Seismic wave fields in a spherically symmetric Earth. Analytical solution

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Abstract

An analytical solution is obtained for seismic wave fields in a spherically symmetric Earth. Asymptotics is used for stable calculation of wave fields. It is shown that the classical asymptotics in the case of a ball of large (in wavelengths) dimensions gives an error in the solution. The original asymptotics is used for efficient calculation of a solution without errors with high detail. A program has been created that makes it possible to carry out calculations for high-frequency (1 hertz and higher) teleseismic wave fields in a discrete (layered) sphere of planetary dimensions. Calculations can be carried out on personal computers with OpenMP parallelization. In the works of V. Yu. Burmina (2010, 2019) proposed a spherically symmetric model of the Earth. It is characterized by the fact that in it the outer core has a viscosity and, therefore, an effective shear modulus other than zero. For this model of the Earth, a highly detailed calculation was carried out with a carrier frequency of 1 hertz. As a result of the analytical calculation, it was found that high-frequency oscillations of small amplitude, the so-called “precursors,” appear ahead of the PKP waves. An analytical calculation showed that the theoretical seismograms for this model of the Earth are in many respects similar to the experimental data. This confirms the correctness of the ideas underlying its construction.

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About the authors

А. G. Fatyanov

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences

Author for correspondence.
Email: fat@nmsf.sscc.ru
Russian Federation, Novosibirsk

V. Yu. Burmin

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: burmin@ifz.ru
Russian Federation, Moscow

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2. Fig. 1. Component Ur of the seismic field with a carrier frequency of 1 Hz for a homogeneous sphere of the Earth's size. The calculation algorithm uses a new (a) and classical (b) asymptotics. Vertically – time in seconds (increases downwards), horizontally – distance in degrees. The letters P and PP denote direct and single longitudinal waves. Noise – interference when using classical asymptotics.

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3. Fig. 2. Component Ur of the seismic field. The vertical axis shows time in seconds (increases upwards), the horizontal axis shows distance in degrees. The emergence of precursors for the Earth model from [7, 8].

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4. Fig. 3. Fragment of a montage of seismograms obtained at seismic stations of the global network.

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