The Study Of Wave Equation Fourier Finite-difference Pre-stack Depth Migration

Migration has been rapidly developed, which is a key technology of seismic data processing to improve horizontal resolution of complex geological targets, particularly in pre-stack depth migration. It can overcome the shortcomings of the time migration and has more accurate image then the time migration for complex geological structure. Recently, there are two methods in pre-stack depth migration. One is based on ray tracing method. Another is the wave field continuation method. Among them, the methods of wave extension are one-way and two-way wave migration. The typical two-way wave migration is reverse time migration. One-way migration is a widely used method. Fourier finite-difference(FFD) migration is a typical one-way migration. It is achieved in frequency- wavenumber domain and frequency- space domain.From the acoustic wave equation, the decomposition condition was discussed, constant of medium speed in the vertical, that was used form the acoustic wave equation to the one-way wave equation. The FFD continuation operator is deduced form the one-way wave equation. The error of Split-Step Fourier(SSF) operator and FFD operator and the advantage of the FFD operator with respect to the SSF operator were analyzed. The time consistent imaging condition of one-way migration was discussed.The wave field continuation, the critical step of migration, was studied. The SSF operator and the FFD operator impulse responses were calculated and analyzed, which intuitively indicated the error of them. The factors of FFD migration were studied, which were border impact of continuation process, frequency of seismic record and step long. These factors by simple models and complex models were analyzed. It has little effect on a simple model having or not attenuation boundary. For complex models, attenuation border is very important. Extension step long is important for the efficiency of pre-stack depth migration. When the extension step selected is too small, migration increases the computational cost. When the extension step selected is too large, you can not get high-quality imaging results. Selecting the appropriate extension steps need to analyze specific issues. The effect of the seismic record efficiency on FFD migration was reached. When you select a smaller frequency bandwidth, it can speed up the computational efficiency, however, the resolution of the results drop. For simple subsurface structure, you can use a smaller bandwidth. For complex media structure, you should choose a larger bandwidth. For a simple model, the low speed has little effect on result. For a complex model, the low speed has little effect on result of shallow part and has much effect on result of deep part. The high speed has much effect on result of whole model.FFD migration method was used for SEG-EAGE salt model and it got a good migration result. It proved the FFD migration was a good depth migration method.