Analysis of Calving Seismicity from Taylor Glacier, Antarctica
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Transcript of Analysis of Calving Seismicity from Taylor Glacier, Antarctica
Analysis of Calving Seismicity from Taylor Glacier, Antarctica
Josh CarmichaelDepartment of Earth and Space Sciences
University of Washington, Seattle
What I will tell YouPart I: Introduction to the science Calving: what it is, why you should care Seismology: what it is, some theory, applied
to glaciology Problem Statement: how to identify a calving
event from a few seismometers The Seismogram: part path, part calving
source1. Calving source as a dislocation on a fault2. Expressed features along the path from a source
to a receiver
What I will tell You (cont…)
Part II: Analysis of Seismograms Interlude: Questions so far? Cross Correlation of waveforms, what it is,
what it might say Polarization analysis: direction energy
comes from Fourier Transforms of time series, power
spectra, interpretation Other ideas
Calving of Dry Land Glaciers Calving: The partial or full collapse of an ice
shelf—usually from free surface evolution Illustration: why read this slide when you
can watch the movie What you just saw:1. 10 days of visible buckling + deformation, prior
to calving2. Complete calving > 3 m thick ice column ~35
meters long in < 1 day
Why Study Calving? (Who Cares?)
Climatologists, Glaciologists: use Antarctica and Greenland to study climate change
Calving is the dominant mechanism for ice loss in Antarctica
Most models don’t assume the existence of ice cliffs, let alone, calving bad
Need way to measure calving frequency!
Why Seismology can Help: Calving Ground Displacement
Calving events shake ice and ground E,N,Z recorded by seismograms
Sensor sample rate = 200Hz Instrumental temperature
resilience: operates to -40 IF calving seismicity is
unambiguous can count events
Can estimate calving locations (inverse problem)
The Array
1000 meters
A Model for Calving Source Decomposition
Pre-Calve: Column loads glacier; deformation time scale ~10 days; damage evolution to crack formation
Precursor events seismically similar
A Model for Calving Source Decomposition
Crack propagation along damaged-weakened regions
Column unloads free surface
A Model for Calving Source Decomposition
Energy scattering from column collapse; incoherent, high frequency
Energy Scatter
Problem Statement
Can a calving event be unambiguously identified in the seismic record?
Can it tell us about seasonal precursor events?Bottom-Up Problem: Seasonal calving statistics realizable given calving waveforms can be recognized
Some Basic Questions Concerning the Problem:
What else excites the sensor? Even if you know ice calved, is it distinct on
the seismogram? (source uniqueness?) The opposing question: Will separate
calving events look similiar? (well-posed?) What does calving look like?
(characterization) The big question
We will come back to this
Enter Non-Global Seismology
Experimental Seismology: using ground motion records to infer structure, or nature of source
Detectable by seismometers: helicopters, tides, landslides, lightening, anything that is loud…
“Seismograms”: ground motion waveforms (velocity usually what is really recorded).
Differences from global seismology: less attenuation, rays sample local structure only, shorter wavelengths, tighter array coverage.
Seismic Waves in Boring Media
Equation of motion
tGctG
fuctu
inknlijkljin
iklijklji
ξx2
2
2
2
Green’s function*
Impulsive force*
dtG
nucdtuq
npjiijpqn
0,;,,,
ξxξx
From Betti’s Rep. Thm. for an internal dislocation on
V
Sx
,ξiu
* If you care: ask me what a delta function really is, or what LG = means rigorously, after this talk
mpq=
What Displacement Solutions Look Like
For an infinite, homogeneous, uniform medium, with no initial motion and a point dislocation:
For half-space, with traction-free boundary conditions, with no initial motion or body forces:
rm
stuffr
mstuffmt
rG
m pqpqpq
q
nppq
)()(1~ 24
tit ZNE 00 exp, xkUUUxu T
The Displacement Field Integral
The displacement field representation is a convolution of two tensors—a smoothing operation
The Green’s function spatial derivative is physically a force couple, with moment arm in the q direction
Units of moment per unit area Time shift convolution
dtG
nucdtuq
npjiijpqn
0,;,,,
ξxξx
q
p
Couple magnitude
Integrand is inner product of 2nd and 3rd order tensor: result is vector
Seismic Waves in Boring Media (continued)
The point: displacement on determines displacement everywhere thru a convolution of the impulse response’s derivative with the slip function
Interpretation: Equivalent to a sum of force couples distributed over internal surface:
,2000,000,
,
3
3
3
ξξ
ξm
ξ
uu
u
mnuc pqkijkpq :tensioninformingcrackaForx3
CLVD Moment Density Tensor
Examples of Moment Tensor Physical Realizations
Respectively, left to right: (1) An explosion or implosion (2) The compensated linear vector dipole (3) mode III failure (4) mode II failure
What’s Seen by the Sensor A seismogram is a convolution of the slip
contribution and the source:
domaintimedmtG
tu pqq
npn
,;, 00 ξx
Green function = source Slip, material effects
domainfreqdSU pqq
npn .,;, 00
ξx
Convolution theorem turns integration into multiplication, but freq. domain loses phase info.
t)
What to Expect Beneath the Glacier and Sand
Sensors close to source see top layer effects If we ignore deeper layering, must ignore arrivals
corresponding to smaller ray parameters
~50m
~30m
~200m-500m
integrand mediaboring
factornattenuatio
timetravelway2
tta
vh
t
TTttRtr
tuttatr
i
j j
ji
jj
i
jjj
N
iiii
2
1
1
11
Summary So Far
Same location events may differ only in source Same source events may differ only in their path Identical calving events at distinct locations have
identical waveforms, minus the path Frequency domain turns temporal convolution into
multiplication
dmtG
trtatu pqq
npn
,;, 00 ξx
Seismogram for an internal dislocation in the ice:
Now For Some Data
Ideas on how to Analyze the Data
Time, Location of a Calving Event
Broken tilt sensors and cables time of calving
GPS locations known
Search through record ~10 days prior to total data loss
Plan: Find Similar Waveforms from Same Location
From previous slides, we expect waveforms for similar events to match;
We know from observation where the most actively calving region is
First off: we find events that arrive @ the cliff-adjacent stations first and compare…(no location necessary)
Cross-Correlation: Test for Waveform Similarity
10;
;
22
Ni
i
iNi
iiNi
Cc
dudw
duwCc
tutwdutwtC
Global maxima of a the cross-correlated function value of t gives max. overlap
High correlation coefficient high waveform similarity
maximizedistCt Ni:
Structure Features or Source?
Spectral peaks obvious on each station Glacial spatial features, wave speed standing
waves trapped in ice could have 23Hz peak
Common Spectral Amplitude
Closer station: rich in high freq.
Distant station: rich in lower freq.
Sam
e Event
Most similar to calving event
Application of Cross Correlation: Categorizing Waveforms
Is this all thermal skin cracking? Is any of this actually calving?
Antarctic D
ayA
ntarctic Day
R > 0.97
Log[ vL 2/v
H2 ] vs. tim
e
Vertical Component
Organizing Multiplets
Multiplet: several events originating from the same location, separated temporally
Polarization: The direction of particle motion for a wave; seismic waves characterized by 3 polarization vectors
Polarization Analysis of Multiplets
1
T
EEU
uuuuuu
uuuuuuVVU
uuuV
V
3
2
1
000000
......
...
.........
ze
nnne
ezenee
zne
izjnie
iZiNiE
iZiNiE
t
t
tNtutNtutNtu
ttuttuttutututu
Construct a matrix of displacement in each direction
Form a 3x3 matrix Perform an eigenvalue
decomposition (SVD also permissible)
The magnitude of the eigenvalue ratio: provides a measure of size of polarization axes
Polarization Data
Eigenvalue RatiosLargest Eigenvectors
rotated
Future Directions (if any)
Model the calving of large ice columns near failure time (“easy part”)
Pre-Cursory event modeling of unstable cliff face (“hard part”)
Hard part involves multiple time scales: Ice wall deformation (~50 days) Crevasse opening (~10 days) Fault plane growth, generation (~ 1 hour?) Rupture (~ 1 sec)
Summary Calving is the most prominent form of ice
loss from Antarctica Sensors: see u = convolution of couple
distribution over plane w/moment density and path
Data shows: Diurnal fluctuations in warm months of seismic
activity Waveforms may be categorized into “similarity”
sets for discerning source differences Polarization shows activity swarms from same
direction
Thanks To...
Ken Creager Erin Pettit Matt Szundy Matt Hoffman Erin Whorton AMATH