The method employed by him for the purpose is no less simple
theoretically than that used for locating the epicentre. If the
position of the latter (E) is known, one accurate measurement of the
angle of emergence EPF, at any other point P would be sufficient to
fix the depth of some point within the focus F (Fig. 11). Here, again,
Mallet relied chiefly on fissures in walls that were fractured but not
overthrown. In detail, these fissures are nearly always jagged or
serrated, for they tend to follow the lines of joints rather than
break through the solid stone, though they sometimes traverse bricks
and mortar alike. But the general course of the fissures, he urged,
would be at right angles to the wave-path, and their inclination to
the vertical should be equal to the angle of emergence.
[Illustration: FIG. 11.--Diagram to illustrate Mallet's method of
determining depth of seismic focus.]
In obtaining measurements of this angle, the buildings to be chosen
are those of large size, with few windows or other apertures, and with
walls made of brick or small short-bedded stones. The cathedral-church
at Potenza perhaps satisfies these conditions more closely than any
other structure examined by Mallet. The plan of the fissures in the
walls and roof has been given in Fig. 5, and Fig. 12 represents the
fissures In the vertical section along the axial line and looking
north, as drawn by the cathedral architect. From these fissures Mallet
calculated the mean angle of emergence at Potenza to be 23° 7'. The
distance of Potenza from Caggiano being seventeen miles, and the
height of the former being 2,580 feet, the depth of the focus
resulting from this observation alone would be 6-3/4 miles below the
level of the sea.
[Illustration: FIG. 12.--Vertical section of Cathedral Church at
Potenza. (_Mallet._)]
_Objection to Mallet's Method._--The weakest point in Mallet's method
is probably his assumption that the wave-paths are straight lines
extending outward from the focus. Even if the depth of the focus is
not more than a few miles, the waves must traverse rocks of varying
density and elasticity, and, at every bounding surface, they must
undergo refraction. If the rocks are so constituted that the velocity
of the earth-waves in them increases with the depth, then the
wave-paths must be bent continually outwards from the vertical, so
that the angle of emergence at the surface may be considerably less
than it would have been with a constant velocity throughout. In this
case, the actual depth will be greater, perhaps much greater, than the
calculated depth. For instance, if the angle of emergence at Potenza
were diminished only 5° by refraction, the calculated depth of the
focus would be too small by 1-3/4 miles.
Public-domain text, read in full here on John Shaqi.
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