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