- Open Access
Numerical simulation of crustal deformation using a three-dimensional viscoelastic crustal structure model for the Japanese islands under east-west compression
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2013
Received: 26 February 2013
Accepted: 6 May 2013
Published: 9 October 2013
The three-dimensional viscoelastic crustal structure beneath Japanese islands was modeled to simulate their crustal deformation by using a finite-element method and applying boundary conditions of the east-west horizontal compression. The result shows that there are relatively narrow zones of high strain rate at shallow depths, whose pattern is similar to that of the Niigata-Kobe tectonic zone revealed by GPS. High strain rates are not necessarily concentrated in regions where the elastic layer is relatively thin, but rather where its thickness changes abruptly.
As for the stress regime of Japanese islands, extensive geological evidence has shown that since the late Neogene (~3 Ma), Japanese islands have been subjected to compressional deformation in the east-west (EW) direction (Chinzei and Machida, 2001). Moreover, geodetic data for the past 100 years and GPS data for the past two decades show that EW compression has been going on in Japanese islands (Sagiya et al., 2000). The data on the stress orientation from focal mechanisms (Heidbach et al., 2010) indicate that Japanese islands are presently located in an EW compressional stress field.
On the basis of the background described above, we first modeled the 3D viscoelastic crustal structure (rheology structure) of Japanese islands and then conducted a 3D finite-element-method (FEM) simulation under boundary conditions of steady-state EW compression assuming time scales of a few decades to a few thousand years.
2.1 Viscoelastic crustal structure model
log A (MPa−n/s)
2.2 Simplification of the model
In the strength structure model thus obtained, there are parts where the strength is markedly low, such as directly below volcanic fronts, even though these parts are shallower than Conrad discontinuity. This feature was also indicated by Shimamoto (1992), who speculated the rheology structure of northeastern Japan on the basis of rock experiments. The viscoelastic crustal model in this study quantifies this idea. Meanwhile, the effective viscosity coefficient of the lower crust in our model takes values roughly on the order of 1020−1021 Pa s.
The distribution of the elastic constants is as described in Section 2.1 and the rigidity μ averages 34 and 67 GPa at 10 and 60 km depth, respectively. The corresponding relaxation time τrelax = η/μ is 930 and 470 years, respectively.
2.3 FEM mesh
Direction of the x-axis
Physical size (L x × L y ×L z [km])
Number of elements
Each element in the target zone
280 × 290 × 46
3.14 × 2.15 × 2.00
616 × 638 × 132
300 × 500 × 46
3.70 × 3.70 × 2.00
660 × 1100 × 264
150 × 250 × 60
1.85 × 1.85 × 1.50
330 × 550 × 132
300 × 250 × 46
3.70 × 1.85 × 2.00
660 × 550 × 132
300 × 250 × 46
3.70 × 1.85 × 2.00
660 × 550 × 132
250 × 150 × 46
3.09 × 1.11 × 2.00
550 × 330 × 132
The 3D distribution of the material properties was given only inside the target zones. The material properties outside the target zones were extrapolated so that those on the side surfaces of the target zones continue without change. Thus, the whole calculation zone consists of an upper elastic layer and a viscoelastic layer beneath it.
2.4 Boundary conditions and calculations
The response of each target zone to uniform compression in the x-axis direction was evaluated using the FEM code PyLith (Williams et al., 2005; Williams, 2006; Aagaard et al., 2007, 2008a, b, 2013). For each mesh, we considered the ground surface to be a free surface and the displacement in the axial direction to be zero at the boundary surfaces of the whole calculation zone other than the x-axis direction (Fig. 4).
Practically, the limit t → ∞ can be regarded as the time after complete relaxation. Giving the compressional unit displacement to the EW sides of the whole calculation zone by a step function and running the model for 100,000 years (>100τrelax), we regarded the calculated displacements factored by V as the steady-state velocity response of the crustal model to the steady-state EW compression. Similarly, we regarded the calculation results of the strain (stress) as the steady-state strain (stress) rate.
Quantitatively, the observed average strain rate in NKTZ according to GPS is 50–75 nanostrain/y, and near central Japan, the peak value is 150 nanostrain/y. In the regions outside NKTZ where the strain rate is low, the value is 25–50 nanostrain/y and there are areas where it is less (Sagiya et al., 2000). On the other hand, our simulation results are scaled to the mean strain rate of EW compression given a priori by the boundary condition. If the applied mean strain rate is 50 nanostrain/y, the strain rates in the NTKZ are 50–80 nanostrain/y, which matches well with the GPS data; There is also a peak exceeding 80 nanostrain/y at almost the same point as the peak in the GPS data; In the part with a low strain rate outside NKTZ, the strain rate is 30–50 nanostrain/y.
In the GPS data of Sagiya et al. (2000), there are zones with high strain rate outside NKTZ on the forearc side, particularly in Shikoku, and the southern coastal areas of Kanto and Hokkaido. However, the strain rate in the corresponding zones in Fig. 5 is not that high. This is likely because, while the strain on the forearc side in the GPS data is considered to largely involve elastic strain that cyclically accumulates during interseismic periods of about 100 years because of the subducting oceanic plates, these effects are not considered in steady-state simulation.
4. Concluding Discussion and Future Problems
4.1 Origin of NKTZ
To the best of our knowledge, this is the first study to indicate the possibility of a shift in the position with high accumulation rate of deep stress and strain relative to the surface (NKTZ). This has not been previously pointed out probably because there has not been an attempt to construct a realistic 3D model of the viscoelastic crustal structure because of the limited information available on the deep crust. The present results show the importance of establishing a method for constructing a realistic model for the viscoelastic crustal structure, which is also three-dimensionally nonuniform. In this paper, we make notice of this important issue, even though this is a preliminary crustal model.
Incidentally, when drawing Figs. 5 and 6, we assumed time scales of a few decades to a few thousand years. When one assumes a time scale much longer than the recurrence times of intraplate earthquakes (e.g., longer than 105 years), plasticity should be incorporated to the crustal model, as done by Shibazaki et al. (2007), (2008). Consequently, the stress distribution within the elastic layer will be significantly different from that in Fig. 6 if plasticity is taken into account: The distribution pattern in Fig. 6 is expected to resemble that of the plastic strain rate.
4.2 On the simplification of the crustal model
In this study, we used a simple crustal model with linear viscous rheology mainly because of the applicability of Matsu’ura and Sato (1989)’s method for simulating the generation of earthquakes as well crustal deformation. The Matsu’ura and Sato (1989)’s method has the following advantages. (i) In their method, the crustal deformation or stress accumulation is divided into a steady-state part and a perturbation part that correspond to steady-state plate motions and earthquake events, respectively. This separation is useful for assessing the system behavior. In the present study, we used the steady-state part only. (ii) The steady-state part is represented by a complete relaxation solution (Section 2.4); therefore, the response in the elastic part does not depend on the viscosity coefficient. This feature can largely solve the problem of ambiguity in the viscosity distribution deep in the crust. (iii) In this respect, a single viscosity coefficient value is adequate for the crustal model, as done in this study. As a result, we can easily adjust the time increments and the end time of the calculations to obtain a steady-state solution, and thus can reduce the computation time.
Of course, we have to separately evaluate the effects of using linear instead of nonlinear rheology in the calculations (e.g., stress/strain localization). However, on the other hand, some simplification of the crustal model is necessary to decrease the calculation time and carry out the items listed in the following section. When focusing on forecasting and considering the ambiguities in the distribution of the various parameters deep in the crust, we believe that the simplification of the crustal model in this study is presently an adequate solution.
4.3 Future problems
It is necessary to perform considerable FEM calculations to examine the effects of variations in the parameters of the constitutive law and of mineral distributions of the crust on the simulation results. The same holds for the parameters related to the simplification of the viscoelastic crustal structure model, e.g., a critical value of the viscosity coefficient to divide the crustal model into an elastic part and a viscoelastic part.
There are regions in Japanese islands that should be modeled with a boundary condition other than EW compression, e.g., the collision zone around the Izu Peninsula or the rift zone in central Kyushu. These areas are excluded from the target zone in this study.
The model needs to incorporate a factor to take into account the elastic strain that cyclically accumulates during interseismic periods of the subduction zone earthquakes occurring along the Japan Trench and the Nankai Trough.
The model also needs to incorporate several factors to take into account the afterslip on a fault plane and the transient viscous relaxation in the crust after large inland earthquakes, as well as the steady slip in the deep part. To achieve this, we need to model the deep extension of the active faults that lie within the inland areas of Japanese islands.
Data on the Conrad and Moho discontinuity depths were provided by Dr. Akio Katsumata. Constructive comments by anonymous reviewers significantly improved the manuscript.
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