Theory of frequency dependent acoustics in patchy-saturated porous media
Theory of frequency dependent acoustics in patchy-saturated porous media
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DOI：
10.1121/1.1381021
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发表时间：
2001-08-01
影响因子：
2.4
通讯作者：
Johnson, DL
中科院分区：
文献类型：
--
作者：
Johnson, DL
多孔岩石的动态体积模量(K) /波浪（omega）理论是在准静态Biot理论的背景下发展起来的，这种岩石的饱和发生在两种不同流体的100%饱和斑块中。该理论描述了低频时Biot-Gassmann-Woods结果与高频时Biot-Gassmann-Hill结果的交叉。给出了接近低频和高频极限的精确结果。基于这些精确的结果，以及(K) /波浪（ω）扩展到复ω平面的性质，给出了一个简单的封闭解析模型。与含气和含水饱和岩石的简单几何精确解的比较表明，解析理论在整个频率范围内是非常精确的。除了Biot理论的常用参数外，该模型还具有两个几何参数，其中一个是斑块的比表面积S/V。在其中一种流体是气体的特殊情况下，第二个参数是一种不同的，但也很简单的，对刚性流体的斑块大小的度量。该理论与相关实验相结合，将允许人们推断出有关斑块大小和形状的信息，或者相反，如果大小和饱和度值大致已知，则可以进行精确的声波到地震的转换。(C) 2001美国声学学会。
The theory of the dynamic bulk modulus, (K) over tilde(omega), of a porous rock, whose saturation occurs in patches of 100% saturation each of two different fluids, is developed within the context of the quasi-static Biot theory. The theory describes the crossover from the Biot-Gassmann-Woods result at low frequencies to the Biot-Gassmann-Hill result at high. Exact results for the approach to the low and the high frequency limits are derived. A simple closed-form analytic model based on these exact results, as well as on the properties of (K) over tilde(omega) extended to the complex omega -plane, is presented. Comparison against the exact solution in simple geometries for the case of a gas and water saturated rock demonstrates that the analytic theory is extremely accurate over the entire frequency range. Aside from the usual parameters of the Biot theory, the model has two geometrical parameters, one of which is the specific surface area, S/V, of the patches. In the special case that one of the fluids is a gas, the second parameter is a different, but also simple, measure of the patch size of the stiff fluid. The theory, in conjunction with relevant experiments, would allow one to deduce information about the sizes and shapes of the patches or, conversely, to make an accurate sonic-to-seismic conversion if the size and saturation values are approximately known. (C) 2001 Acoustical Society of America.