Measurement of the thickness of formations.—When formations still lie in horizontal beds, we may sometimes learn their thickness directly either from the depth of borings to the underlying rock, or by measurements upon steep cañon walls. If the beds stand vertically, the matter is exceedingly simple, for in this case the thickness is the width of the outcrops of the formation between the beds which bound it upon either side. In the general case, in which the beds are neither horizontal nor vertical, the thickness must be obtained indirectly from the width of the exposures and the angle of the dip. The factor by which the exposure width must be multiplied is known as the sine of the dip angle ([Fig. 30]), which is given with sufficient accuracy for most purposes in the following table. It is obvious that in order to obtain the full thickness of a formation it is necessary to measure from the contact with the adjacent formation upon the one side to a similar contact with the nearest formation upon the other.
Natural Sines
| 0° | .00 | 35° | .57 | 70° | .94 | ||
| 5° | .09 | 40° | .64 | 75° | .97 | ||
| 10° | .17 | 45° | .71 | 80° | .98 | ||
| 15° | .26 | 50° | .77 | 85° | 1.00 | ||
| 20° | .34 | 55° | .82 | 90° | 1.00 | ||
| 25° | .42 | 60° | .87 | ||||
| 30° | .50 | 65° | .91 |
Fig. 31.—Combined surface and sectional views of a plunging anticline (after Willis).
Fig. 32.—Combined surface and sectional views of a plunging syncline (after Willis).
The detection of plunging folds.—When the axis of a fold is horizontal, its outcrops upon a plain will continue to have the same strike until the formation comes to an end. Upon a generally level surface, therefore, any regular progressive variation in the strike direction is an indication that the folds have a plunging or pitching character. Many serious mistakes of interpretation have been made because of a failure to recognize this evidence of plunging folds. The way in which the strikes are progressively modified will be made clear by the diagrams of [Figs. 31] and [32], the first representing a pitching anticline and the second a pitching syncline. In both these reciprocal cases the strikes of the beds undergo the same changes, and the dip directions serve to distinguish which of the two structures is present in a given case. There is, however, one further difference in that the hard layers of the plunging anticline, where they disappear below the surface in the axis, will present a domed surface sloping forward like the back of a whale as it rises above the surface of the sea. Plunging folds in series will thus appear in the topography as a series of sharply zigzagging ranges at those localities where the harder layers intersect the surface. Such features are encountered in eastern Pennsylvania, where the hard formations of the Appalachian Mountain system plunge northeastward under the later formations. The pitch of the larger fold is often disclosed by that of the minor puckerings superimposed upon it.
