POROELASTIC BACKUS AVERAGING FOR ANISOTROPIC LAYERED FLUID-SATURATED AND GAS-SATURATED SEDIMENTS

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 flu ids. For a medium consisting of a stack of vertically fractured horizo ntal layers, this effective medium is orthorhombic. We derive the poro elastic constants that define such media in the long-wavelength limit as well as the effective large scale permeability tenser. The permeabi lity shows strong anisotropy for large porosity fluctuations. We obser ve pronounced effects that do not exist in purely elastic media. At ve ry 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 flo w occurs. The effective-medium velocities of the quasi-compressional w aves are higher in the no-flow than in the quasi-static limit. Both ar e lower than the high-frequency, i.e., ray-theory limit. Partial satur ation 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 c ompliant frame tends to increase the anisotropy. In the quasi-static l imit, 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 saturatio n varies, only the ray-theory velocity exhibits anisotropy.