AVO modeling of monochromatic spherical waves: comparison to band-limited waves
Charles P. Ursenbach, Arnim B. Haase
Monochromatic and band-limited spherical waves have differing reflection coefficient curves. To make a comparison of these two paradigms, a new expression for the monochromatic reflectivity is given in terms of a weighting function. The weighting function approach, developed previously for a specific class of band-limited spherical waves (Rayleigh wavelets), shows explicitly how different plane waves contribute to the spherical-wave reflection coefficient. Direct comparison shows that monochromatic waves have oscillatory, non-decaying weighting functions, and thus sample a wide range of plane waves. This contrasts with typical Rayleigh wavelets which have well-localized weighting functions. These two behaviors lead to reflection coefficient curves which are respectively oscillatory and monotonic after the critical angle. A bridge between these two behaviors is constructed by considering unusually narrow Rayleigh wavelets. These show intermediate properties. The benefits of this study are 1) a simple and convenient method for calculating monochromatic spherical-wave reflection coefficients, and 2) a clearer understanding of how spherical-wave reflection coefficients are created from constituent plane-waves.