Abstract - The maximum displacement and the dimensions of single faults are systematically related and the variation in displacement, from a maximum at the centre of a fault to zero at an elliptical tip-line loop, is described by a simple theoretically described expression. These relationships are used to examine the theoretical ranges and distributions of rates of change of displacements on fault surfaces. The dimensions and maximum displacement of a fault can be estimated from a limited number of displacement gradient measurements. Estimates are further constrained by a knowledge of the effective shear modulus of the rocks containing a fault. An understanding of displacement gradients can be applied to problems commonly encountered in mining operations and in the interpretation and use of seismic reflection data, in addition to field problems.
A comparison of theoretical displacement gradients with measured displacement gradients from British Coalfield faults shows that (i) fault surface ellipticities are between 1.5 and 2.5 and (ii) gross displacement gradients, expressed as the ration of maximum displacement/long axis radius of the fault ellipse, range from 0.02 to 0.002. The measured displacement gradients indicate that the shear moduli of the faulted rocks range from 3 to 11 GPa, which is within the known range for Coal Measure rocks.
Displacement gradients along an array of fault segments are similar
to those of single faults. For analysis of displacement gradients it is
necessary to sum the discontinuous and continuous components of displacement;
in extreme cases all the displacement may be accommodated by continuous
deformation.
Journal of Structural Geology 11, 307-316, 1989.