Calculation of wave fields in a layered half-space with absorption based on the Thomson-Haskell method

: 40-49
Received: November 08, 2018
Revised: December 24, 2018
Accepted: December 26, 2018

R. Pak, O. Lanets, "Calculation of wave fields in a layered half-space with absorption based on the Thomson-Haskell method", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 4, no. 2, pp. 40-49, 2018.

Hetman Petro Sahaidachnyi National Army Academy
Lviv Polytechnic National University

This article is devoted to the development of calculation method of seismic waves on the free surface of a horizontally-layered half-space, which are perturbed by local sources. Previous obtained relations for scalar potentials of direct waves P, SV and SH from the simple force in a homogeneous environment are used for this purpose. It let us derive formulas for a complete wave field in the horizontally-layered isotropic elastic half-space, which is perturbed by the point source in the form of the simple time-depend force by using modified Thomson-Haskell’s matrix method. Exact expressions for three-dimensional displacement vector on the free surface are developed. Obtained results are generalized on the case of absorbing environments.

The algorithm is built and the computer program for calculation of three-component synthetic seismograms in the horizontally-layered isotropic environment with absorption is written on the base of developed method of direct problem solving.

In order to verify the efficiency and stability of the algorithm, full synthetic seismograms were calculated  on the test examples.

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