Numerical Simulation Of Elastic Wave Field In The Two Phase-medium Of Coal And Rock

As the earthquake engineering and energy seismic exploration are further developed, the theory of bi-phase medium is introduced for more accurate description of the underground porous medium containing fluid. Biot(1956a, b,1962a, b) has established the foundation of bi-phase medium wave propagation theory. Based on the theory, the elastic wave field in coal-rock medium is simulated, the status of the underground coal-rock medium's geological tectonic characteristics and the changes of porosity size is investigated. It has important significance to effectively control the water and gas outburst and other natural disasters in mines.In this paper, the theoretical model is established on the basis of bi-phase medium, the bi-phase medium constitutive relationship is discussed, and the elastic wave propagation velocity is calculated through the equation of elastic wave propagation in bi-phase medium, which lay a theoretical foundation for the specific numerical simulation. Moreover, the principle of numerical simulation, finite difference, is described and discussed. The finite difference method used in 2-d elastic wave equation is emphatically introduced, the realization of the finite difference is systematically researched, as well as the algorithm of staggered grids difference is given out. In the simulation of wave field, the transmissive absorbing boundary conditions and exciting source of zero-phase wavelet are applied, and the stability condition suitable for four-order spatial, two-order time finite difference in 2-d isotropic medium is proposed. Through the two-order center difference method for displacement equation, the discrete numerical solution of elastic wave equation in two-dimensional bi-phase medium based on the Biot theory is achieved. Then under the help of Matlab programmes, several typical models of elastic wave field are forward simulated respectively, the horizontal and vertical particle displacement vibration graphs of solid and liquid bi-phase medium in the layered model. From the forward simulation results, it is shown that, in the uniform layered coal-rock medium, the amplitude of elastic wave decreases significantly as the porosity increases while the amplitude increase as the porosity decreases. The changes of amplitude are also significant when elastic wave propagates in layered medium as porosity is variable, which is intuitive in the particle displacement vibration graphs.Above all, the bi-phase medium elastic wave field simulation method has great realistic and theoretical value for the understanding of the geological tectonic characteristics and change of porosity size of underground coal-rock medium. It is also proved that the detection technology of elastic wave applied in mine geology work is effective and feasible.