Multidimensional Petrophysical Seismic Inversion Based on Knowledge-Driven Semi-Supervised Deep Learning

Petrophysical seismic inversion is a challenging problem due to its intrinsic nonlinearity and ill-posedness. Deep learning emerges as a promising solution to tackle this intricate problem, with semi-supervised learning proving particularly valuable in scenarios with limited labeled data. However, many existing semi-supervised learning approaches applied to reservoir parameters inversion are unidimensional or focus on single model parameters, potentially hindering the attainment of highly accurate predictions for multiple petrophysical parameters. To this end, we introduce a novel knowledge-driven semi-supervised deep learning approach for multidimensional petrophysical seismic inversion. This framework features a lightweight 2-D UNet, incorporating prior knowledge about the range of model parameters, to parameterize the set of pseudo-inverse operators, enabling effective multitask learning. By leveraging the low-frequency porosity as the sole initial model input, our approach enhances the information-sharing capabilities of the neural network. We also introduce Hermite cubic splines to parameterize source wavelets varying with angles, ensuring smooth and compactly supported waveforms. In addition, we develop a semi-supervised training loss function that integrates deterministic forward operators and sampling operators, allowing simultaneous updating of weights in both forward and pseudo-inverse operators. The proposed method facilitates the simultaneous inversion of wavelets, porosity, water saturation, and clay volume. Synthetic and field data tests are conducted to validate our approach, demonstrating that it significantly enhances inversion accuracy compared to 1-D semi-supervised deep learning methods.