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Optimizing Multidomain Chebyshev Method for Seismic Wave Propagation

This project, led by Peter Daneček, an early-stage researcher, focuses on refining the Multidomain Chebyshev Method to accurately model seismic wave propagation in complex media. The method's design goals include parallel 3D implementation with good scalability, structured implicit topology, and the ability to handle both continental and global scales. By utilizing spherical geometry and overlapping domains, the method aims to overcome the limitations of current Earth models, offering improved grid generation and inversion. The research includes numerical comparisons with other methods, test cases against known solutions, and future enhancements for complex models and boundary conditions.

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Optimizing Multidomain Chebyshev Method for Seismic Wave Propagation

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  1. Overlapping Multidomain Chebyshev Method:Verification

  2. Profile Seismic wave Propagation and Imaging in Complex media: a European network • PETER DANECEK • Early Stage Researcher • Host Institution: INGV Bologna, Italy • Place of Origin: Zlin, Czech Republic • Appointment Time: Juni 2006 • Project: Multidomain Chebyshev Method for Wave Propagation on Continental and Global Scales with Application. • Task Groups: TG Numerical Methods, TG Global Scale • Cooperation: OGS Trieste, Munich University

  3. Overview • Motivation and design goals • Numerical method: OMDC • Geometry • Results • Future work

  4. Design goals • Parallel 3D method with good scalability • Efficient, structured method=> implicit topology • Continental & Global Scale Seismology => spherical geometry • Justification: - current Earth models are smooth- grid generation AND inversion

  5. Numerical method (1) Overlapping Multidomain Chebyshev Method N = 6

  6. Numerical method (2) OMDC N = 6

  7. How does it relate to other methods? Numerical method ? ? ? OMDC ? ? ?

  8. How does it relate to other methods? equal-spaced Fourier method special co-location Chebyshev method Numerical method Increasing order Strong formulation higher order FD low order FD OMDC local global Weak formulation SEM low order FEM FEM with high order ordinary polynomials

  9. Spherical geometry (1) • Uniform mapping by continuous functions for the whole computational domain • Elastic equations solve directly in spherical coordinate system • Orthogonality between coordinate lines • Few pre-calculated/stored parameter

  10. Spherical geometry (2) • Sphere decomposed into six equally shaped chunks • Each chunk has a uniform mapping by continuous functions • Coordinates lines along the surface are no longer orthogonal • Derivatives are coupled • Elastic equations solve directly in the resulting coordinate systems • Still moderate number of pre-calculated/stored parameter

  11. Results (1) • 8 processors • N = 8 • 32x32x40 elements • 226x226x282 points • Unity sphere with r= 0.8..1.0, == -5..+5 degree • Grid spacing: 0.17..1.08 *10-3 • Vs = 0.1, Vp = 0.2 • ca. 10 ppw, c < 0.1, leap-frog • Source: point force in radial direction • Absorbing boundaries

  12. Results (1)

  13. Results (2) • 64 processors • N = 8 • 32x32x40 elements • 226x226x282 points • Unity sphere with r= 0.8..1.0, == -5..+5 degree • Grid spacing: 0.17..1.08 *10-3 • Vs = 0.1, Vp = 0.2 • ca. 10 ppw, c < 0.1, leap-frog • Source: Explosion (stress) • Absorbing boundaries

  14. Results (2)

  15. Results model 1 model 2

  16. Future work • Time histories • Comparison against known solution • Boundary conditions • Complex models • Code extensions and improvements • Test the limits • Comparison with other methods • Applications • More work on Cubed Sphere geometry

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