地震学报2025，Vol.47Issue(2)：153-168,16.DOI:10.11939/jass.20230151
基于相速度预测的FMM弹性TTI介质qP波射线追踪
qP wave ray tracing in FMM elastic TTI media based on phase velocity prediction
摘要
Abstract
Fast and accurate calculation of travel time and ray path of seismic waves are two key problems in the field of seismic imaging and inversion.Solving these two problems plays a key role in the in-depth study of the fine structure of the Earth's interior,the efficient explora-tion of the distribution of different types of resources underground,and even the scientific pre-diction of possible natural disasters.However,the situation becomes more complex when an-isotropic media are involved.In such media,the velocity of seismic waves does not remain constant as in isotropic media,but varies with the propagation direction of seismic waves.This characteristic makes it a challenging task to calculate the propagation time of seismic waves and to determine the ray paths in anisotropic media.The conventional isotropic fast marching method(FMM)shows excellent performance advantages in solving the travel time problem in isotropic media.It is able to produce results relatively quickly and accurately due to its efficient algorithm and stable computational process.However,when we try to apply the method to solve the Eikonal equation under anisotropic conditions,we are faced with a critical aspect:the need for an accurate estimation of the phase velocity.This is because in an anisotropic medi-um,the velocity,anisotropy parameter and stratigraphic dip are not constant,and their dynam-ic changes make the calculation of the propagation direction complicated.The complex calcula-tion of the propagation direction further increases the difficulty of phase velocity estimation.As a key parameter describing the velocity of seismic waves in a given direction,the accuracy of the phase velocity estimation is like the first domino in the chain,which directly affects the sub-sequent propagation time and the final accuracy of the ray path calculation.Any small devi-ation in the phase velocity estimate can be amplified in the subsequent calculations,leading to a large deviation of the final results from the actual situation. In this paper,the fast marching method(FMM)for anisotropic media,which is a mature and widely used method,is taken as a solid basis for an in-depth study.Through rigorous theor-etical derivation and practical verification,a phase velocity estimation method for tilted trans-versely isotropic(TTI)media and an anisotropic ray tracing method based on the principle of phase velocity prediction(PVP)are proposed.The method cleverly inherits the outstanding features of speed and stability of isotropic FMM,while maintaining the same level of computa-tional accuracy as isotropic FMM,ensuring reliability and accuracy of results.A phase velo-city prediction formula for TTI media has been derived.The formula can directly and accur-ately calculate the corresponding changes in phase velocity based on the changes in key factors such as seismic wave velocity,anisotropy parameter and stratigraphic dip.It greatly simplifies the complicated process of solving the anisotropic Eikonal equation and breaks the bottleneck of the previous methods in terms of computational efficiency and accuracy.It also greatly improves the computational efficiency of ray tracing,making the calculation process more efficient and faster,and at the same time significantly improves the computational accuracy,providing a more reliable and accurate basis for subsequent processing and interpretation of seismic explora-tion data. In order to comprehensively and thoroughly verify the computational efficiency and accur-acy of the method in practical applications,simulation experiments are carried out on a number of representative typical models.First,a unified theoretical model is used as the first test ob-ject.The model is relatively simple in structure and has a clear theoretical analytical solution,which can provide a clear reference standard for the accuracy verification of the method.Through comparative analyses,the results clearly show that the computational results obtained by the method are in high agreement with the theoretical results,which strongly verifies the ex-cellent performance of the method in terms of accuracy.Then,the vertical transverse isotropy(VTI)reference model and Marmousi model are further tested.The results show that this meth-od has small calculation error and good stability,and can be applied to ray tracing of complex structures.In addition,in order to further quantify the performance of the method,a multi-source near-surface numerical simulation test is also carried out.A model of complex near-surface structure is designed,and the wave fields of multiple sources are simulated by finite dif-ference method.The seismic record of the model is simulated and its first arrival time is picked up.Then,ray tracing and travel time calculation are carried out by using this method,and the results are compared with those of finite difference simulation.The calculation errors and time of isotropic FMM and anisotropic PVP-FMM are statistically analyzed.The results show that both of them have the same calculation error,and the average error is very small.The error of anisotropic PAP-FMM is 43%less than that of anisotropic FMM without phase velocity predic-tion.A computer with 2.4 GHz CPU is used for ray tracing.The total time consumption of 913 source for isotropic FMM and PAP-FMM are 326 seconds and 372 seconds respectively.Be-cause anisotropic FMM increases the calculation links of phase velocity and group velocity,the time consumption is increased by 10%compared with isotropic FMM.PVP-FMM added a phase angle prediction link,which increased the time consumption by 14%.In summary,this method has the same computational efficiency as isotropic FMM,and also has good adaptabil-ity and stability for near-surface models.关键词
各向异性/快速推进方法/射线追踪/相速度Key words
anisotropy/fast marching method/ray tracing/phase velocity分类
地球科学引用本文复制引用
张志禹,董雪,赵亦群..基于相速度预测的FMM弹性TTI介质qP波射线追踪[J].地震学报,2025,47(2):153-168,16.基金项目
国家自然科学基金联合基金(U21A20485)资助. （U21A20485）
