论文标题
基于Eikonal方程的地下断层扫描的贝叶斯物理信息网络
Bayesian Physics-Informed Neural Networks for the Subsurface Tomography based on the Eikonal Equation
论文作者
论文摘要
获得足够数量的地震数据进行培训的高昂成本限制了在地震层析成像中的机器学习的使用。此外，在传统的地震层析成像文献中，由于嘈杂的数据和数据稀缺而引起的反转不确定性较少。为了减轻不确定性效应并量化其在预测中的影响，采用了所谓的贝叶斯物理信息信息网络（BPINN）基于Eikonal方程式来推断速度场并重建旅行时间领域。在BPINN中，研究了两种推理算法，包括Stein变异梯度下降（SVGD）和高斯变异推理（VI），以进行推理任务。几个基准问题的数值结果表明，可以准确估算速度场，并且可以通过BPINNS合理的不确定性估计来很好地估算旅行时间。这表明BPINN提供的推断速度模型可以作为地震反转和迁移的有效初始模型。
The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in conventional seismic tomography literature. To mitigate the uncertainty effects and quantify their impacts in the prediction, the so-called Bayesian Physics-Informed Neural Networks (BPINNs) based on the eikonal equation are adopted to infer the velocity field and reconstruct the travel-time field. In BPINNs, two inference algorithms including Stein Variational Gradient Descent (SVGD) and Gaussian variational inference (VI) are investigated for the inference task. The numerical results of several benchmark problems demonstrate that the velocity field can be estimated accurately and the travel-time can be well approximated with reasonable uncertainty estimates by BPINNs. This suggests that the inferred velocity model provided by BPINNs may serve as a valid initial model for seismic inversion and migration.
