DYNAMIC-EQUIVALENT MEDIUM APPROACH FOR THINLY LAYERED SATURATED SEDIMENTS

The phase velocity and the attenuation coefficient of compressional se ismic waves, propagating in poroelastic, fluid-saturated, laminated se diments, are computed analytically from first principles. The wavefiel d is found to be strongly affected by the medium heterogeneity. Impeda nce fluctuations lead to poroelastic scattering; variations of the lay er compressibilities cause inter-layer flow (a 1-D macroscopic local h ow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 1 0-100 Hz. The various attenuation mechanisms are found to be approxima tely additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seis mic to sonic frequencies. Blot's global flow (the relative displacemen t of solid frame and fluid) contributes mainly in the range of ultraso nic frequencies. From the seismic frequency range up to ultrasonic fre quencies, attenuation due to heterogeneity is strongly enhanced compar ed to homogeneous Blot models. Simple analytical expressions for the P -wave phase velocity and attenuation coefficient are presented as func tions of frequency and of statistical medium parameters (correlation l engths, variances). These results automatically include different asym ptotic approximations, such as poroelastic Backus averaging in the qua si-static and the no-flow limits, geometrical optics, and intermediate frequency ranges.