A new closed analytical solution for the elastodynamic half-space Green’s function

Abstract

Abstract The elastodynamic half-space Green’s function has been the subject of research for more than a century since the Lamb’s classical solution. Here, we revisit the problem and present a new closed analytical solution, in frequency domain, based upon the Principle of Equipartition (EQP) of Energy. This principle asserts that the imaginary parts of the Green’s tensor components equal the average cross-correlations of the fields generated by the uniform incidence of P and S body waves and by Rayleigh surface waves with amplitudes weighted by partition factors. The real part of the Green’s function is the Hilbert transform of the imaginary part. We validate our results by comparing synthetic seismograms of well-known solutions for surface and buried forces and discuss the implications of this new solution. Constructing synthetic diffuse fields is a first step for identifying them in nature. Graphical Abstract

Keywords

• Elastic half-space
• Elastodynamic Green’s function
• Equipartition
• Cross-correlations
• Synthetic diffuse fields