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.Schedule
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
Syllabus
Introduction to classical seismic rock physics models (a)
Introduction to classical seismic rock physics models (b)
Mathematical stability analysis of wave equations (a)
Mathematical stability analysis of wave equations (b)
Seismic wave propagation model for complex porous media
Some cutting-edge topics related to artificial intelligence
Reference
Bear J. Dynamic of Fluids in Porous Media. Soil Science, 1972.
Carmichael R S. Practical Handbook of Physical Properties of Rocks and Minerals. Boca Raton,Fla., CRC Press, 1989.
Mavko G, Mukerji T, Dvorkin J. The Rock Physics Handbook. 2nd ed, Cambridge University Press, 2009.
巴晶。岩石物理学进展与评述[M]。北京：清华大学出版社，2013。
刘嘉玮。岩石物理学中波传播理论的稳定性分析[D]。北京：清华大学， 2016。
LecturerJiawei Liu (刘嘉玮, Assistant Professor, Tohoku University)Dr. Jiawei Liu is currently an Assistant Professor at the Advanced Institute for Materials Research (AIMR), Tohoku University, Japan. She received her Ph.D. in Applied Mathematics from Tsinghua University and previously worked as a postdoctoral researcher at the School of Geosciences and Info-physics, Central South University. Her research focuses on seismic wave propagation, stability analysis and numerical simulation of partial differential equations, and the development of scientific computing tools based on MATLAB App Designer. She has authored more than ten papers as the first or corresponding author in journals such as Geophysical Journal International and Geophysical Prospecting, and holds three granted Chinese invention patents. Dr. Liu has led a provincial Natural Science Foundation project and contributed to two General Programs supported by the National Natural Science Foundation of China.
