Modeling of Wave Dispersion Using Continuous Wavelet Transforms: Incorporating Causality Constraint with Non Linearly Frequency-Dependent Attenuation

This contribution is concerned with the modeling of wave dispersion using continuous wavelet transforms. The mathematical basis for such modeling was formulated in Kulesh et al., Pure Appl. Geophys, 162(2005) p. 843-855. In that work, we derived the wavelet propagator with the assumption that the attenuation shows a nearly linear frequency dependency without imposing any constraint on the relationship between the phase velocity and the attenuation. In the present work we show how to improve the model to incorporate non-linear frequency dependent attenuation for the Cauchy wavelet while satisfying the causality constraint. We show examples with synthetic and experimental data for illustration.