Low frequency coda decay: separating the different components of amplitude loss. Patrick Smith Supervisor: Jürgen Neuberg School of Earth and Environment, The University of Leeds. ESC WG 2007
Outline of Presentation Background: low-frequency seismicity, quantifying amplitude losses Methodology: Viscoelastic finite-difference model & Coda Q analysis Results and Implications: plus some discussion of future work ESC WG 2007
Low frequency seismicity High frequency onset Coda: harmonic, slowly decaying low frequencies (0-5 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 ESC WG 2007
Source Propagation of seismic energy Conduit Resonance Energy travels as interface waves along conduit walls at velocity controlled by magma properties Top and bottom of the conduit act as reflectors and secondary sources of seismic waves Fundamentally different process from harmonic standing waves in the conduit Trigger Mechanism = Brittle Failure of Melt
Propagation of seismic energy ESC 2007
P-wave S-wave Propagation of seismic energy ESC 2007
Interface waves P-wave S-wave Propagation of seismic energy ESC 2007
Interface waves Propagation of seismic energy ESC 2007
Interface waves Propagation of seismic energy ESC 2007
Interface waves Propagation of seismic energy ESC 2007
Interface waves Propagation of seismic energy ESC 2007
Propagation of seismic energy ESC 2007
reflections Propagation of seismic energy ESC 2007
reflections Propagation of seismic energy ESC 2007
Propagation of seismic energy ESC 2007
Low frequencies High frequencies FAST MODE: I1 NORMAL DISPERSION SLOW MODE: I2 INVERSE DISPERSION Low frequencies High frequencies Acoustic velocity of fluid Propagation of seismic energy ESC 2007
I1 I2 Propagation of seismic energy ESC 2007
I1 I2 S Propagation of seismic energy ESC 2007
S I1 I2 Propagation of seismic energy ESC 2007
S I1 I2 Propagation of seismic energy ESC 2007
‘Secondary source’ I2 Propagation of seismic energy ESC 2007
Surface-wave ‘Secondary source’ Propagation of seismic energy ESC 2007
Surface-wave Propagation of seismic energy ESC 2007
I1R1 Propagation of seismic energy ESC 2007
I1R1 Propagation of seismic energy ESC 2007
I2 I1R1 Propagation of seismic energy ESC 2007
I2 ‘Secondary source’ Propagation of seismic energy ESC 2007
‘Secondary source’ Propagation of seismic energy ESC 2007
Propagation of seismic energy ESC 2007
Propagation of seismic energy ESC 2007
Propagation of seismic energy ESC 2007
Most of energy stays within the conduit Propagation of seismic energy ESC 2007
Most of energy stays within the conduit Propagation of seismic energy ESC 2007
Most of energy stays within the conduit Propagation of seismic energy ESC 2007
Most of energy stays within the conduit Propagation of seismic energy ESC 2007
Propagation of seismic energy ESC 2007
R2 Propagation of seismic energy ESC 2007
R2 Events are recorded by seismometers as surface waves Propagation of seismic energy ESC 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) One of the few tools that provide direct link between surface observations and internal magma processes ESC WG 2007
Conduit Properties seismic signals (surface) Magma properties (internal) Seismic parameters Signal characteristics Context: combining magma flow modelling & seismicity Conduit geometry + Properties of the magma Attenuation via Q ESC WG 2007
Seismic attenuation in magma Why is attenuation important? Definitions: Apparent (coda) Intrinsic (anelastic) Radiative (parameter contrast, geometric spreading) true damping amplitude decay Allows us to link signal characteristics, e.g. amplitude decay of the coda, to properties of the magma such as the viscosity Needed to quantitatively link source and surface amplitudes. ESC WG 2007
Seismometer Quantifying amplitude losses Trigger mechanism: brittle failure at conduit walls Intrinsic attenuation in magma causes some damping of signal amplitude – but how much? Contrast in elastic parameters causes some energy to be transmitted and some to be reflected QiQi R (reflection coefficient) T (transmission coefficient) Q -1 =Q i -1 +Q r -1 Q -1 Q r -1 Total amplitude decay is a combination of these contributions: Further amplitude loss due to geometric spreading – signal travels to seismometer as surface wave ff ff ss ss
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: Intrinsic Q is dependent on the properties of the magma: Viscosity (of melt & magma) Gas content Diffusivity Use in finite-difference code to model frequency dependent Q ESC WG 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 ESC WG 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 (taken from Chouet 1996) Synthetic trace ESC WG 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 ESC WG 2007
Results Apparent (coda) Intrinsic (anelastic) An amplitude battle: competing effects Radiative (parameter contrast, geometric spreading) High intrinsic attenuation overcome by resonance effect – but need better understanding of how energy of interface waves is trapped Determines behaviour at high intrinsic Q – shifts the curve vertically For a fixed parameter contrast Apparent Q greater than intrinsic Q: Resonance dominates Apparent Q less than intrinsic Q: Radiative energy loss dominates ESC WG 2007
Results… in progress! Apparent Q vs. Reflection Coefficient: A Puzzle! Intuitively expect opposite behaviour to what is observed Due to difference between acoustic and interface waves? Apparent Q vs. intrinsic Q for different parameter contrasts: Expect to shift curve vertically Needs further analysis! Apparent (coda) Q vs. Reflection Coefficient Reflection Coefficient (from parameter contrast) Apparent Q from coda analysis Low R → low contrast → expect rapid decay of energy → low Q ?? High R → high contrast → expect slower decay of energy → high Q ?? R = 0.25 R = 0.50 R = 0.75
ESC WG 2007 Future Work and developments Compare attenuation of acoustic waves with interface waves – aim to understand the variation with reflection coefficient ! Want to quantitatively relate amplitudes at surface to slip at source → ‘magma flow meter’ idea. Also need to think about shear source vs. explosive source 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
Thanks for your attention! ESC WG 2007