The actual configuration of the surface.—The foregoing computations relative to the power of shells of the earth to sustain pressures are based on ideal forms and structures that are not realized in fact. How far the earth fails to conform to these conditions must now be considered. When compared with the earth as a whole, the inequalities of its surface are trivial. If the great dynamic forces acted through the whole or the larger part of the body of the earth, the configuration of the surface can be supposed to have done little more than influence the location of the surface deformations and their special phases. But if the forces were limited to a crust of moderate thickness, the configuration of the surface is a matter of radical importance.
Concave tracts.—There is need, therefore, to inquire if any considerable breadth of the crust is outwardly plane or concave, for the principle of the dome is obviously not applicable to a plane or concave surface. To be a source of fatal weakness, the concavity must be broad enough to cause the planes of equal cooling, the isogeotherms, to be concave to considerable depths. For example, if the hypothetical level of no stress is eight miles below the surface, as computed on certain assumptions, the concave portion must be so broad that the isogeotherms will also be concave outward at something near that depth; in other words, the main part of the zone of thrust must be concave. A narrow concavity at the surface, such as an ordinary valley in a portion of the crust that has the average convexity, would not seriously depress the isogeotherms, or affect the zone of thrust, but a valley several times eight miles (level of no stress) in breadth would. For inspecting the surface of the earth in this regard, it is convenient to know what amounts of fall below the level surface give a true plane for given distances. These are shown in the following table:[274]
| Length of arc in miles. | Length of normal to chord at middle point in | Average fall of true plane from level plane per mile, in feet. Greater fall gives concavity. | |
|---|---|---|---|
| Feet. | Fathoms. | ||
25 | 100.3 | 16.7 | 8. |
50 | 432. | 72. | 17.3 |
75 | 913.4 | 152.2 | 24.3 |
100 | 1,684. | 280.7 | 33.7 |
150 | 3,748.8 | 624.8 | 49.9 |
200 | 6,674. | 1,112.3 | 66.7 |
250 | 10,369.9 | 1,728.3 | 82.9 |
300 | 14,942. | 2,490.3 | 99.6 |
400 | 26,664. | 4,444. | 133.3 |
500 | 41,659. | 6,943. | 166.6 |
Applying these criteria to the surface of the lithosphere, it is found that concave tracts from 100 to 300 miles in breadth are not uncommon. The more notable of these are shown in black on the accompanying map, [Fig. 454], and two typical ones are shown in cross-section in Figs. [455] and [456]. It is to be observed that concave tracts border the continents very generally. They are connected with the descent from the continental shelf to the abysmal basins, and are unsymmetrical. Notable concavities are found in some of the great valleys on the continental platforms. The basins of Lake Superior, Michigan, Huron, and Ontario are in part concave; so are Puget Sound, the Adriatic, and the Dead Sea; so also are the valleys of California, of the Po, and of the Ganges, when the adjacent mountains are included. Some of the “deeps” of the bottom of the ocean are notably concave. [Fig. 455], a cross-section of the Challenger Deep, drawn to true scale and convexity, shows the nature of the phenomenon. The breadth is here 300 miles, and the depression below a true plane is 11,400 feet. The lower line of the figure shows the approximate position and form of the normal isogeotherm about ten miles below the surface. Assuming equal conductivity in all parts, it is clear that the isogeotherms must be concave upwards for a considerable distance below ten miles. Unless the shell of thrust is much more than ten miles thick, these concave portions should yield as fast as cooling below them permits, and no stresses arising from convexity could be accumulated.
Fig. 454.—Map of the world, showing in black the chief submarine concavities of the lithosphere. (Prepared by W. H. Emmons.)
Fig. 455.—Section of the Challenger Deep from an island on the Caroline plateau, a, to an island on the Ladrone plateau, b, drawn to a true scale, showing the real concavity of the surface of the lithosphere for a breadth of 300 miles. The upper line represents the sea surface, a natural level. The next line below represents a true plane, eliminating the curvature of the sea surface. The third line represents the bottom of the deep. By comparison with the line above, its true concavity may be seen. The lowest line represents an isogeotherm at about 10 miles below the surface; i.e. appreciably below “the level of no stress,” as usually computed, showing that the whole thrust zone is concave outwards, if it is limited to surface cooling as usually computed. (Prepared by W. H. Emmons.)
Fig. 456.—Section through the Atlantic coastal plain, the continental shelf, and a portion of the abysmal bottom, drawn to a true scale, showing that the surface of the lithosphere drops below a true plane tangent to the continental shelf and the ocean-bottom. The upper line represents the surface of the coastal plain at the left and of the ocean at the right. The lower line represents the sea-bottom, and the middle line a true plane tangent to the shelf and the sea-bottom. The breadth of the concave tract varies from 100 to 150 miles. (Prepared by W. H. Emmons.)