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.
翻译:最近,瓦森斯坦损失功能在应用于确定性全波转换(FWI)问题时被证明是有效的。我们考虑在Bayesian FWI应用这一损失功能,以便在解决方案中捕捉不确定性。还考虑比较实践中通常使用的其他损失功能。Gibbs后遗物的存在和稳定性在先前和模型的假设薄弱的情况下显示在功能空间上。特别是,瓦瑟斯泰因损失造成的分布在数据中高频噪音方面相当稳定。我们然后用Laplace近似值来估计未知速度场和与估计数有关的不确定性,用数字来说明由此产生的分布的差别。