3D generalized nonhyperboloidal moveout approximation

Conclusions

We have introduced an extension of the generalized moveout approximation to 3D. The proposed approximation, similarly to its 2D analog, reduces to several known functional forms with particular choices of parameters. The approximation requires seventeen parameters, which are uniquely defined by zero-offset computations and four addtional finite-offset rays. Our numerical tests show that, in comparison with other known 3D moveout approximations, the proposed approximation produces results with superior accuracy, which is not surprising given the larger number of adjustable parameters. Its advantage becomes more obvious with more complex models. Moreover, the proposed approximation performs well even in the presence of anisotropic axis rotation and multiple layers suggesting that only seventeen parameters are sufficient to describe the reflection traveltime in a model with 3D anisotropic layers. In our experiments, the accuracy can be nearly exact for practical purposes with less than 0.3% in maximum error in both homogeneous and complex layered anisotropic models. The proposed moveout approximation can readily be used for forward reflection traveltime computation or as a basis for inversion for anisotropic parameters from seismic reflection data.

3D generalized nonhyperboloidal moveout approximation