Filtering of a Ricker wavelet induced by anelastic seismic wave propagation and reflection

A varying Q factor with depth induces modifications of seismic wave features due to anelastic propagation but also reflections at the discontinuities. Standard signal analysis methods often neglect the reflection contribution when assessing Q values from seismic data. We have developed an analytical quantification of the cumulative effects of both the propagation and reflection contributions by considering the Kjartansson's model and a seismic plane wave at normal incidence on a step-like discontinuity. We show that the cumulative effects are equivalent to a frequency filter characterized by a bandform and phase that both depend on the ratio between the elastic and anelastic contrasts. When considering this filter applied to a Ricker wavelet, we establish an analytical expression of the peak frequency attribute as a function of propagation and reflection properties. We demonstrate that this seismic attribute depends on the anelastic contrast, which cannot be neglected when assessing Q factors: the error in Q estimate is not linearly dependent on the anelastic contrast and we establish an analytical expression for the case where this contrast is weak. An unexpected phenomenon for a step-like interface is an increase in the peak frequency that is observed when the anelastic and elastic contrasts have opposite signs, with a constraint on the anelastic propagation properties. This behaviour allows assessing the elastic and anelastic parameters