The Study Of Elastic Wave Fresnel Zone Travel-time Tomography

As for the traditional travel-time tomographic velocity inversion is based on ray theory which is a high frequency approximation of wave equation,the sensitivity kernel function and travel-time residual calculated on single ray have limited accuracy.However,conventional ray-based tomography methods are based on the Fermat theory which assumes the frequency of wave is infinitely high,while the actual wave is band-limited and propagates along a ‘tube-like' volume which is called Fresnel zone.To resolve the problems of tomography based on ray theory,Fresnel tomography discards the concept of zero-width geometric ray.Taking into account the seismic signal has a certain bandwidth,high-frequency radiation path not only on the nature of the medium will affect the propagation of seismic waves,rays near the same media features will affect the propagation of seismic waves.I make use of Fresnel volume to describe the wave propagation in complex media.And then,I develop Fresnel volume theory and the corresponding tomographic method(FVT)which is proved more accurate and higher resolution than the traditional raypath tomography.So,this study has important academic meaning,and the corresponding methods will have important practical value.We propose the Fresnel zone travel-time tomography based on multi-band frequencies' combination.This paper starts from the Born and Rytov approximation of frequency-domain wave equation to derive the travel-time sensitivity kernels of wave equation on the band-limite wave-field and the travel-time residual can be obtained based on the Rytov approximation at the same time.Meanwhile,we enhance the resolution and precision by combining multiple frequencies during different stages of iteration.This method can improve the accuracy and efficiency of inversion.Comparing with conventional ray tomography inversion method,it can provide more reliable and accurate travel-time residual which can't be affected by Ray focusing and caustic phenomena based on Rytov approximation.The inverted result proves that our method has a higher resolution and accuracy.