单程波角度域内压制多次波偏移假象

Eliminating migration artifacts in angle domain based on one-way wave equation migration of multiples

多次波偏移中的假象主要来自于不同地震事件之间的互相关,由于这种互相关满足成像条件,很难直接在偏移过程中去除.但是对于准确的速度模型,真实的成像结果在角度域内应该是平直的.根据这个判断准则,可以在角度域内移除多次波偏移中的假象.本文以数据自相关偏移为例,提出了在单程波多次波偏移中移除假象的主要流程:首先在在单程波偏移过程中高效地提取角度域共成像点道集,然后对角度域共成像点道集应用高分辨率的抛物线型Radon变换,用合适的切除函数处理后,反变换回到角度域,最后叠加各个角度成分,得到偏移结果.Marmousi模型的合成数据测试表明,这种方法可以很好地压制多次波偏移过程中产生的假象,有效地提高成像结果的信噪比.

The migration artifacts are mainly introduced by the crosscorrealtion of different seismic events.As they honor the imaging condition,they are difficult to be eliminated directly.However,only the traces of the true events are flat in angle domain common image gathers（ADCIGs）and the artifacts can be identified.To separate signal from noise more explicitly,high resolution parabolic Radon transform is applied.In numerical examples,we show that ADCIGs can be extracted from Fourier finite difference（FFD）migration more effectively than in reverse time migration（RTM）.We followed the workflow proposed by Biondi and Symes（2004）to extract ADCIGs.In oneway wave equation migration,the crosscorrelation imaging condition is applied and the subsurface item is added to upgoing and downgoing wavefields.Then all the shots are stacked to obtain horizontal offset common image gathers（HOCIGs）.Using the formula proposed by Sava and Fomel（2003）,we can transform HOCIGs from offset domain to angle domain and obtainADCIGs.Then the ADCIGs are processed with high resolution parabolic Radon transform.It takes maximum entropy distribution as the constraint condition and uses sparse constrained inversion to improve the resolution.If the migration velocity is correct,the energy of true seismic events is concentrated in the vicinity of zero curvature in the Radon domain,while the energy of artifacts is mapped to nonzero area.Save and Guitton（2005）present their method to suppress multiples in image domain.We modify the method in data to data migration and divide it into five steps：（1）Extract ADCIGs directly from data to data migration;（2）Apply high resolution parabolic Radon transform to ADCIGs;（3）Mute the nonzero components in the Radon domain;（4）Obtain ADCIGs without artifacts using adjoint Radon transform;（5）Stack all different angles to get the final image.In the numerical example,the result of conventional FFD migration using primaries only has no artifacts.It can be improved by muting the low frequency components at large angles.In data to data migration the same muting technique works while the artifacts still exist.After the application of our proposed workflow,most migration artifacts are eliminated and the signal-tonoise ratio of the imaging result is improved effectively.We also show that compared to RTM,FFD is much faster and more efficient to extract ADCIGs.Through the proposed method,the artifacts in the image of data to data migration are mostly eliminated.The final result is comparable to conventional FFD migration.As multiples prediction and wavelet estimation are not needed in data to data migration,it can be significant for real data.The proposed method is mainly aimed at one type of undesired crosscorrelation.How to eliminate the other type of artifacts needs further study.The possible solutions include wide azimuth acquisition technology,least squares migration method and so on.Another point to be addressed is that FFD is suitable to calculate HOCIGs fast while it cannot offer vertical offset common image gathers（VOCIGs）.If we need to combine HOCIGs and VOCIGs to generate stable ADCIGs,the FFD operator should be modified.