Migration imaging technique is commonly used in reconnaissance beyond tunnel or roadway,of which the important part is the travel time calculation.Because the imaging area approximates the whole underground space,such non-penetrating bodies as tunnels or roadways,holes,and mine goaves have a great influence on the travel time of seismic wave.Therefore,based on Fast Marching method (FMM),the authors developed a new algorithm to calculate the travel time of seismic waves for those complex models including the non-penetrating bodies.In this algorithm,a labeling technique is adopted for non-penetrating bodies,and the ray will automatically avoid and bypass the non-penetrating bodies in narrow band of FMM when a ray approaches them,making the seismic wavefront propagation more realistic.Also,this new algorithm can be applicable to the model for irregular ground surface if the above surface area is regarded as a non-penetrating body.Therefore,the new algorithm can deal with the model with non-penetrating bodies and irregular ground surface simultaneously.Compared with the conventional algorithm,the marked point is the only change of the developed algorithm,which maintains the accuracy and efficiency of FMM.The numerical test results show that the improved algorithm can calculate the travel time accurately,and has strong adaptability and good stability to complex model.
蒋锦朋, 朱培民. 非穿透体和起伏地表模型的FMM走时计算[J]. 物探与化探, 2018, 42(1): 166-171.
Jin-Peng JIANG, Pei-Min ZHU. FMM-based travel time calculation in complex model including non-penetrating abnormal body and irregular ground surface. Geophysical and Geochemical Exploration, 2018, 42(1): 166-171.
Julian B R,Gubbins D.Three-dimensional seismic ray tracing[J].Journal of Geophysics Research,1977,43(1):95-114.
[5]
Um J,Thurber C.A fast algorithm for two-point seismic ray tracing[J].Bulletin of the Seismological Society of America,1987,77(3):972-986.
[6]
Prothero W A,Taylor W J,Eickemeyer J A.A fast,two-point,three-dimensional ray tracing algorithm using a simple step search method[J].Bulletin of the Seismological Society of America,1988,78(3):1190-1198.
Vidale J.Finite-difference calculation of travel-times[J].Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[9]
李永博. VTI介质及复杂模型FMM射线追踪方法研究[D].西安:长安大学,2012.
[10]
Podvin P,Lecomte I.Finite difference computation of traveltimes in very contrasted velocity models:A massively parallel approach and its associated tools[J].Geophysical Journal International,1991,105(1):271-284.
[11]
Sethian J A.A fast marching level set method for monotonically advancing fronts[J].Proc. Nat. Acad. Sci.,1996,93:1591-1595.
[12]
Rawlinson N,Sambridge M.Multiple reflection and transmission phases in complex layered media using multistage fast marching method[J].Geophysics,2004,69:1338-1350.
[13]
Rawlinson N,Sambridge M.Wave front evolution in strongly heterogeneous layered media using the fast marching method[J].Geohys. J. Int.,2004,156:631-647.
[14]
Hassouna M S,Farag A A.Multistencils fast marching methods:A highly accurate solution to the eikonal equation on cartesian domains[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(9):1563-1574.
[15]
Sethian J A.Level set methods and fast marching methods[M].Cambridge:Cambridge University Press,1999.