5:15 PM - 7:15 PM
[SGD03-P18] Gravitational effect on temporal evolutions of viscoelastic deformation
Keywords:Postseismic deformation, Viscoelastic deformation, Temporal evolution, Crustal deformation, Gravity change
Viscoelastic deformation is one of the major mechanisms of postseismic deformation. Its time evolution is often assumed to follow a simple time function such as an exponential function. In fact, if a medium is homogeneous, Maxwell viscoelastic half-space without gravitation, the postseismic displacements and gravity changes on the surface follow an exponential time function with a common time constant. This can be confirmed by applying the correspondence principle to elastic solutions (Okada, 1985; Okubo, 1991). A more realistic case would be a medium with gravity and an elastic layer. Fukahata and Matsu'ura (2018) dealt with viscoelastic deformation in this situation and reported that time constants of displacements depend on directions of the displacements and epicentral distances, and that the progression of the displacements is sometimes reversed. However, physical interpretations of these complex temporal evolutions are not clear. Therefore, this study investigated gravitational effects on viscoelastic deformation as a cause of the above complex temporal evolutions. In detail, viscoelastic deformations in a simple situation were numerically calculated, their temporal evolutions were characterized, and the characteristics were physically interpreted.
For a clear interpretation of calculation results, this study assumed a medium with a uniform Maxwell viscoelasticity. A numerical method for the spherical medium with gravitation (Zhou, 2022; Zhou and Wang, 2023) was used to calculate viscoelastic deformations. To avoid missing deformations with long time constants, we dealt with a long time period, up to approximately 16000 years after an earthquake. The dip angle of a point source was set to 10 degrees to simulate earthquakes in subduction zones. The source depth and epicentral distances were changed to discuss spatial scale dependencies. A constant CG was introduced to control the strength of the gravitation. For the situation without the gravitation (NoG), CG was set to 10-10 as a sufficiently small value. We calculated 3 physical quantities, which are horizontal displacements, vertical displacements, and gravity changes. Here, the horizontal displacements are values of a spheroidal component coupled with gravitation, and the gravity changes are values at fixed points in space.
In the NoG case, the deformations showed a simple temporal evolution with a common time constant as expected from the analytical results. The time constant was in the order of the Maxwell relaxation time. On the other hand, in the case with the gravitation, additional deformations occurred in the later part, and the temporal evolutions became complex. In this paper, these additional deformations are referred to as "Gravitational Relaxation (GR)". Estimation of the gravitational effects using the equivalence theorem (Fukahata and Matsu'ura, 2006) suggests that a main cause of the GR is advection of the initial stress. GR's time constants depended on their spatial scales. In particular, the GR's time constants were shorter for larger spatial scales. This dependency may reflect the spatial scale dependency of the strength of gravitational effect (Segall, 2010). Moreover, when the epicentral distance was larger relative to the source depth, the progression of GR was reversed. The reversal can be understood by the spatial scale dependency and is caused by the shorter wavelength components. The characteristics of the temporal evolutions were different for each quantity. In particular, the GR of the gravity changes sometimes dominated earlier than others. The GR of the horizontal displacements had smaller amplitudes, and there were other later deformations.
Acknowledgments: The supercomputer of ACCMS, Kyoto university was used for calculation of viscoelastic deformations.
For a clear interpretation of calculation results, this study assumed a medium with a uniform Maxwell viscoelasticity. A numerical method for the spherical medium with gravitation (Zhou, 2022; Zhou and Wang, 2023) was used to calculate viscoelastic deformations. To avoid missing deformations with long time constants, we dealt with a long time period, up to approximately 16000 years after an earthquake. The dip angle of a point source was set to 10 degrees to simulate earthquakes in subduction zones. The source depth and epicentral distances were changed to discuss spatial scale dependencies. A constant CG was introduced to control the strength of the gravitation. For the situation without the gravitation (NoG), CG was set to 10-10 as a sufficiently small value. We calculated 3 physical quantities, which are horizontal displacements, vertical displacements, and gravity changes. Here, the horizontal displacements are values of a spheroidal component coupled with gravitation, and the gravity changes are values at fixed points in space.
In the NoG case, the deformations showed a simple temporal evolution with a common time constant as expected from the analytical results. The time constant was in the order of the Maxwell relaxation time. On the other hand, in the case with the gravitation, additional deformations occurred in the later part, and the temporal evolutions became complex. In this paper, these additional deformations are referred to as "Gravitational Relaxation (GR)". Estimation of the gravitational effects using the equivalence theorem (Fukahata and Matsu'ura, 2006) suggests that a main cause of the GR is advection of the initial stress. GR's time constants depended on their spatial scales. In particular, the GR's time constants were shorter for larger spatial scales. This dependency may reflect the spatial scale dependency of the strength of gravitational effect (Segall, 2010). Moreover, when the epicentral distance was larger relative to the source depth, the progression of GR was reversed. The reversal can be understood by the spatial scale dependency and is caused by the shorter wavelength components. The characteristics of the temporal evolutions were different for each quantity. In particular, the GR of the gravity changes sometimes dominated earlier than others. The GR of the horizontal displacements had smaller amplitudes, and there were other later deformations.
Acknowledgments: The supercomputer of ACCMS, Kyoto university was used for calculation of viscoelastic deformations.