Wide-angle linear forward modelling of synthetic seismograms

We address the issue of linearity and scale dependence in forward modelling of seismic data from well logs, for large ray parameters, wide angles or large offsets. We present a forward model, within the context of seismic-to-well matching, that is linearized in the elastic properties of the earth. This model preserves linearity at large ray parameters and can handle fine-layering effects such as induced anisotropy. Starting from a low-contrast small-ray-parameter model, we extend it to a large-ray-parameter model by fully linearizing the elastic-property contrasts. Overall linearity of the forward model is extended by partitioning the compressional-wave and shear-wave velocity fields into two fundamental scales: a kinematic scale that governs wavefield propagation effects and a dynamic scale that governs wavefield scattering effects. This analysis reveals that the standard practice in forward modelling of strongly filtering the ratio of compressional-wave velocity to shear-wave velocity is well founded in the underlying physics. The partitioning of the velocity fields also leads naturally to forward modelling that accounts fully for stretch effects, to resolution of the angle-of-incidence versus ray-parameter dichotomy in seismic-amplitude analysis, and to full accounting for induced anisotropy and dispersion effects due to fine-layering of isotropic media. With the onset of routine long-offset acquisition and the compelling need to optimize asset management in order to maximize reserve recovery, this forward model recognizes the physics of seismic wave propagation and enables a more complete exploitation of amplitude information in pre-critical seismic data.