Traveltime approximations for transversely isotropic media with an inhomogeneous background |

The main objective of the newly developed expressions is parameter estimation in complex media. Specifically, the perturbation PDEs developed here are with respect to a background generally inhomogeneous, and possibly anisotropic, medium. If a generally inhomogeneous isotropic velocity field is available (for example from conventional migration velocity analysis), in addition to a map of the well-to-seismic misties, which can be used to develop a vertical velocity field, then an elliptical anisotropic model with a vertical symmetry axis can be constructed. We can use this model to solve for traveltimes in elliptically anisotropic media as a background model, as well as to solve for the expansion coefficients using equations 7. These coefficients can be used with, for example, equation 23 to search explicitly for the , and tilt angles and in 3D that provides the best traveltime fit to the data. This process can be implemented in a semblance-type search or incorporated as part of a tomographic inversion. Though the scans are based on an underline factorized assumption in the perturbation parameters, and the tilt angles, we can allow them to vary smoothly with location, and thus, produce effective values. The conversion of these effective values to interval ones in generally inhomogeneous media is not trivial and might require a tomographic treatment of its own.

etaTheta
The traveltime difference between the TTI model computed using equation 9 and the elliptically
anisotropic with a vertical symmetry axis background model for (a) an offset of 1 km, (b) an offset of 2 km, and (c) an offset of 4 km.
The medium has =2 km/s, =2 km/s (), and a reflector depth, =2 km.
Figure 7. |
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The availability of multi-offset data will increase our chances in resolving both and the tilt angle in 2D. The addition of multi azimuth should help resolve the tilt in 3D. Of course, the accuracy of resolving these parameters will depend mainly on how well we estimate the original elliptically anisotropic background medium. However, we can always go back and improve on our velocity picks once an approximate effective and tilt-angle fields are estimated. There are probably many other more sophisticated ways to explore this parameter matrix, however, the equations introduced here provides the basis for doing so.

Traveltime approximations for transversely isotropic media with an inhomogeneous background |

2013-04-02