1. Analytical and Numerical Modelling of Surface Displacements due to Volcanism Olivia Lewis Supervised by Prof. Jurgen Neuberg School of Earth and Environment University of Leeds

2. Ground Deformation Studies in Volcanology Surface displacements in volcanic regions are measured by: Global Positioning System (GPS) Electronic Distance Measurement (EDM) Tiltmeters Satellite (InSAR) Cyclic signals can aid in eruption forecasting Analytical models can be used to estimate source parameters U surface U chamber P (Dvorak & Dzurisin, 1997) (Massonnet et al., 1995)

3. The Mogi Model Assumptions: »Point source of surface displacement »Linear elastic half-space »Isotropic half-space Vertical Displacements Horizontal Displacements R a d P R o y x o However…… These assumptions limit the model accuracy: –Sources are not always point sources –Non-elastic rheologies and heterogeneities exist in volcanic areas

4. Study Aims To investigate and quantify the inaccuracies introduced into the Mogi model when the assumption of a point source is in question. To investigate the response and the applicability of the Mogi model when employed to model surface displacements due to more than one source. To employ analytical methods to examine the line length changes of the electronic distance measurement (EDM) network covering Soufrière Hills volcano, Montserrat.

5. Analytical Modelling of Surface Displacements Single source models: Source depths of 3-10km Radii that correspond to a/d ratios of 0.1 - 0.5 Double source models: Fixed source radii of 500m – 3km Vertical separation reduced from 5a to 0a Model Physical Properties μ = 0.9 GPa (Voight et al., 1999) P = 20 MPa (Bonaccorso et al., 2005) a 5a 4a 3a 2a 1a 0a a1a1 a2a2 a3a3 a4a4 a5a5 d

6. Finite Element Method (FEM) Sources are pressurised cavities within a solid Physical and dimensional properties used are the same as for the analytical models Boundary conditions: Displacement only on deformable surfaces The only load is a pressure on the cavity walls Numerical Models FE Mesh: Smaller element sizes assigned to deformable 8-node tetraheadral elements decided upon after examination of accuracy and computational time

7. Comparison of Analytical and Numerical Model Results (1) a/d ratio 0.10.30.5 Max U v error (%) -1.231.5913.97 Max U r error (%) -0.720.768.28 Single Source Models

8. (a) (b)(c) (d) (e) (f) Displacements Normal Stress Field

9. Comparison of Analytical and Numerical Model Results (2) Vertical separation of sources (in terms of source radius) 3210 Max U v error (%) 17.319.6 4.6 Max U r error (%) 15.419.221.420.0 Double Source Models

10. (a)(b)(c) (d) (e) (f) Displacements Normal Stress Field

11. Line length changes monitored by 3 EDM stations: Jack Boy Hill – Hermitage Peak Spanish Point – Jack Boy Hill Spanish Point – Hermitage Peak Line length data for JB – HP EDM line kindly provided by the Montserrat Volcano Observatory. Analytical Modelling of Line Length Changes at Soufrière Hills Volcano, Montserrat

12. 7.23cm modelled line lengthening ~97% due to magma chamber only 9.2cm observed shortening Line Length Model Results (1) Conduit OnlyMagma Chamber Only 9.2cm

13. Line Length Model Results (2) Dome growth = eruption Eruption leads to deflation of the magma chamber Deflation included in the analytical line length model results in a change in sign of the line length

14. Conclusions Errors become significant if the a/d ratio is >0.3 If the Urmax/Uvmax ratio deviates by ±0.05% from 0.3849 the Mogi model may have significant errors Use of the principle of superposition in the analytical method introduces significant errors – both magnitudes and patterns of surface displacement differ from numerical model results Changes in EDM line length at Soufrière Hills are predominately induced by changes in magma chamber pressure

15. What next? More complex FE models Topography Rigidity variations FE modelling of line length changes Attempt to calibrate changes to magma chamber volumes Prospects For Further Research