Dynamic-equivalent medium approach for thinly layered saturated sediments

Abstract

S U M M A R YThe phase velocity and the attenuation coefficient of compressional seismic waves, propagating in poroelastic, fluid-saturated, laminated sediments, are computed analytically from first principles. The wavefield is found to be strongly affected by the medium heterogeneity. Impedance fluctuations lead to poroelastic scattering; variations of the layer compressibilities cause inter-layer flow (a 1-D macroscopic local flow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 10-100 Hz. The various attenuation mechanisms are found to be approximately additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seismic to sonic frequencies. Biot's global flow (the relative displacement of solid frame and fluid) contributes mainly in the range of ultrasonic frequencies. From the seismic frequency range up to ultrasonic frequencies, attenuation due to heterogeneity is strongly enhanced compared to homogeneous Biot models. Simple analytical expressions for the P-wave phase velocity and attenuation coefficient are presented as functions of frequency and of statistical medium parameters (correlation lengths, variances). These results automatically include different asymptotic approximations, such as poroelastic Backus averaging in the quasi-static and the no-flow limits, geometrical optics, and intermediate frequency ranges.

Frequency-dependent attenuation as a potential indicator of oil saturation

“…Not accounting for dynamic effects is appropriate for this study because the aim is to better understand the behavior of intrinsic attenuation caused by fluid flow at low seismic frequencies. An analytical solution combining dynamic effects and intrinsic attenuation caused by interlayer flow is given by Gelinsky and Shapiro (1997). As shown in Appendix A, 1/Q (Eq.…”

Wave propagation in micro-heterogeneous porous media: A model based on an integro-differential wave equation

“…The characteristic frequency 0 is can be of order 10-100 Hz for fluid-saturated porous rocks, several orders of magnitude below Biot's characteristic frequency B . 14,41 For signals with the bandwidth in the range 0 Ͻ Ͻ B the real and imaginary part of the wave number vector derived from the Gurevich-Lopatnikov theory can be approximated by the causal frequency-power dispersion law…”

Acoustic Attenuation in Self-Affine Porous Structures

“…Many studies [1][2][3][4][5][6][7][8][9][10] have focused on the effective acoustic properties of fluid-filled porous media in the presence of mesoscopic length-scale heterogeneity. When an acoustic wave compresses a sample of porous material containing mesoscopic heterogeneity, the fluid-pressure response will be relatively large in regions where the compressibility of the framework of grains is large, and small where the framework compressibility is small.…”