IUGG 2007 An amplitude battle: attenuation in bubbly magma versus conduit resonance Patrick Smith and Jürgen Neuberg School of Earth and Environment, The University of Leeds.

IUGG 2007 Outline of Presentation Background: low-frequency seismicity, seismic attenuation in gas-charged magma Methodology: Viscoelastic finite-difference model & Coda Q analysis Results and Implications

Low frequency seismicity High frequency onset Coda: harmonic, slowly decaying low frequencies (1-5 Hz) → Are a result of interface waves originating at the boundary between solid rock and fluid magma What are low-frequency earthquakes? Specific to volcanic environments IUGG 2007

Why are low frequency earthquakes important? Have preceded most major eruptions in the past Correlated with the deformation and tilt - implies a close relationship with pressurisation processes (Green & Neuberg, 2006) Provide direct link between surface observations and internal magma processes IUGG 2007

Conduit Properties seismic signals (surface) Magma properties (internal) Seismic parameters Signal characteristics Incorporate flow model data into wavefield models Combining magma flow modelling and seismicity Conduit geometry + Properties of the magma Attenuation via Q

IUGG 2007 Seismic attenuation in magma (i) Generation of low-frequency events: Can seismic energy travel through a highly viscous magma to produce resonance - or is it too highly attenuated? (ii) Allows us to link signal characteristics, e.g. amplitude decay of the coda, to properties of the magma such as the viscosity. Why is attenuation is important? Definitions: Apparent (coda) Intrinsic (anelastic) Radiative (parameter contrast, geometric spreading)

IUGG 2007 Amplitude decay of coda Comparison of approaches: 1.Kumagai & Chouet: used Sompi method to calculate complex frequencies to derive apparent Q from signals → resonating crack finite-difference model using bubbly water mixture to reproduce signals. Only radiative Q – no account of intrinsic Q 2.Our approach – viscoelastic finite-difference model, with depth dependent parameters: includes both intrinsic attenuation of magma and radiative energy loss due to elastic parameter contrast. Kumagai & Chouet (1999)

IUGG 2007 Intrinsic Q Intrinsic Q is directly dependent on properties of the attenuating material: but if these are unknown can be equivalently calculated from phase lag between applied stress and resulting strain: Q is dependent on the properties of the magma: Viscosity Gas content Diffusivity Amplitude Phase lag Applied stress Resultant strain time Collier et al. (2006)

IUGG 2007 Modelling Intrinsic Q To include anelastic ‘intrinsic’ attenuation – the finite-difference code uses a viscoelastic medium: stress depends on both strain and strain rate. Parameterize material using Standard Linear Solid (SLS): viscoelastic rheological model whose mechanical analogue is as shown: Use parallel array to model Q with frequency

IUGG 2007 Finite-Difference Method Domain Boundary Solid medium (elastic) Fluid magma (viscoelastic) Variable Q Damped Zone Free surface Seismometers Source Signal: 1Hz Küpper wavelet (explosive source) ρ = 2600 kgm -3 α = 3000 ms -1 β = 1725 ms -1 2-D O(Δt 2,Δx 4 ) scheme based on Jousset, Neuberg & Jolly (2004) Volcanic conduit modelled as a viscoelastic fluid-filled body embedded in homogenous elastic medium

IUGG 2007 Determining apparent (coda) Q Coda Q methodology : Decays by factor (1­  Q) each cycle Aki & Richards (2003) Model produces harmonic, monochromatic synthetic signals Time [number of cycles] Amplitude -A 0 A0A0 A1A1 A2A2 A3A3 Take ratio of successive peaks, e.g. A1A1 A2A2  =  Q Q =  A 2 A 1 – A 2

IUGG 2007 Calculation of coda Q Calculating Q using logarithms Gradient of the line given by: Unfiltered data Hence Q is given by: Time [cycles] log(Amplitude) Q value based on envelope maxima Gradient of line = Q value from gradient = Linear Fit Data

IUGG 2007 Results Intrinsic Q Apparent Q Intrinsic Q vs Apparent (coda) Q For a fixed parameter contrast 2 SLS in array Apparent Q less than intrinsic Q: Radiative energy loss dominates Apparent Q greater than intrinsic Q: Resonance dominates

IUGG 2007 Future Work and developments Compare attenuation of acoustic waves with interface waves, both intrinsic & radiative Use flow magma models to derive viscosities – examine impact on seismic amplitude decay Link observables, e.g. coda decay & frequency content to magma properties such as the viscosity, gas content & pressure → ‘magma flow meter’ idea