Geoscience Reference
In-Depth Information
(a)
S
(b)
(c)
i
N
N
O
Lower focal
hemisphere
A
i
S
Figure 4.25.
(a) A schematic cross section through the Earth, centre O. The focal
sphere is an imaginary small sphere centred on the earthquake focus (
◦
). The lower
focal hemisphere is shaded. The ray path for the first arrival at seismograph S
intersects the lower focal hemisphere at an angle
i
from the vertical. (b) Projection of
the lower focal hemisphere onto a horizontal plane. N is north. Seismograph S plots
at (
i
,
A
), where
i
is the angle of incidence shown in (a) and
A
is the geographic
azimuth of S from the earthquake focus. The polarity of the first motion recorded at
Sisthen plotted at (
i
,
A
). (c) The fault-plane solution for the strike-slip earthquake
shown in Fig. 4.18(a). Compression, positive first motion, black; dilatation, negative
first motion, white.
The first P-wave motion to arrive at any particular station from an earthquake
on this fault will either be compressional (the first motion is a push) or dilata-
tional (the first motion is a pull). At each of these six seismograph stations the
polarity of the first-arriving energy is noted. Thus, the polarities at stations A,
C and E are positive (compressional) and those at stations F and B are negative
(dilatational), whereas station D receives no P-wave energy. If the distribution
of compressional and dilatational first motions for many seismograph stations
around the earthquake is plotted, it is seen that they fall into four quadrants
(Fig. 4.22(b)), alternately positive and negative. The length of the arrow in the
lobe represents the relative magnitude of the first P-wave at that location.
Since the Earth is spherical, in practice we must use spherical coordinates,
which slightly complicates the geometry but not the results. Imagine a small
sphere centred on and surrounding the focus of an earthquake. This sphere is
known as the
focal sphere
. The ray that arrives first at each receiver intersects
the
lower focal hemisphere
at an angle from the vertical
i
and at azimuth
A
(Fig. 4.23(a)). To calculate the angle
i
from the vertical at which the ray intersects
the lower focal hemisphere, knowledge of the gross P-wave structure of the Earth
is required in order to trace the ray back from receiver to source (see Section 8.1.1
and Appendix 3). However, in practice the calculations have already been done
and the angle can be obtained from standard seismological tables. The lower
focal hemisphere is then projected onto a horizontal plane using an equal-area
