3D generalized nonhyperboloidal moveout approximation

Homogeneous HTI layer

To test the accuracy of the proposed approximation, we first consider a single horizontal layer of an HTI material over flat reflector with properties given in Table 1 and thickness of 1 $km$ . The accuracy comparison between different approximations is shown in Figure 1with true traveltime computed from ray tracing. The reference rays for the generalized approximation (equation 1) were chosen in terms of different ray parameters $P_{xi}$ and $P_{yi}$ , which then gives $X_i$ , $Y_i$ , and $T_i$ needed to solve for approximation coefficients according to equations 15-20. In this example, the reference rays are associated with $P_{x1} = 0.4$ and and $P_{y1}=0.0$ along $x$ -axis, at and $P_{x2}=0.0$ and $P_{y2} = 0.338$ along $y$ -axis, at $P_{x3}=0.23$ and $P_{y3}=0.153$ along $x=y$ , and at $P_{x4}=0.23$ and $P_{y4}=-0.153$ along $x=-y$ . The proposed approximation shows smaller error than previous approximations (Figure 1c).

onelayerHTInmo,onelayerHTIal,onelayerHTIgma
Figure 1. Error plots in the homogeneous HTI layer of a) NMO ellipse b) approximation by Al-Dajani and Tsvankin (1998) (simlar to Al-Dajani et al. (1998)), and c) the proposed approximation. Note that b) and c) are plotted under the same color scale and $H$ denotes the reflector depth.

3D generalized nonhyperboloidal moveout approximation