared across brittle–ductile faults in the Southern Alps of New Zealand. The technique is based on the assumption that simple shear has dominated the shear zone formation. For input data we require the strikes and dips of the outcrop surfaces, the offset markers, and the shear zones as well as the pitch of the simple shear vector in the plane of the shear zone. The paper develops a set of algebraic and graphical operations that allow one to convert photographs of faulted or sheared planar markers observed on an arbitrary outcrop surface into an equivalent view that is coincident with the movement (m) plane of the fault or shear zone. This view displays the true displacement of the offset marker and delineates its deformed shape as seen in a section that is parallel to the slip vector.