基于波动方程的层间多次波预测方法研究

In exploration geophysics，velocity analysis and migration methods except reverse time migration are based on ray theory or one-way wave-equation. So multiples are regarded as noise and required to be attenuated. It is very important to attenuate multiples for structure imaging, amplitude preserving migration. So it is an interesting research in theory and application about how to predict and attenuate internal multiples effectively. There are two methods based on wave-equation to predict internal multiples for pre-stack data. One is common focus point method. Another is inverse scattering series method. After comparison of the two methods, we found that there are four problems in common focus point method: 1. dependence of velocity model; 2. only internal multiples related to a layer can be predicted every time; 3. computing procedure is complex; 4. it is difficult to apply it in complex media. In order to overcome these problems, we adopt inverse scattering series method. However, inverse scattering series method also has some problems: 1. computing cost is high; 2. it is difficult to predict internal multiples in the far offset; 3. it is not able to predict internal multiples in complex media. Among those problems, high computing cost is the biggest barrier in field seismic processing. So I present 1D and 1.5D improved algorithms for reducing computing time. In addition, I proposed a new algorithm to solve the problem which exists in subtraction, especially for surface related to multiples. The creative results of my research are following: 1. derived an improved inverse scattering series prediction algorithm for 1D. The algorithm has very high computing efficiency. It is faster than old algorithm about twelve times in theory and faster about eighty times for lower spatial complexity in practice; 2. derived an improved inverse scattering series prediction algorithm for 1.5D. The new algorithm changes the computing domain from pseudo-depth wavenumber domain to TX domain for predicting multiples. The improved algorithm demonstrated that the approach has some merits such as higher computing efficiency, feasibility to many kinds of geometries, lower predictive noise and independence to wavelet； 3. proposed a new subtraction algorithm. The new subtraction algorithm is not used to overcome nonorthogonality, but utilize the nonorthogonality's distribution in TX domain to estimate the true wavelet with filtering method. The method has excellent effectiveness in model testing. Improved 1D and 1.5D inverse scattering series algorithms can predict internal multiples. After filtering and subtracting among seismic traces in a window time, internal multiples can be attenuated in some degree. The proposed 1D and 1.5D algorithms have demonstrated that they are effective to the numerical and field data. In addition, the new subtraction algorithm is effective to the complex theoretic models.