基于L_1范数的多次波自适应减方法及应用分析

Adaptive multiple subtraction using L_1-norm and the application analysis

多次波问题在地震勘探中普遍存在。自由表面相关多次波压制(SRME)方法是目前多次波压制方法的主流,使用该方法的重要步骤之一是将由反馈迭代法预测得到的地震多次波经匹配后从原始数据中减去。基于L2范数的多次波自适应减方法有其适用范围,仅在某些情况下才有好的处理结果。这里基于迭代重加权最小二乘法(IRLS算法)的混合L1/L2范数来近似L1范数解,同时结合模型数据和实际数据进行多次波压制处理,并与基于L2范数的自适应减方法进行对比分析。结果显示,本方法不仅有效压制了多次波,而且还相对更好地保持了有效波的能量,这表明本方法可以在不同情况下实现更为普遍的多次波压制。

The multiple problem is widespread in seismic exploration.Surface-related multiple elimination(SRME)is one of the most widely used multiple elimination nowadays.Matching the multiple model which predicted by feedback iteration method is a very important step of this method and then adaptively subtracting this model from the original data.Adaptive reduction method based on L2-norm has its applicable scope,in some cases just have good treatment results.We use the hybrid of L1 / L2 norm which based on the iteratively reweighted least squares(IRLS)method for the adaptive subtraction step.This choice is to realize the adaptive multiple subtraction using L1-norm.In the meantime,we illustrate our method with synthetic and field dataset.We show that the method leads to much improved attenuation of the multiples compare against the method which using L2-norm.In particular,the L1-norm method can not only attenuate the multiples,but also preserve the primaries simultaneously.We also show that this method could give full play to the advantages of the two methods mentioned above and realize the more general cases multiple wave suppression.