A homogeneous anisotropic effective‐medium model for saturated thinly layered sediments is introduced. It is obtained by averaging over many layers with different poroelastic moduli and different saturating fluids. For a medium consisting of a stack of vertically fractured horizontal layers, this effective medium is orthorhombic. We derive the poroelastic constants that define such media in the long‐wavelength limit as well as the effective large‐scale permeability tensor. The permeability shows strong anisotropy for large porosity fluctuations. We observe pronounced effects that do not exist in purely elastic media. At very low frequencies, seismic waves cause interlayer flow of pore fluid across interfaces from more compliant into stiffer layers. For higher frequencies, the layers behave as if they are sealed, and no fluid flow occurs. The effective‐medium velocities of the quasi‐compressional waves are higher in the no‐flow than in the quasi‐static limit. Both are lower than the high‐frequency, i.e., ray‐theory limit. Partial saturation affects the anisotropy of wave propagation. In the no‐flow limit, gas that is accumulated primarily in the stiffer layers reduces the seismic anisotropy; gas that is trapped mainly in layers with a more compliant frame tends to increase the anisotropy. In the quasi‐static limit, local flow keeps the anisotropy constant independent of partial saturation effects. For dry rock, no‐flow and quasi‐static velocities are the same, and the anisotropy caused by layering is controlled only by fluctuations of the layer shear moduli. If the shear stiffness of all layers is the same and only the compressive stiffness or saturation varies, only the ray‐theory velocity exhibits anisotropy.

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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.

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The measured geophysical response of sand–shale sequences is an average over multiple layers when the tool resolution (seismic or well log) is coarser than the scale of sand–shale mixing. Shale can be found within sand–shale sequences as laminations, dispersed in sand pores, as well as load bearing clasts. We present a rock physics framework to model seismic/sonic properties of sub‐resolution interbedded shaly sands using the so‐called solid and mineral substitution models. This modelling approach stays consistent with the conceptual model of the Thomas–Stieber approach for estimating volumetric properties of shaly sands; thus, this work connects established well log data‐based petrophysical workflows with quantitative interpretation of seismic data for modelling hydrocarbon signature in sand–shale sequences. We present applications of the new model to infer thickness of sand–shale lamination (i.e., net to gross) and other volumetric properties using seismic data. Another application of the new approach is fluid substitution in sub‐resolution interbedded sand–shale sequences that operate directly at the measurement scale without the need to downscale; such a procedure has many practical advantages over the approach of “first‐downscale‐and‐then‐upscale” as it is not very sensitive to errors in estimated sand fraction and end member sand/shale properties and remains stable at small sand/shale fractions.