180 H. F. EEID GEOMETRY OF FAULTS 



c' V ; therefore we do not know whether the fault is normal or reversed, 

 nor can we tell whether a horizontal straight line at right angles to the 

 fault-strike has been lengthened or shortened. If we are fortunate 

 enough to find the fault-plane and can determine its dip, we can then 

 determine the dip-shift, for this will be represented by the line be- 

 tween the planes of the disrupted stratum and parallel with the dip 

 of the fault. For example, the dip-shift will be be, which equals 

 as' /cos (8 + h). When the fault and the strata dip to opposite sides of 

 the vertical (the fault is then represented by b' c'), we may use the same 

 expression for the dip-shift, but we must make h negative. The heave, 

 or horizontal throw, is given by the line cd^bc sin h = as' sin h/cos 

 (8 + /i). The vertical throw, bd, equals be cosh = as' cos h/ 'cos 

 (8 + h). We evidently have all the elements of the displacement in the 

 plane at right angles to the strata and to the fault. 



If the movement has a component parallel with the fault-strike, we 

 must use the system of projection given above to represent the observa- 

 tions. As the procedure in this case and in the case of a diagonal fault 

 are exactly similar, we shall take the latter as more general. 



Diagonal faults. — Case I : Given, the traces and the dip of a disrupted 

 stratum. Let us suppose that we have determined the offset between 

 T and t, the traces of a disrupted stratum, figure 7. If no other meas- 

 ures have been made except the dip, we can only determine the strati- 

 graphic throw, which can be found from a vertical section at right angles 

 to the traces of the stratum, as in figure 5. It can also be found in our 

 system of projection as follows : Draw the traces t, f, figure 3, and at t 

 lay off the angle 8, representing the dip, and at V lay off the angld 

 8" = 90° — 8, which will represent the inclination of the perpendicular 

 to the two planes. The angle tcV will be a right angle, ct' will be the 

 amount of the stratigraphic throw, bt' will be its horizontal projection, 

 and 8" will be its inclination. 



Given, in addition, the trace and dip of the fault-plane. If, in addi- 

 tion, we are able to locate the fault-plane and to determine its dip, we 

 can, by the method already given, determine the projection, ed, of the 

 line of intersection of the fault-plane and the stratum, figure 7. A 

 parallel line through e' will be the projection of the intersection of the 

 fault-plane and the displaced part of the stratum. If we have no other 

 observations we can not decide whether the fault is normal or reversed; 

 all we can say is that some point on the original of ed has been moved to 

 some point on the original of e' d'. These lines are parallel and they lie 

 in the fault-plane; one lies in one part of the disrupted stratum and the 



