Observational Seismology
Lecture 3
Seismic Rays and Earth Structure
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History of Seismology
First seismologists were just
interested in earthquake
themselves.
Modern seismology starts in 1883
when John Milne proposed that
earthquakes could be recorded at
teleseismic stations
1889 von Rebeur Paschwitz recorded
Tokyo earthquake at Potsdam
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History of Seismology 2
1897 First breakthrough in determining Earth structure when
Oldham identified:
Large waves
Preliminary tremor
Secondary tremor
T
Large
Preliminary
Milne realised the significance and
used travel time difference to locate
earthquakes → global earthquakes
∆
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History of Seismology 3
1900 Oldham – P & S tremors travelled through the interior of the Earth while
large waves propagated close of the surface
1906 Oldham – made the big leap forward and supplied the seismological
evidence that the Earth has a central core
1909 Mohorovicic use the same argument of a discontinuity in the travel time
curve to identify the crust
To do better required a method of calculating wave velocity from travel time
curve more accurately:
1907 & 1910 Herglotz, Wiechert Bateman inversion
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History of Seismology 4
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History of Seismology 5
1914 Gutenberg calculated depth of the core as 2900km or 0.545R
Solid mantle
103
Liquid outer core
Shear wave shadow zone
Present estimates of core depth are within a few km
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History of Seismology 6
1936 Lehman discovered the Earth’s inner core
103
143
Found P wave reflected
from inner core in P
wave “shadow zone”
Lehman used a geometric argument, but both Gutenberg and
Jeffreys within 2 years had independently calculations of PKP
rays to verify hypothesis
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History of Seismology 7
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Jeffreys-Bullen Travel-Time Diagrams
Plots of travel times of teleseismic rays against epicentral distance ∆ provides the
basic observational data base: Jeffreys-Bullen travel-time diagram for earthquake
phases (1940).
Direct P
LQ Love wave
Direct S
LR Rayleigh wave
Travel time – from source to
station, but depends on reflection,
refraction and diffraction.
Surface wave plots of T vs ∆ are straight lines due to constant velocity along
path. Body wave plots of T vs ∆ are curves because velocity changes with
depth.
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Jeffreys-Bullen Travel-Time Diagrams
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Ray Parameter Definition
r sin i / v = constant = p
Ray Parameter
Constant, irrespective of local wave speed
Definition: The ray parameter is the geometric property of a seismic ray that
remains constant throughout its path. It is invariant in transmission, reflection,
refraction and transformation. It is equal to r sin i / v.
If the ray parameter is different we are talking about a different ray.
The consequence of Snell’s Law (i), that the refracted ray lies in the plane
containing the incident ray and the normal to the plane tangent to the interface,
implies, in spherically symmetric media, that it lies in a diametral plane (one
that contains the centre of the sphere).
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Wave transformation
Wave transformation is unique to seismology. Nothing like it occurs to sound,
light or water waves. It is a consequence of elastic waves crossing boundaries
in solid media.
Refracted S
Hitting a boundary with an incident P will
cause the rock at the point of incidence to be
Refracted P
not only compressed but also sheared.
Likewise when SV hits a boundary
obliquely get reflected and refracted P and
SV. When SH hits boundary obliquely only
get reflected and refracted SH. When P is
normal incident only get reflected and
refracted P.
Reflected P
Incident P
Reflected S
Several transformations can occur on one path leading to a complicated
picture. This complexity can actually be turned to our advantage.
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Seismic Rays in the Earth
PKP Refracted
through the
core
dif P
pP
PcP Reflected off
core
PcP
PcS
PP
Reflected off surface
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Deep earthquakes
Deeper earthquakes > 100km observed
Benioff zones
x
x
x x
xx
Earthquakes cluster on plane
dipping away from trench axis
Obtain accurate depths from surface reflection of seismic waves
Deep: phase
separation seen at
pP
teleseismic station
x
sP
P
Shallow
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Seismic Rays in the Earth 2
S
Secondary wave
J
S wave through inner core
Reflected P wave with 2 legs
SSS
Reflected S wave with 3 legs
pP
P wave with leg from focus to
surface
sS
S wave with leg from focus
to surface
SP
S wave reflected as P wave
PS
P wave reflected as S wave
P
Primary wave
K
P wave through outer core
I
P wave through inner core
P’
Abbreviation for PKP
PP
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Seismic Rays in the Earth 3
c
Wave reflected at outside boundary of outer core (e.g., ScS)
i
Wave reflected at outside boundary of inner core (e.g., PKiKP)
m
No. of reflections inside the outer boundary of outer core is m-1
d
Depth in km from which a seismic ray is reflected
h
Wave that may be reflected from a discontinuity around inner core
dif P,S Diffracted P or S waves around outer core
LQ
Love waves
LR
Rayleigh waves
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Seismic Rays in the Earth 4
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Jeffreys-Bullen Travel-Time Diagrams
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How do we determine Earth
structure from seismology?
Our basic observational data are
travel times for epicentral distance
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P & S velocities from Travel Times
Jeffreys & Gutenberg
PREM
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Rock physics
Once we have velocity profile we can deduce other physical properties.
P wave velocity (from rock physics)
1/ 2
⎛ K S + 4 .µ ⎞
3 ⎟
α = ⎜⎜
⎟
ρ
⎝
⎠
KS adiabatic bulk modulus
µ shear modulus
ρ density of materials
For mathematical convenience we define the Lamé parameters λ, µ:
λ = KS – 2/3. µ
so,
1/ 2
⎛ λ + 2µ ⎞
⎟⎟
α = ⎜⎜
⎝ ρ ⎠
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Rock physics 2
S wave velocity
1/ 2
⎛µ⎞
β = ⎜⎜ ⎟⎟
⎝ρ⎠
For a Poisson solid λ = µ by definition (actually a good approximation), then
α ((λ + 2µ ) / ρ )1/ 2
=
β
(µ / ρ )1/ 2
i.e., α / β = √3 = 1.73 for Poisson solid
P waves are just over 1½ times as fast as S waves
a useful guide
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Rock physics 3
Liquids have no shear strength
µ=0
so β = √(µ/ρ) = 0
Solid rocks have undergone compaction due to overburden & therefore
have greater densities, bulk modulus and shear modulus.
As KS & µ increase more rapidly with depth than ρ, so generally α, β
generally increase with depth (i.e., KS/ρ & µ/ρ both increase with depth)
Example
KS
µ
Granite
2.7x1010 N/m2
1.6x1010 N/m2
surface
3.0x1010 N/m2
at 10km
Water
Granite α ~ 5.5 km/s
β ~ 3 km/s
0.2x1010 N/m2
0
Water α ~ 1.5 km/s
β ~ 0 km/s
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Earth Models
(Bullen)
From seismology we know α, β so we know K/ρ & µ/ρ
What we don’t know is how Earth density varies with depth.
This we can be found by an iterative process using the AdamsWilliamson equation, derived from Newton’s Law of
Gravitation.
Must satisfy known Earth’s mass and moment of inertia.
Input from experimental rock physics/mineral physics, computer
simulations, known composition of universe/meteorites.
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Earth Models 3
(Bullen)
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Earth Models 4
Bullen shells
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Review
What makes seismology difficult?
1) Have to deal with P & S waves, Rayleigh and Love waves. (Other
phases: Stoneley waves and T phases would be covered in advanced
seismology.)
2) Earth is spherical, so have to introduce radius into ray parameter.
3) Earth is a complex structure – velocity varies with depth; discontinuities.
4) Physics of waves in solid media is complicated by transformations, e.g.,
P → P + SV.
However this very complexity necessitates the use of seismology
in determining Earth structure. Seismology has the highest
resolution of any of our geophysical probes in mapping out
Earth structure and composition.
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Review 2
Seismology has had the biggest impact of any discipline on
the Earth sciences and is predominant in geophysics.
•
Because of these complexities seismology is difficult.
•
Jeffreys: “If geophysics requires mathematics for its treatment
it is the Earth that is responsible, not the geophysicist” [1924].
•
The maths is horrendous, but the physics is accessible
(lectures 3 & 4):
1) The physics of waves – particle motion, reflection, refraction
and transformation.
2) Their ray paths and what that means in terms of Earth
structure.
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