Analysis of Calving Seismicity from Taylor Glacier, Antarctica

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Analysis of Calving Seismicity from Taylor
Glacier, Antarctica

• Josh Carmichael
• Department of Earth and Space Sciences
• University of Washington, Seattle

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What I will tell You

• Part 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 source
• Calving source as a dislocation on a fault
• Expressed features along the path from a source
  to a receiver

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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

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Calving of Dry Land Glaciers

• Calving The partial or full collapse of an ice
  shelfusually from free surface evolution
• Illustration why read this slide when you can
  watch the movie
• What you just saw
• 10 days of visible buckling deformation, prior
  to calving
• Complete calving gt 3 m thick ice column 35
  meters long in lt 1 day

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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 dont assume the existence of ice
  cliffs, let alone, calving ? bad
• Need way to measure calving frequency!

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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)

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The Array
1000 meters
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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

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A Model for Calving Source Decomposition

• Crack propagation along damaged-weakened regions
• Column unloads free surface

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A Model for Calving Source Decomposition

• Energy scattering from column collapse
  incoherent, high frequency

Energy Scatter
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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

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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
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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.

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Seismic Waves in Boring Media
S

• Equation of motion

x
S
V
Impulsive force
Greens function
mpq
From Bettis Rep. Thm. for an internal
dislocation on S
If you care ask me what a delta function
really is, or what LG d means rigorously, after
this talk
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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

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The Displacement Field Integral
Units of moment per unit area
Time shift ? convolution
Couple magnitude
xq
Integrand is inner product of 2nd and 3rd order
tensor result is vector
xp

• The displacement field representation is a
  convolution of two tensorsa smoothing operation
• The Greens function spatial derivative is
  physically a force couple, with moment arm in the
  xq direction

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Seismic Waves in Boring Media (continued)

• The point displacement on S determines
  displacement everywhere thru a convolution of the
  impulse responses derivative with the slip
  function
• Interpretation Equivalent to a sum of force
  couples distributed over internal surface

x3
CLVD Moment Density Tensor
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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

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Whats Seen by the Sensor

• A seismogram is a convolution of the slip
  contribution and the source

W(t)
Green function source
Slip, material effects

• Convolution theorem turns integration into
  multiplication, but freq. domain loses phase info.

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What to Expect Beneath the Glacier and Sand
50m
30m
200m-500m

• Sensors close to source see top layer effects
• If we ignore deeper layering, ? must ignore
  arrivals corresponding to smaller ray parameters

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Summary So Far
Seismogram for an internal dislocation in the ice

• 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

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Now For Some Data

• Ideas on how to Analyze the Data

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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

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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 _at_ the
  cliff-adjacent stations first and compare(no
  location necessary)

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Cross-Correlation Test for Waveform Similarity

• Global maxima of a the cross-correlated function
  ? value of t gives max. overlap
• High correlation coefficient ? high waveform
  similarity

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Structure Features or Source?
Closer station rich in high freq.
Distant station rich in lower freq.
Same Event
Common Spectral Amplitude
Most similar to calving event

• Spectral peaks obvious on each station
• Glacial spatial features, wave speed ? standing
  waves trapped in ice could have 23Hz peak

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Application of Cross Correlation Categorizing
Waveforms
Vertical Component
R gt 0.97
Antarctic Day
Antarctic Day
Log vL2/vH2 vs. time

• Is this all thermal skin cracking?
• Is any of this actually calving?

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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

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Polarization Analysis of Multiplets

• 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

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Polarization Data
rotated
Eigenvalue Ratios
Largest Eigenvectors
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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)

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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

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Thanks To...

• Ken Creager
• Erin Pettit
• Matt Szundy
• Matt Hoffman
• Erin Whorton
• AMATH