## SCPY672 Geophysical Forward Modeling and Inversion

Instructor: Chaiwoot Boonyasiriwat (chaiwoot@gmail.com) Class Hours: Monday (3:00PM-4:30PM), Thursday (2:30PM-4:00PM) Classroom: Computer Lab Objectives: Learn how to numerically solve PDEs, and estimate medium physical properties related to geophysical problems Grading: Homework 30, Participation 10, Midterm Exam 30, Final Exam 30 Policies- each homework (report and codes) must be submitted electronically to chaiwoot@gmail.com

- each homework is due in one week

- homework submitted after the due date will not be graded

- each homework has 10 points

- copying homework of others will result in a zero point## Tentative Course Schedule

Lecture Date Lecture Notes Notifications 1 Jan 25, 2016 Class orientation, PDEs and integral equations, overview of relevant mathematical methods, introduction to Fortran programming, OpenGL Redbook codes, introduction to symplectic integration HW1: Solving the Lotka-Volterra model using explicit, implicit, and symplectic Euler methods, MATLAB files 2 Jan 28, 2016 Symplec Euler method and the derivation of Stromer-Verlet method (staggered-grid method) 3 Feb 1, 2016 Computing the Earth magnetic field from a magnetic dipole, Finite difference (FD) approximation HW2: Earth magnetic field and charged particle motion 4 Feb 4, 2016 Finite-difference solutions to Laplace, Poisson, and diffusion equations; implicit finite difference methods HW3: Solving the 2D diffusion equation using Crank-Nicolson method 5 Feb 8, 2016 Direct methods and iterative methods for solving linear systems HW4: Solving a linear system using steepest descent and conjugate gradient methods 6 Feb 11, 2016 Simulation of acoustic wave propagation using explicit FD method: regular and staggered grids 7 Feb 15, 2016 von Neumann stability analysis for an explicit scheme 8 Feb 18, 2016 Absorbing boundary conditions (ABC) and layers (ABL): Clayton-Engquist (CE) ABC, sponge ABL, perfectly matched layer (PML), hybrid methods 9 Feb 25, 2016 Frequency-domain waveform modeling, Simulation of elastic and electromagnetic wave propagation - 10 Feb 29, 2016 EM and modeling of dipole antenna 11 Mar 3, 2016 Adaptive mesh refinement, code Berger and Oliger (1984) 12 Mar 7, 2016 Introduction to finite volume method 13 Mar 10, 2016 Finite volume method (continued) - 14 Mar 21, 2016 Finite volume method (continued) 15 Mar 23, 2016 Finite volume method (continued) - 16 Apr 4, 2016 Grid generation Read Persson and Strang (2004) 17 Apr 4, 2016 Grid generation (continued) - 18 Apr 18, 2016 Artificial neural network 19 Apr 18, 2016 Artificial neural network (continued) - 20 Apr 20, 2016 Eikonal solver 21 Apr 20, 2016 Eikonal solver (continued) - 22 Apr 25, 2016 Fourier spectral method 23 Apr 25, 2016 Chebyshev spectral methods - 24 Apr 27, 2016 Introduction to finite element (FE) method and weighted residual method, FE solution to a 1D steady-state problem, Element point of view in 1D FEM, higher-order FEM, 1D time-dependent problems 25 Apr 27, 2016 FE solution to a 2D steady-state problem, 2D finite element method (continued) - 26 May 4, 2016 TBA 27 May 4, 2016 TBA - ## References

## Books

- Cohen, G. C., 2002, Higher-Order Numerical Methods for Transient Wave Equations, Springer.
- Hairer, E., C. Lubich, and G. Wanner, 2006, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag.
- Heath, M. T., 2002, Scientific Computing: An Introductory Survey, Second Edition, McGraw-Hill.
- Hughes, T. J. R., 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover.
- Inan, U. S., and R. A. Marshall, 2011, Numerical Electromagnetics: The FDTD Method, Cambridge University Press.
- Johnson, C., 2003, Finite Element Methods, Advanced Scientific Computing II Lecture Note, University of Utah. (PDF)
- Landau, R. H., and M. J. Páez, 1997, Computational Physics: Problem Solving with Computers, John Wiley & Sons.
- LeVeque, R. J., 2007, Finite Difference Methods for Ordinary and Partial Differential Equation, SIAM.
- Nocedal, J., and S. J. Wright, 2006, Numerical Optimization, Second Edition, Springer.
- Pain, H. J., 2005, The Physics of Vibrations and Waves, 6th Edition, John Wiley & Sons.
- Rahman, M., 2007, Integral Equations and Their Applications, WIT Press.
- Shearer, P., 2009, Introduction to Seismology, Cambridge University Press.
- Trefethen, L. N. 2000, Spectral Methods in MATLAB, SIAM. (Companion website)
- Wang, Y., 2008, Seismic Inverse Q Filtering, Blackwell Publishing.
- Woolfson, M. M., and G. J. Pert, 1999, An Introduction to Computer Simulation, Oxford University Press.
## Articles

- Abarbanel, S., and D. Gottlieb, 1988, On the construction and analysis of absorbing layers in CEM, Applied Numerical Mathematics, 27, no. 4, 331-340.
- Bérenger, J. P., 1994, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, 114, 185-200.
- Cerjan, C., D. Kosloff, R. Kosloff, M. Reshef, 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equations, Geophysics, 50, no. 4, 705-708.
- Chu, C., and P. L. Stoffa, 2012, Implicit finite-difference simulations of seismic wave propagation, Geophysics, 77, no. 2, T57-T67.
- Clayton, R., and B. Engquist, 1977, Absorbing boundary conditions for acoustic and elastic wave equation, Bulletin of the Seismological Society of America, 67, no. 6, 1529-1540.
- Clayton, R., and B. Engquist, 1980, Absorbing boundary conditions for wave-equation migration, Geophysics, 45, no. 5, 895-904.
- Collino, F., and C. Tsogka, 2001, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, 66, no. 1, 294-307.
- Courant, R., K. Friedrichs, and H. Lewy, 1928, On the partial differential equations of mathematical physics, Physik. Math. Ann., 100, 32-74.
- Einstein, A., 1905, On the motion required by the molecular kinetic theory of heat, of particles suspended in fluids at rest, Annalen der Physik 17, 549-560.
- Johnson, S. G., 2010, Notes on perfectly matched layers, Online MIT Course Notes.
- Keys, R., 1985, Absorbing boundary conditions for acoustic media, Geophysics, 50, no. 6, 892-902.
- Levander, A. R., 1988, Fourth-order finite difference P-SV seismograms, Geophysics 53, no. 11, p. 1425-1436.
- Liu, Y., and M. K. Sen, 2010, A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation, Geophysics, 75, no. 2, A1-A6.
- Robertsson, J. O. A., 1996, A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography, Geophysics, 61, no. 6, 1921-1934.
- Virieux, J., 1984, SH-wave propagation in heterogeneous media: Velocity-stress finite difference method, Geophysics, 49, no. 11, 1933-1957.
- Yee, K., 1966, Numerical solution of initial boundary value problems involving Maxwellâ€™s equations in isotropic media, IEEE Transactions on Antennas and Propagation, 14, no. 3, 302-307.
- Zhou, M., 2003, A well-posed PML absorbing boundary condition for 2D acoustic wave equation, UTAM Annual Report. http://utam.gg.utah.edu/tomo03/03_ann/pdf/mzhou_pml.pdf
## Additional Resources

- MIT Open Courseware: Numerical methods for partial differential equations
- Numerical methods for PDEs