Modeling of wave field, which has been excited of deep or superficial source in horizontally layered half-space
Received: March 04, 2017
Hetman Petro Sahaidachny National Army Academy

Purpose. The aim is to conduct mathematical modeling of disturbances and seismic wave field propagation in horizontally layered isotropic elastic half-space; summarizing the results obtained in the case of absorbing media; numerical implementation of the method of calculation of seismic waves in horizontally layered medium with absorption, perturbed point source in a simple force that depends on time; build sustainable programs and algorithms for numerical calculations for synthetic seismograms; and conducting numerical experiments for verification of results. Methodology. The method comprises administering primary wave fields, perturbed idle power on or within horizontally layered isotropic elastic half-space with absorption. It is based on the use of integrals Bessellya-Mellin, matrix Thomson-Haskell method and its modifications. Results. The effective and sustainable method of calculating synthetic seismograms for stratified horizontally layered isotropic medium with absorption was carried out. The method takes into account the availability of the free surface, the presence of a point source in a simple force placed on or within half-space interference phenomena associated with tonkosharuvatistyu. To increase the stability calculation of the wave field  the transition was made from the characteristic matrix of fourth order matrix to sixth order. The modeling of the phenomenon of resonance in horizontal layered half-space was caused by the presence of low speeds in the upper layer. Originality. After entering primary wave field perturbations idle power on or within the horizontally-layered half-space, the developed numerical and analytical approach to modeling of waves in horizontally layered isotropic elastic media was imperfect. Algorithms and software were used for the calculation of synthetic seismograms at the free surface of environments. Practical significance. The practical significance of the developed method is the ability to analytically and numerically explore the wave processes occurring in layered media. The calculation of synthetic seismograms and allocating them to different types of waves allow analysis and accurate interpretation of the wave pattern that is recorded during seismic observations

1. Molotkov L. A. Matrichnyy metod v teorii rasprostraneniya voln v sloistykh, uprugikh i zhidkikh sredakh [Matrix method in the theory of wave propagation in layered, elastic and liquid media]. Leningrad, Nauka, 1984, 201 p.
2. Roganov Yu. V., Pak R. M. Predstavlenie potentsiala ot tochechnykh istochnikov dlya odnorodnoy izotropnoy sredy v vide integralov Besselya-Mellina [Representation of potentials of point sources for the homogeneous isotropic medium as Bessel-Mellin integrals]. Geofizicheskij zhurnal [Geophysical Journal], 2013, vol. 35, no. 2, pp. 163–167.
3. Abo-Zena A. Dispersion function computations for unlimited frequency values. Geophysical Journal of the Royal Astronomical Society, 1979, vol. 58, pp. 91–105.
4. Aki K., Richards P. Quantitative Seismology, Second Ed. Sausalito, University Science Books, 2002, 700 p.
5. Baumbach M., Grosset H., Schmidt H. G., Paulat A., Rietbrock A., Ramakrishna Rao C. V., Solomon Raju P., Starkar D., Indra Mohan. Study of the foreshocks and aftershocks of the intraplate Latur earthquake of September 30, 1993, India. Latur Earthquake, H. K. Gupta (Editor). Memoir of the Geological Society of India 35, 1994, pp. 33–63.
6. Bouchon M. A. Review of the discrete wavenumber method. Pure and Applied Geophysics, 2003, vol. 160, pp. 445–465.
7. Chapman C. H. Yet another elastic plane-wave, layer-matrix algorithm. Geophysical Journal International, 2003, vol. 154, pp. 212–223.
8. Cormier V. F. Theory and observations - forward modeling/synthetic body wave seismograms. Treatise on Geophysics, 2007, vol. 1, pp. 157–189.
9. Dunkin I. W. Computation of modal solution in layered elastic media at high frequencies. Bulletin of the Seismological Society of America, 1965, vol. 55, pp. 335–358.
10. Kennett B. L. N. Seismic Wave Propagation in Stratified Media. Cambridge University Press, 1983, 342 p.
11. Kennett B. L. N. The seismic wavefield. Introduction and theoretical development. Vol. 1. Cambrige University Press, 2001, 370 p.
12. Müller G. The reflectivity method: a tutorial. Journal Geophysical, 1985, vol. 58, pp. 153–174.
13. Pei D. H., Louie J. N., Pullammanappallil S. K. Improvements on computation of phase velocity of Rayleigh wave based on the generalized R/T coefficient method. Bulletin of the Seismological Society of America, 2008, vol. 98, pp. 280–287.