[论文解读] Separating Simultaneous Seismic Sources using Robust Inversion of Radon and Migration Operators

Amr Ahmed Mahmoud Ibrahim|arXiv (Cornell University)|Jan 1, 2016

Seismic Imaging and Inversion Techniques参考文献 137被引用 11

一句话总结

本文提出一种基于ℓ₁-范数Radon变换与Stolt偏移算子的鲁棒反演框架，用于分离共炮记录地震数据中的叠加源，实现对重叠源数据的高效处理。通过利用渐近线与顶点偏移双曲Radon变换（AASHRT），该方法能有效抑制强干扰噪声，同时保留弱一次波信号与衍射波，显著提升地震成像中的计算效率与信号聚焦能力。

ABSTRACT

The advent of high density 3D wide azimuth survey configurations has greatly increased the cost of seismic acquisition. Simultaneous source acquisition presents an opportunity to decrease costs by reducing the survey time. Source time delays are typically long enough for seismic reflection energy to decay to negligible levels before firing another source. Simultaneous source acquisition abandons this minimum time restriction and allows interference between seismic sources to compress the survey time. Seismic data processing methods must address the interference introduced by simultaneous overlapping sources. Simultaneous source data are characterized by high amplitude interference artefacts that may be stronger than the primary signal. These large amplitudes are due to the time delay between sources and the rapid decay of seismic energy with arrival time. Therefore, source interference will appear as outliers in denoising algorithms that make use of a Radon transform. This will reduce the accuracy of Radon transform de-noising especially for weak signals. Formulating the Radon transform as an inverse problem with an L1 misfit makes it robust to outliers caused by source interference. This provides the ability to attenuate strong source interference while preserving weak underlying signal. In order to improve coherent signal focusing, an apex shifted hyperbolic Radon transform (ASHRT) is used to remove source interferences. ASHRT transform basis functions are tailored to match the travel time hyperbolas of reflections in common receiver gathers. However, the ASHRT transform has a high computational cost due to the extension of the model dimensions by scanning for apex locations. By reformulating the ASHRT operator using a Stolt migration/demigration kernel that exploits the Fast Fourier Transform (FFT), the computational efficiency of the operator is drastically improved.Moreover, the computational efficiency of the Stolt-based ASHRT operator allows us to extend the model dimension to fit seismic diffractions with the same accuracy as seismic reflections. The Asymptote and Apex Shifted Hyperbolic Radon Transform (AASHRT) can better focus diffracted energy by extending the basis functions to account for the asymptote time shift associated with diffractions. This transform is used to interpolate synthetic data that contain significant amount of seismic diffractions. The results of the interpolation tests show that the AASHRT transform is a powerful tool for interpolating seismic diffractions.

研究动机与目标

• 解决叠加源地震数据中强干扰噪声导致传统去噪与偏移方法性能下降的问题。
• 提出一种基于ℓ₁误差的鲁棒Radon变换公式，以减轻重叠源能量引起的异常值影响。
• 通过Stolt偏移/动校正核，提升顶点偏移双曲Radon变换（ASHRT）的计算效率。
• 将Radon变换扩展至使用渐近线与顶点偏移基函数，以更准确地建模地震衍射波。
• 在复杂观测几何条件下，实现对弱反射波与衍射波的高保真插值与分离。

提出的方法

• 将Radon变换建模为带有ℓ₁-范数误差的逆问题，以增强对源干扰引起的振幅异常值的鲁棒性。
• 引入顶点偏移双曲Radon变换（ASHRT），通过可变顶点位置建模反射波旅行时，提升信号聚焦能力。
• 利用Stolt偏移/动校正核对ASHRT进行重构，借助FFT计算，大幅降低计算成本。
• 将ASHRT框架扩展至包含渐近线时间偏移，形成渐近线与顶点偏移双曲Radon变换（AASHRT），以实现对衍射波的精确建模。
• 将AASHRT应用于具有强衍射成分的合成地震数据插值，验证了其在信号恢复方面的优越性能。

实验结果

研究问题

• RQ1 ℓ₁-范数正则化在叠加源强干扰背景下，如何提升Radon变换的鲁棒性？
• RQ2 基于Stolt的ASHRT重构方法在保持精度的同时，能在多大程度上降低计算成本？
• RQ3 AASHRT变换是否能有效建模并重建标准Radon变换难以处理的地震衍射波？
• RQ4 与传统去噪与偏移方法相比，所提方法在强干扰背景下对弱一次反射波的保留能力如何？
• RQ5 在模型维度中引入顶点与渐近线偏移后，对地震信号插值精度有何影响？

主要发现

• ℓ₁-范数Radon变换能有效压制强干扰噪声，同时保留弱一次波信号，在存在异常值时优于标准ℓ₂-基去噪方法。
• 基于Stolt的ASHRT算子通过利用FFT显著降低计算成本，使扩展模型维度的高效处理成为可能。
• AASHRT变换在衍射丰富合成数据中成功实现对地震衍射波的高精度建模与重建，性能优于标准ASHRT。
• 使用AASHRT的插值结果展现出更高的信号保真度与更少的伪影，尤其在波场行为复杂的区域表现更优。
• 该方法可在三维宽方位角地震勘探中实现高质量的叠加源分离，支持更经济高效的地震采集，缩短调查时间。