Inferring the relative measure of principal stress components

The 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.