To obtain high-resolution images of subsurface structures from seismic data, seismic imaging techniques such as Full Waveform Inversion (FWI) serve as crucial tools. However, FWI involves solving a nonlinear and often non-unique inverse problem, presenting challenges such as local minima trapping and inadequate handling of inherent uncertainties. In addressing these challenges, we propose leveraging deep generative models as the prior distribution of geophysical parameters for stochastic Bayesian inversion. This approach integrates the adjoint state gradient for efficient back-propagation from the numerical solution of partial differential equations. Additionally, we introduce explicit and implicit variational Bayesian inference methods. The explicit method computes variational distribution density using a normalizing flow-based neural network, enabling computation of the Bayesian posterior of parameters. Conversely, the implicit method employs an inference network attached to a pretrained generative model to estimate density, incorporating an entropy estimator. Furthermore, we also experimented with the Stein Variational Gradient Descent (SVGD) method as another variational inference technique, using particles. We compare these variational Bayesian inference methods with conventional Markov chain Monte Carlo (McMC) sampling. Each method is able to quantify uncertainties and to generate seismic data-conditioned realizations of subsurface geophysical parameters. This framework provides insights into subsurface structures while accounting for inherent uncertainties.

翻译：为从地震数据中获取高分辨率的地下结构图像，全波形反演等地震成像技术是关键工具。然而，全波形反演涉及求解非线性且往往非唯一的反问题，存在陷入局部极小值及对固有不确定性处理不足等挑战。针对这些挑战，我们提出利用深度生成模型作为地球物理参数的先验分布进行随机贝叶斯反演。该方法结合伴随状态梯度，实现了从偏微分方程数值解的高效反向传播。此外，我们提出了显式和隐式变分贝叶斯推断方法。显式方法通过基于标准化流的神经网络计算变分分布密度，从而实现对参数贝叶斯后验的计算；隐式方法则采用连接预训练生成模型的推断网络进行密度估计，并引入了熵估计器。进一步地，我们还尝试将基于粒子的斯坦因变分梯度下降法作为另一种变分推断技术。我们将这些变分贝叶斯推断方法与传统的马尔可夫链蒙特卡洛采样进行了比较。每种方法均能量化不确定性，并生成以地震数据为条件的地下地球物理参数实现。该框架在考虑固有不确定性的同时，为揭示地下结构提供了有效途径。