<p>Seismic inversion serves as a powerful methodology for estimating subsurface reservoir parameters. In recent years, data-driven approaches have attracted considerable research interest, owing to their robust nonlinear approximation capabilities. Nevertheless, the practical implementation of these methods is frequently limited by the availability of training datasets. Semi-supervised or unsupervised data-driven approaches that incorporate physical laws can, to some extent, alleviate the dependency on training data. Still, factors such as acquisition noise and topographic variations result in insufficient vertical and lateral continuity in inversion results, increasing the difficulty of subsequent interpretation. While quadratic regularization can significantly enhance the continuity of the results, it tends to blur stratigraphic boundaries and may even cause the loss of detailed information. To address these limitations, we integrate a local regularization method termed relativity-of-Gaussian (RoG), building upon semi-supervised seismic inversion. The core of RoG is its capacity to discriminate between noise and stratigraphic boundaries while simultaneously detecting potential edge, which significantly improves the continuity of inversion results while maintaining the fidelity of stratigraphic features across all scales. In this paper, a semi-supervised seismic inversion framework is constructed using a spatiotemporal neural network as an example. The proposed method is evaluated using both synthetic and field datasets and compared with conventional methods, demonstrating superior performance in terms of lateral continuity and structural preservation.</p>