标题： 基于自适应Tikhonov-TV正则化的稳健声波和弹性全波形反演 显示英文标题

标题： Robust acoustic and elastic full waveform inversion by adaptive Tikhonov-TV regularization

摘要： 全波形反演（FWI）是一种强大的基于波的成像技术，但由于其固有的不适定性和非凸性，会导致局部极小值和收敛性差。 正则化方法通过引入先验信息并强制执行平滑变化或分段常数行为等结构约束来稳定FWI。 其中，Tikhonov正则化促进平滑性，而总变差（TV）正则化保留尖锐边界。 然而，在FWI背景下，我们指出了这些正则化方法的两个关键缺点。 首先，地下模型参数（纵波速度、横波速度、密度）通常表现出具有明显间断分隔不同层的复杂地质构造，而在每层内部参数则平滑变化。 单独使用Tikhonov或TV正则化都无法有效约束这种分段平滑结构。 其次，更为关键的是，当初始模型远离真实模型时，这些正则化假设可能导致局部最小值。 为了解决这些问题，我们提出了自适应Tikhonov-TV（TT）正则化，该正则化将模型分解为平滑和块状成分，从而实现对分段平滑结构的鲁棒恢复。 在ADMM框架内实现时，TT正则化结合了基于稳健统计分析的自动化平衡策略。 数值实验表明，对于声学和弹性FWI使用基准地质模型时，与单独应用Tikhonov和TV正则化相比，TT正则化显著提高了收敛性和重构精度。 我们展示了对于复杂模型和远程初始模型，Tikhonov和TV正则化往往趋于收敛到局部最小值，而TT正则化通过其两种正则化策略的自适应组合有效地缓解了循环跳跃问题。 显示英文摘要

摘要： Full Waveform Inversion (FWI) is a powerful wave-based imaging technique, but its inherent ill-posedness and non-convexity lead to local minima and poor convergence. Regularization methods stabilize FWI by incorporating prior information and enforcing structural constraints like smooth variations or piecewise-constant behavior. Among them, Tikhonov regularization promotes smoothness, while total variation (TV) regularization preserves sharp boundaries. However, in the context of FWI, we highlight two key shortcomings of these regularization methods. First, subsurface model parameters (P- and S-wave velocities, density) often exhibit complex geological formations with sharp discontinuities separating distinct layers, while parameters within each layer vary smoothly. Neither Tikhonov nor TV regularization alone can effectively constrain such piecewise-smooth structures. Second, and more critically, when the initial model is far from the true model, these regularization assumptions can lead to a local minimum. To address these issues, we propose adaptive Tikhonov-TV (TT) regularization, which decomposes the model into smooth and blocky components, enabling robust recovery of piecewise-smooth structures. Implemented within the ADMM framework, TT regularization incorporates an automated balancing strategy based on robust statistical analysis. Numerical experiments on acoustic and elastic FWI using benchmark geological models demonstrate that TT regularization significantly improves convergence and reconstruction accuracy compared to Tikhonov and TV regularization when applied separately. We show that for complex models and remote initial models, both Tikhonov and TV regularization tend to converge to local minima, whereas TT regularization effectively mitigates cycle skipping through its adaptive combination of the two regularization strategies.