Chapter 4: Igneous Rocks: Product of Earth's Internal Fire

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Chapter 10: Earthquakes and Earth’s
Interior
Introduction
 When the Earth quakes, the energy stored in
elastically strained rocks is suddenly released.
 The more energy released, the stronger the quake.
 Massive bodies of rock slip along fault surfaces
deep underground.
 Earthquakes are key indicators of plate motion.
How Earthquakes Are Studied (1)
 Seismometers are used to record the shocks and
vibrations caused by earthquakes.
 All
seismometers make use of inertia (慣性), which is
the resistance of a stationary mass to sudden
movement.

This is the principal used in inertial seismometers.
 The seismometer measures the electric current
needed to make the mass and ground move
together.
Figure 10.1
How Earthquakes Are Studied (2)
 Three inertial seismometers are commonly used
in one instrument housing to measure up-down,
east-west, north-south motions simultaneously.
↑
↓
Figure 10.2
→
←
Earthquake Focus And Epicenter
 The earthquake focus (震源) is the point where
earthquake starts to release the elastic strain of
surrounding rock.
 The epicenter (震央) is the point on Earth’s
surface that lies vertically above the focus of an
earthquake.
 Fault slippage begins at the focus and spreads
across a fault surface in a rupture front.
 The rupture front travels at roughly 3 kilometers
per second for earthquakes in the crust.
Figure B10.01
The First Seismogram from a Distant
Earthquake
Seismology (地震學) is a fairly young
science; recordings of earth motion
(seismograms) have only been made for
about 100 years. Shown is what is widely
considered to be the first remote
(teleseismic) seismogram, made on April
17, 1889, in Potsdam, Germany by E.
von Rebeur-Pacshwitz (Nature, 1889).
The instrument was a photographically
recording horizontal pendulum originally
installed for astronomical purposes. The
earthquake was in Japan and had a
magnitude of about 5.8.
Source: http://www.iris.edu
Epicenter
Focus
Figure 10.3
Seismic Waves (1)
 Vibrational waves spread outward initially
from the focus of an earthquake, and continue
to radiate from elsewhere on the fault as
rupture proceeds.
Seismic Waves (2)
 There are two basic families of seismic waves.
 Body waves (體波) can transmit either:


Compressional motion (P waves), or
Shear motion (S waves).
 Surface
waves (表面波) are vibrations that are
trapped near Earth’s surface. There are two types of
surface waves:


Love waves, or
Rayleigh waves.
Body Waves (1)
 Body waves travel outward in all directions from
their point of origin.
 The first kind of body waves, a compressional
wave, deforms rocks largely by change of
volume and consists of alternating pulses of
contraction and expansion acting in the direction
of wave travel.
 Compressional
waves are the first waves to be
recorded by a seismometer, so they are called P (for
“primary”) waves.
P-wave: Longitudinal wave (縱波)
 Dan Russel
Figure 10.4
Body Waves (2)
 The second kind of body waves is a shear wave
(剪力波).
 Shear
waves deform materials by change of shape,
 Because shear waves are slower than P waves and
reach a seismometer some time after P waves arrives,
they are called S (for “secondary”) waves.
S-wave: Transverse wave (橫波)
Figure 10.4
SV motions on the vertical plane parallel to the propagation direction
 Dan Russel
Body Waves (3)
 Compressional (P) waves can pass through solids,
liquid, or gases.
 P waves move more rapidly than other seismic
waves:


6 km/s is typical for the crust.
8 km/s is typical for the uppermost mantle.
Body Waves (4)
 Shear (S) waves consist of an alternating series of
side-wise movements.
 Shear
waves can travel only within solid matter.
 The speed of a S wave is
times that of a P wave. A
1/ 3
typical speed for a S wave in the crust is 3.5 km/s, 5 km/s
in the uppermost mantle.
 Seismic body waves, like light waves and sound
waves, can be reflected and refracted by change in
material properties.
 When change in material properties results in a
change in wave speed, refraction bends the direction
of wave travel.
Figure 10.5
Body Waves (5)
 For seismic waves within Earth, the changes in
wave speed and wave direction can be either
gradual or abrupt, depending on changes in
chemical composition, pressure, and mineralogy.
 If Earth had a homogeneous composition and
mineralogy, rock density and wave speed would
increase steadily with depth as a result of increasing
pressure (gradual refraction).

Measurements reveal that the seismic waves are refracted
and reflected by several abrupt changes in wave speed.
c: reflection at the coremantle boundary
K: P wave in the outer core
I: P wave in the inner core
i: P wave reflection at the
inner-outer core boundary
Figure 10.6
Surface Waves (1)

Surface waves travel along the surface of the ground
or just below it, and are slower than than body
waves, but are often the largest vibrational signals in
a seismogram. The two most important are
Rayleigh and Love waves, named after British
scientists, Lord Rayleigh and A.E.H. Love who
discovered them
Surface Waves (2)


Rayleigh waves combine shear and compressional
vibration types, and involve motion in both the vertical
and horizontal directions. The velocity of Rayleigh
waves is about 0.92 times that of S waves.
Love waves consist entirely of shear wave vibrations
in the horizontal plane, analogous to an S wave that
travels horizontally, so they only appear in the
horizontal component of a seismogram. The velocity
of Love waves is approximately equal to that of S
waves, so they arrive earlier than Rayleigh wave.
Rayleigh wave – particle motions on the vertical plane parallel to the
propagation direction
Propagation direction
Love wave – particle motions on the horizontal plane perpendicular
to the propagation direction
Propagation direction
Rayleigh wave retrograde (counter-clockwise) motions
P > S > Rayleigh wave velocity
Surface Waves (2)

The longer the wave
length of a surface wave,
the deeper the wave
motion penetrates Earth.
Surface waves of different
wave lengths develop
different velocities. This
Behavior is called
Dispersion (色散).
Chi-Chi Earthquake: a shallow earthquake caused by the collision
between the Eurasian and Philippine plate.
Northridge Earthquake: a shallow earthquake occuring along a splay
of the San Andreas fault system near San Fernado Valley, just north of
Los Angeles.
Izmit Turkey Earthquake: a shallow earthquake occuring along the EW trend North Anatolian fault. Starting in 1939, the NA fault has
produced a sequence of major earthquakes, of which the 1999 event is
the 11th with a magnitude M ≥ 6.7.
Bolivia Earthquake: the deepest earthquake of this size (M=8.1,
d=670 km) ever recorded, caused by the Cocos plate subducting
under the south American continent.
Source: http://www.iris.edu/pub/programs/sel/ibmpc/
Seislove and Seiswave
Figure 10.7
Determining The Epicenter (1)

An earthquake’s epicenter can be calculated from
the arrival times of the P and S waves at a
seismometer.

The farther a seismometer is away from an epicenter, the
greatest the time difference between the arrival of the P
and S waves.
Determining The Epicenter (2)

The epicenter can be determined when data from
three or more seismometers are available.


It lies where the circles intersect (radius = calculated
distance to the epicenter).
The depth of an earthquake focus below an
epicenter can also be determined, using P-S time
intervals.
Figure 10.8
Figure 10.9
Earthquake Magnitude (1)



In 1935, Charles Richter at Caltech devised a calibration
scheme, called Richter scale, for describing the size of an
earthquake.
The Richter magnitude (芮氏地震規模) is based on a
logarithmic scaling of energy released by earthquakes and
divided into steps called magnitudes with numerical values M
from 0 to 10.
A large-sized earthquake occurs over a larger fault, requires
more time to rupture, and therefore generate longer-period
seismic waves. Thus, the energy released by an earthquake
affects both the amplitude X and the oscillation period T of
the P wave.
Earthquake Magnitude (2)


Richter’s original magnitude formula depends on the
logarithm of the ratio X/T. One unit of Richter magnitude
corresponds to a tenfold increase in X/T as measured by a
seismometer. A correction factor is added to adjust the
different distance between the earthquake and seismometer.
Later seismologists devised more general magnitude
estimate based on either on P wave (T~1 s), called mb,
surface wave trapped in the crust (T~20 s), or surface
trapped in the upper mantle (T~200 s), called Ms.
Earthquake Magnitude (3)

Lately, earthquake magnitude has been connected more directly to
motions on a fault. In 1977, Hiroo Kanamori at Caltech proposed a
relation between Richter magnitude M and seismic moment M0. The
moment is directly related to the mechanical energy released by fault
motion. The seismic moment is expressed as
M0= μAD
where μ (unit: newtons/m2) is shear stiffness of rock surrounding the
fault, A (unit: m2) is the area of the fault, and D (unit: m) is the
average slip during the earthquake. Seismic moment has the energy
units of newton-m=joules. Kanamori’s relation between moment and
magnitude is
M = (2/3) log10 M0 - 6.0
Figure B10.01
Earthquake Magnitude (4)



Most crustal rocks have shear stiffness μ=3x1010 nt/m2. If an
earthquake slips 3 km on a vertical fault 50 km long that
extends from the surface to 15 km depth, what is the magnitude
of this earthquake?
M0 =(3x1010 nt/m2)(50,000m)(15,000m)(3m)=6.75x1019 joules
M=(2/3)log10 M0 - 6.0=7.2
Each step in the Richter scale, for instance, from magnitude M
= 2 to magnitude M = 3, represents approximately a thirty fold
(101.5=31.6) increase in seismic moment (or energy).
The largest earthquake in 20th century that occurred in 1960 in
the subduction zone beneath Chile has a M=9.5, breaking along
an 800-km-long fault. The average fault slip was estimated to
be 25 m.
Earthquake Frequency (1)



Each year there are roughly 200 earthquakes
worldwide with magnitude M = 6.0 or higher.
Each year on average, there are 20 earthquakes with
M = 7.0 or larger.
Each year on average, there is one “great”
earthquake with M = 8.0 or larger.
Earthquake Frequency (2)

Four earthquakes in the twentieth century met or
exceeded magnitude 9.0.




1952 in Kamchatka (M = 9.0).
1957 in the Aleutian Island (M = 9.1).
1964 in Alaska (M = 9.2).
1960 in Chile (M = 9.5).
Earthquake Frequency (3)

The nuclear bomb dropped in 1945 on the Japanese
city of Hiroshima was equal to an earthquake of
magnitude M = 5.3.

The most destructive man-made devices are small in
comparison with the largest earthquakes.
Earthquake Hazard




Seismic events are most common along plate
boundaries.
Earthquakes associated with hot spot volcanism
pose a hazard to Hawaii.
Earthquakes are common in much of the
intermontane western United States (Nevada, Utah,
and Idaho).
Several large earthquakes jolted central and eastern
North America in the nineteenth century (New
Madrid, Missouri, 1811 and 1812).
Figure 10.10 A seismic risk map based on maxium horizontal acceleration
during an earthquake, expressed as the percentage of the acceleration due to
gravity (9.8m/s2).
Earthquake Disasters (1)

In Western nations, urban areas that are known to be
earthquake-prone have special building codes that
require structures to resist earthquake damage.


However, building codes are absent or ignored in many
developing nations.
In the 1976 T’ang Shan earthquake in China,
240,000 people lost their lives.
Earthquake Disasters (2)


Eighteen earthquakes are known to have caused
50,000 or more deaths apiece.
The most disastrous earthquake on record occurred
in 1556, in Shaanxi province, China, where in
estimated 830,000 people died.
Earthquake Damage (1)


Earthquakes have six kinds of destructive effects.
Primary effects:


Ground motion results from the movement of seismic
waves.
Where a fault breaks the ground surface itself, buildings
can be split or roads disrupted.
Earthquake Damage (2)

Secondary effects:




Ground movement displaces stoves, breaks gas lines, and
loosens electrical wires, thereby starting fires.
In regions of steep slopes, earthquake vibrations may cause
regolith (表土) to slip and cliffs to collapse.
The sudden shaking and disturbance of water-saturated
sediment and regolith can turn seemingly solid ground to a
liquid mass similar to quicksand (流沙) (liquefaction,液化).
Earthquakes generate seismic sea waves, called tsunami
(海嘯), which have been particularly destructive in the
Pacific Ocean.
Modified Mercalli Scale (修正麥卡利震
度階級 ﹐簡稱為MM震度階級)


This scale is based on the amount of vibration
people feel during low-magnitude quakes, and the
extent of building damage during high-magnitude
quakes.
There are 12 degrees of intensity in the modified
Mercalli scale (see Table 10.2)
World Distribution of Earthquakes



Subduction zones have the largest quakes.
The circum-Pacific belt, where about 80 percent of
all recorded earthquakes originate, follows the
subduction zones of the Pacific Ocean.
The Mediterranean-Himalayan belt is responsible
for 15 percent of all earthquakes.
Figure 10.15
Depth of Earthquake Foci


Most foci are no deeper than 100 km. down in the
Benioff zone, that extends from the surface to as
deep as 700 km.
No earthquakes have been detected at depths below
700 km. Two hypotheses may explain this.


Sinking lithosphere warms sufficiently to become entirely
ductile at 700 km depth.
The slab undergoes a mineral phase change near 670 km
depth and loses its tendency to fracture.
Figure 10.16
First-Motion Studies Of The
Earthquake Source



If the first motion of the arriving P wave pushes the
seismometer upward, then fault motion at the
earthquake focus is toward the seismometer.
If the first motion of the P wave is downward, the
fault motion must be away from the seismometer.
S-waves and surface waves also carry the signature
of earthquake slip and fault orientation and can
provide independent estimates of motion at the
earthquake focus.
Figure 10.17
Figure 10.18. Focal mechanism of
earthquakes. Black quadrants indicate
compressional first motion, while white
quadrants tensional first motion.
Earthquake Forecasting And Prediction
(1)


Forecasting (預報) identifies both earthquakeprone areas and man-made structures that are
especially vulnerable to damage from shaking.
Earthquake prediction (預測) refers to attempts to
estimate precisely when the next earthquake on a
particular fault is likely to occur.
Earthquake Forecasting And Prediction
(2)



Earthquake forecasting is based largely on elastic rebound
theory and plate tectonics.
The elastic rebound theory (彈性回復理論) suggests that if
fault surfaces do not slip easily past one another, energy will
be stored in elastically deformed rock, just as in a steel
spring that is compressed. The theory can only explain longterm risk of future earthquakes.
Currently, seismologists use plate tectonic motions and
Global positioning System (GPS) measurements to monitor
the accumulation of strain in rocks near active faults.
Figure 10.19
Earthquake Forecasting And Prediction
(3)


Earthquake prediction has had few successes.
Earthquake precursors:




Suspicious animal behavior.
Unusual electrical signals (1989 Loma Prieta earthquake).
Many large earthquakes are preceded by small earthquakes
called foreshocks (Chinese authorities used an ominous
series of foreshocks to anticipate (the Haicheng earthquake
M=7.3 in 1975).
Not all the large earthquakes are preceded by strong
foreshocks. In 1976, a stronger earthquake struck
Tangshan without warning and killed 240,000 people.
Figure 10.20
Red circles represent the
places where marshes and
swamps suddenly become
tidal flats in a recent
earthquake catastrophe
causing abrupt elevation
changes along coastal lines.
Figure B02
Earthquake Prediction (4)

One hypothesis for earthquake prediction was based on where
earthquakes occur at regular intervals. Elastic rebound theory
could explain short-term risk if the following conditions were
satisfied:
1. The rocks along a fault have a well-defined critical
threshold for strain, above which the fault will slip.
2. Strain accumulates in the fault zone in a steady manner.

If the strain accumulation rate is known from the motions
associated with plate tectonics, one can project when the next
earthquake will occur on the fault.
Earthquake Prediction from Parkfield
Experiment in California

Moderate-size earthquakes of M~6 have
occurred on the Parkfield section of the San
Andreas Fault at fairly regular intervals - in
1857, 1881, 1901, 1922, 1934, and 1966.
The first, in 1857, was a foreshock to the
great Fort Tejon earthquake which ruptured
the fault from Parkfield to the southeast for
over 300 km. Available data suggest that all
six moderate-sized Parkfield earthquakes
may have been "characteristic" in the sense
that they all ruptured the same area on the
fault. If such characteristic ruptures occur
regularly, then the next quake would have
been due before 1993. However, the
predicted earthquake still has not occurred.
Improved Theory for Earthquake
Prediction (1) – Earthquake Triggering

Fault interaction. After a fault slips during an earthquake, the
stresses on all neighboring faults are affected. Every large
earthquake is followed by numerous aftershocks, which are
smaller earthquakes that occur in response to the sudden
release of strain in surrounding rock. Seismologists have
found cases where aftershocks concentrate in area of rock
where the calculated stresses increased. Moreover, some cases
showed that the next large earthquake occurs, sometimes
decades later, in the region where the last earthquake has
increased the local stress. For instance, the focus of the 1994
Northridge earthquake in LA (M=6.8) was located where
stress had been increased by a 1971 earthquake in nearby San
Fernando.
A case where aftershocks
concentrate on areas with
stress increase induced by a
large earthquake. Red and
yellow indicate areas where the
calculated stress increased
slightly after a main shock.
Changes in stress are small, up
to three bars, comparable to a
pressure change of 3
atomspheres.
Figure 10.21
Fig. 1. Overlapping
aftershocks of the 1971 San
Fernando (blue; first year, M
> 2) and 1994 Northridge
(red; first 24 days, M > 3)
earthquakes (Stein et al.,
1994)
Red and yellow are the areas where the
stress increase after the major shocks 1971
San Fernando earthquake and 1994
Northridge earthquake.
Improved Theory for Earthquake
Prediction (2)

Weak fault behavior. Fault zones are weak surfaces within
subsurface rock. Friction on the fault prevents slip as strain
and stress accumulate in surrounding rock. In the laboratory,
geologists have observed that friction on many rock surfaces
decreases greatly once the surfaces start to slip. This effect,
called velocity-weakening behavior, allows slip to accelerate
and to release all the strain of the rock. Incorporating this rock
behavior into computer simulations of fault slips, the
simulations show that small patches of the fault surface can be
stressed by slip on neighboring patches, sometimes causing
large portions of the fault to slip simultaneously. The
simulations match the behavior of real faults, displaying
earthquakes of all sizes at irregular intervals.
Improved Theory for Earthquake
Prediction (3)

Fluid in faults. Subsurface faults form a network of pathways
for water, CO2, and other volatiles in the brittle upper crust.
The volatiles come from (1) rainwater, which percolates
downward through surface fractures and porous rocks, (2)
mantle outgassing, a byproduct of magma migration, eruption,
and emplacement, and (3) metamorphic dehydration reactions.
Fluids in the fault will decrease the friction. Many studies
suggest that water well levels have risen or fallen just before
earthquakes, some open faults have gushed water after an
earthquake, and small earthquakes tend to occur near newly
filled reservoirs. Seismologists have hypothesized that many
earthquakes deeper than 100 km in subducting slabs are
induced by the release of water from hydrated minerals.
Using Seismic Waves As Earth Probes
(1)


Seismic waves are the most sensitive probes we
have to measure the properties of the unseen parts
of the crust, mantle, and core.
Distinct boundaries (or discontinuities) can be
readily detected by refraction and reflection of body
waves deep within Earth.
Using Seismic Waves As Earth Probes
(2)



Early in the twentieth century, the boundary
between Earth’s crust and mantle was demonstrated
by a Croatian scientist named Mohorovicic.
A distinct compositional boundary separated the
crust from this underlying zone of different
composition (the Mohorovicic discontinuity).
Seismic wave speeds can be measured for different
rock types in both the laboratory and the field.
Figure 10.22
Figure 10.23 The
crustal thickness in
NA. This map is
compiled from seismic
wave and gravity
measurements. The
gravity is lower over
regions of thickened
crust because the
density of crustal
rocks is lower than
that of mantle rocks.
Using Seismic Waves As Earth Probes
(3)

The thickness and composition of continental crust
vary greatly from place to place.


Thickness ranges from 20 to nearly 70 km and tends to be
thickest beneath major continental collision zones, such
as Tibet.
P-wave speeds in the crust range between 6 and 7
km/s. Beneath the Moho, speeds are greater than 8
km/s.
Using Seismic Waves As Earth Probes
(4)


Laboratory tests show that rocks common in the
crust, such as granite, gabbro, and basalt, all have Pwave speeds of 6 to 7 km/s.
Rocks that are rich in dense minerals, such as
olivine, pyroxene, and garnet, have speeds greater
than 8 km/s.

Therefore, the most common such rock, called peridotite,
must be among the principal materials of the mantle.
Using Seismic Waves As Earth Probes
(5)

Some evidence can be obtained from rare samples
of mantle rocks found in kimberlite pipes—narrow
pipe-like masses of intrusive igneous rock,
sometimes containing diamonds, that intrude the
crust but originate deep in the mantle.
Using Seismic Waves As Earth Probes
(6)

Both P and S waves are strongly influenced by a
pronounced boundary at a depth of 2900 km.


Geologists infer that it is the boundary between the
mantle and the core.
Seismic-wave speeds calculated from travel times
indicate that rock density increases from about 3.3
g/cm3 at the top of the mantle to about 5.5 g/cm3 at
the base of the mantle.
Figure 10.25
Using Seismic Waves As Earth Probes
(7)


To balance the less dense crust and the mantle, the
core must be composed of material with a density of
at least 10 to 13 g/cm3.
The only common substance that comes close to
fitting this requirement is iron.
Using Seismic Waves As Earth Probes
(8)



Iron meteorites are samples of material believed to
have come from the core of ancient, tiny planets,
now disintegrated.
All iron meteorites contain a little nickel; thus,
Earth’s core presumably does too.
P-wave reflections indicate the presence of a solid
inner core enclosed within the molten outer core.
Layers of Different Physical Properties
in the Mantle


The P-wave velocity at the top of the mantle is
about 8 km/s and it increases to 14 km/s at the coremantle boundary.
The low-velocity zone can be seen as a small blip in
both the P-wave and S-wave velocity curves.


An integral part of the theory of plate tectonics is the idea
that stiff plates of lithosphere slide over a weaker zone in
the mantle called the asthenosphere.
In the low velocity zone rocks are closer to their melting
point than the rock above or below it.
Figure 10.26
Pd: diffractive wave along
the CMB
PKIKP: P wave entering the
inner core
PKiKP: P reflected at the
inner-outer core boundary
The 400-km Seismic Discontinuity


From the P-and S-wave curves, velocities of both P
and S waves increase in a small jump at about 400
km.
When olivine is squeezed at a pressure equal to that
at a depth of 400 km, the atoms rearrange
themselves into a denser polymorph (polymorphic
transition).
The 670-km Seismic Discontinuity


An increase in seismic-wave velocities occurs at a
depth of 670 km.
The 670-km discontinuity may correspond to a
polymorphic change affecting all silicate minerals
present.
Seismic Waves and Heat (1)


Seismic wave speed is affected by temperature.
Seismologists translate travel-time discrepancies
into maps of ‘fast” and “slow” regions of Earth’s
interior using seismic tomography. The principle is
similar to CAT scan (X-ray tomography) of the
human body in medical science.
Figure 10.27
Seismic Waves and Heat (2)


Researchers hypothesize that these “slow’’ regions
are the hot source rocks of most mantle plumes.
Near active volcanoes, seismologists have
interpreted travel-time discrepancies to reconstruct
the location of hot and partially molten rock that
supplies lava for eruptions.
Figure 10.28
Earthquakes Influence Geochemical
Cycles (1)



Earthquakes play an important role in the transport
of volatiles through Earth’s solid interior.
Earthquakes facilitate the concentration of many
important metals into ore deposits.
In the mantle, the carbon and hydrologic cycles are
fed when the subducting slab releases water, CO2,
and other volatiles at roughly 100-km depth beneath
the overriding plate.
Earthquakes Influence Geochemical
Cycles (2)

Some seismologists speculate that water released
from the slab helps cause brittle fracture in the slab
itself, and that water may be necessary for deep
earthquakes to occur in the Benioff zone.
Homework # 2
Due 3/8/2004
1. (25pts)
(a) Explain how seismologists use the seismic moment to estimate the earthquake size.
(b) Suppose a crustal fault 3 km long and 2 km wide slips 10 cm? What is the seismic
moment? (use the shear stiffness of the surrounding rock in the textbook).
(c) What is the Richter magnitude?
(d) How much will seismic moment and magnitude increase if the length, width, and slip of
the fault each grows by a factor of 3.16?
2. (20pts) What are the two types of seismic body waves? What are their main distinguishing
features? What are surface waves?
3. (25pts) Explain the following seismic discontinuities in the earth’s interior and what
causes the change in seismic velocity across them:(a) M-Discontinuity (b) LowVelocity Zone (c) 670-km Discontinuity (d) Core-Mantle Boundary.
4. (30pts) 恰好位在震源位置的地震儀測站記錄到PcP, ScS 和PKiKP三個波相的走時
分別為8分31秒, 15分36秒和16分35秒。另外在地球相反的一側離震源距離180
度的測站記錄到PKIKP波的到時為 20分12秒。繪出這些波相在地球內部傳遞的路
徑,並根據地球的分層,利用這些波相的走時估算地函 (Mantle) P和S波的平均速
度以及外核 (Outer Core) 和內核 (Inner Core) P波的平均速度。
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