178 H. F. REID GEOMETRY OF FAULTS 



it is not strictly accurate, it will not in general introduce any material 

 error. A long fault is apt to have very different strikes in different 

 parts of its course; we can then apply the methods here described to 

 small parts of the fault separately, and we can determine, not only the 

 similarities, but also the differences, of the movements in various parts 

 of the fault. It is quite possible for a fault surface to be curved, even 

 with parallel displacements, provided it is so shaped that one side can 

 slide on the other along the shift without distortion; the surface will be 

 cylindrical, and the contours on the surface will be similar curves all 

 parallel to each other. "We can apply the methods here described to this 

 case, but we must draw the contours of the fault surface instead of merely 

 using the trace and the dip. 



Plastic distortions may change the form of the fault and other sur- 

 faces concerned during the shift or afterwards. It would then be ■ an 

 interesting problem of structural geology to determine, by a consideration 

 of the possible movements of nearly rigid blocks and by a consideration 

 of the forms of the surfaces and the distortions observed, what parts of 

 the displacements were due to plastic movements and what parts to 

 simple shifts on the fault. In some cases an approximate solution could 

 certainly be obtained, though in others it might be impossible. We shall 

 not treat of these complex movements, except in certain very simple 

 cases, but shall consider that the displaced rock, at least over small areas, 

 has moved without distortion, like a rigid body. The comparison of the 

 movements thus determined at different parts of the fault would go far 

 to reveal the plastic distortions. 



Parallel Displacements 

 plane strata 



Data required for determination of shift— 7 The complete determina- 

 tion of the shift which has occurred at a fault requires us to find the 

 horizontal direction of the movement, its inclination to the horizontal 

 plane, and its amount. 4 The determination of these three quantities 

 requires three different measures ; the nature of these measures will differ 

 in different cases, but they must be independent. For instance, the dis- 

 placements of two strata, or of two parallel dikes, or of a stratum and a 

 sill, would only yield one independent measure; but the displacements 

 of a stratum and a dike which have the same strike, but different dips, 



4 We may. if we prefer, determine the components of the total movement in three 

 directions at right angles to each other. 



