Purpose. The aim of study is to create the method of seismic wave fields modeling for a broad class of vertically and horizontally inhomogeneous layered media. Simulation will make it possible to more precisely assess the characteristics of sedimentary strata in the study of the transmission characteristics of the environment under the engineering structures. Methodology. At modeling in engineering seismology should be used a wide frequency range (from 0 to 200 Hz) to study all possible effects on engineering structures. While solving the direct problem need to use mathematical modeling techniques that allow taking into account the different types and forms of inhomogeneities, as well as the complex structure of the sedimentary layer. The research was conducted by solving the direct dynamic problem of seismic with finite element method. This method of mathematical modeling allows calculations for models which are complicated in their structure. When solving the direct dynamic problem of seismicity with this method, wave propagation are calculated for each time point, so do not lose the ability to consider different exchange effects inside the model and also we can calculate models with different complex geometric structure and various inclusions. For simulations were used existing two-dimensional models. When setting signal as close to the -impulse, we get the response in full possible frequency range of model without additional processing output results. Results. The software package for mathematical modeling of seismic wave field was created. A result of modeling are obtained field of displacements, velocities of displacement, acceleration, as well as appropriate frequency characteristics for this model. Originality. The software package obtained allows investigating dynamic characteristics and resonance frequencies of the sedimentary layer in interactive mode. Practical significance. Based on the results of research, the wave field and the frequency response of the sedimentary layer under the engineering structure were obtained. Analysis of frequency characteristics of environment provides a resonant frequency to be considered in the design of large engineering structures.

- 1. Bate K., Vilson E. Chislennye metody analiza i metod konechnyh jelementov [Numerical methods of analysis and finite element method]. Moscow, 1982, Strojizdat, 448 p.

2. Brych T .B. Matematychne modeliuvannia vplyvu protsesu pohlyblennia naftohazovoi sverdlovyny na napruzheno-deformovanyi stan hirskoho masyvu [Mathematical modeling of the influence of deepening of oil and gas well on rock stress-strain state]. Visnyk Lvivskoho universytetu. Seriia fizychna, 2010, no. 45, pp. 135-141.

3. Verbytskyi S. T., Brych T. B., Rozhok N. I., Kuplovskyi B. Ye. Metod Nakamury ta metod skinchenykh elementiv pry doslidzhenni AChKhS [Nakamura's technique and finite element method in solid amplitude-frequency response investigation]. «Heodynamika», 2011, no. 2(11), pp. 38–40.

4. Il'jushin A. A. Mehanika sploshnoj sredy [Continuum mechanics]. Moscow, 1978, Izdatel'stvo Moskovskogo universiteta, 288 p.

5. Kendzera O. V. Seismichna nebezpeka i zakhyst vid zemletrusiv (praktychne vprovadzhennia rozrobok Instytutu heofizyky im. S.I. Subbotina NAN Ukrainy) [Seismic hazard assessment and protection against earthquakes (Practical applications of developments of Subbotin Institute of Geophysics of NAS of Ukraine)]. Visnyk Natsionalnoi akademii nauk Ukrainy. 2015, no. 2, pp. 44–57. Available at: http://nbuv.gov.ua/j-pdf/vnanu_2015_2_10.pdf.

6. Kendzera O., Vrakhuvannia amplitudno-chastotnykh kharakterystyk gruntovoi tovshchi pry seismichnomu mikroraionuvanni budivelnoho maidanchyka v m. Odesi [Considering of amplitude-frequency characteristics of soil thicker under seismic microzoning of building site in Odesa]. Visnyk Kyivskoho natsionalnoho universytetu imeni Tarasa Shevchenka. Seriia Heolohiia. 2010, no. 2(49), pp. 10–13.

7. Kuplovskyi B .Ye., Semenova Yu. Modeliuvannia khvylovoho polia dlia skladnykh seismichnykh rozriziv [Design of wave field for complicated arranged seismic cuts]. Visnyk Lvivskoho universytetu. Seriia fizychna. 2010, no. 45, pp. 141–150.

8. Sedov L. I., Mehanika sploshnoj sredy. 2 t [Continuum mechanics]. Moscow, 1984, Nauka, 560 p.

9. Starodub Yu. P., Brych T. B. Kombinovanyy matrychno-skinchenoelementnyy metod dlya vyvchennya poshyrennya khvyl'ovykh poliv u neodnoridnykh seredovyshchakh [The combined matrix – finite element method to study the propagation of wave fields in heterogeneous media structure]. Materialy naukovo-tekhnichnoyi konferentsiyi profesors'ko-vykladats'koho skladu, naukovykh pratsivnykiv i aspirantiv Ukrayins'koyi Akademiyi Drukarstva. 1995, P. 132.

10. Starostenko V. I., Kendzera O. V., Omelchenko V. D., Verbytskyi S. T., Verbytskyi Yu. T., Amashukeli T. A., Lisovyi Yu. V., Rozhok N. I. Seismolohichni doslidzhennia dlia Chornobylskoi AES [Seismological Investigation for Chernobyl NPP]. Natsionalna akademiia nauk Ukrainy — Chornobyliu: Zbirnyk naukovykh prats. NAN Ukrainy. Natsionalna biblioteka Ukrainy im. V. I. Vernadskoho; Redkol.:O. S. Onyshchenko (hol.) ta in. Kyiv, 2006. Available at: http://www.nbuv.gov.ua/books/2006/chernobyl/svi.pdf.

11. Timoshenko S. P., Gud'er Dzh. Teorija uprugosti [Theory of elasticity]. Moscow, 1975, Nauka, 576 p.

12. Bathe K.-J., Finite element procedures in engineering analysis. New Jersey, 1982, Prentice-Hall, Inc., Englewood Cliffs, 738 p.

13. David V. Hutton, Fundamentals of Finite Element Analysis. New York, 2004, McGraw-Hill, 495 p.

14. Singiresu S. Rao, The Finite Element Method in Engineering. Fourth edition. Miami, 2004, Elsevier Science & Technology Books, 664 p.

15. Zienkiewicz O. C., Taylor R. L. The Finite Element Method for solid and structural mechanics. Six edition. V. 1–3. Oxford, 2005, Elsevier Butterworth-Heinemann. 632 p.

16. Zhangxin Chen, Finite Element Methods and Their Applications. Berlin, 2005, Springer, 411 p.