Page 1 British Crown Copyright 2007/MOD Modelling Earthquake Generated Infrasonic Waveforms using a Fraunhofer Approximation at the Ground-Atmosphere Interface

Page 1British Crown Copyright 2007/MOD

Modelling Earthquake Generated Infrasonic Waveforms usinga 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, UK2. 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 4.2Ica, Chile, Mw 8.0


Introduction

Earthquake generated infrasound

Coupled either(i) Near epicentre local ground motion(ii) Along seismic surface wave path

topographic interaction

(Mutschlecner and Whitaker, 2005)


Introduction (2)

Array processed data• Deduce topographic features involved• e.g., Le Pichon et al. (2003) – Kunlun EQ

Constraints Traveltime Azimuth

Seismic surface wave velocityInfrasound group velocity

Assumptions


From Source to Station

SeismicSource

Topography ReceiverArray

SourceParameters

TopographicParameters

InstrumentResponse

EarthVelocity Structure

AtmosphericVelocity

Structure

SeismicWaves

InfrasoundWaves

CouplingProblem


The Coupling Problem

Rayleigh Integral

• Pressure due to a moving piston related to the acceleration of the piston


Towards Synthetics

Fraunhofer Approximation

Assumptions

• Iso-phaseThe whole diffractor vibrates in phase

• Far-fieldDistance to observation point is much greaterthan the dimensions of diffractor

(Formulation tested against analytic results of Freedman, 1960)


Diffraction Pattern

Off-axisAngle

(Formulation tested against analytic results of Freedman, 1960)

• Correct spatial pattern• Correct axial pressure values


Two example Earthquakes

Folkestone EQ, UK28/04/2007ML = 4.2 (BGS)Very little local topography

Ica EQ, Peru15/08/2007MW = 8.0 (USGS)In area of high topography (Andes)


Folkestone Earthquake, UK, 28/04/2007


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 =


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


Folkestone EQ - Reconstructing thesource

Celerity used = 0.340km/s

TT = vs.ds+vi.di

• Travel time is sum ofseismic and infrasoundpropagation times

(assuming tropospheric propagation)


Folkestone EQ - Reconstructing thesource

Celerity used = 0.300km/s

TT = vs.ds+vi.di

• Travel time is sum ofseismic and infrasoundpropagation times

(assuming stratospheric propagation)


Folkestone EQ – Modelling Idea

White cliffs of Dover• Only prominent topographic feature in proximity to earthquake


Folkestone EQ – Acceleration records

Strong motion seismometer within 5km of epicentreGood constraints on local ground motion

Z

N

E


Folkestone EQ – Position of Sea Cliffs

Mean height in section betweenFolkestone and Dover: 75m

(Data coutesy of Beaches at RiskProject (BAR), University of Sussex)

www.brittanica.com


Modelling Method

Seismic sourcemodel

CliffParameterization

Pressure waveformsfor each cliff section

Waveform atreceiver

Syntheticseismograms

Couplingequations

Geometricalspreading &summation overcliff sections

Near-field accelerationrecords

Cliff height andorientation data

Constraining the problem


Folkestone EQ – Synthetic PressureWaveforms

Data

Model(filtered 2-8Hz – black)(unfiltered– blue)

Model vs Data

• Order of magnitude agreement• Duration• Amplitude


Ica EQ, Peru – 15/08/2007

Common area for large EQ’s generatingInfrasound.

Ica

(Le Pichon et al., 2002, 2006)

Mw = 8.0

1.5 Hours

Azi.

Vel.

Azimuths = 250 to 300 degrees

Phase Speeds = 0.34 to 0.38 km/s


Ica EQ – Reconstructing the source

Extended source region in Western Andes ~ 1000km long


Ica EQ – Topography Gradients

High density areas of detections Large topographic gradients

BUT: Large gradients in Eastern Andes No observed infrasound


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 topography more difficult to explain waveforms

Waveforms provide physical meaning for signal structure

• However, individual topographic diffractors can be identified

amplitudesduration

• Poorly constrained problem


Conclusions

Fraunhofer approximation to Rayleigh IntegralNon-computationally expensive routineAdapted to give ground-to-air coupling waveforms

Folkestone Earthquake, UK, 2007Example of isolated topographic interactionSatisfactory model for signal amplitude & duration

Ica Earthquake, Peru, 2007More complicated example of topographic interactionComplications – require good seismic model to resolve


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


Comparison with previous Earthquakes

Amplitudes are consistent with previously found trend

Low magnitude event has shorterduration than expected. Influenceof noise?

(Le Pichon et al. 2006 – Surface Mag used)


Folkestone EQ – Incorporating CoastlineVariability

= Max angle in perturbationsof cliff angle (100m sections)

The higher the angle – the less regular the cliff face

Higher angle =More scattering and higheramplitude synthetics


Folkestone EQ – Influence of EQ FocalMechanism

Changing fault orientation changesamplitudes by < 1 order of magnitude


Ica EQ – Infrasonic Observations


Ica EQ – Towards Synthetic Waveforms

Data

Increasing azimuth overtime



Data compared to Model

Picks out correct azimuthsBUTmany more predictedthan observed

Modelled amplitude~ order of magnitude too low



Map of modelled reflectors

Eastern Andes- Influence not observed in data.

Predicted reflectors close toStation- probably in shadow zone


Discussion / Implications

Future Work

• Implications of earthquake source directivity

• Insight into ground motion on steep slopes surrounding largeearthquakes

• Physics behind the empirical relationships

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Page 1 British Crown Copyright 2007/MOD Modelling Earthquake Generated Infrasonic Waveforms using a Fraunhofer Approximation at the Ground-Atmosphere Interface