Multilevel adaptive mesh modeling for wave propagation in layered media

In this paper, we apply an adaptive mesh refinement method for numerical modeling of two-dimensional wave propagation in blocky models. A blocky model consists of patches with homogeneous properties. A series of nested-type adaptive meshes of local rectangular finer or finest mesh patches is used to control the solution accuracy at each level. The high-resolution simulation of wave propagation can be obtained effectively from coarser mesh to finer mesh level. Numerical experiments show good performance of the proposed algorithm to obtain fine characteristics of wave propagation (in particular reflected, transmitted, diffracted energy) while avoiding numerical dispersion.
- Barad, M. and Colella, P., 2005. A fourth-order accurate local refinement method for Possion’sequation. J. Comput. Phys., 209: 1-18.
- Berger, M., 1982. Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. Ph.D.Thesis, Stanford University.
- Berger, M. and Oliger, J., 1984. Adaptive mesh refinement for hyperbolic partial differentialequations. J. Comput. Phys., 53: 484-512.
- Berger, M., 1986. Data structures for adaptive grid generation. SIAM J. Sci. Stat. Comput., 7:904-916.
- Berger, M. and Colella, P., 1989. Local adaptive mesh refinement for shock hydrodynamics. J.Comput. Phys., 82: 64-84.
- Berger, M. and Rigoutsos, L., 1991. An algorithm for point clustering and grid generation. IEEE.T. Syst. Man. Cy., 21: 1278-1286.
- Berger, M. and Leveque, R., 1998. Adaptive mesh refinement using wave-propagation algorithmsfor hyperbolic systems, SIAM J. Numer. Anal., 35: 2298-2316.
- Bishop, T., Bube, K., Cutler, R., Langan, R., Love, P., Resnick, J., Shuey, R., Spindler, D. and
- Wyld, H., 1986. Tomographic determination of velocity and depth in laterally varyingmedia. Geophysics, 50: 903-923.
- Bolstad, J., 1982. An Adaptive Finite Difference Method for Hyperbolic Systems in One SpaceDimension. Ph.D. Thesis, Stanford University.
- Calhoun, D., Helzel, C. and LeVeque, R., 2008. Logically rectangular grids and finite volumemethods for PDEs in circular and spherical domains. SIAM Review, 50: 723-752.
- Debreu, L., Vouland, C. and Blayo, E., 2008. AGRIF: Adaptive grid refinement in Fortran.Comput. Geosci-UK, 34: 8-13.
- Griebel, M. and Zumbusch, G., 1998. Adaptive space grids for hyperbolic conservation laws. Proc.of the 7th Internat. Conf. on Hyperbolic Problems, Basel, Switzerland.
- Horning, R. and Trangenstein, J., 1997. Adaptive mesh refinement and multilevel iteration for flowin porous media, J. Comput. Phys., 136: 522-545.
- Ketcheson, D. and LeVeque, R., 2008. WENOCLAW: A higher order wave propagation method,
- Hyperbolic Problem: Theory, Numerics, Applications. Springer Verlag, Berlin: 609-616.
- Lanseth, J. and LeVeque, R., 2000. A wave propagation method for three-dimensional hyperbolicconservation laws. J. Comput. Phys., 165: 126-166.
- LeVeque, R., 1997. Wave propagation algorithms for multidimensional hyperbolic systems. J.Comput. Phys., 131: 327-353.
- LeVeque, R., 2002. Finite volume methods for hyperbolic problems. Cambridge University Press,Cambridge.
- Ma, J., Gang, T. and Hussaini, M.Y., 2007. A refining estimation for adaptive solution of waveequation based on curvelets. In: Van De Ville, V., Goyal, K. and Papadakis, M. (Eds.),Wavelets XII, Proc. SPIE Vol. 6701, 67012J.
- Mi, T. Ma, J. and Yang, H., 2009. Adaptive grid simulation of wave equations based on secondgeneration wavelet transform. Submitted to Geophysics.
- Mitra, S., Parashar, M. and Browne, J., 1997. DAGH: User’s Guide, Dept. of Computer Sciences.
- Univ. of Texas at Austin. http://www.caip.rutgers.edu/ ~ parashar/DAGH/136 MI, MA, CHAURIS & YANG
- Pancheshnyi, S. Segur, P., Capeilere, J. and Bourdon, A., 2008. Numercial simulation offilamentary discharges with parallel adaptive mesh refinement. J. Comput. Phys., 227:6574-6590.
- Qian, J. and Symes, W., 2002. An adaptive finite-difference method for traveltimes and amplitudes.Geophysics, 67: 167-176.
- Trangenstein, J., 1995. Adaptive mesh refinement for wave propagation in nonlinear solid. SIAMJ. Sci. Comput., 16: 819-839.