Abstract:

Seismic travel-time calculation is significant in numerical modeling,tomography inversion and migration. In this paper, integrated using wave-front construction and Lie algebra integral, we proposed a new method, called wave-front construction-Lie algebra integral(WFC-LAI)method， which is applicable to unsymmetrical travel-time calculation in laterally velocity variant medium. We make coordinate conversion by travel-time of image rays computed by wave-front construction and convert the lens item of single square root operator in depth domain to a constant, then in the ray coordinates we determine analytical expression of paraxial travel-time using Lie algebra integral and exponent mapping. Through numerical experiments we know our result coincides with the theoretical value in the medium with linear laterally variant velocity. Comparing with wavefront construction we can conclude that in laterally velocity variant medium, WFC-LAI method is applicable to travel-time calculation and saves storage space and computing time, which is extremely beneficial to improve the precision and efficiency of Kirchhoff pre-stack depth migration.

Key words: lateral velocity variation, Lie algebra integral, exponent mapping, wave-front construction, unsymmetrical travel-time, seismic