1. Combining magma flow models with seismic signals
Patrick Smith
M.Res. Physics of the Earth and Atmosphere (2005/6)
Supervisor: Prof. Jürgen Neuberg
School of Earth and Environment,
The University of Leeds

2. Outline of Presentation
Background: low frequency seismicity
Project split into 3 sections:
Incorporating flow model data (main focus)
Conduit geometry and stiffness factor
Comparison of a 30m and 50m wide conduit
Motivation & Aims → Method → Results
Conclusions

3. Low frequency seismicity
What are low-frequency earthquakes?
Specific to volcanic environments
Weak 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

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

5. Trigger Mechanism = Brittle Failure of Melt
Conduit Resonance
Propagation of seismic energy
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
Source
Trigger Mechanism = Brittle Failure of Melt

6. Propagation of seismic energy

7. Propagation of seismic energy
S-wave
P-wave

8. Propagation of seismic energy
Interface waves
S-wave
P-wave

9. Propagation of seismic energy
Interface waves

10. Propagation of seismic energy
Interface waves

11. Propagation of seismic energy
Interface waves

12. Propagation of seismic energy
Interface waves

13. Propagation of seismic energy

14. Propagation of seismic energy
reflections

15. Propagation of seismic energy
reflections

16. Propagation of seismic energy

17. Propagation of seismic energy
FAST MODE: I1
NORMAL
DISPERSION
Low frequencies
Acoustic velocity of fluid
High frequencies
High frequencies
SLOW MODE: I2
INVERSE
DISPERSION
Low frequencies

18. Propagation of seismic energy

19. Propagation of seismic energy

20. Propagation of seismic energy

21. Propagation of seismic energy

22. Propagation of seismic energy
‘Secondary source’

23. Propagation of seismic energy
Surface-wave
‘Secondary source’

24. Propagation of seismic energy
Surface-wave

25. Propagation of seismic energy
I1R1

26. Propagation of seismic energy
I1R1

27. Propagation of seismic energy
I1R1 I2

28. Propagation of seismic energy
‘Secondary source’

29. Propagation of seismic energy
‘Secondary source’

30. Propagation of seismic energy

31. Propagation of seismic energy

32. Propagation of seismic energy

33. Propagation of seismic energy
Most of energy
stays
within the conduit

34. Propagation of seismic energy
Most of energy
stays
within the conduit

35. Propagation of seismic energy
Most of energy
stays
within the conduit

36. Propagation of seismic energy
Most of energy
stays
within the conduit

37. Propagation of seismic energy

38. Propagation of seismic energy

39. Propagation of seismic energy
Events are recorded by seismometers as surface waves R2

40. Incorporating flow model data
Motivation
Properties of the magma
Seismic parameters
Signal characteristics
Incorporate flow model data into wavefield models
Magma properties
(internal)
seismic signals
(surface)

41. Incorporating flow model data
Aims & Methodology
Flow model data
Derive seismic parameters
Use in wavefield models

42. Magma flow models
A 2-D finite-element model for magma flow has recently been developed (Collier & Neuberg, 2006)
Magma properties resolved at all depths and lateral positions within a volcanic conduit

43. Incorporating flow model data
Seismic (acoustic) velocity
Weighted average of components from the three different phases
Acoustic velocity → calculated from gas volume fraction, pressure & bulk density

44. Incorporating flow model data
Seismic (acoustic) velocity
Acoustic velocity profiles calculated for models with:
30m wide conduit
two different exsolved gas contents
______
Lower gas content
Higher gas content

45. Wavefield Models (horizontal component)
System of differential equations (elasto-dynamic equations)
(horizontal component)
Solved numerically using a finite-difference method

46. Finite-Difference Method
Domain Boundary
Solid
medium
Liquid magma
Damped Zone
Free surface
Seismometers
Source Signal:
1Hz Küpper wavelet
100m below top of conduit
ρ = 2600 kgm-3
α = 3000 ms-1
β = 1725 ms-1

47. Results Introducing flow models based parameters produces:
more noise and higher frequencies
horizontal components
Magma model
Average
less regular spacing of sub-events
vertical components
large amplitude of sub-events transmitted from the bottom of the conduit

48. Results Impedance Contrast Flow Model:
High contrast at the top, low at the bottom
more energy transmitted from bottom of conduit
Magma model
Average

49. Constant averaged values
Results
Constant averaged values

50. Flow model derived values
Results
Flow model derived values

51. Conduit Geometry and Stiffness factor
Resonance characteristics depend on:
Contrast in physical properties of fluid and solid
2. Geometry of conduit μ B L h
(Aki et al. 1977)

52. Adjusting acoustic velocity Adjusting density
Method
Varied parameter contrast part by:
Adjusting acoustic velocity
Adjusting
density μ B

53. Results Both increase stiffness → but opposite behaviour!
Increasing the stiffness factor by increasing the acoustic velocity produces a shift to higher frequencies
acoustic velocity
density
Increasing the stiffness factor by increasing the density produces a shift to lower frequencies
Both increase stiffness → but opposite behaviour!

54. Comparison of a 30m and 50m wide conduit
Motivation and Aims
Recent evidence for widening of conduit from 30m to 50m (M.V.O., 2006)
Expect to shift to higher frequencies in the amplitude spectra with increasing width.
Aim: to see if this prediction is validated by results of numerical modelling

55. Synthetic Seismograms
Results
Synthetic Seismograms
Vertical component seismograms
30m wide
Faster decay of amplitude for wider conduit
50m wide

56. Results
Amplitude Spectra
horizontal component
______
Show a clear shift to higher frequency peaks with increasing width
30m
50m
vertical component
______
30m
50m

57. Incorporating flow model data
Conclusions
Incorporating flow model data
More complex seismograms
Steep gradients in impedance contrast → more energy transmitted from bottom of conduit
Less regular spacing of sub-events in time and frequency domains

58. Conduit geometry and stiffness
Conclusions
Conduit geometry and stiffness
Stiffness factor does not fully define the resonance characteristics
→ using a single parameter contrast B/μ within the stiffness factor is not justified.
Better approach to consider effects of component ratios individually

59. Conclusions Widening of conduit
Results show expected shift to higher frequencies
Provides further evidence and validation for widening of upper conduit
Larger width implies reduced rise rate of magma → more time for gas to escape → reduced likelihood of explosions (M.V.O., 2006)

60. References and Acknowledgements
I would like to thank my supervisor Professor Jürgen Neuberg for his help and guidance throughout this research. I would also like to acknowledge the support of Dr. Marielle Collombet and thank her for providing the magma flow model data that was used in this project. This M.Res. was funded by a NERC studentship.
Aki, K., Fehler, M. & Das, S., 1977, Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 Kilauea eruption. J. Volcanol. Geotherm., 2, pp
Collier, L. & Neuberg, J., 2006, Incorporating seismic observations into 2D conduit flow modelling. J. Volcanol. Geotherm., 152, pp
Green, D. N. & Neuberg, J., 2006, Waveform classification of volcanic low-frequency earthquake swarms and its implication at Soufrière Hills Volcano, Montserrat. J. Volcanol. Geotherm., 153, pp51-63.
M.V.O. (Montserrat Volcano Observatory), 2006, Assessment of Hazard and Risks Associated with Soufrière Hills Volcano, Montserrat. Sixth Report of the Scientific Advisory Committee, March Part Two - Technical Report (available at
Neuberg, J., Tuffen, H., Collier, L., Green, D., Powell T. & Dingwell D., 2006, The trigger mechanism of low-frequency earthquakes on Montserrat. J. Volcanol. Geotherm., 153, pp37-50.