  Seismic impedance inversion can be performed with a semi-supervised learning
algorithm, which only needs a few logs as labels and is less likely to get
overfitted. However, classical semi-supervised learning algorithm usually leads
to artifacts on the predicted impedance image. In this artical, we improve the
semi-supervised learning from two aspects. First, by replacing 1-d
convolutional neural network (CNN) layers in deep learning structure with 2-d
CNN layers and 2-d maxpooling layers, the prediction accuracy is improved.
Second, prediction uncertainty can also be estimated by embedding the network
into a Bayesian inference framework. Local reparameterization trick is used
during forward propagation of the network to reduce sampling cost. Tests with
Marmousi2 model and SEAM model validate the feasibility of the proposed
strategy.
