Widening of Conduit The results provide further evidence and validation for the increase in the width of the conduit which may mark a significant change in the volcano’s behaviour. An increase in conduit width may imply a reduced magma rise rate allowing gas more time to escape (M.V.O., 2006) Incorporating flow model data The seismic (acoustic) velocity in a three-phase magma is given by where B is the bulk modulus of the magma (melt, crystals & gas) and ρ is the bulk density. (Neuberg & O’Gorman, 2002) Bulk modulus of the magma depends on bulk moduli of the phases weighted by their volume fractions. The expression derived and used to calculate the acoustic velocity was: for ρ the bulk density, ρ m density of the melt, ρ c density of the crystals, α mc seismic velocity of the melt-crystal mixture, χ g the gas volume fraction and P the pressure. Combining Magma Flow Models with Seismic Signals Patrick Smith - M.Res. Physics of the Earth and Atmosphere (2005/6) Supervisor: Jürgen Neuberg School of Earth and Environment, University of Leeds, Leeds. LS2 9JT 5. Conclusions 6. 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 Levander, A.R., 1988, Fourth-order finite-difference P-SV seismograms. Geophysics, 53, pp 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. & O’Gorman, C., 2002, A model of the seismic wavefield in gas-charged magma: application to Soufrière Hills volcano, Montserrat. In: Druitt, T.H. & Kokelaar, B. (Eds), The Eruption of the Soufrière Hills volcano, Montserrat, from 1995 to 1999, Geological Society of London, Memoir 21, pp Virieux J., 1986, P-SV wave-propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics, 51, pp Summary Low frequency seismic events have been observed on many volcanoes worldwide and are considered key tools in volcanic monitoring and eruption forecasting. The seismic parameters in a volcanic environment are strongly dependent on the properties of the magma which control the character of the low frequency seismicity. Spatial distributions of the acoustic velocity and density within a volcanic conduit were derived from a 2-D finite- element model of magma flow. These parameter distributions were then incorporated into a 2-D finite-difference model of the seismic wavefield. Hence a better approach is to consider the effect of its three component ratios (velocity, density and aspect ratio) individually. There is recent evidence (M.V.O., 2006) for a widening of the conduit of Soufrière Hills volcano on Montserrat from 30m to 50m. Results of finite-difference numerical modelling validated the expected shift to higher frequencies of the spectral peaks. Widening of the upper section of the conduit may mark a significant change in the volcano’s behaviour with reduced likelihood of explosions. 2. Motivation and aims Aims: To improve the understanding of how introducing spatial variations in seismic parameters derived from flow models influences the behaviour of the propagating wavefield. Widening of Conduit Recent evidence from measurements of a spine squeezed out of the upper conduit (M.V.O., 2006) has suggested a widening of the conduit of Soufrière Hills volcano on Montserrat. A shift towards higher frequencies in the amplitude spectra is expected as the conduit width is increased. The aim is to see if this prediction is validated by the results of numerical simulations. 3. Methodology 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 Figure 1: Schematic diagram showing the setup of the finite-difference scheme grid Conduit Geometry and Crack Stiffness Resonance characteristics depend on the geometry and on contrast in physical properties between solid and fluid. Summarised by the Crack Stiffness Factor: where B is the bulk modulus of the fluid, μ the rigidity of the solid, L length and h the width. (First introduced by Aki et al. (1977)) Can be rewritten in terms of the ratios of velocities and densities as: for ρ f and ρ s the densities of the fluid and solid, α f the acoustic velocity of the fluid and β s the S-wave velocity of the solid. Effects of varying the stiffness factor were examined by adjusting the either acoustic velocity or density for a range of conduit widths. 4. Results Figure 5: Amplitude spectra for the 30m wide and 50m wide conduit produced using an FFT window length of 2 18 Large vertical gradients in the impedance contrast within the conduit allowed more energy to be transmitted from the lower part of the conduit, reflected in a larger amplitude of the corresponding sub-events within the synthetic signals. The arrival times of the sub-events and hence also the spacing of the spectral peaks in frequency were found to be less regular. The role of the so-called ‘crack stiffness factor’ in controlling the resonance characteristics was also examined for a range of narrower more dyke-like conduits. It was shown that the stiffness factor does not completely define the resonant frequencies, as increasing the stiffness factor by adjusting the either acoustic velocity or density displayed opposite effects. Data were taken from finite-element conduit flow models with varying exsolved gas contents (Fig. 2) Figure 2: Depth profiles of acoustic velocity in the conduit for the two different flow models with high and low exsolved gas contents Finite-Difference Method 2-D, scheme based on work of Virieux (1986) and Levander (1988) Volcanic conduit modelled as a fluid-filled body embedded in homogenous solid medium (Fig. 1). Figure 3: Synthetic seismograms for sets of flow-model based seismic parameters compared to constant average values. Based on a parameter distribution for 30m wide conduit derived from the lower-gas content magma flow model. Figure 4: Amplitude spectra for a 10m wide conduit, showing the contrasting effects on the spectral peaks of varying the stiffness factor by adjusting either the acoustic velocity or the density. Fixed values used for velocity and density: ρ = 2000 kgm -3 and α = 1500 ms -1. The only parameter varied was the conduit width. Amplitude spectra reveal expected shift to higher frequencies with larger width (Fig. 5) Faster decay of the signal amplitude for larger width (Fig. 6) Figure 6: Synthetic seismograms for a 30m wide and 50m wide conduit. The amplitudes of both seismograms are normalised relative to the 30m wide conduit which has the larger amplitude signal. Widening of Conduit Conduit Geometry and stiffness Increasing the stiffness factor by increasing the acoustic velocity produces a shift to higher frequencies (due to higher phase velocity) (Fig. 4) and also a more monochromatic signal. Increasing the stiffness factor by increasing the density produces a shift to lower frequencies (due to lower phase velocity) (Fig. 4) and also a slower decay of the amplitude of the resonance. Incorporating Flow Model data Results from models using flow model based parameter distributions were compared to those with average values. Very low acoustic velocities means the sub-events are separated by several seconds. (Fig. 3) Large vertical gradient in impedance contrast implies more energy escapes from the lower end of the conduit where contrast is lowest. Incorporating flow model data Introducing the flow model derived spatial distributions of the seismic parameters produces more complex seismograms with more noise and higher frequencies. The arrival times of the sub-events and hence also the spacing of the spectral peaks in frequency were found to be less regular. Conduit Geometry and stiffness The crack stiffness factor does not fully define the resonance characteristics and using a single parameter contrast B/μ within the stiffness factor is not justified. Better approach to consider the effect of each of the three component ratios on the resonance individually. Conduit geometry and stiffness Consider the effects of adjusting both the geometry and the seismic parameters together according to the stiffness factor. Reduce the width of the body to a more dyke -like size. Incorporating Flow Model data Motivation: The magma properties control the seismic parameters. Therefore it is necessary to incorporate information on the spatial distribution of magma properties into wavefield models of low-frequency events. Important to be able to link seismic signals directly to the magma properties: implications for monitoring and hazard assessment.