1. Page 1 British Crown Copyright 2007/MOD Modelling Earthquake Generated Infrasonic Waveforms using a Fraunhofer Approximation at the Ground-Atmosphere Interface Green, D. N. 1, Guilbert, J. 2, Le Pichon, A. 2, Sebe, O. 2 and Bowers, D. 1 1.AWE Blacknest, UK 2.CEA/DASE, Bruyeres-le-Chatel, France www.brittanica.com geoinfo.amu.edu.pl Ground-to-air coupling Fraunhofer approximation to the Rayleigh integral Two example earthquakes : Folkestone, UK, Ml 4.2 Ica, Chile, Mw 8.0

2. Page 2 British Crown Copyright 2007/MOD Introduction Earthquake generated infrasound Coupled either (i)Near epicentrelocal ground motion (ii) Along seismic surface wave path topographic interaction (Mutschlecner and Whitaker, 2005)

3. Page 3 British Crown Copyright 2007/MOD Introduction (2) Array processed data Deduce topographic features involved e.g., Le Pichon et al. (2003) – Kunlun EQ Constraints Traveltime Azimuth Seismic surface wave velocity Infrasound group velocity Assumptions

4. Page 4 British Crown Copyright 2007/MOD From Source to Station Seismic Source Topography Receiver Array Source Parameters Topographic Parameters Instrument Response Earth Velocity Structure Atmospheric Velocity Structure Seismic Waves Infrasound Waves Coupling Problem

5. Page 5 British Crown Copyright 2007/MOD The Coupling Problem Rayleigh Integral Pressure due to a moving piston related to the acceleration of the piston

6. Page 6 British Crown Copyright 2007/MOD Towards Synthetics Fraunhofer Approximation Assumptions Iso-phase The whole diffractor vibrates in phase Far-field Distance to observation point is much greater than the dimensions of diffractor (Formulation tested against analytic results of Freedman, 1960)

7. Page 7 British Crown Copyright 2007/MOD Diffraction Pattern Off-axis Angle (Formulation tested against analytic results of Freedman, 1960) Correct spatial pattern Correct axial pressure values

8. Page 8 British Crown Copyright 2007/MOD Two example Earthquakes Folkestone EQ, UK 28/04/2007 M L = 4.2 (BGS) Very little local topography Ica EQ, Peru 15/08/2007 M W = 8.0 (USGS) In area of high topography (Andes)

9. Page 9 British Crown Copyright 2007/MOD Folkestone Earthquake, UK, 28/04/2007

10. Page 10 British Crown Copyright 2007/MOD Folkestone Earthquake, UK, 28/04/2007 Back Azimuth: 21±3° Trace Velocity : 332±6m/s Time elapsed from seismic origin time: 840s Epicentre to Station range: 284km Infrasonic Parameters 284/840 = 0.338km/s If infrasound generated local to epicentre, approx. celerity =

11. Page 11 British Crown Copyright 2007/MOD Folkestone EQ: atmospheric parameters Atmospheric Profile -European Centre for Medium-Range Weather Forecasts (ECMWF) Weak stratospheric waveguide Also thin tropospheric waveguide Both waveguides confirmed by ray-tracing

12. Page 12 British Crown Copyright 2007/MOD Folkestone EQ - Reconstructing the source Celerity used = 0.340km/s TT = v s.d s +v i.d i Travel time is sum of seismic and infrasound propagation times (assuming tropospheric propagation)

13. Page 13 British Crown Copyright 2007/MOD Folkestone EQ - Reconstructing the source Celerity used = 0.300km/s TT = v s.d s +v i.d i Travel time is sum of seismic and infrasound propagation times (assuming stratospheric propagation)

14. Page 14 British Crown Copyright 2007/MOD Folkestone EQ – Modelling Idea White cliffs of Dover Only prominent topographic feature in proximity to earthquake

15. Page 15 British Crown Copyright 2007/MOD Folkestone EQ – Acceleration records Strong motion seismometer within 5km of epicentre Good constraints on local ground motion Z N E

16. Page 16 British Crown Copyright 2007/MOD Folkestone EQ – Position of Sea Cliffs Mean height in section between Folkestone and Dover: 75m (Data coutesy of Beaches at Risk Project (BAR), University of Sussex) www.brittanica.com

17. Page 17 British Crown Copyright 2007/MOD Modelling Method Seismic source model Cliff Parameterization Pressure waveforms for each cliff section Waveform at receiver Synthetic seismograms Coupling equations Geometrical spreading & summation over cliff sections Near-field acceleration records Cliff height and orientation data Constraining the problem

18. Page 18 British Crown Copyright 2007/MOD Folkestone EQ – Synthetic Pressure Waveforms Data Model (filtered 2-8Hz – black) (unfiltered– blue) Model vs Data Order of magnitude agreement Duration Amplitude

19. Page 19 British Crown Copyright 2007/MOD Ica EQ, Peru – 15/08/2007 Common area for large EQ’s generating Infrasound. Ica (Le Pichon et al., 2002, 2006) M w = 8.0 1.5 Hours Azi. Vel. Azimuths = 250 to 300 degrees Phase Speeds = 0.34 to 0.38 km/s

20. Page 20 British Crown Copyright 2007/MOD Ica EQ – Reconstructing the source Extended source region in Western Andes ~ 1000km long

21. Page 21 British Crown Copyright 2007/MOD Ica EQ – Topography Gradients High density areas of detections Large topographic gradients BUT: Large gradients in Eastern Andes No observed infrasound

22. Page 22 British Crown Copyright 2007/MOD Discussion / Implications Folkestone Earthquake, UK Instructive because of simple topography High amplitude accelerations / proximity to cliffs observable infrasound from small EQ Ica Earthquake, Peru Non-trivial topographymore difficult to explain waveforms Waveformsprovide physical meaning for signal structure However, individual topographic diffractors can be identified amplitudes duration Poorly constrained problem

23. Page 23 British Crown Copyright 2007/MOD Conclusions Fraunhofer approximation to Rayleigh Integral Non-computationally expensive routine Adapted to give ground-to-air coupling waveforms Folkestone Earthquake, UK, 2007 Example of isolated topographic interaction Satisfactory model for signal amplitude & duration Ica Earthquake, Peru, 2007 More complicated example of topographic interaction Complications – require good seismic model to resolve

24. Page 24 British Crown Copyright 2007/MOD Acknowledgements and References NERIES - Network of Research Infrastructures for European Seismology CEA/DASE – For hosting me during July 2007 Freedman, A., Sound Field of a rectangular piston, 1960, JASA, 32(2) 197-209 Le Pichon, A. et al., Infrasonic imaging of the Kunlun Mountains for the great 2001 China earthquake, 2003, GRL, 30(15) 1814 Le Pichon, A. et al., Ground-coupled air waves and diffracted infrasound from the Arequipa earthquake of June 23, 2001, 2002, GRL 29(18), 1886 Mutschlecner, J. P. and Whitaker, R. W. Infrasound from earthquakes, 2005, JGR, 110 D01108

25. Page 25 British Crown Copyright 2007/MOD Comparison with previous Earthquakes Amplitudes are consistent with previously found trend Low magnitude event has shorter duration than expected. Influence of noise? (Le Pichon et al. 2006 – Surface Mag used)

26. Page 26 British Crown Copyright 2007/MOD Folkestone EQ – Incorporating Coastline Variability = Max angle in perturbations of cliff angle (100m sections) The higher the angle – the less regular the cliff face Higher angle = More scattering and higher amplitude synthetics

27. Page 27 British Crown Copyright 2007/MOD Folkestone EQ – Influence of EQ Focal Mechanism Changing fault orientation changes amplitudes by < 1 order of magnitude

28. Page 28 British Crown Copyright 2007/MOD Ica EQ – Infrasonic Observations

29. Page 29 British Crown Copyright 2007/MOD Ica EQ – Towards Synthetic Waveforms Data Increasing azimuth over time

30. Page 30 British Crown Copyright 2007/MOD Ica EQ – Towards Synthetic Waveforms Data compared to Model Picks out correct azimuths BUT many more predicted than observed Modelled amplitude ~ order of magnitude too low

31. Page 31 British Crown Copyright 2007/MOD Ica EQ – Towards Synthetic Waveforms Map of modelled reflectors Eastern Andes - Influence not observed in data. Predicted reflectors close to Station - probably in shadow zone

32. Page 32 British Crown Copyright 2007/MOD Discussion / Implications Future Work Implications of earthquake source directivity Insight into ground motion on steep slopes surrounding large earthquakes Physics behind the empirical relationships