186 H. F. REID GEOMETRY OF FAULTS 



Not infrequently the strata on one or both sides of the fault-plane 

 have been bent up in a direction opposite to their displacements. In 

 finding the displacements we must use the position of the strata outside 

 this distorted portion; the shift thus determined refers to the relative 

 displacement of the rock in general on opposite sides of the fault and not 

 to the actual slip on the fault-plane, which may be somewhat less. 



Case V ': Given, the total shift, in amount, direction, and inclination; 

 to determine the displacement of any plane, such as a stratum or vein. 

 Let ff r , figure 10, be the projection of the shift, its inclination being 8', 

 and /'being the projection of the higher point; the difference of level of 

 these two ends of the shift is fg. Suppose a plane is given by its trace, 

 T, and by its dip, 8. A point of this trace, which was originally at d, 

 has been moved to the original of d', a distance equal to and parallel 

 with the original of ff', the height of the original of d! above d equals fg. 

 The displaced part of the stratum passes through the original of d' and 

 dips to the north at an angle 8. It will reach the horizontal plane at a 

 point, T', found by drawing d' T' at right angles to the trace T, and 

 erecting d' g' = fg at right angles to d' V ', and at g' laying off the angle 

 90° — 8; g' T' meets d' T' on the trace of the displaced plane; for if the 

 triangle d' g' T' be rotated about d' T' until g' is vertically above d\ 

 the line g' T' will lie in the dip of the displaced plane and will cut the' 

 horizontal plane at T'. The trace, T', can then be drawn parallel with 

 T. If the trace, F, of the fault is given, we can find the fault-dip, 8", 

 and consequently the projections he and h' e' of the fault intersections 

 with the strata T and T'j the stratum T will not extend to the right of 

 he, nor T' to the left of h' e' . 



FOLDED OR CONTORTED STRATA 



The changes in the shape of the strata prevent us in this case from 

 using the very simple construction given above, and if the fault should 

 be a strike-fault it is in general necessary to make a pretty complete geo- 

 logical section in order to compare the two sides and determine the move- 

 ment which has taken place at right angles to the fault-strike. The 

 movement parallel with the fault-strike would have to be determined as 

 in the former case, by the dislocation of a dike or of some other plane. 

 In the case of diagonal or dip-faults our problem is somewhat easier. 

 The crest of an anticline or the trough of a syncline furnishes a line 

 which has been dislocated by the fault, equivalent, in our former case, to 



