Wollner & Dvorkin 15 discussed a method for estimating the effective solid bulk modulus and fluid bulk modulus of a layered poroelastic package from fine-scale measurements. Berryman 12 deduced the compliance form expression for stratified porous media under the same assumptions used in GassmannвЂ™s equations. Gelinsky & Shapiro 9 derived the analytical expressions for effective stiffness tensors of a layered porous package at no-flow and quasi-static conditions. Multiple methods exist for the upscaling of elastic properties from finer-scale measurements. Much effect has been devoted to estimating the effective properties of heterogeneous composites in the geophysical literatures 7, 8, 9, 10, 11, 12, 13, 14. Stratified poroelastic materials are typical heterogeneous composites. Determining the valid relationship between poroelastic constants and the effective fluid bulk modulus of heterogeneous systems at seismic scale remains challenging. Laboratory measurements have shown that the Biot-Gassmann equation may have different behavior for heterogeneous systems 4, 6. The prediction of Biot and GassmannвЂ™s equations 2 have been confirmed by both laboratory and field experiments 3, 4, 5 however, this theory has been limited by the explicit assumptions of homogeneous fluids and solid phases, and it is often used to establish the relationship between undrained poroelastic constants and the pore-fluid bulk modulus for centimeter-scale rocks or porous layers (such as reservoirs). The commonly used theory describing wave propagation in fluid-saturated media is BiotвЂ™s equation of poroelasticity 1, which forms the basis for relating poroelastic constants with the fluid bulk modulus for homogeneous media.

However, one issue with this is that the relationship between undrained elastic constants and pore-fluid bulk modulus established in the laboratory or well can be different and may not be directly used in interpreting seismic data whose spatial scale is much coarser. Seismic signatures are important sources of information on the physical properties of subsurface and commonly used to infer reservoir fluid properties, based on the relationship between undrained elastic constants and pore-fluid bulk modulus established at local scale. Seismic methods are among the principle tools used in oil and gas exploration, CO 2 sequestration monitoring, mineral exploration and other areas. The findings will help us understand the upscaling of rock-physics transform, which will improve the accuracy of geological property predictions from seismic-scale elastic constants. To interpret seismic-scale elastic constants for petrophysical properties, the rock physics relationship need to be carefully calibrated. The results of numerical simulations show that LamГ© moduli provide more insight into rock properties and pore-fluid contents than P-wave impedances, and that the relationship between the upscaled elastic constants and the effective fluid bulk moduli at the seismic scale is usually not perfectly preserved at the reservoir scale. The seismic-scale results reveal that the identification of reservoir fluid properties is improved using elastic constants that is more sensitive to pore fluid properties. After conducting a two-dimensional marine seismic survey over the physical model, the physical modeling data ware then used to retrieve the elastic constants of the layered package. To understand this problem, we built a scaled physical model comprised of artificial porous layers with different pore fluids. However, the spatial heterogeneity of rock physical properties at the local scale has a significant impact on this relation. Elastic constants derived from seismic-scale measurements are often used to infer subsurface petrophysical properties based on rock-physics relationships established from either theoretic model or core-scale measurements.

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