ABSTRACT The conventional impedance inversion method ignores the attenuation effect, transmission loss and inter‐layer multiple waves; the smooth‐like regularization approach makes the corresponding impedance solution excessively smooth. Both fundamentally limit the resolution of impedance result and lead to the inadequate ability of boundary characterization. Therefore, a post‐stack impedance blocky inversion method based on the analytic solution of viscous acoustic equation is proposed. Based on the derived recursive formula of reflections, the 1D viscous acoustic wave equation is solved analytically to obtain zero‐offset full‐wave field response. Applying chain rule, the analytical expression of the Frechet derivative is derived for gradient‐descent non‐linear inversion. Combined with smooth constraints, the blocky constraints can be introduced into the Bayesian inference framework to obtain stable and well‐defined inversion results. According to the above theory, we firstly use model data to analyse the influence of incompleteness of forward method on seismic response, and further verify the effectiveness of the proposed method. Then the Q‐value sensitivity analysis of seismic trace is carried out to reduce the difficulty of Q‐value estimation. Finally, the real data from Lower Congo Basin in West Africa indicate that the proposed approach provide the high‐resolution and well‐defined impedance result. As a supplement and development of linear impedance inversion method, the non‐linear viscous inversion could recover more realistic and reliable impedance profiles.

中文翻译：

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基于粘性声波方程解析解的叠后阻抗块状反演

摘要 传统的阻抗反演方法忽略了衰减效应、传输损耗和层间多波；类似平滑的正则化方法使相应的阻抗解过于平滑。两者都从根本上限制了阻抗结果的分辨率，导致边界表征能力不足。为此，提出了一种基于粘性声学方程解析解的叠后阻抗块状反演方法。基于导出的反射递归公式，解析一维粘性声波方程以获得零偏移全波场响应。应用链式法则，推导出梯度下降非线性反演的 Frechet 导数的解析表达式。结合平滑约束，可以将块状约束引入贝叶斯推理框架以获得稳定且定义明确的反演结果。根据上述理论，我们首先利用模型数据分析了正演方法的不完备性对地震响应的影响，进一步验证了所提方法的有效性。然后进行地震道的Q值灵敏度分析，以降低Q值估计的难度。最后，来自西非下刚果盆地的真实数据表明，所提出的方法提供了高分辨率和明确定义的阻抗结果。作为线性阻抗反演方法的补充和发展，非线性粘性反演可以恢复更真实可靠的阻抗曲线。