Berryman JG, Berge PA, Bonner BP
Lawrence Livermore National Laboratory, Livermore, California 94551-9900, USA.
J Acoust Soc Am. 2000 Jun;107(6):3018-27. doi: 10.1121/1.429331.
For wave propagation at low frequencies in a porous medium, the Gassmann-Domenico relations are well-established for homogeneous partial saturation by a liquid. They provide the correct relations for seismic velocities in terms of constituent bulk and shear moduli, solid and fluid densities, porosity and saturation. It has not been possible, however, to invert these relations easily to determine porosity and saturation when the seismic velocities are known. Also, the state (or distribution) of saturation, i.e., whether or not liquid and gas are homogeneously mixed in the pore space, is another important variable for reservoir evaluation. A reliable ability to determine the state of saturation from velocity data continues to be problematic. It is shown how transforming compressional and shear wave velocity data to the (rho/lambda, mu/lambda)-plane (where lambda and mu are the Lame parameters and rho is the total density) results in a set of quasi-orthogonal coordinates for porosity and liquid saturation that greatly aids in the interpretation of seismic data for the physical parameters of most interest. A second transformation of the same data then permits isolation of the liquid saturation value, and also provides some direct information about the state of saturation. By thus replotting the data in the (lambda/mu, rho/mu)-plane, inferences can be made concerning the degree of patchy (inhomogeneous) versus homogeneous saturation that is present in the region of the medium sampled by the data. Our examples include igneous and sedimentary rocks, as well as man-made porous materials. These results have potential applications in various areas of interest, including petroleum exploration and reservoir characterization, geothermal resource evaluation, environmental restoration monitoring, and geotechnical site characterization.
对于低频波在多孔介质中的传播，在液体均匀部分饱和的情况下，加斯曼 - 多梅尼科关系已得到充分确立。它们根据组分的体积模量和剪切模量、固体和流体密度、孔隙度和饱和度，给出了地震波速度的正确关系。然而，当已知地震波速度时，要轻易地反演这些关系来确定孔隙度和饱和度是不可能的。此外，饱和度的状态（或分布），即液体和气体在孔隙空间中是否均匀混合，是储层评价的另一个重要变量。从速度数据确定饱和度状态的可靠能力仍然存在问题。本文展示了如何将纵波和横波速度数据转换到（ρ/λ，μ/λ）平面（其中λ和μ是拉梅参数，ρ是总密度），从而得到一组用于孔隙度和液体饱和度的准正交坐标，这极大地有助于解释地震数据以获取最感兴趣的物理参数。对相同数据进行的第二次变换随后可分离出液体饱和度值，并提供有关饱和度状态的一些直接信息。通过在（λ/μ，ρ/μ）平面中重新绘制数据，可以推断出数据采样区域中存在的斑块状（非均匀）与均匀饱和度的程度。我们的示例包括火成岩和沉积岩，以及人造多孔材料。这些结果在包括石油勘探和储层表征、地热资源评估、环境恢复监测以及岩土工程场地表征等各个感兴趣的领域都有潜在应用。
