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Fig. 1. Elasticity and phase velocities of diopside as a function of pressure. Parts (a) and (b) show the evolution of elements of the elasticity matrix with pressure as calculated using density functional theory. (In part (a): squares: C 11 , unfilled circles: C 22 , filled circles: C 33 right pointing triangle: C 44 , left pointing triangle: C 55 , downwards pointing triangle: C 66 . In part (b) squares: C 12 , unfilled circles: C 13 , filled circles: C 23 , right pointing triangles: C 15 , left pointing triangles: C 25 , downwards pointing triangles: C 65 , upwards pointing triangles: C 43 .) Contours in parts (c), (d) and (e) show the variation in the velocity of the qP (left column) and difference in the velocity of the qS1 and qS2 phases (centre and right column) with propagation direction (upper hemisphere pole figures created with MS plot with the cartesian axis system and approximate location of the crystallographic a axis shown in the inset) and pressure. Tick marks in the right hand column indicate the polarisation direction of the fast shear wave (qS1). 36
Fig. 2. Classifications of models of lowermost mantle anisotropy. Both panels show variations in properties extracted from a combined flow and texture model of the D ′′ (Walker et al., 2011). The upper panel shows the proportion of the predicted anisotropy which is captured by an assumption of vertical transverse isotropy (VTI). The lower panel shows the universal anisotropy index of Ranganathan and Ostoja-Starzewski (2008). The proportion of hexagonally is not well correlated with the overall anisotropy. However, over the majority of the globe more than 70% of the norm of the elasticity can be described with an hexagonal approximation. 37
Page 1 and 2: MSAT - A new toolkit for the analys
Page 3 and 4: ing and modelling the seismic conse
Page 5 and 6: where the repeated indices on the r
Page 7 and 8: Weng, 1984) or cracks which are uni
Page 9 and 10: two values place an upper (Voigt) a
Page 11 and 12: 3.1 Design, development and documen
Page 13 and 14: toolkit we group the functions toge
Page 15 and 16: confirms that an elasticity matrix
Page 17 and 18: the mantle a possible mechanism for
Page 19 and 20: Figure 2 a) can exhibit both large
Page 21 and 22: on the observed effective splitting
Page 23 and 24: azimuthal anisotropy from shear wav
Page 25 and 26: 116, B08307. Kustowski, B., Ekströ
Page 27 and 28: Ranganathan, S. I., Ostoja-Starzews
Page 29 and 30: irefringence in nine-component VSP
Page 31 and 32: Function name MS VRH MS axes MS dec
Page 33 and 34: 1 % Loop over p r e s s u r e s , r
Page 35: 1 % i n t e r r o g a t e e l a s t
Page 39: 0.1 A L1 Az = 30; L2 dip = 00 B L1

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