Numerical Modeling of Seismic Wave Propagation

Published in Feb 02, 2023 06:23 PM

-- Elective Course; 3 credits ---

Topics:

Review of Fortran90:declaration of variables and constants; programming elements, reading and writing formatted and unformatted (binary files) data, use of modules, dynamic allocation, functions and subroutines;
Review of equations of elasticity and acoustics: first order equations in tension and velocities, second-order equations in displacements; transverse vertical isotropic (VTI) media and the isotropic media; simplification for the acoustic case, the first order equations, acoustic equation wave for general media and for media with small density gradient;
The finite difference method (MDF): simple and staggered grid formulations, finite difference operators; explicit and implicit schemes, properties of difference equations, stability and numerical dispersion.

Acoustic modeling with MDF: schemes in single and staggered grids (in second and fourth orders in space), application of seismic source, non-reflective boundary condition (CCNR), absorbing boundary conditions (ABC); stability criteria, criterion to avoid numerical dispersion;
ElasticmodelingwithMDF:simplesandstaggeredgridformulations,formulationsforsecond- order equations in displacements (or velocities) and formulations for the first-order equations in terms of stresses and velocities; formulations for isotropic media and VTI media;
Reverse time migration (RTM): basic processing review, stacking, zero offset section; the explosive reflector model and principle of imaging, zero-offset RTM and RTM with offset (post- and pre-stack); computational implementation and practical aspects.

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Bibliography:

- Cunha, R.D., 2011, Programação Científica em FORTRAN 95, Clube dos Autores.
- Di Bartolo, L., 2013, Introdução à Modelagem Sísmica utilizando o MDF, Apostila Minicurso UNICAMP (6h).
- Chapman, C.H., 2004, Fundamentals of seismic wave propagation, Cambridge University Press.

- Strikwerda, J.C., 2004, Finite difference schemes and partial differential equations, Siam.
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- Di Bartolo, L., 2010, Modelagem sísmica anisotrópica através do método das diferenças finitas utilizando sistemas de equações em 2a ordem. Tese de Doutorado, COPPE/PEC.
- Di Bartolo, L., 2012, A new family of finite-difference schemes to solve the heterogeneous acoustic wave equation, Geophysics, v 77, n. 5, pp.T187-T199.

- Virieux, J., 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics, v 51, n. 4, pp.889-901.