3D generalized nonhyperboloidal moveout approximation

Homogeneous orthorhombic layer with azimuthal rotation

Figure 3 shows the relative error plots of several approximations in a similar homogeneous orthorhombic model as in the previous example but with additional 30 $\,^{\circ}$ azimuthal rotation with respect to the global coordinates. Assuming the rotation azimuth is known, the approximations by Al-Dajani et al. (1998) and Xu et al. (2005) behave largely similar to the original case with the error plots rotated (Figures 3b and 3c). The proposed approximation is implemented based on the global coordinate system regardless of the azimuthal orientation of the orthorhombic symmetry plane and leads to a significantly more accurate result (Figure 3d). The reference rays were shot at $P_{x1} = 0.289$ and $P_{y1}=0.004$ along $x$ -axis, at $P_{x2} = 0.032$ and $P_{y2}=0.282$ along $y$ -axis, at $P_{x3}=0.2$ and $P_{y3}=0.206$ along $x=y$ , and at $P_{x4}=0.2$ and $P_{y4}=-0.163$ along $x=-y$ .