Earth as a Planet: Surface and Interior 201
FIGURE 11 (a) Ray paths of the compressional waves (P) in the
mantle, including their conversion to shear waves (S). (b) Ray
paths of the P waves interacting with the outer and inner core.
(c) Ray paths of the S waves interacting with the core; the S
waves are converted into P waves in the outer core.
40% lower than at the bottom of the mantle; also, there
are no S waves. The inner core is solid, with a composition
similar to that of the outer core. Figure 11b shows the rays
(mostly P waves) that are reflected from the core–mantle
boundary (CMB; a letter c is inserted, e.g., PcP) or that are
transmitted through the outer core (letter K: PKP) or also
through the inner core (letter I: PKIKP). Figure 11c shows
S-wave rays interacting with the CMB: reflected (ScS) or
converted at the CMB into a P wave and then again recon-
verted into a S wave: SKS and SKKS. The latter indicates
one internal reflection from the underside of the CMB.
Figure 12 shows an example of an earthquake recorded
on a three-component seismograph system and then rotated
such that the “radial” component shows horizontal motion
along the great circle from the earthquake to the station;
“transverse” component is also horizontal motion but in
the direction perpendicular to the ray path, and “vertical”
component shows up-and-down motion.
Figure 13 compares observed travel times, reported
by the International Seismological Centre with those pre-
dicted by an Earth model. The scatter around the predicted
values is caused by the effects of lateral heterogeneity and
measurement errors.
Measurements of the travel times of the waves such as
shown in Figures 11 and 13 have led to the derivation of
models of the seismic wave speed as a function of depth.
These, in turn, were used to improve the location of earth-
quakes and further refine the models. The first models were
constructed early in the 20th century; the models published
by Beno Gutenberg and Sir Harold Jeffreys in the 1930s
are very similar in most depth ranges to current ones. The
model of Jeffreys is compared with a recent model (iasp91)
in Figure 14. The upper mantle (the topmost 700 km) with
its discontinuities and the inner core are exceptions.
In addition to the body waves, which propagate through
the volume of the Earth, there are also surface waves, whose
amplitude is the largest at the surface and decreases expo-
nentially with depth. Surface waves are important in study-
ing the crust and upper mantle and, in particular, their lat-
eral variations, as the Earth is most inhomogeneous near the
surface. There are Rayleigh waves with the particle motion
in the vertical plane (perpendicular to the surface; second
and third trace in Figure 12) and Love waves whose particle
motion is in the horizontal plane (parallel to the surface).
Surface waves are dispersed in the Earth because of the
variation of the physical parameters with depth; notice that
the longer period surface waves in Figure 12 arrive before
shorter period waves.
Very long period surface waves (>100 sec) are some-
times called “mantle waves,” have horizontal wavelengths
in excess of 1000 km, and maintain substantial amplitudes
(and, therefore, sensitivity to the physical properties) down
to depths as large as 600–700 km. Because of their long
periods, mantle waves are attenuated relatively slowly and
can be observed at the same station as they travel around
the world several times along the same great circle (both
in the minor and major arc direction). Figure 15 shows a
three-component recording of mantle waves (note the time
scale); the observed seismograms are shown at the top of
each pair of traces; the bottom trace is a synthetic seismo-
gram computed for a three-dimensional Earth model.
Superposition of free oscillations of the Earth (known
also as the normal modes) in the time domain will yield
mantle waves. First spectra of the vibrations of the Earth
were obtained following the Chilean earthquake of 1960;
the largest seismic event ever recorded on seismographs.
The measurements of the frequencies of free oscillations
lead to the renewed interest in the Earth’s structure. In par-
ticular, they, unlike body waves, are sensitive to the density