Three-dimensional modeling of temporal field by radial and finite-differential methods for solving the problems of seismology


  • V.N. Pilipenko Subbotin Institute of Geophysics, National Academy of Sciences of Ukraine, Ukraine
  • A.O. Verpakhovskaya Subbotin Institute of Geophysics, National Academy of Sciences of Ukraine, Ukraine



seismology, three-dimensional modeling, temporal field, finite-differential continuation, eikonal equation.


Three-dimensional modeling of temporal field allows reconstructing the kinamatics of wave processes observed in the Earth during seismic studies and determine in such a way spatial position into it of the studied objects. Modeling is also an important tool for inspection of correctness of methods for solving the inverse problem during the process of interpretation both seismological and seismic exploration data. 

Seismic rays which determine the direction of the flow of high-frequency part of seismic wave field energy are very important in seismology.  Tracking the rays and their calculation allows solving different problems of seismology as well as checking the accuracy of results obtained while different methods of processing and interpretation of data observed on the Earth surface are used.

A version of finite-differential modeling of temporal field in three-dimensional spherical Earth is based on direct net approximation of the eikonal equation and it is this approach to reconstruction of values of seismic waves arrivals to any point of Earth depths is the most stabile and as a result can guarantee correctness of solving lots of applied problems of seismology. At the same time continuation of temporal field is a part of calculative process of finite-differential migration designed at the Institute of Geophysics named after S.I.Subbotin of NAS of Ukraine and is used while processing seismic exploration data.

Development of computer technologies during recent decades brought the appearance of theories, algorithms, and software-based complexes realizing the solving of three-dimensional geophysical in particular seismological problems.  The paper gives theoretical foundations, algorithms, and results of application  of three-dimensional temporal fields modeling developed for both radial and finite-differential methods by practical examples.


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How to Cite

Pilipenko, V., & Verpakhovskaya, A. (2019). Three-dimensional modeling of temporal field by radial and finite-differential methods for solving the problems of seismology. Geofizicheskiy Zhurnal, 41(5), 3–26.