Research And Application Of Travel-time Tomography Based On Fast Sweeping Method

As a geophysical inversion method to effectively restore the formation medium velocity model,travel-time tomography has been deeply studied and applied for a long time because of its advantages of a small amount of calculation and high computational efficiency.In this paper,the basic principle and method of X-ray travel time tomography are discussed in detail.For the travel time calculation method,the fast sweeping method(FSM)based on the process function equation is used.The calculation amount of this algorithm is only O(N),compared with The traditional fast march method(FMM)and the shortest path method(SPM)has higher calculation efficiency and can guarantee sufficient calculation accuracy.In this paper,the principle and numerical implementation of the algorithm is derived in detail,and the efficiency and accuracy of the FSM algorithm are verified through various models.In terms of tomographic inversion,the adjoint-state method based on the FSM algorithm is used to obtain the Fréchet derivative matrix,which reduces the amount of calculation and memory consumption.This travel time tomography method without a ray path has the advantage of being fast and robust compared to SPM-based travel time tomography.This paper adopts several velocity models with different degrees of complexity,and through two tomography inversion schemes,highlights that the travel time tomography based on the FSM algorithm will be an important development direction of first arrival travel-time imaging.At the same time,in the application of velocity modeling,this paper applies the velocity model constructed by FSM travel time tomography to reverse time migration to obtain an accurate underground medium structure.The main research achievements of this paper are as follows:(1)To realize the SPM,FMM,and FSM to solve the model travel time field;(2)To derive the numerical calculation method of the gradient by adjoint-state method,and realize the tomography based on the SPM or the non-ray tomography based on the FSM;(3)To realize prestack reverse time migration algorithm based on 2D acoustic equation;(4)The joint imaging of FSM travel time tomography and reverse time migration is realized to obtain effective stratum structure features.