1. Analysis of Calving Seismicity from Taylor Glacier, Antarctica Josh Carmichael Department of Earth and Space Sciences University of Washington, Seattle

2. 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 1. Calving source as a dislocation on a fault 2. Expressed features along the path from a source to a receiver

3. 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

4. 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 moviemovie What you just saw: 1. 10 days of visible buckling + deformation, prior to calving 2. Complete calving > 3 m thick ice column ~35 meters long in < 1 day

5. 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!

6. 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)

7. The Array 1000 meters

8. 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

9. A Model for Calving Source Decomposition Crack propagation along damaged- weakened regions Column unloads free surface

10. A Model for Calving Source Decomposition Energy scattering from column collapse; incoherent, high frequency Energy Scatter

11. 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

12. 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

13. 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.

14. Seismic Waves in Boring Media Equation of motion Green’s function * Impulsive force * From Betti’s Rep. Thm. for an internal dislocation on  V S x  * If you care: ask me what a delta function really is, or what LG =  means rigorously, after this talk m pq =

15. 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:

16. 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 qq pp Couple magnitude Integrand is inner product of 2 nd and 3 rd order tensor: result is vector

17. 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: x3x3 CLVD Moment Density Tensor

18. 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

19. What’s Seen by the Sensor A seismogram is a convolution of the slip contribution and the source: Green function = sourceSlip, material effects Convolution theorem turns integration into multiplication, but freq. domain loses phase info.  t)

20. 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

21. 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 Seismogram for an internal dislocation in the ice:

22. Now For Some Data Ideas on how to Analyze the Data

23. 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

24. 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)

25. 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

26. 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. Same Event Most similar to calving event

27. Application of Cross Correlation: Categorizing Waveforms Is this all thermal skin cracking? Is any of this actually calving? Antarctic Day R > 0.97 Log[ v L 2 /v H 2 ] vs. time Vertical Component

28. 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

29. 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

30. Polarization Data Eigenvalue Ratios Largest Eigenvectors rotated

31. 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)

32. 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

33. Thanks To... Ken Creager Erin Pettit Matt Szundy Matt Hoffman Erin Whorton AMATH