On the other hand, the two basic prerequisites given above for the formation of submarine valleys conform to definite global patterns. If our purpose is given a broader formulation (i.e., if we try to encompass the largest possible number of submarine valleys and the most extensive territories of their occurrence), local factors may be neglected and we may base our analysis of the phenomenon solely on the main factors. We may then trace the principal regularities which are instrumental in the formation of submarine canyons and their distribution over the Earth. We shall now examine these main factors separately.
Fluctuations in ocean level. A deflection of the rotation axis within the Earth's body causes fluctuations of the ocean level of the entire surface of our planet. However, the magnitude and size of these fluctua tions differ at different points on the globe. Variations in the magnitude and direction of the fluctuations in the ocean level conform to certain patterns. Simultaneous fluctuations are of the same sign in opposite quadrants of the globe separated by "indifferent" meridians and parallels. Following along the parallel in any quadrant the fluctuations reach their maximum values on the meridian of the shift of poles, attenuating gradually in both directions away from this meridian toward the "indifferent" meridians.
Similarly, in every quadrant, following along the meridian, the fluctua tions reach their maximum values in the middle latitudes, their amplitudes diminishing toward the poles and the equator. In this case we are interested in the latter phenomenon, i. e., the regularity governing the amplitudinal variation of the fluctuations in ocean level in the meridional direction.
Table 1 lists variations in the length of the Earth's radius between the equator and the poles at intervals of 5° lat. The differences in length of every adjacent pair of radii listed in the table govern the amplitude of the fluctuation in ocean level on approaching the poles (or withdrawing from them) by 5°. For instance, the Earth's radius is 6369.6 km at a latitude of 40°, and 6367.7 km at a latitude of 45°. The difference in the length of the radii is 6369.6 — 6367.7 = 1.9 km. This means that as the pole comes 5° closer to any point situated at the latitude of 40° the ocean level there will fall by 1.9 km. At a point situated at a latitude of 55° the approach of the pole by 5° will depress the ocean level by 1.7km; the
fall will be 1.1 km at a latitude of 15°, and so on.
The third column of Table 1 lists the magnitudes of the fluctuation in the ocean level at different latitudes of the Earth when the poles approach the point (or withdraw from it) by 5°. The tabulated data can be used for plotting a graph by marking the y-axis with the values listed in the last column of the table (on any convenient scale). The resultant curve will display the pattern governing the amplitudinal variation of the fluctuations in ocean level at different terrestrial latitudes. It will be seen from Figure 1 that the maximum fluctuations in ocean level occur in the middle latitudes, decreasing at lower and higher latitudes.
In the geological past the Earth's poles shifted in several directions, and therefore it is possible to conclude that the maximum fluctuations of the ocean level in different epochs occurred in different areas of the Earth's surface situated in the middle latitudes, so that eventually large fluctuations occurred in all areas along these parallels. Areas in the polar regions and in the equatorial zone must have undergone fluctuations of considerably smaller amplitudes.
Hence it follows that conditions favoring the formation of submarine canyons by erosion must have occurred primarily in the middle latitudes. If the submarine valleys were indeed incised by rivers at low ocean levels, then they must be most numerous in the middle latitudes.
The fluctuations in ocean level are small about the poles and along the equator, and are practically zero for small deflections of the rotation axis. However, this does not indicate that appreciable fluctuations of the ocean level did not occur in the polar regions and in the equatorial zone of the Earth.
The depth of the largest submarine canyons (such as those discovered along the shores of North America) often reach 2 —2.5 km. Assuming that these canyons were incised by rivers when the ocean level was low, we must admit a shift of the poles within 5-6°, in order to allow for a depression of the surface of the oceanic spheroid by an amount corresponding to the depth of these canyons in the middle latitudes. Such a deflection of the rotation axis would also produce appreciable fluctuations in the ocean level in the equatorial zone and in the high latitudes, although they would be far more limited than in the middle latitudes.