Numerical simulations

2D and 3D numerical simulations of the 2D and 3D zero-offset experiments with the Marseille model are currently performed using two kinds of numerical methods : a Spectral-Element Method (SEM) and the Tip-Wave Superposition Method (TWSM).

The SEM is based upon a high-order piecewise polynomial approximation of the weak formulation of the wave equation. It combines the accuracy of the pseudospectral method with the flexibility of the finite-element method (Tromp et al., 2008). In this method, the wave field is represented in terms of high-degree Lagrange interpolants, and integrals are computed based upon Gauss-Lobatto-Legendre quadrature. This combination leads to a perfectly diagonal mass matrix, which in turn leads to a fully explicit time scheme that lends itself very well to numerical simulations on parallel computers. It is particularly well suited to handling complex geometries and interface matching conditions.

The TWSM is a hybrid method based on the combination of the Kirchhoff-type propagation and convolution-type reflection operators. The complete description and derivation of the formulas of the TWSM for the acoustic case can be found in Ayzenberg et al. (2007). The detailed physical explanation of the method based on Huygens’ principle is presented in Ayzenberg et al. (2009). Details on implementation of the method, together with the computing resources needed for simulations, can be found in Tantsereva et al. (2013).

If you want to test your code (or the method you used to work with) with our experimental data, do not hesitate to contact us!

References cited above :

• M.A. Ayzenberg, A.M. Aizenberg, H.B. Helle, D.K. Klem-Musatov, J. Pajchel and B. Ursin (2007) 3D diffraction modeling of singly scattered acoustic wavefields based on the combination of surface integral propagators and transmission operators Geophysics 72, SM19-SM34.
• J. Tromp, D. Komatitsch and Q. Liu (2008) Spectral-Element and Adjoint Methods in Seismology. Communications in Computational Physics 3, 1-32.
• M.A. Ayzenberg, A.M. Aizenberg and B. Ursin (2009) Tip-wave superposition method with effective reflection and transmission coefficients: A new 3D Kirchhoff-based approach to synthetic seismic modeling. The Leading Edge 28, 582-588.
• A. Tantsereva, B. Ursin, N. Favretto-Cristini, P. Cristini, D. Komatitsch A.M. Aizenberg (2013) Numerical modeling of zero-offset acoustic data by the Tip-Wave Superposition Method. 75th EAGE Conference & Exhibition, London (UK).