We study the combined effect of (1) attenuation caused by interlayer-flow and (2) tuning on the reflection coefficient of a layer embedded in an elastic medium in one dimension. Both attenuation and tuning are frequency dependent. We only consider a contrast in attenuation between the layer and the non-attenuating medium. We use the analytical interlayer-flow model, which is based on Biot’s theory of poroelasticity, to model attenuation in the layer. The resulting complex velocity for the attenuating layer is used in the analytical solution for the complex reflection coefficient of a layer embedded in an elastic medium. Attenuation combined with tuning in layers can generate reflection coefficients with significant (1) amplitude (> 10 %) and (2) frequency dependence. Our results can be applied to hydrocarbon reservoirs with high attenuation but low acoustic impedance contrast to the surrounding rock.
We present a study on the frequency-dependent reflection coefficient of a layer exhibiting attenuation caused by interlayer flow (White et al., 1975). Quintal et al. (2009) showed that, for a wide range of realistic petrophysical parameters for sandstones partially saturated with water and gas, the quality factor, Q (wave attenuation can be defined as Q-1), can be as small as 2 in the interlayer-flow model. They applied the interlayer-flow model to study the reflection coefficient, R, of a thin (compared to the wavelength) layer partially saturated with water and gas, exhibiting such high attenuation. The amplitude of the reflection coefficient of such a layer, due to contrast in attenuation to the non-attenuating background medium, but no acoustic (real part of) impedance contrast, can be greater than 10 % for a value of Q lower than 4.
In this paper, we extend the study made by Quintal et al. (2009), taking also into account the influence of the layer thickness on the amplitude of the reflection coefficient. The reflection coefficient of an elastic layer is frequency-dependent due to constructive and destructive interferences of waves reflected from the top and bottom of the layer (e.g., Kallweit and Wood, 1982). This effect is referred to as tuning. The reflection coefficient of a layer with frequency-dependent attenuation is then influenced by two frequency-dependent mechanisms: tuning and attenuation.
The reflection coefficient of an attenuating layer has a maximum when the transition and the tuning frequencies are identical. The transition frequency is the frequency at which attenuation is maximal; and the tuning frequency occurs when the positive and negative interferences result in the maximum amplitude of the reflected wave.
Here we study the combined effect of attenuation and tuning on the reflection coefficient of a layer exhibiting high attenuation contrast to the background medium, but no acoustic impedance contrast. To investigate the combined effect of frequency-dependent attenuation and tuning on the reflectivity of a layer, we use: (1) the analytical solution of the interlayer-flow model (White et al., 1975; Carcione and Picotti, 2006), simulating the influence of the frequency-dependent attenuation; and (2) a 1D analytical solution of the reflection coefficient of a layer embedded in an elastic medium (Brekhovskikh, 1980), where we vary the layer thickness with respect to the wavelength, simulating the influence of tuning.