The Calculation Of Seismic Traveltime Based On FMM In 3-D Random Medium

Self-organization exists widely in the earth medium,the influence of rock mineral composition's heterogeneity and diagenetic process such as temperature,pressure and tectonic movement,physical parameters of strata bound to show heterogeneity.Traditional velocity modeling is difficult to describe heterogeneity,but the appearance of random medium modeling makes it easy.As a tool to study the propagation of seismic wave in random medium,wave field simulation has played a important role.However,the diffraction of wave field in random medium is more serious,which is not conducive to analysis propagation rules.As an important parameter of seismic wave kinematics information,the seismic wave travel time is more intuitive.The calculation of seismic travel time is divided into finite difference method based on Eikonal equation and ray tracing method based on ray theory,It's effective and accurate to obtains seismic travel time in finite difference by solving Eikonal equation which is obtained from high frequency approximation of wave equation.Aiming at the deficiency of the conventional finite difference method,Fast Marching Method(FMM)adopts the upwind difference to solve the problem of instability.The two key techniques of FMM are narrow band expansion and Heap sort.Narrow band expansion is used to simulate the propagation of wave front,and the heap sort is used to select the minimum travel point in the narrow band.Through the Organic combination of both can complete calculation of the hole space with high precision and high efficiency.Since narrow band expansion needs to select the minimum travel time every time,so the efficiency of heap sorting directly affects the efficiency of FMM.In general,heap sort algorithm is based on the complete binarytree.But,this kind of heap sort is not optimal,and the heap sorting method can be improved to fit the characteristics of upwind difference calculationAiming at random medium modeling and FMM,related researchs were carried out and effective improvement strategies were put forward.The main contents of this paper are as follows:(1)the superposition velocity modeling based on statistics random process of spectrum decomposition theory is extended from 2-D to 3-D.This paper mainly focused on 3-D random medium modeling and analysed the effects of self correlation function and self correlation length in three direction and variance to 3-D(stationary)random medium modeling results;(2)the heap sort in FMM is improved,traditional heap sort based on complete binary tree was extended to complete ternary tree heap sort,and on the base of complete ternary tree used the space sinking method,which is combined with upwind difference effectively.Then,the improved algorithm is applied to the uniform model and compare computational efficiency with before.(3)the improved FMM seismic traveltime calculation was applied to 3-D complex random medium,3-D FMM based on upwind was stated in detail,which is mainly including the strategy to realize the3-D local algorithm and narrowband propagation.The computational accuracy and computational efficiency of the algorithm are analyzed in 3-D homogeneous medium model,and then the three-dimensional complex medium model(including random medium)is calculated and analyzed.The result show that the implementation of scheme of random complex medium modeling is feasible,it can describle the velocity of the stratigraphic information effectively,FMM based on complete trigeminal tree Heap sort whatever in 2-D and 3-D random seismic travel time computation in complex medium are stable and efficient.