Comment on ‘Deformation of the NE Basin and Range Province: the response of the lithosphere to the Yellowstone plume?’ by R. Westaway

Abstract

(i) Westaway assumes that a general horizontal deformation in the crustal layer, accommodated on a single set of parallel faults with parallel slip vectors, can closely correspond with that in an underlying fluid which is deforming with a horizontal uniaxial strain rate tensor. This is incorrect. The bulk horizontal deformation in the brittle crust, accommodated on a single set of straight and parallel faults with parallel slip vectors, always has a biaxial strain rate tensor, except in the special case when there is no strike-slip component on the faults. This is easy to show, because such deformation can always be divided into a component of simple shear parallel to the faults, with a biaxial strain rate tensor, uniaxial extension or compression perpendicular to the faults, and a rigid-body rotation about a vertical axis of the whole fault system. Therefore, except when there is no strike-slip motion on the faults, the bulk deformation must have a biaxial strain rate tensor. Unfortunately, Westaway’s theory specifically deals with the case when there is strike-slip motion. (ii) Westaway derives a general relation between the orientation of fault slip vectors and the asymmetrical component of the velocity gradient tensor [equation (2.19) in Westaway (1989)]. This is incorrect. The relative motion between parallel fault blocks can only give information about internal changes in shape, which are described by the strain rate tensor (symmetrical component of velocity gradient tensor). Information about rotation of the whole fault system about a vertical axis is contained in the asymmetrical part of the velocity gradient tensor and can only be determined relative to an external frame of reference. Jackson & McKenzie (1988) have dealt with this important point in some detail. However, if it is assumed that a material line in a particular direction in the deforming mne does not rotate with respect to some frame of reference, then it is possible to determine the asymmetrical component in this frame of reference. Thus, McKenzie & Jackson (1983) assumed that a line parallel to the length of the zone of deformation did not rotate relative to the margins, and calculated the asymmetrical component of the velocity gradient tensor in this frame of reference. Westaway makes no such assumptions. His relation between the vorticity and extensional strain rate is invalid in all frames of reference except one where the vorticity is zero. In this case, his relation predicts correctly that there will be no strike-slip component on the faults. (iii) Westaway asserts that a set of long fault blocks will always rotate about vertical axes at a rate equal to half the vorticity of the velocity gradient tensor of the underlying continuously deforming fluid. This is incorrect. There are always two possible cases when the motions of long straight fault blocks will correspond closely with those of an underlying fluid deforming with constant velocity gradients: (a) when the faults are parallel to the length of a zone of deformation with no velocity gradients along its length, relative to the margins, in which case the fault blocks will not rotate about vertical axes but translate relative to the margins of the zone; and (b) when the faults are perpendicular to the azimuth of the relative velocity vectors in the deforming zone, in which case the blocks will translate relative to h c h other and rotate about vertical axes relative to the margins of the zone at a rate equal to the vorticity of the velocity gradient tensor.