Other methods of calculation which have been employed are based on time observations, as, for instance, the method of Seebach, the method of co-ordinates, the method of hyperboloids or spheres (see pages 200–212).
By means of a number of lines parallel to twenty-six angles of emergence, drawn in towards the seismic vertical, Mallet found that twenty-three of these intersected at a depth of 7⅛ geographical miles. The maximum depth was 8⅛ geographical miles, and the minimum depth 2¾ geographical miles.
The mean depth was taken at a depth of 5¾ geographical miles where, within a range of 12,000 feet, eighteen of the wave paths intersected the seismic vertical.
The point where these wave paths start thickest is at a depth not greater than three geographical miles, and this is considered to be the vertical depth of the focal cavity itself.
For the Yokohama earthquake of 1880, from the indications of seismometers, and by other means, certain angles of emergence were obtained, leading to the conclusion that the depth of origin of that earthquake might be between 1½ and 5 miles.
Possibly, perhaps, the earthquake may have originated from a fissure the vertical dimensions of which was comprised between these depths.
A source of error in a calculation of this description is that the vertical motions may have been a component of transverse motions or perhaps due to the slope of surface waves.
The following table of the depths at which certain earthquakes have originated has been compiled from the writings of several observers.
| In feet | ||||
|---|---|---|---|---|
| Minimum | Mean | Maximum | ||
| Rhineland | 1846 (Schmidt) |
| 127,309 |
|
| Sillien | 1858 (Schmidt) |
| 86,173 |
|
| Middle Germany | 1872 (Seebach) | 47,225 | 58,912 | 70,841 |
| Herzogenrath | 1873 (Lasaulx) | 16,553 | 36,516 | 56,477 |
| Neapolitan | 1857 (Mallet) | 16,705 | 34,930 | 49,359 |
| Yokohama | 1880 (Milne) | 7,920 | 17,260 | 26,400 |
A table similar to this has been compiled by Lasaulx.[87]