狭义的地震反演专指地震波阻抗反演，通过反演可以将频带有限的地震数据中还原为宽频带的波阻抗数据。反演问题的数学表达式是一个病态方程，同样的地震数据对应多个可能的波阻抗反演结果。本文分析并量化了基于深度学习的地震反演方法的不确定性，发现并验证了误差与不确定性之间存在一定的正相关关系，不确定性可以用来评价反演结果的好坏，通过反传不确定性还可以进一步提升了反演精度和空间连续性，具有很大的实际应用价值。论文的主要工作如下： （1）首次提出了闭环地震反演不确定性分析网络（Closed-loop Uncertainty Analysis Network，CUAN）。所提出的网络结合了闭环卷积神经网络（Closed-loop CNN）和深度证据回归（Deep Evidential Regression，DER）方法。CUAN既保留了Closed-loop CNN可以使用无标签数据进行训练的优点，又可以同时估计反演结果的不确定性，还进一步提升了反演效果。CUAN可以估计出真实波阻抗的边缘分布，然后计算出预测波阻抗和反演结果的不确定性。CUAN的主干网络为U-Net和门控循环单元（Gated Recurrent Unit，GRU）的组合，GRU主要提取时序特征，可以更好的预测低频信息，U-Net重在提取空间特征，能更好的预测高频信息。GRU和U-Net相互结合，能够从地震数据中提取更多信息，提升反演效果。 （2）首次提出了不确定性反传地震反演网络（Uncertainty Backpropagation Network，UB-Net）。发现并证明了反演不确定性与误差存在一定的正相关关系，这种关系在误差较大的时候更强，不确定性能更好捕捉反演误差较大的地方。UB-Net根据估计的反演结果的不确定性对无标签数据进行加权，使网络更注重学习不确定性较大区域的映射关系，从而提升反演结果的精度。反演精度的提升进一步说明本文所提反演不确定性估计方法是可靠的，正确反映了误差和不确定性的关系。 （3）在三维地震数据上验证了一维UB-Net的有效性，参考二维反演网络，分析并反传不确定性，进一步提出了二维UB-Net。输入为二维地震数据，用一维UB-Net产生的预测结果作为伪标签预训练网络，输出为绝对波阻抗，再用测井标签数据微调网络，最后反传不确定性得到最终预测结果。相较一维UB-Net，二维UB-Net能从二维地震数据中提取更多空间信息，降低了反演问题的多解性，使得反演不确定性降低，反演结果也更加准确。

Seismic inversion in a narrow sense refers to seismic impedance inversion, through which broadband impedance data can be recovered from limited bandwidth seismic data. The mathematical expression of the inversion problem is an ill-conditioned equation, and the same seismic data corresponds to multiple possible impedance inversion results. This paper analyzes and quantifies the uncertainty of the seismic inversion method based on deep learning, and finds and verifies that there is a certain positive correlation between the error and uncertainty. The uncertainty can be used to evaluate the quality of the inversion results. The inversion accuracy and spatial continuity can be further improved by backpropagating uncertainty, which has great practical application value. The main work of the paper is as follows: (1) The Closed-loop Uncertainty Analysis Network (CUAN) is proposed for the first time. The proposed network combines Closed-loop CNN and Deep Evidential Regression methods. CUAN not only retains the advantage that Closed-loop CNN can use unlabeled data for training, but also estimates the uncertainty of predicted impedance at the same time, and further improves the inversion effect. CUAN can estimate the marginal distribution of impedance, and then calculate the uncertainty of predicted impedance. CUAN can estimate the marginal distribution of true impedance, and then calculate the uncertainty of predicted impedance. The backbone network of CUAN is a combination of U-Net and Gated Recurrent Unit (GRU). GRU mainly extracts time series features, which can better predict low-frequency information. U-Net focuses on extracting spatial features, which can better predict high frequency information. The combination of GRU and U-Net can extract more information from seismic data and improve the inversion effect. (2) The Uncertainty Backpropagation Network (UB-Net) is proposed for the first time. It is found and proved that there is a certain positive correlation between the inversion uncertainty and the error. This relationship is stronger when the error is larger, and the uncertainty is better to capture the place where the inversion error is larger. UB-Net weights the unlabeled data according to the uncertainty of the estimated inversion results, so that the network pays more attention to learning the mapping in the region with large uncertainty, thereby improving the accuracy of the inversion results. The improvement of inversion accuracy further shows that the inversion uncertainty estimation method proposed in this paper is reliable, and correctly reflects the relationship between error and uncertainty. (3) The effectiveness of one-dimensional UB net is verified on three-dimensional seismic data. Referring to two-dimensional inversion network, the inversion uncertainty is analyzed and backpropagated, and two-dimensional UB net is further proposed. The input is two-dimensional seismic data. The prediction results generated by one-dimensional UB net are used as pseudo label to pretrain network, and the output is absolute wave impedance. Then the network is fine-tuned with logging data. Finally, the uncertainty is backpropagated to obtain the final prediction result. Compared with one-dimensional UB net, two-dimensional UB net can extract more spatial information from two-dimensional seismic data, reduce the multiplicity of solutions of inversion problems, reduce the uncertainty of inversion and make the inversion results more accurate.