188 H. F. REID GEOMETRY OF FAULTS 



mine the rotations of lines in the plane of rotation, and see if these rota- 

 tions are equal in different parts of the fault. If the fault surface is 

 nearly plane, its intersections with the strata afford excellent lines for 

 determining the rotations. 



Small rotations, of limited extension, and with the axes at right angles 

 to the fault surface, apparently occur in all ordinary faults. If we fol- 

 low along a fault we finally come to a point where it dies out, and we 

 find in different parts of its course that the amount of the vertical throw 

 has varied. This, of course, requires a certain amount of bending of the 

 strata, and this bending constitutes a rotation of that part. The rotation 

 is not the same at different parts of the fault's course, and may even vary 

 in its direction, in which case we should have gentle folds whose axes are 

 at right angles to the fault-strike. The rotation, of course, is greatest 

 where the rate of variation of the vertical throw is greatest, and this is 

 very apt to occur near the ends of the fault. If the strata are nearly 

 horizontal, a slight rotation will make a great difference in the direction 

 of the strike, and thus the strata on opposite sides of the fault will strike 

 at each other. If, however, the strata are highly inclined, the variation 

 in the strike will be extremely small. Where the rotation is small, the 

 error introduced by treating the displacement as a simple translation, 

 without considering the rotation, would be unimportant. 



Where the rotation is appreciable, it is best to suppose the strata 

 rotated back through an angle until they become parallel on opposite 

 sides of the fault. We can then determine the displacements by the 

 methods already given ; and we must add, as a part of the description of 

 the fault, the amount of rotation which has taken place. We must decide 

 by general conditions, such as the relation of the strike and dip of the 

 strata to the same quantities beyond the ends of the fault, whether one or 

 both sides have been rotated. As this is a case of rotation and transla- 

 tion, it might be treated by the method of the next section; but the 

 method just given is simpler and might be preferable, where the main 

 part of the displacement is a translation accompanied by rotations un- 

 evenly distributed in the various parts of the mass. 



When the axis does not intersect the fault surface, the fault usually 

 occurs only on one side of the axis, and on the other the rocks yield by 

 plastic bending. Movements of this kind apparently take place when 

 large blocks, like the Sierra Nevada mountains, for instance, are tilted 

 up. A section of the fault surface in a vertical plane at right angles to 

 the axis would be circular, but its ground plan might have almost any 

 shape, dependent upon the distribution of the forces causing the move- 



