压缩感知框架下特征地震波提取与反演成像方法研究

The subsurface velocity estimation is the target of seismic data inversion imaging. The typical method for inversion imaging is full waveform inversion (FWI), which usually suffers no convergence because of the non-convexity objective function. This application focus on characteristic expression of seismic data primarily, where the band-limited local time-space domain directional wave-field is defined as the characteristic wave. Then the characteristic wave imaging can establish the relation between the characteristic wave-field and imaging space. Subsurface parameters (velocities) estimation is the target of seismic data inversion imaging. One popular and typical inversion imaging method, full waveform inversion (FWI), usually suffers no convergence because its objective function is non-convex. This application is mainly focused on characteristic expression of seismic wave (not full wave-field) to improve the convexity of objective function. The characteristic wave decomposition (CWD) method can be developed via compressed sensing primarily based on the local linear property of the seismic data, where the band-limited local time-space domain directional wave-field is defined as the characteristic wave. Then the corresponding inversion imaging method will be developed based on this characteristic wave. This inversion imaging includes the characteristic wave imaging (CWI) in attenuation media using local-beam propagating operator, which establishes the relation between the characteristic wave-field and imaging space. The kernel function between characteristic imaging perturbation and macro velocity perturbation can be deduced, and the background velocity (low wavenumber part) will be updated iteratively in characteristic imaging domain. Finally, the ultimate high wavenumber imaging results can be obtained by using the updated velocity. At this point, a complete characteristic wave inversion imaging work flow can be constructed. This inversion imaging method is a development of imaging theory and also a potential method for felid seismic data processing.

以全波形反演为代表的面向参数（速度）估计的反演成像方法是勘探地震学的研究热点与难点之一，其主要挑战来自该反问题目标泛函非凸函数，从而导致反演不收敛和不稳定等问题。本项申请拟从特征地震波场（非全波场）入手构建凸性更好的反演成像方法技术体系。首先基于叠前地震数据具有的局部线性特征，定义局部时空域方向带限波场为特征波场，在压缩感知框架下，发展有效的特征地震波提取方法。基于该特征地震波提出相应的反演成像方法。包括发展与特征波传播相适应的考虑吸收衰减补偿的局部平面波传播算子进行特征波成像；建立特征像扰动与背景速度扰动之间的核函数，并分析射线束传播算子下该敏感度核函数的性态；研究优势照明的特征射线束层析速度反演，更新背景速度（低波数部分）；最后利用更新的速度得到高波数的像，形成一套特征波反演成像方法技术，并在实际应用中取得成效。

随着勘探技术的反正，地震数据处理中的核心步骤之一，偏移成像，已经逐渐从传统构造偏移发展到反演成像。本次研究从叠前地震数据出发，在压缩感知框架下发展特地震数据特征波分解方法，并发展了局部平面波传播算子建立特征波场与特征像的桥梁，从而进行特征波成像。基于角度域特征波成像发展了特征波层析速度反演，最后利用更新的速度进行最后的成像，形成特征波反演成像流程，并应有于模型和实际资料处理。具体完成了以下五方面研究内容：①压缩感知框架下特征波分解方法研究，②吸收衰减介质的特征波成像，③带限局部平面波传播及成像，④特征像域层析速度反演，⑤特征波成像实际资料处理。在项目支持下，发表了12篇期刊论文和4篇会议论文，并完成了相关研究生的培养。另外，基于研究过程开发的方法模块，尝试靶区实际地震资料处理，证明本项研究的方法在应用上有一定的潜力。

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