Scientific and technical journal

«Proceedings of Gubkin University»

ISSN 2073-9028

Proceedings of Gubkin University

UDC: 550.832.044+519.688
DOI: -


Arseniyev-Obraztzov Sergey S.1

1 Gubkin Russian State University of Oil and Gas

Keywords: seismic waves, absorbing boundary conditions, adaptive grids, method of lines


The paper presents a mathematical model and the results of testing of parallel software for computer clusters, designed to simulate the propagation of seismic waves in continuous linear media. The generalized method of direct second-order accuracy in space and time allows the conditionally stable evaluation of the synthetic seismograms for absorbing media with strongly varying parameters. The developed software allows to set the boundary conditions of the free surface for any smooth topography of solids. To reduce the effect of the ref- lected waves from the fictitious boundaries energy-absorbing boundary conditions were used. The program provides for the possibility of local refining of computational grid in areas where high-frequency waves are of particular interest. In order to justify the adequacy of the mathematical and computational models these were applied to solve problems with an analytical solution.


1. Арсеньев-Образцов С.С., Жукова Т.М. Поглощающие граничные условия для численного решения задач теории вязкоупругости//ЖВМ и МФ. – 1987. – Том 27. – № 2. – С. 301–306.
2. Арсеньев-Образцов С.С. Генерация кода программ для численного моделирования сложных междисциплинарных задач термогазодинамического воздействия на пласты баженовской свиты//Труды Российского государственного университета нефти и газа имени И.М. Губкина. – 2009. – № 3 (254). – С. 114–120.
3. Арсеньев-Образцов С.С. Численное моделирование междисциплинарных задач кодогенерацией обобщенного метода прямых на подвижных, адаптивных сетках//Труды Российского государственного университета нефти и газа имени И.М. Губкина. – 2010. – № 2 (259). – С. 120–131.
4. Clayton R., Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations// Bull. Seismo. Sos. Amer. – 1977. – Vol. 67. – P. 1529–1540.
5. Higdon R.L. Absorbing boundary conditions for acoustic and elastic waves in stratified media//J. Comput. Phys. – 1992. – Vol. 101. – P. 386–418.
6. Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves// J. Comput. Phys. – 1994. – Vol. 114. – P. 185–200.
7. Lamb H. On the propagation of tremors over the surface of an elastic solid//Phil. Trans. Roy. Soc. London. Ser. A. – 1904. – Vol. CCIII. – P. 1–42.