用乘子的交替方向法实现扩展全波形反演中的边界约束和全变差正则化：应用于大对比度介质
Implementing bound constraints and total-variation regularization in extended full waveform inversion with the alternating direction method of multiplier: application to large contrast media
摘要：
全波形反演（FWI）是一种波形匹配过程，它可以提供具有波长尺度分辨率的地下模型。然而，这种高分辨率使得FWI易于循环跳跃，当初始模型不够精确时，这将反演驱动到局部极小值。非线性和不适定性的其他来源是噪声，不均匀的照明，近似波物理和参数串扰。所有这些误差源都需要强大且通用的正则化优化方法来减轻它们对FWI的影响，同时保持其固有的分辨率。为了实现这一目标，我们实现了边界约束和全变差（TV）正则化在所谓的频域波场重建反演（WRI）与乘子的交替方向法（ADMM）。在ADMM框架中，WRI依赖于增强的拉格朗日函数，惩罚函数和拉格朗日函数的组合，通过在早期迭代期间放松波动方程约束来扩展FWI搜索空间。此外，ADMM分解的联合波场重建加上参数估计问题成一系列的两个线性子问题，其解决方案是协调提供的解决方案的全球问题。ADMM的可分解性被进一步利用，通过变量分裂和邻近算子，以直接的方式将约束约束和TV正则化与WRI接口。我们的正则化WRI制定的弹性周期跳跃和噪声，以及其分辨率的能力说明了两个目标的大对比度BP盐模型。从3Hz频率和原始初始模型开始，扩展的搜索空间允许以高保真度重建盐和盐下结构。
英文摘要：
Full waveform inversion (FWI) is a waveform matching procedure, which can provide a subsurface model with a wavelength-scale resolution. However, this high resolution makes FWI prone to cycle skipping, which drives the inversion to a local minimum when the initial model is not accurate enough. Other sources of nonlinearities and ill-posedness are noise, uneven illumination, approximate wave physics and parameter cross-talks. All these sources of error require robust and versatile regularized optimization approaches to mitigate their imprint on FWI while preserving its intrinsic resolution power. To achieve this goal, we implement bound constraints and total variation (TV) regularization in the so-called frequency-domain wavefield-reconstruction inversion (WRI) with the alternating direction method of multipliers (ADMM). In the ADMM framework, WRI relies on an augmented Lagrangian function, a combination of penalty and Lagrangian functions, to extend the FWI search space by relaxing the wave-equation constraint during early iterations. Moreover, ADMM breaks down the joint wavefield reconstruction plus parameter estimation problem into a sequence of two linear subproblems, whose solutions are coordinated to provide the solution of the global problem. The decomposability of ADMM is further exploited to interface in a straightforward way bound constraints and TV regularization with WRI via variable splitting and proximal operators. The resilience of our regularized WRI formulation to cycle skipping and noise as well as its resolution power are illustrated with two targets of the large-contrast BP salt model. Starting from a 3Hz frequency and a crude initial model, the extended search space allows for the reconstruction of the salt and subsalt structures with a high fidelity.
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