基于贝叶斯理论的Shearlet域一次波与多次波分离

Primary and multiple separation in Shearlet domain based on Bayesian theory

多次波的去除效果很大程度上决定了地震成像的质量,尽管表面相关多次波的压制(SRME)研究方法取得了很大进步,但预测出来的多次波在相位和振幅上的混乱仍然是一个难题,因此减去的效果好坏尤为关键。常规的最小平方匹配方法并不能很好地处理这种预测的误差,利用Shearlet变换的多尺度、多方向特性,可以使预测的信号在Shearlet域变得稀疏、圆滑。以此为前提,结合贝叶斯概率最大化理论,建立了一个有效的一次波与多次波分离算法。以SRME预测的多次波为例,从贝叶斯预测角度出发,通过精确求解最优化问题就可以达到一次波与多次波分离的目的,该算法能够更好地控制预测信号和实际信号的误差。理论和实际数据的实验表明,相比最小平方匹配减去方法,该方法可以有效地提高减去效果,更好地压制多次波以及高频混叠,并且可以更好地估计一次波。

The quality of seismic imaging is greatly determined by the effect of multiple elimination.Despite great advances in the surface-related multiple elimination method,the chaos in phase and amplitude of predicted multiples remains a difficulty,so that the effect of multiple subtraction is critical.The conventional least-squares matching method is unable to handle this prediction error well.Using multi-scale and multi-direction Shearlet transform,the predicted signals become sparse and smooth in Shearlet domain.On the premise of this method in combination with Bayesian probability maximum theory,an effective primary and multiple separation algorithm has been created.Taking the multiples predicted by SRME as example and from the perspective of Bayesian prediction,the target primary and multiple separations can be achieved by precisely solving the optimization problem.This method is able to better control the errors between predicted and actual signals.The experiments on theoretical and actual data indicate that compared with least-squares matching subtraction method,this method is able to efficiently improve the subtraction effect,preferably suppress multiple and high-frequency aliasing and better estimate primaries.