1:45 PM - 2:00 PM
[STT38-01] Objective estimation of deformation structure in the crust based on inversion of moment density tensor
★Invited Papers
Keywords:GNSS velocity data , Moment density tensor, Bayesian inference, Niigata–Kobe Tectonic Zone
The Niigata-Kobe Tectonic Zone (NKTZ) found by GNSS observations is one of the locations with the highest strain rates in the Japan Islands. In Japan, high strain rates are basically observed along the Pacific coast, which are explained by the coupling on the upper surface of the subducting oceanic plates. On the other hand, high strain rates in the NKTZ cannot be explained by the interplate coupling and are considered to be caused by inelastic deformation such as brittle fracture and plastic flow in the crust (Sagiya & Meneses-Gutierrez, 2022). However, a common view on the processes of inelastic deformation in this region has not yet been established.
A crustal block modeling approach has often been used to understand high strain rates concentrated in the crust. This approach first divides the plate into several crustal blocks based on information on the distribution of active faults and seismic activity and then explains the strain concentration by the mechanical interactions at the boundaries between the crustal blocks. In the NKTZ, however, the division of crustal blocks varies widely among studies, which means that the locations where inelastic deformation occurs cannot be objectively determined.
In this study, to flexibly model the spatial distribution of inelastic deformation, we represent inelastic deformation as a generalized mechanical expression, i.e., moment density tensor. We then developed an inversion method to estimate the 3-D distribution of the moment density tensor from GNSS displacement rate data. The inversion method of moment density tensor has been proposed by Noda & Matsu'ura (2010), but this study makes the following two improvements: The first is that the ratio of the six components of the moment density tensor is fixed, and only the magnitude of the moment density is estimated as unknown parameters. Based on the constitutive law of plastic flow, the ratio of components of the moment density tensor is assumed to be the same as that of the background stress tensor obtained from the focal mechanisms of small and moderate-size earthquakes occurring in the study region. This reduces the number of degrees of freedom in the model to one-sixth of the original. The second is to formulate the inverse problem as a Bayesian model. The probability density function (pdf) representing the relation of the moment density distribution to the displacement rate data is combined with the prior pdf of the model using Bayes' theorem, and the posterior pdf is obtained by sampling using the Hamiltonian Monte Carlo (HMC) method. The prior pdf for the moment density is assumed to be the half-normal distribution with zero peak and the scale parameter is estimated as an unknown parameter. Negative values are not allowed in the prior pdf because inelastic deformation in the opposite direction to the background stress is physically unreasonable. The Bayesian model allows us to evaluate the estimation error of the inversion result. In addition, the HMC method made it easy to introduce prior information based on the tectonophysics.
We applied this method to horizontal displacement rate data from GNSS observations from March 2005 to February 2011 to estimate the moment density distribution per year. The moment density distributions estimated in the shallow part (0-10 km depth) and deep part (10-20 km depth) of the crust show different spatial characteristics. The deep part shows a single band-like distribution along the NKTZ, whereas the shallow part shows a complex distribution along the active fault traces at the surface. This result can be interpreted as that the lower crust is simply separated into two basement blocks, whereas the upper crust is dragged by the basement blocks to form a complex deformation structure. By using the moment density tensor, a generalized expression of inelastic deformation, this study succeeded in objectively estimating the depth-dependent deformation structure in the NKTZ.
A crustal block modeling approach has often been used to understand high strain rates concentrated in the crust. This approach first divides the plate into several crustal blocks based on information on the distribution of active faults and seismic activity and then explains the strain concentration by the mechanical interactions at the boundaries between the crustal blocks. In the NKTZ, however, the division of crustal blocks varies widely among studies, which means that the locations where inelastic deformation occurs cannot be objectively determined.
In this study, to flexibly model the spatial distribution of inelastic deformation, we represent inelastic deformation as a generalized mechanical expression, i.e., moment density tensor. We then developed an inversion method to estimate the 3-D distribution of the moment density tensor from GNSS displacement rate data. The inversion method of moment density tensor has been proposed by Noda & Matsu'ura (2010), but this study makes the following two improvements: The first is that the ratio of the six components of the moment density tensor is fixed, and only the magnitude of the moment density is estimated as unknown parameters. Based on the constitutive law of plastic flow, the ratio of components of the moment density tensor is assumed to be the same as that of the background stress tensor obtained from the focal mechanisms of small and moderate-size earthquakes occurring in the study region. This reduces the number of degrees of freedom in the model to one-sixth of the original. The second is to formulate the inverse problem as a Bayesian model. The probability density function (pdf) representing the relation of the moment density distribution to the displacement rate data is combined with the prior pdf of the model using Bayes' theorem, and the posterior pdf is obtained by sampling using the Hamiltonian Monte Carlo (HMC) method. The prior pdf for the moment density is assumed to be the half-normal distribution with zero peak and the scale parameter is estimated as an unknown parameter. Negative values are not allowed in the prior pdf because inelastic deformation in the opposite direction to the background stress is physically unreasonable. The Bayesian model allows us to evaluate the estimation error of the inversion result. In addition, the HMC method made it easy to introduce prior information based on the tectonophysics.
We applied this method to horizontal displacement rate data from GNSS observations from March 2005 to February 2011 to estimate the moment density distribution per year. The moment density distributions estimated in the shallow part (0-10 km depth) and deep part (10-20 km depth) of the crust show different spatial characteristics. The deep part shows a single band-like distribution along the NKTZ, whereas the shallow part shows a complex distribution along the active fault traces at the surface. This result can be interpreted as that the lower crust is simply separated into two basement blocks, whereas the upper crust is dragged by the basement blocks to form a complex deformation structure. By using the moment density tensor, a generalized expression of inelastic deformation, this study succeeded in objectively estimating the depth-dependent deformation structure in the NKTZ.