Sparsity- and continuity-promoting seismic image recovery with curvelet frames
Sparsity- and continuity-promoting seismic image recovery with curvelet frames
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DOI：
10.1016/j.acha.2007.06.007
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发表时间：
2008-03
影响因子：
2.5
通讯作者：
F. Herrmann;P. Moghaddam;C. Stolk
中科院分区：
文献类型：
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作者：
F. Herrmann;P. Moghaddam;C. Stolk
提出了一种在稀疏性和连续性约束下的非线性保奇异性地震图像恢复方法。我们观察到，曲波，作为一个有方向的框架扩展，导致稀疏的地震图像和线性化成像问题的正常运营商下表现出不变性。基于这一观察，我们推导出一种方法，从噪声数据的迁移幅度的稳定恢复。该方法在偏移之后的后处理步骤期间校正幅度，使得主要的附加成本是正常算子的一个应用，即，一个建模，然后是迁移。渐近这个正常的运营商对应于一个pseudodifferential运营商，其中一个方便的对角线近似curvelet域推导出，包括其误差的范围和一种方法，用于估计的对角线从一个复合运营商组成的离散实现的散射运营商及其伴随的迁移运营商。该解决方案被制定为一个非线性优化问题，在曲波域的稀疏性以及连续性沿着成像的反射体共同促进。为了增强稀疏性，曲波系数上的N1范数被最小化，而连续性通过最小化图像上的各向异性扩散范数来促进。在SEG/EAGE AA′盐模型的模拟数据集上，用逆时波动方程偏移程序对恢复方案的性能进行了评价。
A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for stable recovery of the migration amplitudes from noisy data. The method corrects the amplitudes during a post-processing step after migration, such that the main additional cost is one application of the normal operator, i.e., a modeling followed by a migration. Asymptotically this normal operator corresponds to a pseudodifferential operator, for which a convenient diagonal approximation in the curvelet domain is derived, including a bound for its error and a method for the estimation of the diagonal from a compound operator consisting of discrete implementations for the scattering operator and its adjoint the migration operator. The solution is formulated as a nonlinear optimization problem where sparsity in the curvelet domain as well as continuity along the imaged reflectors are jointly promoted. To enhance sparsity, the ℓ1-norm on the curvelet coefficients is minimized, while continuity is promoted by minimizing an anisotropic diffusion norm on the image. The performance of the recovery scheme is evaluated with a reverse-time ‘wave-equation’ migration code on synthetic datasets, including the complex SEG/EAGE AA′ salt model.