MODEL ANALYSIS: THEORETICAL GLOBAL SEISMOLOGY
Construction and analysis of equations
- Calculus of variations and elastic-gravitational deformations
- Linearized variational model of elastic-gravitational deformations
- Analysis of the system of elastic-gravitational equations
- Dynamic ruptures generating seismic waves
Spectrum
- Characterization of the spectrum and seismic normal modes
Analysis of solutions
- WKB eigenfunctions and EBK quantization in SNREI models, not yet available
- Microlocal analysis of body waves
- Semiclassical analysis of surface waves
Viscoelasticity and dashpot-spring models
- ‘Resolvent estimates for viscoelastic systems of extended Maxwell type and their applications’, SIAM J. Math. Anal. (2024) in print, with M. Kimura, C.-L. Lin and G. Nakamura
- ‘Anisotropic extended Burgers model, its relaxation tensor and properties of the associated Boltzmann viscoelastic system’ (2024), with M. Kimura, C.-L. Lin, G. Nakamura and K. Tanuma View
Scattering and interfaces
- ‘Diffraction from conormal singularities’, Annales Scientifiques de l’ENS 48 (2015) 351-408, doi:10.24033/asens.2247, with G. Uhlmann and A. Vasy
- ‘Nonlinear responses from the interaction of two progressing waves at an interface’, Annales de l’Institut Henri Poincaré/ Analyse non linéaire 36 (2019) 347-363, doi:10.1016/j.anihpc.2018.04.005, with G. Uhlmann and Y. Wang
- ‘Robin surface waves conversion to body waves at an edge’, with G. Uhlmann and A. Vasy – not available yet
Fractures, flow and friction
- ‘Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium’ (2023), with K. Kumar View
- ‘Nonlocal friction coupled to the elastic wave equation‘, with K. Kumar – not available yet
Numerical Schemes in Seismology
- ‘Generalized-screen approximation and algorithm for the scattering of elastic waves’, Q. J. Mech. Appl. Math. 56 (2003) 1-33, doi: 10.1093/qjmam/56.1.1, with J.H. Le Rousseau
- ‘Multi-scale discrete approximation of Fourier Integral Operators’, Multiscale Modeling and Simulation 10(1) (2012) 111-145, doi: 10.1137/100808174, with F. Andersson and H. Wendt
- ‘Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations with limited smoothness’, Applied and Computational Harmonic Analysis 33 (2012) 330-353, doi: 10.1016/j.acha.2012.01.001, with S.F. Holman, H. Smith and G. Uhlmann
- ‘A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves’, Geoph. J. Int. 205 (2016) 1267-1289, doi: 10.1093/gji/ggw070, with R. Ye, C.L. Petrovitch, L.J. Pyrak-Nolte and L.C. Wilcox
- ‘A high order discontinuous Galerkin method with penalty fluxes for the symmetric form of the anisotropic viscoelastic wave equation’, Computers and Mathematics with Applications 99 (2021) 113-132, doi:10.1016/j.camwa.2021.08.003, with K. Shukla and J. Chan
- `A discontinuous Galerkin method for quasi-static viscoelastic relaxation’, with K. Shukla, not available yet
- ‘A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: Penalty fluxes and micro-heterogeneities’, J. Comp. Phys. 403 (2020) 109061, doi:10.1016/j.jcp.2019.109061, with K. Shukla, J. Chan and P. Jaiswal
- ‘Mixed approach for coupled flow and mechanics in a fractured medium’, ArXiv (2024), with O. Duran, K. Kumar and S. Stefansdotti
- ‘A multi-rate iterative coupling scheme for simulating dynamic ruptures and seismic waves generation in the prestressed earth’, J. Comp. Phys. 405 (2020) 109098, doi:10.1016/j.jcp.2019.109098, with R. Ye, K. Kumar and M. Campillo
- ‘Non-perturbative approach to computing seismic normal modes in rotating planets’, J. Sci. Comput. 91 (2022) 67, doi:10.1016/j.camwa.2021.08.003, with J. Shi, R. Li, Y. Xi and Y. Saad
- ‘Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3D anisotropic media’, Geoph. J. Int. 191 (2012) 346-366, doi: 10.1111/j.1365-246X.2012.05634.x, with S. Wang, J. Xia and X.S. Li
