自适应加权混合L1/L2范数匹配相减多次波压制方法

Adaptive subtraction for multiples suppression using hybrid L1/ L2 norm

基于波动方程的自由表面多次波和层间多次波压制时,自适应匹配相减方法的选取是关键的环节。L2范数自适应匹配相减方法适用于多次波强而有效波弱的情况,L1范数自适应匹配相减方法则适用于多次波弱而有效波强的情况,L2范数自适应匹配相减方法的运算速度明显较L1范数自适应匹配相减方法更快。自适应加权混合L1/L2范数匹配相减方法需要构建联合L1范数和L2范数的目标函数,再根据地震数据中有效波与多次波的能量比自适应地调整目标函数中L1范数和L2范数所占权值。该方法充分利用了L1范数和L2范数压制多次波时对地震数据不同的要求,既不需要L2范数自适应匹配相减方法的有效信号与噪声正交的假设,又克服了L1范数自适应匹配相减方法运算效率较低的缺点,在保证压制效果的同时提高了计算效率。多层水平层状模型及SEG/EAGE Pluto模型的测试结果表明,相较于常规方法,该方法明显提升了多次波的压制效果。

Adaptive subtraction is a key step in the suppression of free surface related multiples and internal multiples based on wave equations.The commonly used L2 norm adaptive matching subtraction method is applicable to the case where the multiple is strong and effective signal is weak.The L1 norm adaptive matching subtraction method is applicable to the case where the multiple is weak and effective signal is strong.The L2 norm method is much faster than the L1 norm method in terms of computational speed.In this paper,a hybrid L1/L2 norm adaptive matching subtraction method is proposed.Firstly,this method constructs a joint L1 norm and L2 norm objective function.Then,the weights of L1 norm and L2 norm in the objective function are adaptively adjusted according to the energy ratio of effective wave to multiples in seismic data.This method does not require the assumption that the effective signal and the noise are orthogonal required in the L2 norm method.Meanwhile,this method overcomes the shortcomings of low efficiency of L1 norm method.Test results using multilayer horizontal model and SEG/EAGE Pluto model show its superiority.Compared with conventional method,the method could improve the multiples suppression with higher calculation efficiency.