T分布起伏地表最小二乘逆时偏移

Least-squares reverse time migration on undulated surface based on T-distribution

在复杂构造、复杂岩性、复杂地表条件等地区进行油气地震勘探面临诸多难题,其中剧烈起伏的地表已成为制约上述地区地震勘探发展的瓶颈之一。最小二乘逆时偏移(Least-Squares Reverse Time Migration,LSRTM)相对于常规偏移具有更高的成像分辨率、振幅保真性及均衡性等优势,但基于矩形网格的LSRTM在面对复杂地表时无法很好地适用山前带等剧烈起伏地形。此外,山前带地震资料中包含较多的噪声,T分布相比Huber范数和混合模,在缺失数据的条件下更稳健,且没有多余参数,因而简单实用,而Huber范数和混合模的结果严重依赖参数选取,需要大量的尝试。为此,将全交错网格引入贴体网格,将T分布推广到起伏地表LSRTM,进一步推导了贴体网格线性Born正演方程,在此基础上提出了基于贴体全交错网格的起伏地表LSRTM算法,较好地克服了起伏地形的影响。模型试算验证了算法的有效性和对复杂模型的适应性。

The hydrocarbon seismic exploration in areas with complex structure,complex lithology,and complex surface conditions has many difficulties,among which the severely undulating surface is one of the bottlenecks.The least-squares reverse time migration(LSRTM)has higher imaging resolution,amplitude fidelity,and balance than conventional migration methods.However,the LSRTM based on rectangular grid cannot deal with complex surface and overcome severe undulating terrains such as piedmont zones.In addition,seismic data in these areas often contain a lot of noise.Compared with Huber norm and mixed norm,the T distribution has a better performance in incomplete data,and it has no redundant parameters.So it is simple and practical.The results of Huber norm and mixed norm methods depend heavily on the parameter selection,which requires a lot of attempts.Therefore,a fully-staggered grid is introduced into the body-fitted grid,and the T distribution is extended to LSRTM with undulating surfaces.The linear Born forward equation of body-fitted is further deduced.On this basis,the LSRTM algorithm for undulating surface based on body-fitted fully staggered grid is proposed,which can better solve influences of undulating surfaces.Model tests verify the effectiveness and complex-model suitability of the proposed algorithm.