## Estimation of Thomsen's anisotropic parameters from geophysical measurements using equivalent offset gathers and the shifted-hyperbola NMO equation

### Pavan Kumar Elapavuluri

In order to study and understand the complex Earth, exploration geophysicists make many assumptions. One of them is that the Earth is perfectly isotropic while in fact it is fundamentally anisotropic. This faulty assumption results in erroneous imaging of subsurface strata and thus faulty interprepsilontions. To extend the seismic processing techniques to anisotropic media, it is required that we have a measure of the different anisotropy parameters.

In this thesis I propose a method for estimation of Thomsen's P-wave anisotropy parameters ( and ) for Vertical Transverse Isotropic (VTI) media using Castle's shifted-hyperbola Normal Moveout (NMO) equation. The method was first tested on a synthetic data and then applied to the field data.

I have shown in this thesis that the shifted hyperbola NMO equation (SNMO) gives better estimate of NMO velocities than Dix's NMO equation, as it is a fourth-order Taylor series approximation while Dix NMO equation is a second-order approximation. A Monte-Carlo Inversion technique was used for the inversion of traveltime data for both NMO velocity and the shift parameter S. I have applied this SNMO inversion technique to both Equivalent Offset (EO) and CMP (Common Midpoint) gathers. It was found that the velocity analysis on EO gathers gives comparatively more accurate velocity estimates due to their better signal-to-noise ratio.

After the velocity analysis the NMO velocity and the shift parameter can be used to estimate the anisotropy parameters. I estimated the values of and on synthetic seismic data. The values of were estimated quite accurately while the estimation of the parameter was less accurate. The errors in the estimation of varied from 5-10% while the error in estimation of varied from 20-30%. I then applied this technique to the field dataset acquired over the Blackfoot Field in Alberta and the anisotropic parameters of formations of interest were estimated and were found compare reasonably with expectations based on known lithology.