Random boundary condition for low-frequency wave propagation |

The first parameter is the size of grains. A simple way to determine the grain size is:

where is the effective length of the random velocity grain, is the dominant frequency in the RTM that uses the random boundary condition, and is the dominant low frequency used in modeling. The above equation holds because of the inverse relationship between frequency and wavelength at a given velocity. The second parameter is the shape of grains, the easiest to implement of which is cubic, with side lengths equal to the effective length . Although this works much better than a single-cell random velocity anomaly, its effectiveness is diminished by its regular shape. To further increase the randomness of reflected and scattered wavefields, we propose randomly shaped grains in place of cubic grains. We generate randomly shaped grains by perturbing cubic grains of certain lengths. In this case, the effective length of such a randomly shaped grain is equal the the side length of the cubic grain being perturbed. The perturbed grains will have similar volume or grain size to the cubic grains, but have random shapes that more effectively scatter coherent wavefields. It will be shown next that randomly shaped grains also work well with higher-frequency signals, because the irregular, small-scale features at grain boundaries scatter shorter wavelengths effectively.

Random boundary condition for low-frequency wave propagation |

2011-05-24