  Deep learning (DL) techniques have been widely used in prestack
three-parameter inversion to address its ill-posed problems. Among these DL
techniques, Multi-task learning (MTL) methods can simultaneously train multiple
tasks, thereby enhancing model generalization and predictive performance.
However, existing MTL methods typically adopt heuristic or non-heuristic
approaches to jointly update the gradient of each task, leading to gradient
conflicts between different tasks and reducing inversion accuracy. To address
this issue, we propose a semi-supervised temporal convolutional network (STCN)
based on Nash equilibrium (Nash-MTL-STCN). Firstly, temporal convolutional
networks (TCN) with non-causal convolution and convolutional neural networks
(CNNs) are used as multi-task layers to extract the shared features from
partial angle stack seismic data, with CNNs serving as the single-task layer.
Subsequently, the feature mechanism is utilized to extract shared features in
the multi-task layer through hierarchical processing, and the gradient
combination of these shared features is treated as a Nash game for strategy
optimization and joint updates. Ultimately, the overall utility of the
three-parameter is maximized, and gradient conflicts are alleviated. In
addition, to enhance the network's generalization and stability, we have
incorporated geophysical forward modeling and low-frequency models into the
network. Experimental results demonstrate that the proposed method overcomes
the gradient conflict issue of the conventional MTL methods with constant
weights (CW) and achieves higher precision than four widely used non-heuristic
MTL methods. Further field data experiments also validate the method's
effectiveness.
