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Zero-offset ray

The Taylor expansion of equation 1 around the zero offset

$\displaystyle t^2(x,y) \approx t^2_0 + W(x,y) + \frac{A(x,y)}{2 t_0^2} + ...$ (14)

allows for a direct evaluation of nine coefficients: $ t_0$ , $ W_i$ , and $ A_i$ by matching equation 14 with the expansion of the exact traveltime in vector offset.

Sample $ c_{11}$ $ c_{22}$ $ c_{33}$ $ c_{44} $ $ c_{55}$ $ c_{66}$ $ c_{12}$ $ c_{23}$ $ c_{13}$
HTI 5.06 7.086 7.086 2 2.25 2.25 1.033 3.086 1.033
Layer 1 9 9.84 5.938 2 1.6 2.182 3.6 2.4 2.25
Layer 2 11.7 13.5 9 1.728 1.44 2.246 8.824 5.981 5.159
Layer 3 12.6 13.94 8.9125 2.5 2 2.182 2.7 3.425 3.15

Table 1. Normalized stiffness tensor coefficients (in $ km^2$ /$ s^2$ ) from different anisotropic samples: HTI is from Al-Dajani and Tsvankin (1998), layer 1 is from Schoenberg and Helbig (1997), layer 2 is from Tsvankin (1997), and layer 3 is a modifed sample based on the same fracture model as layer 1.


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Next: Finite-offset rays Up: General method for parameter Previous: General method for parameter

2017-04-20