Seismic Raypath and Wavefront Models in the Lithofacies of the Niger Delta, Nigeria

Abstract

Seismic raypaths and wavefronts model in the vertically anisotropic lithofacies of the Niger Delta are presented. These models based on the linear increase of velocity with depth are defined by the parametric equations: For raypaths \(\left[\mathrm{x}(\theta)=\mathrm{R}_{\mathrm{r}} \operatorname{Cos} \theta+\mathrm{x}_{\mathrm{rc}}\right.\) (centre) and \(z(\theta)=R, \operatorname{Sin} \theta-z_{\mathrm{rc}}\) (radii)]; and for Wavefronts \(\left[x(\theta)=R_w \operatorname{Cos} \theta\right.\) (centre) and \(z(\theta)=R_w \operatorname{Sin} \theta+z_w\) (radii)]. The take-off velocity, \(\mathrm{V}_0=1656 \mathrm{~ms}^{-1}\) and vertical velocity gradient, \(k=0.44 \mathrm{~s}^{-1}\) previously determined for the Niger Delta served as input to these equations to generate the models in Graph (version 4.3) software. Raypaths are at offsets from 400 to 2000 m at 400 m intervals while the wavefronts are at travel times from 20 to 100 ms at 20 ms intervals. Raypaths are observed to be different from straight lines and travel in circular paths while wavefronts are circular arcs travelling greater distance in the vertical direction than in the horizontal for equal travel times. These models provide a basic framework in the Niger Delta for accurate ray tracing, velocity models development and traveltime calculations in seismic processing.