Inversion of velocity field and anisotropic elastic parameters for layered VTI media

Abstract

Numerical modelling studies have been used to devise a way to recover the average P-wave velocity field and the following anisotropic elastic parameters for layered transversely isotropic media: the vertical P-wave velocity (a0), the vertical S-wave velocity (b0), the P-wave anisotropy (e) and the near-vertical P-wave anisotropy (d ). Horizontally layered models comprising transversely isotropic materials with vertical symmetry axes (VTI materials) and isotropic materials were used in computer simulation experiments. It is difficult, even under ideal conditions, to obtain average values of e and d experimentally from multi-layered media. Hence in our numerical simulations, these were obtained by inversion of transmission data. A new double precision inversion code has been developed to invert travel time data to recover the average elastic parameters e and d. The average vertical P and S-wave velocities, a0, b0 were directly determined from travel time data. Subsequently, using the average parameters to the top and to the bottom of a layer of interest, the interval parameters of that layer were recovered using a new least-squares algorithm. From the individual parameters for each layer, we may also compute the overall average velocity field and parameters for the whole multi-layer model. Comparison of the inversion results with directly calculated averages indicated that such multilayered media can be described as a single layer VTI medium except at large incident angles. Simple relationships between the individual and overall average layer parameters were found. A good knowledge of both the individual layer and the overall layer anisotropic parameters, and velocity field may lead to improved seismic data processing and hence, more accurate data interpretation. We expect that this will result in a significant enhancement in seismic resolution and delineation of reservoir volume estimates.