166 Seismology and Earth Structure
earthquakes are used for body wave studies, because they
generate only small surface waves.
Finally, it is worth remembering that travel time tables are
compiled from observations of seismic arrivals. Although most
arrivals on seismograms can be identified today from existing tables, important results are still found by noticing and
explaining a previously unrecognized arrival.
3.5.2 Core phases
The contrast in properties between the solid mantle and the
liquid core, which has lower velocity than the mantle above,
makes the core well suited to seismological study using reflected,
transmitted, converted, and diffracted arrivals.
Core reflections are of great interest because the core–mantle
boundary (CMB) is a solid–liquid boundary, and thus a strong
reflector for shear waves. Reflections off the CMB are denoted
by a lower-case “c,” so ScS is an S-wave reflection and PcP is
a P-wave reflection. Conversions at the CMB also occur. ScP
goes down through the mantle as a shear wave and returns as
a compressional wave, whereas PcS does the reverse. Some
phases undergo multiple reflections at both the core and the
surface; ScSScS (or ScS2) bounces twice at the CMB and once at
the surface. Such reflections, known as multiple ScS, are shown
in Fig. 1.1-4.
ScS is a more distinct arrival than PcP, because the liquid
core does not transmit shear waves. The SH part of the motion
in the incident ScS cannot convert to P waves at the CMB, so is
totally reflected. Hence ScS is often well recorded on the transverse component (Section 2.4.4) of a seismometer. By contrast,
the PcP reflection is generally weak, because the impedance
contrast (Section 2.6.6) is small, so most P energy incident
on the CMB is transmitted. The small impedance contrast
(about 5%) arises because the P-wave velocity decrease going
from the mantle to the core (about 13.7 km/s to 8.1 km/s) is
offset by the density increase (about 5.5 g /cm 3 to 9.9 g/cm 3 ).
Core reflections, especially ScS, are useful in studies of earth
structure, because they give a vertical average velocity for the
mantle. The travel time curves for these phases are concave
upward (Fig. 3.5-4), like that for the reflection off the top of a
layer in a flat geometry (Section 3.2.1). Similarly, they have
finite travel time at zero distance because of the time needed to
get down to the core and back.
The travel times and amplitudes of core phases are also used
to study structure near and within the core, because their ray
paths are sensitive to the structure. To illustrate this idea, consider P-wave ray paths (Fig. 3.5-7, top left) within the earth.
Rays leaving the source at progressively smaller angles of
incidence (closer to the vertical) bottom deeper in the mantle
and so reach greater distances. As the bottoming depth approaches the core–mantle boundary, the travel times of P
and PcP converge (Figs 3.5-3 and 4). Eventually, at about 98°
(the precise distance depends on the depth of the earthquake
and the exact velocity structure), P grazes the core–mantle
boundary, and P and PcP are identical.
An intuitive way to view minimum- and maximum-time
phases is to consider ray paths for surface reflections in a
homogeneous medium (Fig. 3.5-6, bottom). An ellipse defines
the set of points whose summed distances to two points, or
foci, are equal. Thus, if an earthquake and a receiver were the
foci, the travel time for a reflection from any point on the ellipse
would be the same. Hence, if the surface were elliptical, the
reflected phase would be neither a minimum- nor a maximumtime phase, because all the energy would arrive at the same
time. If the surface were flat, and thus had less curvature than
the ellipse, waves that reflect off the surface slightly closer or
further than the midpoint travel further, making the reflection
a minimum-time phase. However, if the surface were circular
and more curved than the ellipse, waves reflected off the surface
slightly closer or further than the midpoint travel a shorter distance, making the reflection a maximum-time phase. This last
case is analogous to that for PP and SS in the spherical earth.
Although PP and SS are maximum time phases with respect
to distance, they are minimum travel time phases with respect
to azimuth, as are most phases. Thus waves with a bounce
point off the great circle path between the source and the
receiver arrive later. This combination of maximum time with
respect to distance and minimum time with respect to azimuth
makes the surface reflections sample an “X”-shaped region of
the surface, known as the Fresnel zone (Section 3.7.3), near the
bounce point. The fact that these are maximum-time phases
also causes them to undergo a π /2 phase shift 3 (Fig. 2.6-5).
Each successive bounce at the surface causes another π /2 phase
shift, so SSS is phase-shifted by π and inverted with respect to
direct S. S4 undergoes a 3π /2 phase shift, and S5 has a 2π shift,
giving it the same shape as the original S.
Figure 3.5-5 is drawn for an earthquake beneath the earth’s
surface. Because earthquakes occur to depths of 700 km, seismic ray paths go up from earthquakes as well as down. Lowercase “p” and “s” identify upgoing compressional and shear
waves (Fig. 3.5-2). pP goes up as a P wave and reflects near
the epicenter, whereas sP goes up as an S wave and converts to
a P wave at the surface. These reflections are useful because
the travel time difference between direct P and pP, for example,
indicates the depth of the earthquake. After an upgoing wave
reflects at the free surface, it can undergo later conversions,
so pPP, sPS, etc. are possible arrivals.
Many other body wave phases have been identified and are
included in travel time tables. In addition, some tables give
arrival times for Love and Rayleigh surface waves. As shown in
Fig. 2.7-4, these surface waves are dispersive, so different frequencies have different arrival times, making the time shown
approximate. This time is still useful for various purposes,
including allowing earth structure studies to avoid phases
that may be obscured by surface waves. In many cases, deep
3 This phase shift, also known as a Hilbert transform, can be viewed by thinking of
the pulse as made up of sine and cosine functions and turning each into the other.
earthquakes are used for body wave studies, because they
generate only small surface waves.
Finally, it is worth remembering that travel time tables are
compiled from observations of seismic arrivals. Although most
arrivals on seismograms can be identified today from existing tables, important results are still found by noticing and
explaining a previously unrecognized arrival.
3.5.2 Core phases
The contrast in properties between the solid mantle and the
liquid core, which has lower velocity than the mantle above,
makes the core well suited to seismological study using reflected,
transmitted, converted, and diffracted arrivals.
Core reflections are of great interest because the core–mantle
boundary (CMB) is a solid–liquid boundary, and thus a strong
reflector for shear waves. Reflections off the CMB are denoted
by a lower-case “c,” so ScS is an S-wave reflection and PcP is
a P-wave reflection. Conversions at the CMB also occur. ScP
goes down through the mantle as a shear wave and returns as
a compressional wave, whereas PcS does the reverse. Some
phases undergo multiple reflections at both the core and the
surface; ScSScS (or ScS2) bounces twice at the CMB and once at
the surface. Such reflections, known as multiple ScS, are shown
in Fig. 1.1-4.
ScS is a more distinct arrival than PcP, because the liquid
core does not transmit shear waves. The SH part of the motion
in the incident ScS cannot convert to P waves at the CMB, so is
totally reflected. Hence ScS is often well recorded on the transverse component (Section 2.4.4) of a seismometer. By contrast,
the PcP reflection is generally weak, because the impedance
contrast (Section 2.6.6) is small, so most P energy incident
on the CMB is transmitted. The small impedance contrast
(about 5%) arises because the P-wave velocity decrease going
from the mantle to the core (about 13.7 km/s to 8.1 km/s) is
offset by the density increase (about 5.5 g /cm 3 to 9.9 g/cm 3 ).
Core reflections, especially ScS, are useful in studies of earth
structure, because they give a vertical average velocity for the
mantle. The travel time curves for these phases are concave
upward (Fig. 3.5-4), like that for the reflection off the top of a
layer in a flat geometry (Section 3.2.1). Similarly, they have
finite travel time at zero distance because of the time needed to
get down to the core and back.
The travel times and amplitudes of core phases are also used
to study structure near and within the core, because their ray
paths are sensitive to the structure. To illustrate this idea, consider P-wave ray paths (Fig. 3.5-7, top left) within the earth.
Rays leaving the source at progressively smaller angles of
incidence (closer to the vertical) bottom deeper in the mantle
and so reach greater distances. As the bottoming depth approaches the core–mantle boundary, the travel times of P
and PcP converge (Figs 3.5-3 and 4). Eventually, at about 98°
(the precise distance depends on the depth of the earthquake
and the exact velocity structure), P grazes the core–mantle
boundary, and P and PcP are identical.
An intuitive way to view minimum- and maximum-time
phases is to consider ray paths for surface reflections in a
homogeneous medium (Fig. 3.5-6, bottom). An ellipse defines
the set of points whose summed distances to two points, or
foci, are equal. Thus, if an earthquake and a receiver were the
foci, the travel time for a reflection from any point on the ellipse
would be the same. Hence, if the surface were elliptical, the
reflected phase would be neither a minimum- nor a maximumtime phase, because all the energy would arrive at the same
time. If the surface were flat, and thus had less curvature than
the ellipse, waves that reflect off the surface slightly closer or
further than the midpoint travel further, making the reflection
a minimum-time phase. However, if the surface were circular
and more curved than the ellipse, waves reflected off the surface
slightly closer or further than the midpoint travel a shorter distance, making the reflection a maximum-time phase. This last
case is analogous to that for PP and SS in the spherical earth.
Although PP and SS are maximum time phases with respect
to distance, they are minimum travel time phases with respect
to azimuth, as are most phases. Thus waves with a bounce
point off the great circle path between the source and the
receiver arrive later. This combination of maximum time with
respect to distance and minimum time with respect to azimuth
makes the surface reflections sample an “X”-shaped region of
the surface, known as the Fresnel zone (Section 3.7.3), near the
bounce point. The fact that these are maximum-time phases
also causes them to undergo a π /2 phase shift 3 (Fig. 2.6-5).
Each successive bounce at the surface causes another π /2 phase
shift, so SSS is phase-shifted by π and inverted with respect to
direct S. S4 undergoes a 3π /2 phase shift, and S5 has a 2π shift,
giving it the same shape as the original S.
Figure 3.5-5 is drawn for an earthquake beneath the earth’s
surface. Because earthquakes occur to depths of 700 km, seismic ray paths go up from earthquakes as well as down. Lowercase “p” and “s” identify upgoing compressional and shear
waves (Fig. 3.5-2). pP goes up as a P wave and reflects near
the epicenter, whereas sP goes up as an S wave and converts to
a P wave at the surface. These reflections are useful because
the travel time difference between direct P and pP, for example,
indicates the depth of the earthquake. After an upgoing wave
reflects at the free surface, it can undergo later conversions,
so pPP, sPS, etc. are possible arrivals.
Many other body wave phases have been identified and are
included in travel time tables. In addition, some tables give
arrival times for Love and Rayleigh surface waves. As shown in
Fig. 2.7-4, these surface waves are dispersive, so different frequencies have different arrival times, making the time shown
approximate. This time is still useful for various purposes,
including allowing earth structure studies to avoid phases
that may be obscured by surface waves. In many cases, deep
3 This phase shift, also known as a Hilbert transform, can be viewed by thinking of
the pulse as made up of sine and cosine functions and turning each into the other.