Seismic inversion is essential for geophysical exploration and geological assessment, but it is inherently subject to significant uncertainty. This uncertainty stems primarily from the limited information provided by observed seismic data, which is largely a result of constraints in data collection geometry. As a result, multiple plausible velocity models can often explain the same set of seismic observations. In deep learning-based seismic inversion, uncertainty arises from various sources, including data noise, neural network design and training, and inherent data limitations. This study introduces a novel approach to uncertainty quantification in seismic inversion by integrating ensemble methods with importance sampling. By leveraging ensemble approach in combination with importance sampling, we enhance the accuracy of uncertainty analysis while maintaining computational efficiency. The method involves initializing each model in the ensemble with different weights, introducing diversity in predictions and thereby improving the robustness and reliability of the inversion outcomes. Additionally, the use of importance sampling weights the contribution of each ensemble sample, allowing us to use a limited number of ensemble samples to obtain more accurate estimates of the posterior distribution. Our approach enables more precise quantification of uncertainty in velocity models derived from seismic data. By utilizing a limited number of ensemble samples, this method achieves an accurate and reliable assessment of uncertainty, ultimately providing greater confidence in seismic inversion results.

翻译：地震反演对于地球物理勘探和地质评估至关重要，但其本质上存在显著的不确定性。这种不确定性主要源于观测地震数据所提供信息的有限性，而这很大程度上是数据采集几何约束所导致的结果。因此，多个合理的速度模型往往能够解释同一组地震观测数据。在基于深度学习的地震反演中，不确定性来源于多个方面，包括数据噪声、神经网络设计与训练，以及数据固有的局限性。本研究提出了一种通过集成方法与重要性采样相结合来量化地震反演不确定性的新方法。通过结合集成方法与重要性采样，我们在保持计算效率的同时，提升了不确定性分析的准确性。该方法通过为集成中的每个模型初始化不同的权重，引入预测的多样性，从而提高了反演结果的鲁棒性和可靠性。此外，重要性采样的使用对每个集成样本的贡献进行加权，使我们能够利用有限数量的集成样本来获得更准确的后验分布估计。我们的方法能够更精确地量化从地震数据推导出的速度模型中的不确定性。通过使用有限数量的集成样本，该方法实现了对不确定性的准确可靠评估，最终为地震反演结果提供了更高的可信度。