Beijing Institute of Mathematical Sciences and Applications

This class aims to present a mathematical analysis of the stability of several classical seismic wave propagation models, including Biot's theory, the double-porosity model, the Biot-Rayleigh model, and the BISQ (Biot/squirt-flow) model. While these models are widely used in rock physics and reservoir geophysics, our results show that under reasonable physical conditions, they may all admit exponentially growing solutions, indicating linear instability. In particular, the BISQ model is shown to be unstable at low frequencies, providing the first theoretical explanation for a well-known empirical observation. We further construct first- and second-order finite difference schemes for the BISQ model and prove the stability of the first-order scheme using the energy method. Numerical experiments confirm that model instability leads to divergence in simulations, while the proposed schemes are stable under proper conditions and suitable for long-time wave propagation modeling.

・ 4.27(Sunday), 13:30-16:00, A3-1-301, 787 662 9899
・ 4.28(Monday), 13:30-16:00, A3-1-301, 518 868 7656
・ 4.30(Wednesday), 13:30-16:00, Online, 928 682 9093
・ 5.7(Wednesday), 13:30-16:00, Online, 928 682 9093
・ 5.8(Thursday), 13:30-16:00, A3-1-301, 638 227 8222
・ 5.9(Friday), 13:30-16:00, A3-1-305, 928 682 9093