Accuracy and limitations of the near-offset P-wave NMO velocity estimation in transversely isotropic media

The accuracy and limitations of the near-offset P-wave NMO velocity estimation in transversely isotropic media have been studied using numerical and physical modelling studies. An expression for the near-offset P-wave NMO velocity for a single horizontal reflector in a vertically transversely isotropic layer has been previously obtained:

where αo and δ respectively represent the vertical P-wave velocity and the P-wave critical anisotropy at oblique angles. The above equation is presented as being valid for any degree of anisotropy. The accuracy of this expression is subject to practical testing in this paper.

Single layered horizontal models were used to carry out the numerical modelling studies. A computer program that calculates P-wave NMO velocities in transversely isotropic media was used. This program uses the exact ray and phase velocity equations in generating velocity functions to be used in ray tracing and is known to give accurate results. Using the elastic parameters for measured anisotropy in sedimentary rocks, the near-offset NMO velocities are computed using our computer program and the above expression. The results obtained at varying degrees of P-wave anisotropy are compared. The degree of anisotropy varied from very weak to strong and contrasting velocity functions were used in numerical modelling simulations.

Phenolite materials with contrasting velocity functions were used to simulate transversely isotropic media with vertical axes of symmetry in physical modelling tests. Experimental reflection data were collected and velocity analysis was conducted for near-offset traces, and the NMO velocity determined by the maximum stack response. The elastic parameters, αo, and δ, of the Phenolite materials were recovered by an iterative inversion of first arrival travel times. These parameters were used to estimate the nearoffset P-wave NMO velocity in Phenolite using the NMO expression and also with our computer program. The NMO velocities obtained from these two methods were compared to that obtained from velocity analysis of the experimental seismic data. These comparisons enabled the validity of the above expression in yielding an accurate P-wave NMO velocity to be tested, in the limit of small offsets.

Numerical and physical modelling results obtained from this study indicate that the accuracy of the near-offset P-wave NMO equation depends on the nature and degree of anisotropy encountered in a given area, and is not valid for all degrees of P-wave anisotropy. Since this equation is commonly used in estimating the near-offset P-wave NMO velocity when processing seismic data acquired over anisotropic sedimentary basins, processing geophysicists should proceed with caution when using this equation.