Kinematic source models for long-period ground motion simulations of megathrust earthquakes: validation against ground motion data for the 2003 Tokachi-oki earthquake
- Asako Iwaki^{1}Email author,
- Takahiro Maeda^{1},
- Nobuyuki Morikawa^{1},
- Shin Aoi^{1} and
- Hiroyuki Fujiwara^{1}
Received: 17 February 2016
Accepted: 16 May 2016
Published: 1 June 2016
Abstract
In this study, a method for simulating the ground motion of megathrust earthquakes at periods of approximately 2 s and longer was validated by using the characterized source model combined with multi-scale spatial heterogeneity. Source models for the M _{W} 8.3, 2003 Tokachi-oki earthquake were constructed, and ground motion simulations were conducted to test their performance. First, a characterized source model was generated based on a source model obtained from waveform inversion analysis. Then, multi-scale heterogeneity was added to the spatial distribution of several source parameters to yield a heterogeneous source model. An investigation of the Fourier spectra and 5 % damped velocity response spectra of the simulated and observed ground motions demonstrated that adding multi-scale heterogeneity to the spatial distributions of the slip, rupture velocity, and rake angle of the characterized source model is an effective method for constructing a source model that explains the ground motion at periods of 2–20 s. It was also revealed how the complexity of the parameters affects the resulting ground motion. The complexity of the rupture velocity had the largest influence among the three parameters.
Keywords
Introduction
Megathrust (\(M_{\rm W} > ~8\)) earthquakes have occurred and will potentially occur in the vicinity of the islands of Japan, including along the Kurile Trench, the Japan Trench, the Sagami Trough, the Nankai Trough, and the Ryukyu Trench. Past megathrust earthquakes have repeatedly brought strong ground motion to land areas; thus, seismic hazard evaluation for future megathrust earthquakes is an urgent issue today. In particular, long-period components of ground motion are expected to be significantly amplified in distant sedimentary basins during future megathrust earthquakes, as observed in recent earthquakes such as the 1985 Michoacan earthquake (e.g., Anderson et al. 1986) and the 2003 Tokachi-oki earthquake (e.g., Koketsu et al. 2005). During the 2011 M9 Tohoku earthquake, the velocity response spectra observed in the Osaka sedimentary basin, approximately 600 km from the source area, exceeded 50 cm/s at periods of 6–7 s (Sato et al. 2012), which caused damages to elevators and non-structural elements of high-rise buildings.
In general, long-period components of ground motion are computed using a deterministic approach with a theoretical representation of the rupture and wave propagation processes; therefore, it is important to construct an appropriate source model and a three-dimensional (3D) velocity structure model. 3D long-period ground motion simulations for future megathrust earthquakes have been presented by numerous works (e.g., Olsen et al. 2008; Pulido et al. 2015). The authors recently studied long-period ground motions for future events at the Nankai and the Sagami Troughs, with the goal of performing seismic hazard evaluation considering the uncertainties of the source parameters (Maeda et al. 2013; Iwaki et al. 2013). These simulations used the 3D Japan integrated velocity structure model (JIVSM; Koketsu et al. 2009) and kinematic source models based on the concept of characterized source models (Irikura and Miyake 2001, 2011). The lower limit of the period range of these simulations was 3 s, as determined by the resolution of both the velocity structure model and the source model.
The characterized source model, which consists of multiple asperities and a background area (e.g., Somerville et al. 1999; Miyake et al. 2003), performs well for both short- and long-period ground motions, particularly in reproducing the rupture directivity pulses, as demonstrated in studies on the 1995 Kobe earthquake (e.g., Kamae and Irikura 1998). It is used in the broadband ground motion prediction scheme (called the “recipe”) by the Earthquake Research Committee (ERC) of the Headquarters for Earthquake Research Promotion of Japan (ERC 2009; Fujiwara et al. 2009). In the recipe, the long- and short-period components of the ground motion are computed using the 3D finite-difference method (FDM) and the stochastic Green’s function method, respectively. The performance of the recipe has been validated mainly for crustal earthquakes with moment magnitudes 6–7 (e.g., Morikawa et al. 2011; Iwaki et al. 2016).
However, the recipe may not be valid for megathrust earthquakes with magnitudes 8 and larger because the characterized source model lacks heterogeneity smaller than asperities, which may not be negligible in simulating ground motion for engineering purposes. Because the characterized source model generates ground motion at periods longer than the corner period T _{C} of the asperities, ground motion at periods shorter than T _{C} may not be sufficiently evaluated when combined with a deterministic computation method for long-period ground motion simulations, as noted by Sato et al. (2006). T _{C} is approximately 10 s for M _{W} 8 earthquakes and 2–3 s for M _{W} 7 earthquakes. The deterministic computation method should be used in the period range at which the 3D velocity structure model is valid, which is usually 1–3 s and longer in Japan, and thus, the crossover period T _{cross} at which the deterministic and stochastic methods are matched is usually approximately 1–3 s. Because the source model lacks heterogeneity with corresponding periods shorter than T _{C}, ground motion tends to be underestimated in the period range between T _{C} and T _{cross} for M _{W} 8 earthquakes. Therefore, heterogeneities that are smaller than the asperities should be included in the characterized source model to account for the ground motion at periods shorter than T _{C} of the asperities.
To overcome this issue, Sekiguchi and Yoshimi (2006) proposed a source model with multi-scale heterogeneity, which was applied to the ground motion prediction of future megathrust earthquakes at the Nankai Trough (Sekiguchi et al. 2008). They considered multi-scale spatial heterogeneity to the spatial distributions of two source parameters, the slip and rupture velocity, on the fault. The resultant source model agrees with the omega-square model of the source spectra and the slip spectra model by Mai and Beroza (2002). Spatial heterogeneities in the slip and rupture velocity are theoretically necessary for the omega-square model as presented by Hisada (2001).
The aim of this study is to validate a method for generating ground motion for megathrust earthquakes in the period range of approximately 2 s and longer by using the characterized source model combined with multi-scale spatial heterogeneity. Source models are constructed for the 2003 M _{W} 8.3 Tokachi-oki earthquake, which occurred off the southeastern coast of Hokkaido, Japan, at the Kuril Trench. Long-period ground motion simulations are then conducted using a 3D FDM with the source model and a 3D velocity structure model, and their performance was tested by comparing the simulated ground motion with the observed records. The effects of heterogeneity of each source parameter on the predicted ground motion are revealed by comparing the heterogeneous models with the characterized models without heterogeneity. In addition, we refer to a slip-inversion model to examine which parameter’s heterogeneity is the most important for reproducing the complicated observed ground motion.
Source models
Model 0: Inversion model (reference model)
Model C: Characterized source model
Source parameters considered in the characterized source model
Outer source parameter | Inner source parameter | Others |
---|---|---|
Fault configuration^{#} | Total area of asperities \(S_{a}\)* | Slip velocity function |
Fault area \(S\) ^{#} | Asperities | Rupture velocity \(V_{R}\)* |
Seismic moment \(M_{0}\) ^{#} | Area \(S_{ai}\)* | Rake angle |
Average stress drop \(\Delta \sigma\) | Stress drop \({{\Updelta }}\sigma_{ai}\)* | |
Average slip \(D\) | Average slip \(D_{ai}\) | |
Background area | ||
Area \(S_{b}\) | ||
Stress drop \({\Updelta}\sigma_{b}\) | ||
Average slip \(D_{b}\) |
The fault configuration, the fault area S, and the seismic moment \(M_{0}\) of Model C are taken from Model 0. The average stress drop Δσ is set to 3.2 MPa, based on the circular crack model of Eshelby (1957), in which \(\Delta \sigma = \left( {7/16} \right) \cdot M_{0} /R^{3}\) where R is the radius of the circular fault. Although the Tokachi-oki earthquake is too large to assume a circular fault, this average stress drop was adopted because it is close to the value of 3.0 MPa proposed by Allman and Shearer (2009). The average slip \(D\) is given by \(D = M_{0} /\left( {\mu S} \right)\), where the rigidity \(\mu\) is set to \(6.48 \times 10^{10}\) N/m^{2}.
After preliminary analysis by trial and error, three rectangles that approximately cover the areas with large moment release in Model 0 are defined as the asperities A1, A2, and A3 (gray rectangles in Fig. 3), and the remaining area is defined as the background area (BA). The strong motion generation area (SMGA) models of Kamae and Kawabe (2004) and Morikawa et al. (2006) are also referred to determine the approximate locations of the asperities. The total area of the asperities \(S_{a}\) is set to 20 % of the fault area S. In the recipe, the average stress drop of the asperities is given by \(\Updelta \sigma_{a} = \left( {S/S_{a} } \right)\Updelta \sigma\) (Madariaga 1979), which is 16 MPa in this case. On the other hand, both Kamae and Kawabe (2004) and Morikawa et al. (2006) suggested relatively high stress drops (25–50 MPa) in the asperities. Therefore, using \(\Updelta \sigma_{a}\) as a baseline, several values of the stress drop are considered for each asperity using \(\Delta \sigma_{ai} = \alpha_{i} \times\Delta \sigma_{\text{a}}\), with \(\alpha_{i} = 1,1.5, 2, 2.5, 3\), where i = 1, 2, 3 correspond to the asperity number. The average slip within each asperity is given by \(D_{ai} = \left( {{{\gamma_{j} } \mathord{\left/ {\vphantom {{\gamma_{j} } {\sum\nolimits_{J} {\gamma_{j} } }}} \right. \kern-0pt} {\sum\nolimits_{J} {\gamma_{j} } }}} \right) \cdot \xi D\), where \(\gamma_{i} \equiv \sqrt {S_{ai} /S}\) and \(\xi = 2.2\) (Somerville et al. 1999).
Source parameters for Model C
Area \(S\) (km^{2}) | Seismic moment \(M_{0}\) (Nm) | Average slip \(D\) (m) | Average stress drop \({\Updelta}\sigma\) (MPa) | Rupture velocity \(V_{\text{R}}\) (m/s) | |
---|---|---|---|---|---|
21,038 | 3.98E + 21 | 2.92 | 3.18 | 3600 |
Asperities | Area \(S_{ai}\) (km^{2}) | Seismic moment \(M_{0}\) (Nm) | Average slip \(D_{ai} , D_{b}\) (m) | Average stress drop \({\Updelta}\sigma_{ai} , {\Updelta}\sigma_{b}\) (MPa) | \(\alpha_{i}\) |
---|---|---|---|---|---|
A1 | 1098 | 3.56E+20 | 5.01 | 16.0 | 1 |
A2 | 2561 | 1.27E+21 | 7.65 | 32.0 | 2 |
A3 | 549 | 1.26E+20 | 3.54 | 40.0 | 2.5 |
BA | 16,381 | 2.23E+21 | 2.04 | 1.48 |
Models H1–H3: Heterogeneous source models
To construct the heterogeneous source models (Models H1, H2, and H3), multi-scale heterogeneity was cumulatively added to the spatial distributions of the slip D, rupture velocity \(V_{\text{R}}\), and rake angle \(\lambda\), using Model C as the initial model. Seven scales of heterogeneity were considered using circular patches with different radii. At each scale (\(k = 1, 2, \ldots , 7\)), \(n_{k}\) circular patches with radii of \(r_{k}\) are distributed randomly on the fault. The radius of the largest patches (\(k = 1\)) is chosen such that their area was nearly equal to that of the smallest asperity A3, i.e., \(r_{1} \sim \sqrt {S_{a3} /\pi }\). The radius at the (\(k + 1)\)th scale is given by \(r_{k + 1} = r_{k} /a\) where the constant a is set to 1.5. The total area of the patches at each scale is constant and almost equal to the total area of the asperities.
Fluctuation of the parameters for the heterogeneous models
Slip (m) | Rupture velocity (m/s) | Rake angle | |
---|---|---|---|
Model H1 | \(\pm 0.5 D/\left( {a^{k - 1} } \right)\) | – | – |
Model H2 | \(\pm 400\) | – | |
Model H3 | \(\pm 45^\circ\) |
The same spatial distributions in the patches are used for the slip and rupture velocity. Therefore, the rupture velocity is assumed to increase when the slip increases. This is similar in principle to other source models for ground motion prediction (e.g., Frankel 2009; Graves and Pitarka 2010), in which a positive correlation between slip and rupture velocity is assumed. This assumption is consistent with several dynamic rupture models (e.g., Day 1982; Song and Somerville 2010), whereas Schmedes et al. (2010, 2013) reported that such correlation is unclear at least under certain conditions of dynamic rupture models. Therefore, it should be noted that it remains unclear whether this assumption is appropriate.
Models S1–S3: Simplified source models
Ground motion simulation
Layers of the velocity structure model by Aoi et al. (2008)
Layer | V _{P} (m/s) | V _{S} (m/s) | \(\rho\) (kg/m^{3}) | Q |
---|---|---|---|---|
1 | 1800 | 500 | 1900 | 100 |
2 | 2100 | 700 | 2000 | 250 |
3 | 2500 | 1100 | 2200 | 1000 |
4 | 3300 | 1700 | 2300 | 1000 |
5 | 4000 | 2200 | 2450 | 1000 |
6^{a} | 6000–8200 | 3550–4630 |
In the following section, the simulated and observed ground motions at a total of 15 K-NET and KiK-net stations (locations indicated in Fig. 2) are examined after band-pass filtering between 0.05 and 0.5 Hz. KiK-net stations have sensors on the ground surface and in boreholes, but only the borehole records are used in this study. The K-NET stations used in this study are located on relatively stiff site conditions, where the effects of nonlinear site responses are assumed to be small.
Results
Validation of heterogeneous source models
Effects of simplification
Discussion and conclusion
This study validated a method for constructing a kinematic source model for ground motion simulations of megathrust earthquakes in the period range of approximately 2 s and longer by combining multi-scale heterogeneity (Sekiguchi and Yoshimi 2006) with the characterized source model. Source models were constructed for the 2003 M _{W} 8.3 Tokachi-oki earthquake, and ground motion simulations were conducted to study the performance of the source models. In deriving the characterized source model (Model C), some parameters (i.e., the total area of the asperities \(S_{a}\), the area \(S_{ai}\) and stress drop \(\Updelta \sigma_{ai}\) of each asperity, and the rupture velocity \(V_{\text{R}}\)) were estimated by a trial-and-error approach, deviating somewhat from the recipe. As a result, the stress drops of asperities A2 and A3 were larger by a factor of 2 and 2.5, respectively, than those determined by the recipe. Similarly, the rupture velocity was set to 0.8 V _{S}, which is higher than that indicated by the recipe (0.72 V _{S}). These results suggest that the kinematic characteristics of an individual earthquake may deviate substantially from those indicated by the recipe, although the recipe represents the averaged characteristics of past earthquakes.
Multi-scale heterogeneity was added to the spatial distribution of the slip, rupture velocity, and rake angle of the characterized source model to yield heterogeneous source models (Models H1–H3). By investigating the FASRs of the simulated and observed ground motion, we demonstrated that the heterogeneous Model H3 is able to effectively explain the ground motion at periods of 2–20 s. The spatial distribution of the 5 % damped Sv of Model H3 also agreed well with the observation, especially in the southeastern region of Hokkaido. It is suggested that adding multi-scale heterogeneity to the spatial distribution of the slip, rupture velocity, and rake angle of the characterized source model is an effective method for constructing a source model for a future megathrust earthquake that can appropriately generates the ground motion at periods of 2–20 s.
Among the three parameters to which heterogeneity was added, the spatial distribution of the rupture velocity showed the largest influence on the ground motion, which is consistent with Watanabe et al. (2008). We also demonstrated that the distributions of the other two parameters, the slip and rake angle, can also largely alter waveforms and even the PGV. Because it is difficult to precisely model the spatial variation of these parameters, it is important to use a set of source parameters with numerous patterns of heterogeneity.
In this study, source models of a past earthquake were studied. When applying such models to ground motion prediction, it is unrealistic to expect that the precise parameters of the scenario source model can be known before an earthquake occurs because of the complexity of the nature of earthquakes. Therefore, two approaches will be important as future works. One is to comprehend the variability of the source parameters by analyzing the ground motion records of past earthquakes. The other is to introduce probabilistic source models that cover the variability generated by a Monte Carlo sampling method (e.g., Yamada et al. 2011) and perform large amount of ground motion computation.
Declarations
Authors’ contributions
AI conducted the simulations, analyzed the data, and drafted the manuscript. TM, NM, and HF participated in the conception and design of the study and helped interpret the results. SA contributed to constructing the FDM code, the source model (Model 0), and the 3D velocity structure model and helped interpret the results. All authors read and approved the final manuscript.
Acknowledgements
Comments from Dr. Kim B. Olsen and an anonymous reviewer helped us improve the manuscript. This study was supported by the “Support Program for Long-period Ground Motion Hazard Maps of Japan” of the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Most figures were drawn using the Generic Mapping Tools software (Wessel and Smith 1998).
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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