Transcript Structure of the Earth`s Deep Interior

Geology 5640/6640 13 Apr 2015
Introduction to Seismology
Last time: Ray-Tracing in a Spherical Earth
• In a spherical geometry, the angle of incidence for a ray at the
top of a uniform-velocity layer is slightly different than the
angle at the bottom.
• We account for this by re-writing Snell’s law to account for the
change in angle of incidence, as:
r1 sin 1 r2 sin 2

p  ui ri sin i
1
2
• Instead of units of slowness, the ray parameter p = dT/d has
units of time per angle in radians
• The
ray-tracing relations become (for  = r/v):
T p
r0
 uds  2 
rp
 2 dr
r  p
2
r

p 2 p 
0
2
rp
r0
dr
r  p
2
2
Read for Wed 15 Apr: S&W 177-184 (§3.6)
 p 2 
rp
 2  p2
r
dr
© A.R. Lowry 2015
Note that part of the T vs  slope in a spherical geometry is just
geometry,
while part
reflects the
change in
velocity with
depth…
And note that
our early
understanding
of travel-times
for the various
phases in the
Earth (and
hence
structure of
the Earth’s
interior) relied
on ray theory
in a spherical
Earth!
Structure of the Deep Earth’s Interior
Region
A
B
C
D
D’
D”
E
F
Depth (km)
33
413
670
2898
1000-2700
2700-2900
4982
6371
1940
1991
Description
Crust
Upper mantle
Transition region
Lower mantle
Lower mantle
2-3% velocity jump
Outer Core
Inner Core
Recent additions to knowledge
of the deep Earth’s interior (in
the last several decades) from
seismology include recognition
of phase boundaries at ~410
and 670 km depths, and phase
and/or compositional
boundary(ies?) in the
lowermost mantle
Understanding the velocities observed at these depths requires
a combination of high P-T lab measurements, geodynamical
modeling and geochemical measurements of surface magmas
Getting this
kind of
information
is of course
easier at the
shallower
depths…
Schmandt et al., Science, 2014
Schmandt et al., Science, 2014
Colors are flow model predictions of upwelling (red)/
downwelling (blue) for two different global shear wave velocity
models… White squares indicate where Ps converted waves
suggest very low vS just below the transition zone!
Measurements of
P-T conditions for
formation of postperovskite are a bit
uncertain, and the
existence or not of
this phase depends
on the (poorly
known) geotherm at
the core-mantle
boundary…
Tomograms at
2811 km depth
The combination of geodynamical modeling and geochemistry
with the seismic data suggests thermochemical convection
(plumes arise from a thin, compositionally distinct layer near
CMB) modulated by slabs which may enter PPv phase nearby
But how did we get this info?
Practical
note:
Traveltime T &
distance
 depend
on source
depth!
T p 
 uds
Body Wave Studies
use the various P and S
 body wave paths through
crust, mantle and core to
image variations… with
emphasis on lateral
perturbations.
A quick reminder of seismic phase designations:
Each path provides a slightly different piece of information…
Most body waves are
minimum travel-time
phases… But surface
reflections in a spherical
Earth are called
“maximum time” because
they take longer to arrive
than would any other
travel path reflected off
the surface!
Consider a ray reflected
from a point  away:
   
T   T     T    
2
 2

   
T   T     T    
2
 2





We can use a Taylor series
expansion to write:
2
    dT
2 d T
T    T

Ý   
2
 2  d
d2
2
    dT
2 d T
T    T

Ý   
2
 2  d
d2
and summing:
  2 d 2T
T  2T
Ý   
2 
d2
The travel-time
curve is concave-down
d 2T
 2 0
d
So all other paths would be
faster!
Core phases:
Reflections off the core-mantle boundary also can be useful
for imaging lateral variations in mantle velocity…
We denote with a “c”, e.g. PcP, ScS
As the liquid outer core cannot transmit S, all SH motion is
reflected (both at the CMB and at the surface) resulting
in a particularly strong ScS phase (relative e.g. to PcS
and PcP).
Much of the P wave
energy by contrast is
transmitted.
Consider:
• From 0-98°, rays
refract within the
mantle
• Rays with slightly
smaller angle of
incidence are
refracted downward
(and the large
decrease in velocity
results in some
unusual moveout in
PKP! With increasing
i get C  B  A).
• As angle of
incidence and ray
parameter p decrease
the reflection off the
inner core (PKiKP)
is retrograde
• Rays with even
smaller angle of
incidence transmit
through the inner core
(PKIKP) in a
progressive direction
• The diffracted core
phase is also strongly
observed (Pd or
Pdiff).