Wavefield Analysis-oriented Wave Equation Finite Difference Forward Modeling

With the increasing complexity of prospecting target, the model media that we research are more and more complex, in order to look into the wavefield of complex media in detail, it is necessary to conduct the numerical simulation of the seismic wavefield. The wave equation finite difference method is one of the most prevalent and the most popular numerical simulation methods in recent years, and its advantages are that analog wavefield is information-rich and simple to accomplish, computation speed is fast, etc.Wave equation finite difference method has many advantages, but there are also some shortcomings, among which is the stability condition, a very important problem and need to be solved urgently. Stability condition directly dominates the success or failure of the forward simulation results, in the wave equation finite difference solutions of the visco-elastic medium, the visco-elastic properties of the medium will increase the instability of numerical solutions. Based on the visco-elastic theory, this paper researches the stability condition of the Kelvin-Voigt and Maxwell visco-elastic models under the different accuracies of difference scheme, and numerical solution of stability condition with velocity and quality factor for the Standard-Linear visco-elastic model.The time step used in forward modeling is determined by the maximum speed when the spatial grid step is set, the greater the speed, the smaller the time step, then it is a large amount of computation. On the assumption of not affecting the result, in order to improve the efficiency of the wave equation difference simulation, this paper realize the wave equation finite-difference variable time-step numerical simulation.The main feature of the near-surface is low-speed, low-density and low-quality factor. With the development of seismic exploration in the mountains, desert and other areas which have complex surface, near-surface seismic numerical simulation technique has been widespread concerned by geophysicist. This part of the simulation adopts a free boundary condition, and combinate the above-mentioned results to simulate and analyze the near-surface effects of seismic wave field, the near-surface Rayleigh wave has been simulated and then conduct a quantitative analysis to determine the simulated Rayleigh surface wave. Visco-elastic medium is more accord with the actual media, so numerical simulation is conducted under a free boundary condition in visco-elastic media which contain a low-velocity layer. And this paper discusses the effect of viscoelastic media on the attenuation of the seismic wave quantitatively in terms of the Q value of the size and the frequency of source wavelet and so on.The actual media (reservoir-related) are often non-uniform, there are many small anomalies and their distributions are extremely irregular in non-uniform media (this can be found through logging data and core samples). In this case, we can construct a random medium to simulate, and can obtain the wave field in the non-uniform medium. Finally, several numerical simulations of the actual velocity model can be run to get the full-wave field in complex reservoir (containing holes, cracks, etc.) and the wavefield in reservoir that under different water saturations, and then carry on the spectrum analysis and time-frequency analysis, but also study the low-velocity layer and the effects of near-surface on the wave field simulation.