2D/3D multi-phase Fresnel volume rays and applications to simultaneously update both velocity model and reflector geometry

Abstract

Theoretically, Fresnel volume ray theory is more suitable for handling real seismic propagation problems because the traveltime depends not only on the velocity distribution along a traditional geometric ray but also on the velocity distribution within a vicinal region (referred to as first Fresnel volume, abbreviated as FFV) which embraces the geometric ray. In this study, we used an exact solution to calculate multi-phase FFV rays for both 2-D and 3-D cases and introduced a normalized coefficient to account for different contributions inside the FFV ray on the traveltimes. Furthermore, we draw a new formula to calculate the partial traveltime derivatives with respective to the velocity variations and depth changes of the reflectors and finally present a simultaneous inversion method for updating both velocity field and reflector geometry by using these multi-phase FFV rays for both in 2-D and 3-D cases. Using synthetic data examples, we compare the reconstructions of the velocity field and the reflector geometry using the FFV ray tomographic methods and the traditional ray tomography approaches. The simulated inversion results for both 2-D and 3-D cases show that the FFV ray tomographic method is advantageous over the traditional ray tomography method, especially when the ray density is relatively low. The other advantage for the FFV ray tomography method is that it can capture the coarse velocity structure and reflector geometry by starting with a low-frequency data set and then map the fine velocity structure and the detailed reflector geometry by using a high-frequency data set.