10:45 AM - 11:00 AM
[SSS09-04] Energy partitioning among strain components in diffuse wave fields (4)
Keywords:Energy partitioning, strain, diffuse wave field, seismic interferometry
The equipartition refers to an equilibrated state where energy is equally distributed in all modes. This state is expected for diffuse wave fields, which are wave fields that have undergone multiple conversion scatterings. For the equipartition state, energy partitioning among different displacement components is known to be theoretically calculated (e.g., Weaver, 1985; Sanchez-Sesma et al., 2008; Margerin, 2009). According to recent developments in distributed acoustic sensing (DAS) techniques, we can measure strain time series at very dense spatial points. However, only a single component of strain tensors, axial strains along optical fibers, can be recorded. Therefore, we need to know how seismic energy is partitioned into this single component. We are especially curious about the (late) coda of DAS records in which multiple conversion scattering occurs. To address these questions, we have so far studied energy partitioning among different strain components for various media: 2D infinite homogeneous media by Nakahara (2023JpGU), 3D infinite homogeneous media by Nakahara and Emoto (2023SSH), and the free surface of 3D homogeneous half-space by Nakahara (2024SSJ). In this study, we extend Nakahara (2024SSJ) to arbitrary depths in 3D homogenous half spaces and consider how the energy partitioning changes with depth.
Nakahara (2024SSJ) formulated the energy partitioning into strain components in 3D homogeneous half-spaces by extending Weaver (1985), which formulated the energy partitioning into displacement components at the free surface of homogeneous half-spaces. However, Nakahara (2024SSJ) focused on the energy partitioning at the free surface. In the present study, we focus on the depth dependence of the energy partitioning. We investigate how the energy is partitioned into different strain components and how the partitioning changes with depth. The following results are obtained: Normal strains of exx and eyy, which can be measured by surface DAS, are mainly composed of SH waves and Rayleigh waves at very shallow depths. However, as the depth increases, Rayleigh-wave contribution quickly decays, and SH-wave contribution remains. Shear strain components of exz and eyz are zero at the free surface ( z=0 ) due to boundary conditions. However, their amplitudes rapidly grow with depth with some fluctuations and are stabilized at depths of more than twice the S-wavelength. SH and SV waves contribute to these shear components. Another shear component, exy, is dominated by SH waves at any depth. Regarding ezz component, which can be measured with borehole DAS, Rayleigh waves are far more dominant at the free surface. However, the amplitude of Rayleigh waves quickly decays within depths of one S-wavelength, and the SV wave contribution becomes dominant.
Nakahara and Emoto (2023SSH) predicted that the energy ratio of exy/exx (the ratio of the shear strain to the normal strain) is 0.713 for 3D infinite homogeneous media. Based on the present formulation, our results at depths far from the free surface (more than three times shear-wave length away) approach the expected value. This agreement corroborates our present calculations.
This study clarifies how the energy partitioning into different strain components in diffuse wave fields changes with depth in 3D homogeneous half-spaces. This leads to a better understanding of DAS record codas, which will help us interpret borehole DAS data especially.
Nakahara (2024SSJ) formulated the energy partitioning into strain components in 3D homogeneous half-spaces by extending Weaver (1985), which formulated the energy partitioning into displacement components at the free surface of homogeneous half-spaces. However, Nakahara (2024SSJ) focused on the energy partitioning at the free surface. In the present study, we focus on the depth dependence of the energy partitioning. We investigate how the energy is partitioned into different strain components and how the partitioning changes with depth. The following results are obtained: Normal strains of exx and eyy, which can be measured by surface DAS, are mainly composed of SH waves and Rayleigh waves at very shallow depths. However, as the depth increases, Rayleigh-wave contribution quickly decays, and SH-wave contribution remains. Shear strain components of exz and eyz are zero at the free surface ( z=0 ) due to boundary conditions. However, their amplitudes rapidly grow with depth with some fluctuations and are stabilized at depths of more than twice the S-wavelength. SH and SV waves contribute to these shear components. Another shear component, exy, is dominated by SH waves at any depth. Regarding ezz component, which can be measured with borehole DAS, Rayleigh waves are far more dominant at the free surface. However, the amplitude of Rayleigh waves quickly decays within depths of one S-wavelength, and the SV wave contribution becomes dominant.
Nakahara and Emoto (2023SSH) predicted that the energy ratio of exy/exx (the ratio of the shear strain to the normal strain) is 0.713 for 3D infinite homogeneous media. Based on the present formulation, our results at depths far from the free surface (more than three times shear-wave length away) approach the expected value. This agreement corroborates our present calculations.
This study clarifies how the energy partitioning into different strain components in diffuse wave fields changes with depth in 3D homogeneous half-spaces. This leads to a better understanding of DAS record codas, which will help us interpret borehole DAS data especially.