Simultaneous traveltime inversion using the multi-phase Fresnel volume rays

Traditional ray tomography method based on high frequency assumption is unable to obtain a high resolution tomographic picture with sparse rays. In contrast, the finite-frequency ray theory is more suitable for real seismic propagation law, that is to say that the travel time is dependent not only on the velocity distribution along a central ray (or traditional geometric ray), but also on the velocity anomaly within a region (referred as the first Fresnel volume), which embraces the central ray. In this paper we first put forward an algorithm to calculate the multi-phase Fresnel volume finite-frequency ray, and then give a inversion method to simultaneously invert both velocity and reflector geometry by using these multi-phase arrival time information. In synthetic example, both the traditional ray tomographic and finite-frequency ray tomographic methods are used to simultaneously update both velocity field and reflector geometry with multi-phase arrival times, the results show that the finite-frequency ray tomographic method is advantageous over the traditional ray tomographic method in terms of velocity reconstruction and reflector geometry updating when the ray density is relatively low. The finite-frequency ray tomographic method with varying frequency is a good choice in real seismic tomographic application.