Elimination of numerical dispersion in finite‐difference modeling and migration by flux‐corrected transport

Abstract

DI_LIL_RThis report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Referenoe herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom. menA..ation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. ABSTRACTFinite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitary variatious in velocity and density, and can handle turning waves well. However, conventional finite-difference methods for solving the acousticwave equation suffer from numerical dispersion when too few samples per wavelength are used. Here, we present two flux-correctcd transport (FCT) algorithms,

Prediction of Margin Stratigraphy

“…for P-and S-waves) allows the complete propagation path of seismic waves to be simulated, i.e. their departure from the source, their passage through multilayered strata and their arrival at surface receivers (Fei & Larner, 1995). This more realistic form of modelling accounts for such additional effects as geometrical spreading, multiples, refractions and reflections at interfaces.…”

3D weak-dispersion reverse time migration using a stereo-modeling operator

“…Classical FD methods suffer from serious numerical dispersion when too few samples per wavelength are used (Yang et al, 2006). To minimize or eliminate numerical dispersion, many researchers have attempted to develop new algorithms by redefining the operators for spatial and temporal differentiation or making some special treatments (Kosloff and Baysal, 1982;Dablain, 1986;Fei and Larner, 1995;Zhang et al, 1999;Mizutani et al, 2000;Zheng and Zhang, 2005). However, as discussed in our previous work (Yang et al, 2007), the theoretical properties of these methods or techniques have some disadvantages.…”

“…However, as discussed in our previous work (Yang et al, 2007), the theoretical properties of these methods or techniques have some disadvantages. For example, although the so-called flux-corrected transport technique can suppress the numerical dispersion (Fei and Larner, 1995;Zhang et al, 1999;Yang et al, 2002;Zheng et al, 2006), it is unable to fully recover the resolution lost by the numerical dispersion when the grid size is too coarse (Yang et al, 2002). The spatial operator for the pseudospectral method (Kosloff and Baysal, 1982;Fornberg, 1987) can be exact up to the Nyquist frequency, but it requires the fast Fourier transform of the wavefield, which needs additional computation and introduces difficulties of how to handle nonperiodic boundary conditions and implementation in parallel computing environments (Mizutani et al, 2000).…”

High accuracy wave simulation – Revised derivation, numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic wave equation

“…These methods serve as powerful tools in exploration seismology. However, some FD methods such as the conventional finite-difference methods with second-and fourth-order accuracies often suffer from the numerical dispersion when too few samples per wavelength are used or when models have large velocity contrasts or artifacts caused by sources at grid points (Fei and Larner, 1995;Yang et al, 2002). Numerical dispersion, which is an un-physical phenomenon caused by discretizing the wave equation (Sei and Symes, 1994;Yang et al, 2002), is an important issue in numerical seismic simulations.…”