Shiann-Jong Lee 1, Dimitri Komatitsch 2,3, Yu-Chang Chan 1, Bor-Shouh Huang 1 and Jeroen Tromp 4 1 Institute of Earth Science, Academia Sinica, Taipei, Taiwan 2 CNRS and INRIA Magique-3-D, Laboratoire de Mod é lisation et d'Imagerie en G é osciences UMR 5212, Universit é de Pau et des Pays de l'Adour, France 3 Institut universitaire de France, 103 boulevard Saint-Michel, Paris, France 4 Department of Geosciences, Princeton University, Princeton, New Jersey, USA Effects of realistic topography on seismic wave propagation: Small- and large-scale topography effects in northern Taiwan The Next Generation of Research on Earthquake-induced Landslides: An International Conference in Commemoration of the 10th Anniversary of the Chi-Chi Earthquake September 21~26, 2009

Outlines Introduction Introduction topography effect Small-scale topography effect topography effect Large-scale topography effect Topography effect vs. source complexity Topography effect vs. source complexity Discussions and Summary Discussions and Summary

Introduction Topography influences ground motion as is observed from data recorded during and after real earthquakes and from numerical simulations. However, the effects of realistic topography on ground motion have not been clearly characterized in numerical simulations. Topography influences ground motion as is observed from data recorded during and after real earthquakes and from numerical simulations. However, the effects of realistic topography on ground motion have not been clearly characterized in numerical simulations. To accommodate high-resolution realistic topography data from the LiDAR Digital Terrain Model (DTM), which has a resolution close to 2 m, we use the SEM to simulate seismic wave propagation for frequencies up to 10 Hz in the Shamao Mountain area. To accommodate high-resolution realistic topography data from the LiDAR Digital Terrain Model (DTM), which has a resolution close to 2 m, we use the SEM to simulate seismic wave propagation for frequencies up to 10 Hz in the Shamao Mountain area. Furthermore, recent publications have mainly focused on implications for ground motion in the mountainous regions themselves, whereas the impact on surrounding low-lying areas has received less attention. Furthermore, recent publications have mainly focused on implications for ground motion in the mountainous regions themselves, whereas the impact on surrounding low-lying areas has received less attention. In order to investigate the detailed interaction between large-scale topography and nearby areas, we study on an example of Taipei basin and the Central Mountain Range (CMR) which are located in northern Taiwan. In order to investigate the detailed interaction between large-scale topography and nearby areas, we study on an example of Taipei basin and the Central Mountain Range (CMR) which are located in northern Taiwan.

Small-scale topography effects Shamao Mountain area LiDAR DTM data (1m) 40-m DEM LiDAR DTM (1m) LiDAR DSM (1m) Aerial topographic map

The Spectral-Element Method (SEM) Pseudospectral MethodAccuracy of a Pseudospectral Method Flexibility of a Finite-element Method Finite-element Method Develop more then 20 years ago in Computational Fluid Dynamics 27 nodes element

Spectral-element meshes Lee et al., 2009

Snapshots P wave S wave Shamao mountain North component, frequency up to 10hz Positive velocity Negative velocity Hypothetical source: Magnitude: M L 5.0 Double-couple source Strike 40°; dip 80°; rake -90° Located at 4.92 km depth

Synthetic waveform comparison Vertical component Velocity waveforms

Peak Ground Acceleration (a) LiDAR DTM (2 m) (b) 40 m DEM * The PGA values are calculated from the norm of the three components of the acceleration vector.

Realistic topography effects on ground motion PGA amplification factor: subtract the PGA value for the model without topography from the value for the model with topography, dividing the result by the PGA value for the model without topography, and multiplying it by 100 to obtain a percentage Relative change in PGA Source frequency Wavefield type Source depth Subsurface model

Summary of small-scale topography effects LiDAR DTM spectral-element mesh Yangminshan region For small-scale topography study, we combined LiDAR DTM data and an improved spectral-element mesh implementation to accommodate high- resolution topography in the Yangminshan region in northern Taipei. The average distance between points at the top of the SEM mesh was approximately 2 m, which enabled us to calculate the response of seismic waves up to a maximum frequency of approximately 10 Hz. PGA increases at mountain tops and ridges, whereas valleys usually have a reduced PGA. In some locations the PGA value decreases rapidly just beneath the tops of mountain ridges. Increased PGA values are also found in parts of valleys where brooks have eroded the ground surface, resulting in steep topography. Topographic effects also strongly depend on the source frequency and wavefield type. These results demonstrate that high-resolution, realistic surface topography needs to be taken into account for seismic hazard analysis, especially in dense population mountainous areas.

Large-scale topography effects Lee et al., 2009 Taipei basin SEM mesh Realistic topography

Snapshot and PGV distribution 3-D wave-speed model + topography + basin (b) – (a) = Residual Snapshot (T = 14 sec) PGV PGV amplification factor: subtract the PGA value for model (b) from the value for the model (a), dividing the result by the PGA value for the model (a), and multiplying it by 100 to obtain a percentage.

Synthetic waveforms along A-A’ profile

Topography effect vs. source depth 15 km depth 40 km depth2 km depth

Topography effect vs. source complexity Large subduction zone earthquake scenarios For finite-fault rupture scenarios (b), (c) and (d): The fault plane is 51 x 31km, divided into 1581 subfaults (of size 1 km x 1 km) The slip on the fault plane is considered uniform (84 cm) with a constant rake angle of 121°. The rupture velocity is assumed to be constant and equal to 2.5 km/s. For each subfault we use a Gaussian source time function with a half-duration of 1 second. Central mountain range (CMR)

Snapshots Vertical component, Velocity wavefield Frequency up to 1Hz in acceleration Positive velocity Negative velocity Rupture area of finite-fault source fictitious seismic station located in CMR

Synthetic waveforms Vertical component of velocity waveforms Point source Bilateral rupture Eastward rupture Westward rupture Synthetic waveformsFrequency spectra PSV

Topography effect vs. source complexity Point sourceBilateral ruptureEastward ruptureWestward rupture

Summary We investigated the effects of large-scale topography associated with the Central Mountain Range (CMR) in northern Taiwan on strong ground motion in the Taipei basin. Results show that variations in source depth modulate the influence of topography on ground motion in neighboring low-lying areas. If a shallow earthquake occurs in the I- Lan region, we find that the CMR significantly scatters the surface waves and therefore reduces ground motion in the Taipei basin. However, when we move the hypocenter deeper, topography scatters the body waves, which subsequently propagate as surface waves and spread into the Taipei basin. We also investigated several hypothetical rupture scenarios of subduction zone earthquakes occurring off the northeast coast of Taiwan. Results shown that the effects of topography on ground motion vary depending on the source rupture process. Our simulations show that topography has different effects depending on the scenario: it may or may not reduce ground motion in Taipei depending on the directivity, location, and depth of the event. These results illustrate the fact that topography should be taken into account when assessing seismic hazard.

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23 Cumulative kinetic energy (E k )

24 Influence of attenuation