Abstract
AbstractA 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 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 characterised 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 for assessment of the elastic and anelastic parameters.
Highlights
In the framework of exploration seismology, wave propagation in attenuating media has been extensively studied to understand amplitude loss, frequency content reduction and phase distortion induced by anelastic processes (Kolsky 1956; Futterman 1962; ToksĂśz & Johnston 1981)
The cumulative filter is characterised by an asymmetrical frequency behaviour that depends on the ratio REâΡ between the elastic reflection coefficient of the reflector and the anelastic contrast between the upper and lower layers
In order to quantify the impact of the cumulative filter on an incoming seismic wave at normal incidence, we have developed analytical expressions for a Ricker source wavelet defined by a peak frequency
Summary
In the framework of exploration seismology, wave propagation in attenuating media has been extensively studied to understand amplitude loss, frequency content reduction and phase distortion induced by anelastic processes (Kolsky 1956; Futterman 1962; ToksĂśz & Johnston 1981). The motivation in studying anelastic reflections, related to the imaginary part of the complex seismic impedance controlled by the quality factor (White 1965; Lines et al 2008; Morozov 2011), is better interpreting reflected wave amplitude (BourbiĂŠ & Nur 1984) and phase rotation (Lines et al 2014) These studies do not deal with an anelastic upper layer, i.e. anelastic propagation is not considered before the reflection and the impact of the Q-contrast magnitude on the reflected wave is still not quantified. Insights and pitfalls related to the use of the peak-frequency attribute when estimating Q values or interpreting seismic data
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