The Study Of Tomography Velocity Inversion Based On Fat Ray Method

Travel time tomography based on ray theory is one of the most effective way to estimate the near surface velocity model. However, conventional ray-based tomography methods rely on Fermat theory which assumes the frequency of wave is infinitely high, thus seismic wave travels through a zero-width ray-path and only the velocity of point which falls on this ray path make contribution to the travel time. While the actual wave is band-limited and propagates along a ‘tube-like’ volume which is called Fresnel zone. Hence, it conflicts with the conventional ray theory and leads to an unstable inversion result. Meanwhile, the traditional ray can only cover a limited space in the media, which results in the sparseness of the tomography matrix. The sparseness cause the tomography matrix to be poorly conditioned and affect the imaging resolution. All these problems cause severe harm to the quality of the tomography result which can not be overlooked.To resolve the problems mentioned above, we propose the fat ray travel-time tomography method based on first Fresnel zone and multiple-frequency-combination. First of all, discarding the concept of zero-width geometric ray, we use fat ray which has a certain width thus extend the coverage of velocity model. By comparing all the defining methods of fat ray, we settled on using Fresnel zone to broaden the conventional ray, which accords with the laws of propagation of seismic wave because of the fact that the majority of energy travels within the first Fresnel zone and constructive interference takes place within it. In this way. the ray-covered space is enlarged and gives a more realistic representation of wave propagation.Different from the conventional ray tomography, it is considered that the spatial points distunbance contribute differently to travel time in fat ray. By taking the contribution made by the points nearby the ray path into consideration, the influence of each point in the media is well quantified by using the weight factor modifying kernel function, thereby giving a more realistic representation of the relationship between slowness perturbation and travel time perturbation. In the meantime, to obtain a better inversion result with a smallest amount of time, a optimal acceleration factor is brought in which speed up convergence. With these modification of the kernel funciton the outcome is much more stable and accurate.The core of tomography inversion is the calculation of sensitive kernel function while ray tracing is the very tool we need. By comparison, we choose the shortest path raytracing based on parabolic traveltime interpolation. As calculation of the path is completely avoided, efficiency is greatly improved. Tests on synthetic models demonstrate the precision and stability of this method. Fouthly, frequency is an important factor determining resolution of band-limited seismic wave, because fat ray with different frequency has a corresponding width of fresnel zone and the area influenced by the travel time delay in velocity thus varies. So this part worth an indepth study.Finally, the idea of a combination of different frequency is brought up in the inversion process. By analyzing the results of using different frequency to do fat ray tomography in the iteration, we can see fat ray with different frequency has its own advantage. So we combine the low and high frequency in iterations by using the low frequency at the starting of iteration to gain a faster convergence and using the high frequency in the following stages of iteration to obtain a higher precision. The output of each time of iteration serves as input of next iteration and the frequency is raised gradually. The combination of different frequency can well improve the precision and resolution of the inversion process. Synthetic data tests show this method of fat ray tomography based on first fresnel zone and multiple frequency combination has a better inversion result when compares to the ray-based tomography and traditional fat ray tomography.We apply our method to real seismic data to estimate velocity model and calculate statics and show promising result comparing to the result of traditional ray-based tomography method.