Generalized nonhyperbolic moveout approximation

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### Linear velocity and linear sloth

We start with two analytical isotropic three-parameter models: linear velocity model (described in Appendix A) and linear sloth model (described in Appendix B). In both models, it is possible to compute the exact moveout analytically and thus to compare directly the accuracy of different approximations with the exact moveout. We show this comparison in Figures 1 and 2, where the relative absolute approximation error is plotted for different approximations against a large range of the offset-to-depth ratio and the maximum-to-minimum velocity ratio. As evident from the figures, three-parameter approximations (shifted-hyperbola and Alkhalifah-Tsvankin) improve the accuracy of the two-parameter hyperbolic approximation. However, the proposed five-parameter generalized approximation brings a more significant improvement and reduces the error by several orders of magnitude.

linvel
Figure 1.
Relative absolute error of different traveltime approximations as a function of velocity contrast and offset/depth ratio for the case of a linear velocity model. (a) Hyperbolic approximation, (b) Shifted hyperbola approximation, (c) Alkhalifah-Tsvankin approximation, (d) Generalized nonhyperbolic approximation. The proposed generalized approximation reduces the maximum approximation error by several orders of magnitude.

linsloth
Figure 2.
Relative absolute error of different traveltime approximations as a function of velocity contrast and offset/depth ratio for the case of a linear sloth model. (a) Hyperbolic approximation, (b) Shifted hyperbola approximation, (c) Alkhalifah-Tsvankin approximation, (d) Generalized nonhyperbolic approximation. The proposed generalized approximation reduces the maximum approximation error by several orders of magnitude.

 Generalized nonhyperbolic moveout approximation

Next: Curved reflector in a Up: Analytical examples Previous: Analytical examples

2013-03-02