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.

Outline of Presentation Background: low-frequency seismicity, project context, quantifying amplitude losses Methodology: Viscoelastic finite-difference model & Coda Q analysis Results and Implications: plus some discussion of future work

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

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

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

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

depth of brittle failure slip plug flow gas loss parabolic flow Seismic trigger mechanism Collier & Neuberg, 2006; Neuberg et al., 2006 Stress threshold:   Pa 7 

Swarm structure Increased event rates Linked to magma extrusion Similar earthquake waveforms Swarms preceding dome collapse

Photo : R Herd, MVO V m/s Towards a Magma Flow Meter

Seismic attenuation in magma Why is attenuation important? Definitions: Apparent (coda) Intrinsic (anelastic) Radiative (parameter contrast) true damping amplitude decay Needed to quantitatively link source and surface amplitudes. Allows us to link signal characteristics, e.g. amplitude decay of the coda, to properties of the magma such as the viscosity (Aki, 1984)

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: ff ff ss ss Further amplitude loss due to geometric spreading – signal travels to seismometer as surface wave: but DOES NOT contribute to apparent Q !

Amplitude decay of coda Comparison of approaches: 1.Kumagai & Chouet: used 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. Figure from Kumagai & Chouet (1999)

BGA 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: Intrinsic Q is dependent on the properties of the magma: Viscosity (of melt & magma) Gas content Diffusivity Use in finite-difference code to model intrinsic Q

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

Calculation of coda Q Calculating Q using logarithms Gradient of the line given by: Hence Q is given by:

Results Apparent (coda) Intrinsic (anelastic) An amplitude battle: competing effects Radiative (parameter contrast) 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

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

Future Work and developments Short-Term: Amplitudes Quantitatively relate amplitudes at surface to slip at source → ‘magma flow meter’ idea. Compare attenuation of acoustic waves with interface waves – aim to understand the variation with reflection coefficient ! Longer Term: Calculate apparent Q for real data? Can we constrain intrinsic Q or conduit properties? Wavefield models: refine to fit Q with frequency at each point. Look at other geometries? Magma flow modelling: work on including gas-loss and crystallisation processes. Simulate loading due to build up of extruded material (dome growth) Incorporating flow modelling results into wavefield models…

Thanks for your attention!

IUGG 2007 Quality Factor, Q Widely used in seismology, inverse of attenuation 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 Taken from Collier et al. (2006)

Seismometer at surface A T Seismometer at source A SRC A R Layer 1: solid  s  s Layer 2: fluid or solid  f  f 4000 m 6000 m 500 m 2500 m 3000 m