论文标题
贝斯林损失的吉布斯后期稳定性用于贝叶斯全波形反演
Stability of Gibbs Posteriors from the Wasserstein Loss for Bayesian Full Waveform Inversion
论文作者
论文摘要
最近，将Wasestein损失函数用于确定性全波反转（FWI）问题时，已被证明是有效的。我们考虑在贝叶斯FWI中应用此损失函数，以便可以在解决方案中捕获不确定性。在实践中通常使用的其他损失函数也被考虑进行比较。在先验和模型的弱假设下，在功能空间上显示了所得Gibbs后期的存在和稳定性。特别是，与数据中的高频噪声相对于高频噪声而言，沃斯坦损失产生的分布非常稳定。然后，我们使用拉普拉斯近似值来估计未知速度场以及与估计值相关的不确定性，从数值上说明了结果分布之间的差异。
Recently, the Wasserstein loss function has been proven to be effective when applied to deterministic full-waveform inversion (FWI) problems. We consider the application of this loss function in Bayesian FWI so that the uncertainty can be captured in the solution. Other loss functions that are commonly used in practice are also considered for comparison. Existence and stability of the resulting Gibbs posteriors are shown on function space under weak assumptions on the prior and model. In particular, the distribution arising from the Wasserstein loss is shown to be quite stable with respect to high-frequency noise in the data. We then illustrate the difference between the resulting distributions numerically, using Laplace approximations to estimate the unknown velocity field and uncertainty associated with the estimates.
