Wave Propagation In Two-phase Media Research Articles

Rock moduli estimation of inhomogeneous two-phase media with finite difference modeling algorithm

Digital rock physics (DRP) builds a bridge between pore-scale physical processes and the macroscopic physical properties of rock. Its key paradigm is to image and digitize the pore space and mineral matrix of rock, then to simulate the response of various physical fields and calculate the equivalent elastic parameters of rocks through digital rocks and mathematical methods. In this paper, a new approach is proposed to estimate the rock moduli of two-phase media with the staggered-grid high-order finite difference method (FDM) of the Biot theory based on DRP. This new method not only takes into consideration the impact of fluid on elastic wave propagation in two-phase media, but it is also easy to understand and implement, improving the calculation accuracy, requiring less memory and improving on the weaknesses of conventional rock physics experiments which are time consuming and expensive. In order to estimate the rock moduli, we establish two models, and the digital rock sample is embedded in one of those. Using this method, it is possible to model the dynamic wave propagation and measure the time delay of the peak amplitude caused by the inhomogeneous structure of the digital rock sample, with the receivers set at the bottom of the two models. The time delay allows us to estimate the effective velocity of both compressional and shear waves, and therefore calculate the rock moduli. Additionally, comparison between the numerical simulated results obtained through this method and experimental results indicates that they agree well. Comparison with the numerical simulated results obtained via another method tests and verifies the accuracy and feasibility of the new method. Also, the equivalence conditions between this new method and the various rock physics models are inferred.

Wave field in two-phase media by the convolutional differentiator method

This paper applies the convolutional differentiator method, based on generalized Forsyte orthogonal polynomial (CFPD), to simulate the seismic wave propagation in two-phase media. From the numerical results we can see that three types of waves, fast P-waves, S-waves and slow P-waves, can be observed in the seismic wave field. The experiments on anisotropic models demonstrate that the wavefront is elliptic instead of circular and S-wave splitting occurs in anisotropic two-phase media. The research has confirmed that the rules of elastic wave propagation in fluid-saturated porous media are controlled by Biot’s theory. Experiment on a layered fault model shows the wavefield generated by the interface and the fault very well, indicating the effectiveness of CFPD method on the wavefield modeling for real layered media in the Earth. This research has potential applications to the investigation of Earth’s deep structure and oil/gas exploration.

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocities and attenuation of ultrasonic waves in two-component media are determined. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results for effective moduli, velocity and/or attenuation as functions of concentration of spherical inclusion material, or porosity, are graphically displayed.

Statistical Theory of Sound Wave Propagation in Two-Phase Media : Effective Sound Velocity, Effective Viscosity and Effective Heat Conductivity

ニ相系の音波伝ぱについて、新しい統計理論を適用し、この波動の長波長の平均的挙動を支配する基礎方程式を導いた。この結果、二相系の音速について厳密な表現式をえ、さらにニ相系の有効物性値並びに有効粘性率、有効熱伝導率の表現式をえた。これらの物性の有効値は希薄分散系の厳密解と一致することを見い出し、分散粒子濃度が高い場合についても、ほかの解析と比較検討を行った。

Interaction model for elastic wave propagation in two-phase media : Kuster, G T Geophys Prospect, V25, N3, Sept 1977, P481–495

Interaction model for elastic wave propagation in two-phase media : Kuster, G T Geophys Prospect, V25, N3, Sept 1977, P481–495