Download Tracing rays through the Earth

Tracing rays through the Earth
• Ray parameter p:
receiv er
source
i1
sin i1 = sin i2= …= sin in = const. = p
V1
V2
Vn
⇒ p is constant for a given ray
V1
i2
V2
i3
V3
i4
V4
i c ritical
• If V increases continuously
with depth ⇒ the ray flattens
and eventually bends upwards
until critical refraction is
reached
critical ref raction
receiv er
source
Velocity increases
continuously with depth
Tracing rays through the Earth
• If we know the variation
in seismic velocity with
depth, given the ray
parameter p, we can:
– Determine the ray trajectory
– Determine the ray travel
time
• Repeating this for all
possible take-off angles ⇒
graph of travel time versus
distance
Velocity-depth structure
• In general:
– We do not know the velocity
variation with depth
– We measure the travel time
(from epicenter to seismic
station)
⇒Inverse problem to get
velocity at deepest point
on the ray path (using a
large number of travel
time observations)
• sin i = Vdt ⇒ R sin i = dt
RdΔ
V
dΔ
Velocity-depth structure
•
Applied to the Earth:
– Major discontinuities in the seismic structure of the Earth ⇔ discontinuities
in mineralogy/petrology
• Moho, 410 km, 660 km, D”, CMB
– IASP91 model (below), PREM (Preliminary Reference Earth Model)
– These models assume perfect spherical symmetry.
Wave propagation in the Earth
P
S
K
I
J
c
i
a P-wave in the mantle
an S-wave in the mantle
a P-wave through the outer core
a P-wave through the inner core
an S-wave through the inner core
a reflection from the CMB
a reflection from the OCB-ICB
• A classic black and white picture….
Wave propagation in the Earth
•The travel-time of waves to a
given epicentral distance is
affected by the focal depth of the
earthquake, up to several hundred
kilometers.
•Most t vs. Δ curves assume:
- a perfectly spherical Earth
- same vertical structure
underneath each location
•Works fairly well, but lateral
velocity variations exist – leads to
seismic tomography
A more dynamic view of wave propagation in the Earth…:seismic wave animation
(seiswave.exe, http://www.geol.binghamton.edu/faculty/jones/ )
Seismic tomography
•
Spherical symmetry not perfectly valid:
– There are lateral variations of seismic velocities
⇒Travel time deviations in comparison to theoretical calculated values
⇒Travel-time residuals or anomalies
•
•
– Causes for anomalies:
- focal depth of earthquake not zero
- local velocity-depth distribution under a particular network
- spherical symmetry not perfectly valid due to Earth’s ellipticity
Travel times can be classified as “early” or “late” depending on whether the
wave passes through a “slow” or “fast” region
On global scale, anomalies interpreted in terms of temperature and rigidity
– “slow” or “warm” regions ⇒ above average temperature and lower rigidity
– “fast” or “cold” regions ⇒ below average temperature and higher rigidity
Tomographic Imaging
• Using travel time
information from many
stations ⇒ reconstruction
of 2D and 3D velocity
structures
• Various scales:
– Global
– Regional
– Local
3D view of the mantle, with
orange surfaces surrounding warm
blobs of mantle, assumed to be
rising plumes.
Tomographic Imaging
• Can be done using body
waves or surface waves
• Inversion of body-waves
data only method to view
lateral variations in
velocity in deep interior
• Velocities in lithosphere
correspond to plate
movement, lower mantle
corresponds to long
wavelength features
Crust and crust-mantle boundary
Mohorovicic, 1909:
– Close to epicenter: single P-wave arrival (Pg)
– Beyond ~200 km from epicenter: Pg was overtaken by
another P-wave arrival (Pn) which traveled faster
– Pg = direct wave, propagates in the crust (5.6 km/s)
– Pn = refracted wave (head wave), propagates through the
upper mantle (7.9 km/s)
– Estimated there was an increase in velocity at 54 km depth
– Mohorovicic discontinuity = Moho
Earth’s Crust
• Strong lateral variations in crust, can’t use inversion of
body wave travel-times to get velocities (why?)
– can use seismic refraction profiles and deep crustal reflection
sounding
• On a global scale, crustal thickness is variable
– Continental vs. oceanic crust
– global average is 33 km
• Variation of velocity with depth depends on location
– ancient continental crust very different than young continental or
oceanic crust
Oceanic Crust
• Oceanic crust
– averages 5-10 km
– under average water depth
of 4.5 km
• Layers
– oceanic sediments
• increase in thickness away
from ridges
– igneous basement
• thin upper layer of basaltic
lava flows over a complex
of basaltic intrusions
– gabbroic rocks
Oceanic crust
Continental Crust
• Continental crust
– stable continents average thickness 3540 km
– under young mountains, 50-60 km thick
– much more complicated than oceanic
• Layers
– crustal sediments
– upper crust basement (granitic)
– seismic discontinuity (not everywhere)
• sialic low velocity layer – laccolithic
intrusions?
– middle crust (migmatites)
– lower crust (amphibolites/granulites)
• has a high velocity upper layer
Continental crust
The Mantle
•
•
•
Upper limit = Moho
Lower limit = CMB (core-mantle boundary)
Layers:
–
–
–
–
–
–
–
rigid upper lid
low-velocity layer (LVL)
transition zone – 220-410 km
transition zone – 410-670 km
transition zone – 670-770 km
D’
D’’
Upper Mantle
• Upper mantle:
– spherical symmetry does not hold well due to lateral variations
– peridotites with olivine as dominant mineral
– Moho to 80-120 km – rigid lid
• paired with lower crust ⇒ lithosphere – layer that participates in plate
tectonics
– 120-220 (+/- 30) km = low velocity zone
• attenuation (viscosity) = asthenosphere
• body waves do not bottom out in LVZ, must use long-period surface waves
• layer is not sharply defined
– 400 km: discontinuity, velocity increase (petrological change, olivine
→ spinel phase transition)
– 400-660 km: phase change, β-spinel → γ-spinel
– 650-670 km: discontinuity, velocity increase (γ-spinel → perovskite)
Lower Mantle
• Lower mantle
– Everything below 670 km
– Composition poorly known
• oxides of Fe, Mg, Fe-Mg silicates with perovskite structure
– 670-770 km: high, positive velocity gradient
– D’ layer: most of the lower, “normal” mantle
• smooth velocity gradients
• no seismic discontinuities
– D” layer: thin layer just above core-mantle boundary
• 150-200 km thick
• lateral variations of velocity (positive and negative):
– fast regions below subductions (positive)
– slow regions below ocean, i.e. Pacific Basin (small or negative)
• Source of mantle plumes?
The Core
•
Gutenberg, 1914:
– Shadow zone for P-waves (105143 degrees)
– Core-mantle boundary = 2900 km
– Gutenberg discontinuity
•
•
Mostly iron, + up to 10% nickel
Lehman, 1936:
– Weak P-wave arrivals within
shadow zone
– Inner core with higher velocities
⇒ solid
– Liquid-inner core boundary =
5000 km
•
Core
– Outer = liquid
• Viscosity ~ water
• Source of the Earth’s magnetic
field
– Inner = solid
Seismic anisotropy
• Definition - dependence of seismic velocity on
direction a seismic wave travels through a crystal
– seismic waves traveling parallel to the a-axis of an
olivine crystal travel faster than waves traveling
perpendicular to the a-axis
• Mantle flow aligns the olivine crystals with the a
axes parallel to the flow
⇒ measuring anisotropy will tell flow direction:
horizontal flow (shields) or vertical flow (MOR)
• Lower mantle mostly isotropic but D” layer
locally anisotropic (currently under investigation)
Anisotropy of the Core
•
Inner core is anisotropic
– may be due to inner core flow aligning the iron crystals like olivine in the
mantle
– velocities 2-4% higher than expected
– symmetry about the axis that is approx. aligned with Earth’s N-S spin axis
– can measure this by travel times of body waves
• paths parallel to spin axis are fastest
•
•
Repeated measurements of P-waves through inner and outer core ⇒
position of inner core’s fast axis has moved w.r.t. to crust and mantle
over last 3 decades
Core movement is a rotation
– inner core rotating faster than rest of the Earth
– several tenths of a degree/year ⇒ complete revolution would take
centuries
What have we learned?
• As waves propagate, they can undergo:
– Reflection
– Refraction (special case of critical refraction)
– Snell’s law applies ⇒ ray-tracing
• Using the propagation of seismic waves in the Earth, one can
show that:
– The structure of the Earth has a spherical symmetry
– There are major discontinuities in seismic velocities in vertical
direction, lateral variations give rise to seismic anisotropy and direction
of flow
– These discontinuities separate layers (shells) of ~homogeneous
petrological composition
•
•
•
•
Crust (granite – basalts/dolerite/gabbros)
Mantle, with LVZ = asthenosphere (peridotite)
Liquid outer core (Earth’s magnetic field), iron (+ nickel)
Solid inner core, iron (+ nickel)