ABSTRACT Ill‐posedness is one of the most common and intractable issues that arise when solving geophysical inverse problems. Ill‐posedness could be induced by various factors such as noise, band‐limited intrinsic property of seismic data and inappropriate forward operators. Regularization has been proven to be an effective method widely accepted for mitigating the adverse effects of ill‐posedness. Aiming to improve the stability and fidelity of the pre‐stack seismic inversion process, we implement the inversion in a Bayesian framework, with a logarithmic absolute criterion taken as a likelihood function, and an l1−2‐norm metric as a priori constraint. Here, we exploit the linear approximation as the forward operator, and optimize the regularized misfit function by the alternating direction method of multipliers. Applications of the method to synthetic and real data sets yielded improved inversion results in terms of accuracy and resolution, and demonstrated the robustness of the method to noise.

中文翻译：

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基于ℓ 1-2-范数正则化对数绝对失配函数的叠前地震反演

摘要 不适定性是解决地球物理反问题时出现的最常见和最棘手的问题之一。不适定性可能由各种因素引起，例如噪声、地震数据的带限固有特性和不适当的前向算子。正则化已被证明是一种被广泛接受的有效方法，可减轻不适定性的不利影响。为了提高叠前地震反演过程的稳定性和保真度，我们在贝叶斯框架中实现了反演，以对数绝对准则作为似然函数，以l1-2范数度量作为先验约束。在这里，我们利用线性近似作为前向算子，并通过乘法器的交替方向方法优化正则化的错配函数。