Interpreting spatial variations in anisotropy from waveform modelling

1. Interpreting spatial variations in anisotropy from waveform modelling J. O. S. Hammond, J-M. Kendall, D. Angus, J. Wookey

2. Variability in shear-wave splitting parameters • 2-layer (Savage and Silver, 1993, Silver and Savage, 1994)

3. Variability in shear-wave splitting parameters • Lateral and depth variations (Rumpker et al., 2003, transform fault)

4. Motivation • Variation in splitting parameters between the Ethiopian plateau and the rift valley (Kendall et al., 2005). • Stations only 10s of km apart have markedly different parameters • Kendall et al., 2005, estimated, based on simple Fresnel zone calculations, that anisotropy is confined to <100km. • Can we place more accurate estimates on the anisotropy characteristics in a rift setting by using finite-frequency modeling

5. One-way solution • Models 3-component wavefront in anisotropic and heterogeneous 3D media (Angus et al., 2004) One-way wave equation Full solution (Finite Difference) • Pros: • Models finite-frequency signals • Handles variations and averaging in medium properties from large down to sub-Fresnel scale • Models coupling of shear waves even within singular regions of slowness surface • Cons: • limited to <15 degrees of direction of propagation • only models transmitted waves

6. Calculate elastic constants for peridotite containing vertically aligned melt pockets (Hudson, 1981) • Build model with anomalous ‘rift’ zone in centre with rotated elastic constants (based on results of Kendall et al., 2005) • One-way wave equation generates synthetic primary arrivals, from which splitting estimates are calculated • Parameters tested • Width of ‘rift’ zone • Anisotropy % • Depth of anisotropic zone • Frequency of wave • Initial shear-wave polarisation Hammond et al., GJI, 2010

7. width 10% anisotropy Width of anisotropic region Period = 8s Initial polarisation = 45º 45km • Vary width of ‘rift’ zone • Large variation in both  and t • Transition of  occurs over ~20km, and ‘rift’ width is defined by inflexion points • Complicated pattern in t profile, similar to that seen in inhomogeneous anisotropic media • 3-D plume model - Rumpker and Silver, 2000 • transform fault - Rumpker et al., 2003)

8. 40km anisotropy Varying amount of anisotropy Period = 8s Initial polarisation = 45º 45km • Vary amount of anisotropy • Large variation in t,  shows consistent pattern • Transition of  occurs over ~20km, and ‘rift’ width is defined by inflexion points • Pattern in t is consistent, with peaks-troughs constant for all models

9. 40km 10% anisotropy Varying depth of anisotropic region Period = 8s Initial polarisation = 45º depth • Vary depth of anisotropic layer • Large variation in t, small variation in  • Transition of  occurs over ~20km-40km, and ‘rift’ width is defined by inflexion points • The peaks and troughs in t move out with depth

10. 40km 10% anisotropy Varying frequency of incoming wave Period Initial polarisation = 45º 45km • Vary frequency of wave • Large variation in t for low frequencies, small variation in  • Transition of  occurs over ~0km-20km, and ‘rift’ width is defined by inflexion points • The peaks and troughs in t are consistent (except the 0.5s wave)

11. 40km 10% anisotropy Varying initial source polarisation Period = 8s Initial polarisation 45km • Vary initial polarisation of the shear wave • Variation in t strongly dependent on initial polarisation • Initial polarisation has a small effect on  and ‘rift’ width is defined by inflexion points

12. Modelling conclusions • SKS splitting can identify sharp lateral changes in splitting (~20-40km) • ‘Rift’ width is always defined by the inflexion points in the  profile • Anisotropy depth is defined by the moveout in the peaks/troughs of the t profile • Initial polarisation dependent • Amount of anisotropy is determined by the background t, far from the ‘rift’ • At stations close to the transition t varies as a function of initial polarisation, whereas  shows little variation. • Possible indicator of sharp lateral variations in anisotropy • For higher frequencies the modelled splitting approaches the ray theoretical limit and shows little variation in t • Frequency dependence of t could indicate sharp lateral variations in anisotropy

13. Eagle data • Inflexion points of  profile define ‘rift’ width • Eagle - 100km • Variation in t profile defines depth (for a given initial polarisation) • Eagle - ~90km • Background t defines amount of anisotropy • Eagle - ~7%

14. Main Ethiopian Rift anisotropy 100km 90km • Good fit to the data • Model - 9-7% anisotropy, 90km depth, 100km wide 7% 9%

15. Transition from 9% to 7% anisotropy Transition from 30° to 20° Depth extent of anisotropy (~90km)

16. MER Conclusions • Simple rotation in anisotropy characteristics can explain MER splitting results • ~90km deep, 100km wide, 7-9% anisotropy • Assuming anisotropy is derived from oriented melt pockets (Kendall et al., 2005), melting beneath the MER is aligned at ~90km • Supports tomography (low velocities) (Bastow et al., 2008) • Supports geochemistry (depth of appreciable melt initiation) Rooney et al., 2005) • Larger anisotropy on western margin of MER • Supports asymmetry in: • Crustal conductivities (Whaler and Hautot, 2006) • Magmatic underplate (Mackenzie et al., 2005, Cornwall et al, 2010) • Supports ideas of focussed melt at this margin (Holtzmann and Kendall, In review)