Shunhua Cao

Finite-difference solution of the eikonal equation using an efficient, first-arrival, wavefront tracking scheme

First‐break traveltimes can be accurately computed by the finite‐difference solution of the eikonal equation using a new corner‐node discretization scheme. It offers accuracy advantages over the traditional cell‐centered node scheme. A substantial efficiency improvement is achieved by the incorporation of a wavefront tracking algorithm based on the construction of a minimum traveltime tree. For the traditional discretization scheme, an accurate average value for the local squared slowness is found to be crucial in stabilizing the numerical scheme for models with large slowness contrasts. An improved method based on the traditional discretization scheme can be used to calculate traveltimes in arbitrarily varying velocity models, but the method based on the corner‐node discretization scheme provides a much better solution.

2.5-D modeling of seismic wave propagation; boundary condition, stability criterion, and efficiency

The modeling of 3-D wave propagation in media having only 2-D variation in the elastic properties—so‐called 2.5-D modeling—is achieved using the wavenumber transform, in which multiple 2-D problems are solved, each one associated with a different strike‐direction wavenumber (ky). We derived a 2.5-D transmitting boundary condition in the frequency domain, which has no simple representation in the time domain. It yields significantly improved results over existing boundary conditions. For time‐domain methods, attenuating boundary conditions must be applied. The 2.5-D stability criterion changes from the 2-D to the 3-D criterion as the wavenumber increases from zero to the maximum value for traveling waves, respectively. In the frequency‐wavenumber (ω-ky) domain at a given spatial location, the wavefield for a fixed frequency (ω) oscillates at progressively higher rates as wavenumber (ky) increases from zero to the maximum value for traveling waves. A nonuniform sampling scheme in wavenumber space, to exploi...

Attenuating boundary conditions for numerical modeling of acoustic wave propagation

Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one-wavelength wide zone. The Neumann-attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.