Seismic wavefront evolution of multiply reflected, transmitted, and converted phases in 2D/3D triangular cell model

Conventionally grid-cell-based schemes for simulating seismic wavefront propagation, such as the finite difference eikonal equation solver or the shortest-path method, usually adopt regular grids or cells in model parameterization to obtaining (but not exclusively) first arrivals only. However, later arrivals, which often result from the velocity interfaces or discontinuities, can be prevalent and significant (sometimes of large amplitude), making them potentially important additional information to use in practical applications. To better approximate the data acquisition geometry and the irregular interfaces, we exploit a triangular shortest-path method (TSPM; that is to use triangular cells in model parameterization) to simulate seismic wavefront evolution, comprising any kind of transmissions, reflections (or refractions), mode conversions, and combinations thereof, in 2D/3D heterogeneous media. A practical procedure, known as the multistage scheme, was incorporated with the TSPM to propagate seismic wavefronts from one interface (or subsurface in 3D) to the next. By treating each separate layer that the wavefront enters as an independent computational domain, one can simulate wavefront transmission and mode conversion by reinitializing it in the adjacent layer and wavefront reflection (and/or conversion) by reinitializing it in the incident layer. To further improve the computational accuracy, a second level of forward star scheme, previously defined in the grid model, is introduced into the triangular cell model. Several examples (including the Marmousi model) are used to demonstrate the viability and versatility of the multistage TSPM in heterogeneous media, even in the presence of high-velocity contrasts involving interfaces of relatively high curvature. With the introduction of the second level of forward star scheme, the total numbers of nodes are reduced sufficiently, and hereafter the computer memory is less required. Most important is that the computing accuracy with the second-level forward star scheme can be largely improved over those with the first level of forward star scheme applied in the multistage TSPM scheme.