Geoscience Reference
In-Depth Information
Appendix 3
Geometry of ray paths and
inversion of earthquake body-wave
time-distance curves
To be able to use the travel-time-distance curves for teleseismic earthquakes (Fig. 4.16)to
determine the internal structure of the Earth, it is necessary to devise equations relating
seismic velocity and depth to travel time and distance.
Initially, consider an Earth assumed to consist of spherically symmetrical shells, each shell
having constant seismic velocity. Consider part of the particular seismic ray (Fig. A3.1)which
traverses three of these layers. Applying Snell's law (Section 4.3.2)tointerface 1 gives
sin
i
1
v
1
sin
j
1
v
2
(A3.1)
=
and applying it to interface 2 gives
sin
i
2
v
2
sin
j
2
v
3
(A3.2)
=
However, from the right-angled triangles OP
1
Q and OP
2
Q, we can write
OQ
=
OP
1
sin
j
1
=
r
1
sin
j
1
(A3.3)
Figure A3.1.
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