The Research On Finite-difference Method Of Wave Equations System In A Two-phase Medium

In modern production and life,human life and social development cannot do without the support of the energy.Most of the energy is buried in the lithosphere of the earth.Due to historical reasons such as the changes of the times,it does not accurately reflect the actual situation and cannot grasp the accurate information if a simple model is constructed to study for the formation of oil and gas.Therefore,it is of great significance to study the actual wave equation.Firstly,the background and research status of seismic waveform are introduced,and the two-phase medium model is selected.Because the model is a good approximation of the physical property parameters.Two kinds of medium and liquid phase are considered in the model based on the Biot theory.Compared with the theory of elastic media,the results will be more accurate.Secondly,the model is based on two-phase medium wave equations.The discrete form is given when the parameter of the equation is the multivariate function.It proved that it is stable the computational format in theory.In the process of solving the wave equation of two-phase medium,in traditional finite-difference methods,in the case of the discrete process,the step is too large to produce a large error.The paper is aimed at this problem;the unit processing of grid area is carried out.In this method can not only ensure that the step size is small enough to guarantee the rationality of finite difference,but also the general rectangle area can be processed to increase the use range of the algorithm.Lastly,the numerical simulation is given in the case of a given three-layer model parameter in the paper.And the wave field snapshot and displacement simulation are given to verify the accuracy of the forward simulation.The difference method presented in this paper can well perform the propagation of transverse and longitudinal waves in solid and liquid media from the results.In this way,this method can reflect the propagation law of underground waves in the stratum,and it has practical significance for seismic exploration.