Energy partitions in 2D and 3D curved boundaries during the seismic wave propagation: Numerical results

Energy partitions during the propagation of seismic waves is a topic of current interest in the field of Seismology and Geophysics. Energy partitions have recently been derived through concepts of diffuse fields, correlations of seismic noise and Green's functions. In this work, the use of Boundary Element Method is introduced to calculate energy partitions for various numerical models that allow to identify the behavior of seismic waves and their associated energy partitions in 2D and 3D curved boundaries. The results are consistent with previously published results and show that most of the energy, regardless of the material, is propagated by Shear waves, reaching in some cases up to 100% of the propagated energy. For an infinity 2D Poisson solid (ν = 0.25), the energy partitions have a distribution of 25% for P-waves and 75% for SV-waves, while for a solid with a ratio of ν = 0.5 the energy is totally propagated by SV-waves thus, P-waves are none existent. Additionally for a halfspace with ν = 0.25, the energy ratio, defined as the quotient of the energy calculated on the surface with respect to that corresponding to an infinite space, has a value of 2.0 for a horizontal free surface while for a curved one such ratio is 1.79. For an infinity 3D Poisson solid, P-, SV- and SH-waves have a distribution of energy partitions of 8.78%, 45.61%, and 45.61%, respectively. Moreover, the energy ratio for a horizontal 3D free surface is 2.39 while for a 3D curved free surface the ratio is 2.68.