O the Foundations of the Dynamical Theory of Fractured Porous Media and the Gravity Variations Caused by Dilatancies.
This thesis investigates the dynamical theory of multiphase fractured porous media, by which the shear wave velocities can now be obtained that are in agreement with experiments, which were against the prediction of the Biot theory. The anisotropy, P and S wave velocities, and also waveforms can now be explicitly expressed as functions of structural, physical, and reservoir parameters such as porosity and pore fluid content, which are the key for the enhancement of seismic resolution and the determination of detailed subsurface structures and in-situ physical properties of subsurface materials, and so are essential for reservoir characterization and reservoir modeling. In addition, there generally exist 2 times A kinds of waves in an A-phase fractured porous medium, i.e., A kinds of P (compressional) waves and A kinds of S (shear) waves. The theory includes the Biot theory and the squirt mechanisms as special cases. The theory is developed using topological spaces and the principle of covariance. The basic theory of 3A -dimensional Riemannian manifold of an A-phase fractured porous medium is given. The equations governing the structural evolution and the interactions between physical properties and structural changes in space and time are also derived, which are needed to understand many new phenomena associated with structural aggregated systems in many fields such as the studies of multiphase structural media, non-Newtonian fluids, and condensed-matter physics. The thermo-dynamics of structural media is also discussed. The deformation, fracturing, and stress relaxation with or without fluid invasion cause dilatations of the fractured porous medium under a tectonic stress. The gravity change caused by these dilatancies has been formulated using the variational principle. The concept of mepicentroid is developed, which, differing from the concept of epicenter, is an essential concept for understanding the association of gravity variation in space and time with the occurrence of earthquakes. In conclusion, this thesis intends to present the general mechanics of structural media, including the general laws of fluid mechanics of multiphase fractured porous media, which is the foundations of the unified theory of dynamic fields of structural media. It contains applications to high resolution modeling, simulation, characterization, and inversion of the in-situ physical properties and structures of multiphase structural media. It also includes topics on dynamic monitoring of motions of subsurface matters.
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- Geophysics; Physics: General; Mathematics