The Elastic Medium Of Seismic Wave Field Simulation

There are two aspects, containing mathematical simulation and physical simulation,in the seismic forward modeling.Forward problem is analytical basis of three links containing seismic data acquisition,data processing and interpretation.This paper mainly discusses numerical simulation of seismic wave field which is one of the important research subjects of prospecting seismology and is also the important tool of researching propagation rules of seismic wave and the validity of detecting all kinds of processing methods.What is more,it is the basis of seismic inversion.So it is the important significance of this technology in the exploration and development of oil and gas field.Research methods of seismic numerical simulation technology include the three kinds of integral equation,ray tracing method and wave equation method.Integral equation is established on the basis of the principle of wave superposition on the basis of the Huygens theory;The main theoretical basis of ray tracing method which belong to geometrical seismology methods is geometrical optics.The main energy of seismic wave spread along the ray path in the approximate high frequency condition.Its main advantage is fast on computing speed.The seismic wave travel time we can get is accurate,but it is lack of seismic wave dynamical information;Numerical simulation method of wave equation is the basis on wave equation of seismic wave,retaining kinematics and dynamics characteristics of seismic wave compared with ray tracing method.Firstly,the paper introduces wave theory on the basis of wave equation methods of seismic wave field,discusses all kinds of solving methods of wave equation and deduces separately the formula of solving methods. We choose the finite difference method of staggered grids which has the simple programming,a fast calculation speed,and can obtain complete elastic wave field information.This method is applied on theoretical research and deduces a wave equations in fields of speed-stress such as stage grid discrete, get difference wave equations defined on the grid point.Then I discuss the compatibility,convergence and stability of discrete difference format, and get stability condition of the difference wave equations, ensure the numerical solution converging to the real solution..It is very important to process source conditions and boundary conditions in the wave numerical simulation.Then I discuss importantly the processing method of source and boundary in the isotropic medium models.Lastly,I establish all different kinds of models in order to analysis the wave field.The synthetic seismic records of P wave and P-SV wave of2d complex inhomogeneous medium,including VSP records,CSP records,CMP records and seismic stacked profile,are calculated by writing computer programs. Finally,the theory and calculated practical model are roughly comformed.