表面多次波最小二乘逆时偏移成像

Least-squares reverse-time migration of surface-related multiples

使用相同的炮记录,多次波偏移能提供比反射波偏移更广的地下照明和更多的地下覆盖但是同时产生很多的串声噪声.相比传统逆时偏移,最小二乘逆时偏移反演的反射波成像结果具有更高的分辨率和更均衡的振幅.我们主要利用最小二乘逆时偏移压制多次波偏移产生的串声噪声.多次波最小二乘逆时偏移通常需要一定的迭代次数以较好地消除串声噪声.若提前将一阶多次波从所有阶数的多次波中过滤出来,使用相同的迭代次数,一阶多次波的最小二乘逆时偏移能够得到具有更高信噪比的成像剖面,而且能够提供与多次波最小二乘逆时偏移相似的有效地下结构成像.

Surface-related multiples are traditionally treated as noise and are attenuated using surface-related multiples elimination（SRME）and/or radon-based multiple-elimination methods.Multiples penetrate into the subsurface several times and contain abundant reflection information of small angles.Compared with migrating of primaries,migrating of multiples extends all the receivers as second sources and sometimes provides additional subsurface illumination.For reverse-time migration（RTM）of all-order multiples,however,the main challenge is that undesired crosscorrelations between forward and backward propagated seismic waves generate so many crosstalk artifacts.The crosstalks may distribute in the whole image profile,which can destruct the true image of reflectors and mislead the interpreting result of a migrated image.Compared with conventional RTM,least-squares reverse-time migration（LSRTM）can invert recorded primaries as an image with more balanced amplitude and higher resolution.Moreover,we develop the conventional LSRTM to invert multiples as an image while iteratively suppressing crosstalk artifacts.However,LSRTM of multiples can′t totally attenuate the artifacts in the image of multiples,and usually many iterations are required to invert a well-accepted image.Alternatively,if first-order multiples can be separated from all-order multiples in advance,LSRTM of first-order multiples can be developed to reduce the iteration number.With the same iterations used,compared with LSRTM of multiples,LSRTM of first-order multiples can provide a much cleaner image section and a similar true image of reflectors.The motivation to develop LSRTM of first-order multiples can be further summarized as：（1）conventional migration of first-order multiples can avoid the most undesired crosscorrelations between forward and backward propagated wavefields and can maintain some advantages of imaging multiples at the same time;although the subsurface information contributed by higher-order multiples is neglected,RTM of first-order multiples have already avoided most artifacts.（2）There are still some crosstalk artifacts in the RTM image of first-order multiples;then,compared with RTM of first-order multiples,LSRTM of first-order multiples can further enhance the image in detail by suppressing the crosstalk artifacts,balancing the amplitude,and improving the resolution.In order to invert primaries as an image,LSRTM iteratively solves a misfit function that is the L2 norm of the amplitude residual between the modeled and observed primaries.Born modeling is a linear two-step procedure and synthesizes primaries perturbed by an image,which bases the LSRTM.Conventional RTM is the adjoint of Born modeling,whereas the analytical solution of the misfit function is the generalized-inverse of the Born modeling.The analytical solution is hard to be obtained because the Hessian matrix is so large,so a nonlinear optimal scheme,e.g.,the steepest-descent method,can be used to iteratively solve the misfit function.Taking the released Sigsbee2 bdata as an example,we can intuitively conclude that LSRTM provides an image with higher resolution and more balanced amplitude and suppresses the migration artifacts compared with conventional RTM.Different with the misfit function for the conventional LSRTM,the misfit function for the LSRTM of multiples is the L2 norm of the amplitude residual between the modeled multiples and estimated multiples during the regular seismic data processing.The accurate calculation for the modeling of multiples is crucial for the success of this method,where a modified Born modeling procedure and an accurate background velocity are utilized.Instead of a point source,the recorded data including primaries and multiples are forward propagated and stacked as the downgoing wavefield.Each discrete point of the image is seen as a scatter.The two-order time derivative of downgoing wavefield is scattered by the RTM image of multiples,and upgoing wavefield is the stack of scattered waves.Surfacerelated multiples are modeled by recording the upgoing wavefield at receivers.Similar to the conventional LSRTM,LSRTM of multiples also can iteratively seek the reflectivity model using a nonlinear optimal method.Moreover,to invert first-order multiples as an image,the misfit function based on the L2 norm of the amplitude residual between the observed and Born modeled first-order multiples should be built.Compared with the Born modeling of all-order multiples,instead of total recorded data,only primaries are forward propagated for the Born modeling of first-order multiples.The observed first-order multiples are estimated by a modified SRME,which includes two steps：（1）predicting higher-order multiples by the convolution of primaries and multiples;（2）adaptively subtracting higher-order multiples from all multiples.RTM of all-order multiples,LSRTM of all-order multiples,RTM of first-order multiples and LSRTM of first-order multiples have been tested on a three-layer and the Marmousi2 model.Only 16 shot gathers are used for imaging on the three-layer model.RTM image of multiples provide wider illumination and higher fold for subsurface,whereas there are a lot of artifacts in the image of multiples.After 10 iterations,LSRTM attenuate most of the artifacts in the image of multiples,except the artifacts at bottom.Moreover,LSRTM of first-order multiples provide amore cleaner section than LSRTM of all-order multiples.There are artifacts in the modeled data using the RTM image of multiples,whereas the modeled data using LSRTM image of multiples have a good match with the estimated multiples using SRME and avoid most artifacts.On the Marmousi2 model,there are many artifacts in the RTM image of multiples,which are mostly attenuated by LSRTM after 5iterations.However,after 5iterations,there are still residual artifacts in the LSRTM image of multiples,which disappear in LSRTM image of first-order multiples.On above two experiments,LSRTM of multiples and LSRTM of first-order multiples both converge very fast and robust.Compared with RTM,LSRTM provides image with more balanced amplitude and better resolution and suppresses the migration artifacts.RTM of multiples can provide a wider illumination and higher fold for subsurface.However,there are many crosstalk artifacts in the RTM image of all-order multiples.LSRTM can attenuate most of the crosstalk artifacts in the image of multiples but costs huge computation of many iterations.A modified SRME is proposed to filter first-order multiples.With the same iterations used,LSRTM of first-order multiples provide a much cleaner section,and provider a similar true image of reflectors compared with LSRTM of all-order multiples.Prior to LSRTM of first-order multiples,first-order multiples are needed to be estimated by a modified SRME.