Energy partitioning into the strain tensor components for diffuse elastic waves in three-dimensional homogeneous isotropic half-space

Thanks to recent advancements in distributed acoustic sensing (DAS) techniques, we can measure the time series of axial strains along an optical fiber at extremely dense spatial intervals. However, only a single component of a strain tensor is measured, and the partitioning of seismic energy into this component is unknown. In this study, we address this problem by formulating energy partitioning into different strain components for diffuse waves in a three-dimensional homogeneous isotropic half-space, building upon previous studies on energy partitioning into displacement components. We investigate how the contributions of both body and surface waves to the six independent components of a strain tensor change with depth. The results show that the horizontal normal strains, which surface DAS observation can measure, are primarily composed of shear horizontal-waves and Rayleigh waves at the free surface. The vertical normal strain, which borehole DAS observation can measure, is dominated by Rayleigh waves at the free surface. However, that contribution quickly decays within the depth of one shear wave-wavelength, and the shear vertical-wave contribution remains. This study serves as a reference for further extension to more realistic media, such as horizontally layered media, and opens a way to interpret the late coda of DAS strain seismograms quantitatively.