Identification of Basin Topography Characteristic Using Multivariate Singular Spectrum Analysis: Case Study of the Taipei Basin

    Identification of Basin Topography Characteristic Using Multivariate Singular Spectrum Analysis: Case Study of the Taipei Basin Yu-Wen Chang, Phung Van Bang, Chin-Hsiung Loh PII: DOI: Reference:

S0013-7952(15)30058-2 doi: 10.1016/j.enggeo.2015.08.027 ENGEO 4142

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

4 November 2014 9 July 2015 25 August 2015

Please cite this article as: Chang, Yu-Wen, Van Bang, Phung, Loh, Chin-Hsiung, Identification of Basin Topography Characteristic Using Multivariate Singular Spectrum Analysis: Case Study of the Taipei Basin, Engineering Geology (2015), doi: 10.1016/j.enggeo.2015.08.027

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ACCEPTED MANUSCRIPT Identification of Basin Topography Characteristic Using Multivariate

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Singular Spectrum Analysis: Case Study of the Taipei Basin

Taiwan.

Ph.D. student, National Taiwan University, Department of Civil Engineering, Taipei 10617,

Professor, National Taiwan University, Department of Civil Engineering, Taipei 10617,

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Taiwan.

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Taiwan. e-mail: [email protected]

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Ph.D. candidate, National Taiwan University, Department of Civil Engineering, Taipei 10617,

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Yu-Wen Chang1 , Phung Van Bang2 , and Chin-Hsiung Loh3

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ACCEPTED MANUSCRIPT Identification of Basin Topography Characteristic Using Multivariate Singular Spectrum Analysis: Case Study of the Taipei Basin by

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Yu-Wen Chang1 , Phung Van Bang2 , and Chin-Hsiung Loh3

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ABSTRACT

The effects of earthquake-induced basin amplification are caused by the interaction of

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wave-fields with a basin boundary, which depend on complex source to site distances, basin

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geometry (topography), and sediments distribution within the basin. In this study the identification of long-period waves induced by strong earthquake motions through basin

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topography together with local site effects of the basin is investigated. Through multivariate

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singular spectrum analysis (MSSA), a unique analysis tool for extracting tendencies and harmonic components in geophysical time series, is used to extract the long-period wave of

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basin response caused by the seismic events. Seismic response data of Taipei Basin were used to examine the existing of the lowest dominant frequency of the basin caused by basin topography. Finally, the seismic-induced ground motion data can be separated to local site effects and the basin motion caused by the effect of topography. Keywords: Multivariate Singular Spectrum Analysis, Taipei Basin, Basin topography characteristic, Local site effect

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ACCEPTED MANUSCRIPT INTRODUCTION

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Taiwan is characterized with complex geological structures, resulted from the oblique

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convergence of Philippine Sea plate toward the Eurasian plate at Taiwan at a rate of about 70

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to 80 mm/yr (Angelier et al., 1986). This tectonic environment results in high seismicity in and around the island of Taiwan. Taipei City, the capital of Taiwan, is a sediment-filled basin

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which covers an area of about 20 km × 20 km and is made up of Quaternary alluvium and

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lake deposits. During the 1999 Chi-Chi Earthquake (ML7.3; epicenter 150km to the south) and the eastern Taiwan offshore earthquake of 31 March 2002 (also called the 2002 331

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suffered severe damage.

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Earthquake; ML6.8; epicenter 110km to the southeast), many buildings in the Taipei Basin

Previous researches indicate that even if the earthquakes have mostly occurred outside

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the basin (the earthquake characteristics refer to foregoing indication), the thick recent deposits in the “soft” basin have caused significant damage due to the site amplifications (Wen and Peng, 1998; Wang et al., 2004). However, basin topography and local site characteristic influenced ground motion in the basin and have a strong correlation with amplitude, duration, and frequency contents in a basin structure (Komatitsch et al., 2004). In general, the seismic energy that may be trapped at basin edges is the cause of amplification of seismic waves. Figure 1 presents an example that shows the recorded velocity response spectra (with 5% damping ratio) from two stations (TAP017 and TAP035) that located in and 3

ACCEPTED MANUSCRIPT around the Taipei Basin during three earthquake events (i.e. the Chi-Chi earthquake, 2002 331

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Earthquake, and 1994 Nan-Ao earthquake). The velocity response spectrum from the three

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events of these two stations and the distribution of shear wave velocity from borehole data of

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these two stations are also shown in Figure 1. It indicates that an obvious long-period energy composition can be identified from station in the basin (Loh et al., 2003; Huang et al., 2010).

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TAP017

94 95 422

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96 4

87

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51 6 3

93

52

92

37

TRB01354 43 44

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18 110 2324

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13 12 TRB001 108 1 20 99 100 116

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115 33 48 53

TRB012

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22 89

TAP035 71

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67

86

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109 102

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97 31 117 29

26 32

91 90 15MND015

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TAP017 17

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MND021

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MND003 8

7 10

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TAP035 35

Figure 1. Velocity response spectra at station of TAP017 and TAP035 (in and around the Taipei Basin) during the Chi-Chi Earthquake, 2002 331 Earthquake, and 1994 Nan-Ao Earthquake. The thin black line denotes the boundary of the Taipei Basin. The distribution of SPT-N and shear wave velocity from borehole data of these two stations is also shown. In particular, incoming seismic waves are affected by the presence of the irregular basin sediment and bedrock interface; the latter may induce the long-period surface waves in the sediments if significant earthquake event was triggered. To investigate the dominant frequency of the basin sediment layer, observations from micro-tremor measurements can 4

ACCEPTED MANUSCRIPT provide an effective means to achieve the dominant frequency of local site condition. The

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local site effects of the Taipei Basin had been studied using shallow earthquake data (Sokolov

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et al., 2009) as well as via numerical simulations (Huang et al., 2010; Lee et al., 2008a). The

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results showed a relatively low-frequency (< 1~2 Hz) wave across the basin. Many researches adopted the single-station horizontal-to-vertical-spectra-ratio (HVSR) method to investigate

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the site response under earthquakes or micro-tremor recordings (Lermo and Chavez-Garcia,

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1993; Wen et al., 2006). Based on the single-station HVSR method and data, it is fact that the dominant period of the basin at a frequency of 1~2 Hz is related to the distribution of the

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Sungshan Formation (see Figure 2) (Yamazaki et al., 1997; Huang, 2009). On the other hand,

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Kuo et al. (2014) indicated that there existed another peak at a frequency of 0.4~0.7 Hz, as represented by the single-station HVSR using micro-tremor measurement. These studies

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indicated that the variation of local site effects as well as the topography of the Taipei Basin is quite complicated and cannot be clearly dissociated. The research objective of this paper is to utilize a novel signal decomposition method to extract the long-period wave that is produced by basin topological structure during large earthquakes. The site effect of the Taipei Basin on strong ground motions could then be clearly identified.

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ACCEPTED MANUSCRIPT 25.2

N

The depth contours of the Sungshan Formation which is the topmost strata of the basin(Wang et al, 2004)

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-100m -80m

25.05

Period(S)

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Latitude,(N)

25.1

-60m

2.0

-40m

1.8 1.6

-20m

24.95

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1.4

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contuor:dominant period by H/V spectral ratio method(Huang J.Y., 2009)

121.35

121.4

121.45

121.5

121.55

121.65

1.0 0.8 0.6 0.4 0.2 0.0

121.7

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Longitude,(E)

121.6

1.2

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Figure 2. The distribution of dominant period of the Taipei Basin, as represented by single-station HVSR using micro-tremor measurement. (revised from Huang, 2009). To analyze the ground motion data from a time-frequency domain analysis, there are

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several methods for signal decomposition. The short-time Fourier transform, wavelet

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transform (also called the wavelet packet transform) (Coifman et al., 1992; Misiti et al., 1996),

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or empirical mode decomposition (Huang et al., 1998) can provide signal decomposition from a single component of data. For multivariate signal analysis, principal component analysis

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(PCA) is an important statistical tool in many fields of data analysis (Jolliffe et al., 2002; Boe et al., 2003). In order to acquire the macrocosm basin response characteristic of the Taipei Basin during earthquake excitations, a novel signal processing technique called multivariate singular spectrum analysis (MSSA) is used to analyze the array data from earthquake-induced ground motions. The MSSA is a model-free and nonparametric analysis method in cooperation with multivariate signal processing technique. MSSA procedures mainly involve two stages: decomposition and reconstruction. It takes the singular value decomposition (SVD) 6

ACCEPTED MANUSCRIPT of the data matrix embedded by the analyzed time series and decomposes the data into several

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simple, independent, and identifiable components from singular values and singular vectors.

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MSSA had been applied to many diverse areas such as climate change and geophysical

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phenomena, (Castagnoli et al., 2005; Vautard et al., 1989; 1992) and mineral processing (Jemwa et al., 2006). The basic capabilities of MSSA include finding trends, extracting

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periodic components, smoothing, and de-noising time series data. In contrast to other signal

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decomposition methods that utilize a single record to decompose the seismic data, this algorithm focuses on using a multivariate data set to extract the principal components of

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ground motion.

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Under the Taiwan Strong Motion Instrumentation Program (TSMIP), operated by the Central Weather Bureau (CWB) in Taiwan, in Taipei Basin a denser array with a spacing of

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approximately 5 km was widely deployed (Liu et al, 1999). Seismic ground motion data (two horizontal and one vertical direction) collected by this dense array in the basin provides a good opportunity to identify the dominant period of the basin topography. The number of stations in the basin makes it possible to observe the complete trends of the seismic waves traveling across the basin. For example, during the Chi-Chi Earthquake and the 331 Earthquake (31 March, 2002), a large number of data was collected from this basin (Loh et al. 2000; 2003) which can be used to investigate the basin response characteristic and the site amplification effect of the Taipei Basin 7

ACCEPTED MANUSCRIPT GEOGRAPHY AND GEOLOGY OF THE TAIPEI BASIN

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Taipei Basin located in Northern Taiwan contains the metropolitan areas with the highest

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population densities. The tectonic expansion could have been induced by pure tension, which

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caused the basin to assume its triangular shape with an area of about 20 km × 20 km. The basin is surrounded by a varied topography, including mountains, tablelands, and a group of

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volcanoes. This one-sided subsidence made the basin’s Tertiary basement into a half-graben

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shape (see Figure 3). During the Pliocene and the Pleistocene age, gravels and conglomerates

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were widely deposited in the Linkou area which was a delta fan produced by reverse faulting

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activities. About 400,000 years ago, the area became a tensile environment and caused the

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Hsinchuang fault to alter its sense of movement and become a normal fault, (it has now been renamed as the Sanchiao fault). The normal faulting activities of the Sanchiao fault caused the

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sinking and took shape the Taipei Basin. Thus, the deepest part of the basin is along the northwestern border, where the Sanchiao fault is located (Teng et al., 2001). Four deposited unconsolidated strata were overlaid the basement of the Taipei Basin. The top near-surface layer, called the Sungshan Formation, is thought to dominate the site effects due to its loose sand and silt content (Wang et al., 2004). The Chingmei Formation beneath the Sungshan Formation is mainly composed of gravels and overlies the sand-and-silt Wuku Formation. The fourth Quaternary stratum is the gravel-rich Banchiao Formation that overlays on the Tertiary Basement. Based on the data of drilling wells and shallow reflection seismic 8

ACCEPTED MANUSCRIPT lines, the two major discontinuities in the basin, the bottom of the Songshan Formation and

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the basement, were described by Teng et al. (2001) and Wang et al. (2004), respectively. The

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Songshan Formation is relatively thin (about 50 m) with a very low S-wave velocity. The

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deepest part of the Tertiary Basement is about 700m to 1000 m along the western border of

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the Taipei Basin.

Figure 3. Topography and geology of the Taipei Basin and the locations of TSMIP network stations. The depth contours denote the Tertiary basement in the basin (Wang et al., 2004). The deepest part of the basement exceeds 700 m (Teng et al., 2001). The distribution of SPT-N and shear wave velocity from borehole data of these stations located on A-A’ profile is also shown.

DAMAGE EARTHQUAKES OF TAIPEI BASIN It has been reported that near-fault ground motions may induce many seismic disasters 9

ACCEPTED MANUSCRIPT (Shin and Teng, 2001). However, far-field earthquakes may also induce a significant impact

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on ground motion, particularly to a basin, such as the Taipei Basin because of the long-period

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dominant mode. Based on the seismic hazard analysis, the hazard contribution corresponding

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to a specific magnitude and distance of the controlling earthquakes at the 10% probability of exceedance within 50 years level of the Taipei Basin is shown in Figure 4. Compared to

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seismicity damage, it is concluded that these controlling earthquakes are located in the

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subduction zone of the northeastern part of Taiwan. The distance and magnitude of these controlling earthquakes are greater than 70 km and ML 6.8, respectively (Chang et al., 2008).

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According to the aforementioned information, the seismic observations of three shallow

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earthquakes are used to study the basin characteristic and topography effect of the Taipei Basin (Table 1). The local site effects are also investigated in this study. First, the ground

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motion data of the Chi-Chi Earthquake (21 September, 1999) with local magnitude of 7.3 are considered in this study. Second, the ML 6.8 eastern Taiwan offshore earthquake which occurred on 31 March 2002 with its epicenter 110 km away is the second event for this study. This earthquake caused minor damage near its epicenter but significant damage in Taipei. These seismic events triggered the most number of stations of TSMIP network in the northern part of Taiwan. The third earthquake is a medium earthquake that occurred on 5 June, 1994 in northwestern Taiwan and referred to as the Nan-Ao Earthquake (ML 6.5). Figure 5 shows the locations of the epicenters of these earthquakes. The seismic data (recorded by the TSMIP 10

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network) used are listed in Table 1.

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Figure 4. Distribution of the hazard contribution for the Taipei Basin. The figure on the left shows the locations of the controlling earthquakes and their hazard contribution percentages. The figure on the right illustrates the magnitudes and distance values of the controlling earthquakes.

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Table 1. The information of earthquakes used in this study Time

ML

Chi-Chi Earthquake

1999 /09 /21

7.3

331 Earthquake

2002 /03/ 31

6.8

1994 /06 /05

6.5

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Earthquake

Nan-Ao Earthquake

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Depth(km) Lon.( °E) Lat.( °N) Data in Basin 32 stations 8.0 120.81 23.85 (64 horizontal recordings) 44 stations 13.8 122.18 24.14 (88 horizontal recordings) 34 stations 5.3 121.84 24.46 (68 horizontal recordings)

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Taipei Basin

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Figure 5. Distribution of the epicenters of earthquakes used in this study.

MULTIVARIATE SINGULAR SPECTRUM ANALYSIS

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The singular spectrum analysis (SSA) is a multidisciplinary signal analysis tool which

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works similar to the familiar Principal Component Analysis (PCA). Besides, it allows a time series to be decomposed into different components, (e.g., the signal itself as well as various

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noise components), which can be subsequently removed from the data and can extract information from time series without prior knowledge of the dynamics affecting the time series (Golyandina, 2001; Alonso et al., 2005). The method of SSA can be applied to a single series or jointly to several series and it is referred to as multivariate SSA (MSSA). The basic procedure of MSSA consists of four steps, namely embedding, singular value decomposition, grouping, and diagonal averaging. The first two steps are referred to as the decomposition stages, and the final two steps are referred to as the reconstruction stages. 1st step: Embedding 12

The embedding procedure is a mapping technique that translates

ACCEPTED MANUSCRIPT the original time series into a sequence of multi-dimensional lagged vectors. Assume ym[n] is

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the observed data from mth channel at nth time step, and y[n] is an observed data vector from

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, n=1~N

(1)

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 y1[n]   y [ n]  y[n]   2        y M [n]

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all M channels at nth time step as expressed below:

where N is the total number of time steps of the observed data. The data matrix Y of the

y[ K ]   y[ K  1]      y[ N ]  

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 y[ 1 ] y[2]  y[2] y[3] Y     y[ L] y[ L  1]

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observed data with a row size of ML and a column size K is then embedded as follows:

K=N-L+1 and L
(2)

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Let L be an integer and 1 < L < N. The length of L must be large enough to allow separation into the components,. The embedding procedure forms K lagged vectors (K = N – L

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+ 1) and maps the time series with length N to an ML time delay series with length K (Bozzo et al., 2010).

2nd step: Singular value decomposition (SVD)

Singular value decomposition of the

data matrix Y is conducted as follows: * Y US V

(3)

where U represents a unitary matrix with dimensions ML×ML, S denotes a diagonal matrix with nonnegative real numbers on the diagonal with dimensions ML×K, and V* (the conjugate

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ACCEPTED MANUSCRIPT transpose of V) represents a unitary matrix with dimensions K×K. The diagonal entries of S

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are known as the singular values of matrix Y. The columns of U and V are called the left

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singular vectors and the right singular vectors of Y, respectively. There denote U = [u1, u2, …,

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uML], V = [v1, v2, …, vK] and S=[diag(σ1, σ2, …, σML), 0] with σ1 > σ2 > … > σML. By using singular value decomposition, it is possible to write Y as a sum of all elementary matrices Y1

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~ YnL as follows:

Y  Y1  Y 2    Y ML

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  1u1 v 1T   2u 2 v T2     nLu ML v TML  u p  u 2p    u MLp T 1 1

T 2

(4)

T ML

The grouping procedure partitions ML elementary matrices into

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3rd step: Grouping

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where p1 ~ pML are the principal components of the time delay series with a length K.

several subsets as follows:

(5)

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Y  Y1  Y 2    Y D

where Y i is the dth subset matrix grouped by several elementary matrices and d=1~D. The method of grouping depends on the objectives of MSSA. For example, if one wants to de-noise a time series, elementary matrices can be grouped into two subsets of a matrix (D=2). One subset of the matrix would contain the first p elementary matrices corresponding to a large singular value, while the other elementary matrices corresponding to a small singular value are involved in the other subset of the matrix as follows:

Y1  Y1  Y2    Yp 14

(6a)

ACCEPTED MANUSCRIPT Y 2  Yp1  Yp2    YML

(6b)

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Generally, elementary matrices with small singular values denote noise. The de-noise

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signal can be recovered from the subset of matrix Y 1 . Selection of p can refer to the

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signal-to-noise ratio or singular value distribution. More information about how to group elementary matrices can be found in the work of Golyandina et al. (2001). After the 3rd step, the data matrix is divided into several

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4th step: Diagonal averaging

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subsets of the matrix as shown in Equation (5). The original time series y can then be divided into several subsets of the time series y1~yD as follows:

y  y1  y 2    y D

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(7)

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where each subset of the time series can be derived by diagonal averaging of each subset of matrix (1) as follows:

1 n d y [n]   y q,nq1 n q 1

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d

1 n d y [n]   y q,nq1 L q 1 d

for 1 ≤ n < L-1

for L ≤ n < K

N  K 1 1 y [ n]  y q,d nq1  N  n  1 qn K 1 d

for K ≤ n < N

where y l,dk is the submatrix of matrix Y d with dimensions M×1 as expressed below:

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(8)

ACCEPTED MANUSCRIPT  y1,d K    y 2,d K     d   y L, K 

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(9)

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d d  y1,1 y1,2  d d y 2,1 y 2,2 d  Y      d d  y L,1 y L,2

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The first two steps are considered as the decomposition stage of MSSA while the last

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two steps are regarded as the reconstruction stage. The result of the first stage is a representation of the data matrix as a sum of several resultant matrices. The last stage

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transfers each resultant matrix into a time series, which is one additive component in the

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initial series. The corresponding operation is called diagonal averaging, which is a linear

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operation and maps the data matrix of the initial series into the initial series itself. In this way

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one can obtain a decomposition of the initial series into several additive components. In contrast to other signal decomposition methods that use a single record to decompose the

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seismic data, this algorithm focuses on using a multivariate data set to extract the principal components of ground motion. Processing of the multi-location measurement data by using MSSA is to perform eigen-structure identification by merging all the spatially distributed records and processing them using all multi-location measurements globally instead of using each item of data individually provides a very important data analysis technique for extracting common features of a basin.

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ACCEPTED MANUSCRIPT IDENTIFICATION OF BASIN CHARACTERISTICS

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Analysis using seismic data from down-hole measurement

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The Taipei Basin Down-hole Seismic Network (TBDSN), which was established by the

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Institute of Earth Sciences (IES), is a local down-hole seismic array network in the Taipei

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Metropolitan Area (Huang et al., 2010). The down-hole array is composed of eight boreholes at depths in excess of 300 m. To investigate the dominant frequency induced by the basin

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topography effect or the local site effect, in this section, two borehole sites were chosen for

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study. The first selected borehole location was drilled at the Panchiao Vocational Advisory

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Committee for Retired Servicemen (TF) and the second one is at the Minquan Park, Songshan

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District, Taipei City (MP), which are located at the western and eastern part of the Taipei Basin, respectively. The depth of the two stations at the bottom of the borehole is below the

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bedrock interface. Table 2 lists the parameters for the down-hole seismic arrays and their emplacement depths used in this study. Table 2. Parameters of down-hole seismic array at MP and TF stations. Earthquake

Station

Lon. (°E)

Lat. (°N)

Depth(m) 0

MP

121.557

25.062

100*

2002/03/31 earthquake

0 TF

121.445

* depth of boreholes down to the bedrock.

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25.028

300*

Location Minquan Park, Songshan District, Taipei City Vocational Advisory Committee for Retired Servicemen, Panchiao City

ACCEPTED MANUSCRIPT Consider the down-hole data collected at the TF site and the MP site from the 31 March,

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2002 earthquake. Figures 6(a) and 6(b) present the distribution of the singular spectrum from

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MSSA using velocity data (integrated from the recorded acceleration data) of both the down

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hole bedrock (Figure 6(a)) and the ground surface (Figure 6(b)) at stations MP and TF in the Taipei Basin. The Fourier amplitude spectrum of the extracted major principal components

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using velocity seismic wave from these data through MSSA is also shown in Figures 6(c) and

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6(d). Figure 6(c) shows the comparison on the Fourier amplitude spectrum of the reconstructed signal of the 1st and 2nd major principal components of two down-hole bedrock

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sites through MSSA. One can identify the only one major dominant period at T=2~3 sec

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which confirmed that the basin topography has a long dominant period and this period can be excited during earthquake. Figure 6(d) shows the comparison on the Fourier amplitude

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spectrum of the reconstructed signal of the four major principal components (from 1st to 4th components and 5th to 6th components ) using data collected from two ground surface sites through MSSA. The dominant periods from both the local site effect (around 1.0 sec) and the basin topography effect (from bedrock motion with a period of 2~3 sec) can be identified. Although, the dominant period at T=2~3 sec also was identified (extracted components from 5th and 6th singular value), but the energy of this period is smaller than the down-hole data. The difference of the period contents of the major principal components from both down-hole data and the ground surface are obvious. The seismic ground motion at ground surface 18

ACCEPTED MANUSCRIPT contains both the basin topography and the site amplification effects. It demonstrated that a

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dominant period of 2~3 sec can be identified from the down-hole bedrock data, while on the

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ground surface not only the dominant period of 2~3 sec which corresponding to basin

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movement but also the local site effect with dominant period about 1.0 sec can be identified. From the comparison of down-hole data shows that existence of dominant period of basin

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topography can be excited when a significant earthquake (large, shallow, and far field

Singular Spectrum, L = 150 14

25.45%

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Data : 2002 331 earthquake MP station@100m(EW, NS directions) TF station@300m(EW, NS directions)

1st & 2nd singular value

Data : 2002 331 earthquake MP station@100m(EW, NS directions) TF station@300m(EW, NS directions)

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8

6

4

2

(a) 0 0

20

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Eigenvalue (%)

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earthquake event) with a large magnitude occurs.

40

60

(c) 80

100

Eigenvalue Number

Singular Spectrum, L = 150 8

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Data : 2002 331 earthquake MP station@0m(EW, NS directions) TF station@0m(EW, NS directions)

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23.71 %

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Eigenvalue (%)

1st ~ 4th singular value

Data : 2002 331 earthquake MP station@0m(EW, NS directions) TF station@0m(EW, NS directions)

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5th & 6th singular value

3 2 1 0

(d)

(b) 0

20

40

60

80

100

Eigenvalue Number

Figure 6. Distribution of singular values using seismic velocity data on the basement and surface of 2002 331 Earthquake recorded at stations MP and TF in the Taipei Basin. Figures (a) and (b) show the singular spectra of the basement and surface in the Taipei Basin; Figures (c) and (d) show the frequency spectra of bedrock and surface ground motion which show the dominant frequencies induced by both the basin structure and the sediment. 19

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Seismic Response Analysis from Basin Earthquake Monitoring Array

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To further proved the influence of basin topography on surface ground motion during

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earthquake, seismic response data from the Taipei Basin triggered by three historical earthquake events (listed in Table 1) are used to discuss the basin response characteristic.

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First, the seismic observations of the Chi-Chi Earthquake are used to extract the dominant period of the Taipei Basin, with particular focus on the effect of topography on ground

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motions. Following the procedures of MSSA as described in the previous section, the data

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matrix (using velocity waveforms) is formed where each yi denotes the measured acceleration

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at station “i” with dimensions 64×1 (from 32 recorded stations, and each with 2 directions of

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east-west and north-south) and set L=50. The distribution of singular values (from singular

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value decomposition) is then generated, as shown in Figure 7.

Figure 7. Plot of the distribution of singular spectrum (use L=50) from seismic data of the Taipei Basin of 1999 Chi-Chi Earthquake (32 stations, 64 recordings). Figure 8 shows that the ground motion response using the 1st and 2nd largest singular 20

ACCEPTED MANUSCRIPT values (or major principal components) as well as the 3rd and 4th singular values (or principal

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components) for the Chi-Chi Earthquake at station TAP003 are reconstructed. It is observed

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that the reconstructed signal from the first two major principal components contained the

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longest period in the recorded data. This shows that the surface ground motion contains a long-period seismic wave. This long-period seismic wave is consistent with the observed data

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from the down-hole measurements at the bedrock. With the same approach on all the recorded

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data in the basin, the extracted principal components from each station can be generated. A stable dominant period of 2~3 sec can be identified from the acceleration response spectrum

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(with 5% damping ratio) of the extracted dominant principal components from all stations on

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the basin, as shown in Figure 9. It shows that even from data collected from shallow soil deposit, if the data is from the basin response, the long period seismic waves induced by basin

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topography do exist. The result indicated that a significant long-period ground motion (or principal components) of 2~3 sec was contained in the record in the Taipei Basin from the analysis of the Chi-Chi Earthquake. The identified dominant period remains unchanged across the basin. By using the extracted principal components from the basin, the velocity trajectories at each station across the basin can be constructed as shown in Figure 10. Figure 10(a) shows that the trajectory of the principal components (from all instruments that was activated in the basin) and Figure 10(b) shows the trajectory of the residual components. The trajectory of the major principal components, the dominant motion of the Taipei Basin, 21

ACCEPTED MANUSCRIPT demonstrated the motion of the basin bedrock structure induced by basin topography during

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earthquake. On the other hand, the variation of the trajectory of the residual components

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across the basin became obvious. The residual components can be explained as the earthquake

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induced vibration cause of local site effects (influence of local soft layers), as illustrated in

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Figure 10(b).

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Figure 8. Velocity waveforms of TAP003 station on the Chi-Chi Earthquake of the extracted principal component motion of north-south (NS) direction and east-west (EW) direction, including in the (a),(c) using 1st and 2nd singular values; (b),(d) using 3rd and 4th singular values.

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ACCEPTED MANUSCRIPT Figure 9. Acceleration response spectra with 5% damping ratio of the extracted principal

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components of each station of the Chi-Chi Earthquake, including in the: left is east-west direction, and the right is north-south direction. It shows that a common long-period wave of about 2~3 sec is identified from the seismic data of the Taipei Basin.

(b) the residual components

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(a) the extracted principal components

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Figure 10. Plot of the 2-dimensional velocity trace, the extracted principal components, and the residual components of each strong motion station in the Taipei Basin during the Chi-Chi Earthquake using MSSA.

Furthermore, seismic response data from the 331 Earthquake (31 March, 2002, ML=6.8)

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and the Nan-Ao Earthquake (5 June, 1994, ML=6.5) were also investigated. The trajectory matrices of the two earthquakes for MSSA were constructed and each data vector yi was set with dimensions 88×1 and L=50 and dimensions 68×1 and L=300, respectively. Based on the data of the 31 March, 2002 earthquake, Figure 11(a) shows the distribution of the singular values of the earthquake. To extract the long-period waves the principal component from the 1st and 2nd singular values for the earthquake was also reconstructed. These extracted long-period waves were induced by the basin topology. The acceleration response spectra 23

ACCEPTED MANUSCRIPT with 5% damping ratio (see Figure 11(b)) of the extracted principal components from each

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station shows the stable dominant period of 2.44 sec for the 331 Earthquake. It can be

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observed that the extracted components perform the stable peaks from station to station (did

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not change with respect to the depth of the basement) at period 2.44 sec are almost unchanged. Therefore, this identified period can be defined as the dominant period caused by basin

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topography. Figure 11(c) also plots the velocity trajectories of the principal component of the

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identified dominant mode from all instruments in the Taipei Basin for 31 March, 2002 earthquake. The movement of each trajectory is very similar which also confirms that the

2002, 331 Earthquake L=50

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identified principal component belongs to the basin dominant mode.

Figure 11(a). The distribution of singular spectrum of the 331 Earthquake (L=50, 44 stations, 88 recordings).

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Figure 11(b). Plot the acceleration response spectra of the extracted major principal

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component motions for east-west direction and north-south direction on the 331 Earthquake.

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Figure 11(c). Plot of the 2-dimensional velocity trace, the extracted principal components, and the residual components of each strong motion station in the Taipei Basin during the 2002/3/31 Earthquake using MSSA.

A similar approach was applied to the seismic response data of the Nan-Ao Earthquake. When the length L is large enough, the singular vectors present a frequency content information of the analysed signal, and the singular values present the energy information of the analysed signal corresponding to each frequency component (Bozzo et al., 2010). In order to get more content information of the analysed signal in the moderate-magnitude earthquake, the large L was used for this earthquake. From the distribution of the singular values of the 25

ACCEPTED MANUSCRIPT Nan-Ao Earthquake as shown in Figure 12(a), instead of using the 1st and 2nd principal

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components, the 3rd to 6th principal components were selected to reconstruct the ground

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motion. The acceleration response spectrum of the different principal components

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reconstructed from the basin is shown in Figure 12(b) to Figure 12(d). It is observed that the identified dominant periods longer than 2 sec are from four major principal components. One

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is the period of seismic wave at 5~6 sec that was identified from the 1st and 2nd principal

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components. This identified dominant period is much longer than the result from the Chi-Chi Earthquake as well as the 331 Earthquake (i.e., T=2~3 sec), but the energy of this period is

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smaller than the other two seismic events from components of the period at 2~3 sec. It is believed that a very long period of basin topography effect can be generated from the Nan-Ao

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Earthquake. Reconstruction of the ground motion from the 5th and 6th singular values was also

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conducted and the acceleration response spectrum of the signal is shown in Figure 12(d). The result shows another dominant period of the reconstructed signals from the 5th and 6th singular values is around 2~3 sec which is consistent with the dominant period identified from the Chi-Chi Earthquake and the 331 Earthquake. The difference on the identified dominant periods between this event and the other two events is because the hypocenter of the Nan-Ao Earthquake is much closer to the Taipei Basin than the 331 Earthquakes and also located on the convergent plate boundary, therefore, the basin topography effect is even more significant. The acceleration response spectra with 5% damping ratio of the extracted principal 26

ACCEPTED MANUSCRIPT component motions (with periods longer than 2.0 sec) reconstructing from four singular

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values of the 1st to 2nd and 5th to 6th on the Nan-Ao Earthquake is shown in Figure 13.

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Figure 14 also plots the velocity trajectories of the principal components of the

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identified dominant modes (from the 1st to 2nd and 5th to 6th singular values) and the residual components of all instruments in the Taipei Basin from the Nan-Ao Earthquake. It is observed

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that the velocity trajectories of the two long-period principal components represent the

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movement consistent in station to station. It demonstrates that the extracted signals may belong to the response of basin topography effect. The basin topography and the local site

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effect can also be observed from the analysis.

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Singular Spectrum 2.5

1994, Nan-Ao Earthquake L=300

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0.5

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Eigenvalue (%)

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1.5

1st & 2nd

1st, 2nd  4.15%

3rd, 4th  2.51% 5th, 6th  2.44%

(b)

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(a)

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50

100

150

200

250

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Eigenvalue Number

5th & 6th

(d)

3rd & 4th

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Figure 12. The reconstruction of the acceleration response spectra of the Nan-Ao Earthquake. Figures (a) show the distribution of the singular spectrum (using L=300, 34 stations, 68 recordings); Figures (b), (c), and (d) show the acceleration response spectrum of the different principal components reconstructed from 1st to 6th singular value, respectively.

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ACCEPTED MANUSCRIPT 1st & 2nd 5th & 6th

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5th & 6th

1st & 2nd

Figure 13. Acceleration response spectra with 5% damping ratio of the extracted principal component motions (with periods longer than 2.0 sec) including the east-west

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direction and the north-south direction on the Nan-Ao Earthquake.

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(a) the principal component from 1st and 2nd singular values

(b) the principal component from 5st and 6nd singular values

(c) the residual components Figure 14. Plot of 2- dimensional velocity trace of the strong motion station in the Taipei 28

ACCEPTED MANUSCRIPT Basin from the extracted principal components and residuals of the 1994 Nan-Ao Earthquake.

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DISCUSSION OF RESIDUAL COMPONENTS FROM MSSA

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Considering the Taipei Basin as an example, it is confirmed that the earthquake induced

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ground motion recorded from the basin surface generally depends not just on the peculiarities of topography but also on the source, path, and local site effects. In this study, the peculiarities

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of topography or basin response characteristic can be extracted from the major principal

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components through the proposed MSSA. The residual signals can then be used for the study of local site effects of the basin.

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Since from the MSSA of seismic data from the Taipei Basin, the identified major

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principal component with a period of 2~3 sec corresponds to the topography effect of the basin response characteristic. The residual signals of the surface ground motion from MSSA

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will then be used to examine the variation of local site effects across the basin. According to the principle of MSSA, after removing the long-period signal (effect of basin topography) from the recorded ground motion data (i.e. the Chi-Chi Earthquake, the 331 Earthquake and the Nan-Ao Earthquake) on the Taipei Basin, the acceleration response spectrum of the residual signal is calculated. The characteristic of site effect can certainly reflect the variation of the dominant period according to the depth of local soil deposit. Station of TAP017, TAP026, and TAP034 are classified into three different groups based on the depth of the soil deposit, i.e. soil deposit 29

ACCEPTED MANUSCRIPT depth larger than 200m, between 100m and 200m, less than 100m. These acceleration

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response spectra of the residual signals of the above mentioned three earthquakes are

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compared, as shown in Figure 15. The variation of the dominant period from the acceleration

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response spectrum with respect to the different depth of soil deposit is obvious. Since the dominant period of the basin topography was extracted from MSSA, the results shown in

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Figure 14 demonstrated the effect of local site deposit in the basin. The residual signal can

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certainly reflect the variation of the dominant period to reflect the local soil deposit. Thus, it is confirmed that the ground motion recorded from the basin surface generally depends not just

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on the source, path, and local site effects; but also on the peculiarities of basin topography.

87

5

98

6 3 0 -50 0 -60

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96 4

51 -3 00

0 -40

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95

C

52

44

94 422

16

37

92 11

TAP017 -200

12 TRB001 108 1 99 100

19

18

38

110 2324

25

TAP026 26

-150

TRB01354 43

32

-100

9

MND003 8

7 10

17 MND021

93

-25 0

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20 116

91 90 15 MND015

14

13

21

97 31 117 29

109 102 22 89

71

101

30

115 -50

33

67

48

The boundary of the Taipei Basin

53 34

86

TAP034 35

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(a) Chi-Chi Earthquake

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TRB012

88

74

The depth of the Tertiary basement in the basin

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(b) 331 Earthquake

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(c) Nan-Ao Earthquake

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Figure 15. Acceleration response spectra of the residual signals in the Taipei Basin (from the Chi-Chi Earthquake, the 331 Earthquake, and the Nan-Ao Earthquake).

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CONCLUSIONS

In order to investigate the local site effects of the Taipei Basin, the shallow earthquake data or micro-tremor recordings were used to identify the characteristic of the dominant frequency in basin, for example, numerical simulation, the single-station horizontal to vertical spectra ratio (HVSR) method, etc. However, the complex interactions between topography and sedimentary basin structure, as well as the influence of source location, cannot perfectly be separated from micro-tremor measurements.

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ACCEPTED MANUSCRIPT In contrast to other signal decomposition methods using a single record to decompose the

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seismic data, this algorithm focuses on using a multivariate data set to extract the principal

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components of ground motion. In the application based on the algorithm of MSSA, the

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dominant period of the Taipei Basin was identified using earthquake response data from the Taipei Basin. The identified dominant period of basin topography effect (2.0 sec ~6.0 sec)

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from three earthquake events is quite consistent. This basin dominant period can also be

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proved from the seismic response data collected from the down-hole array in the basin. The trajectory of the principal component for the three earthquakes is quite consistent with the

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topography of the basin, which confirms that the motion of the long-period is induced by the

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basin topography. For the design of long-period structures in the basin, it is necessary to consider the effect of long-period waves (> 2.0 sec) induced by the basin topography.

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Different from the long-period waves (basin response characteristic), the local site effects can be identified after removing the long-period signals caused by the basin topology. The corner periods for local site effects noted in the response spectra associated with the earthquake data observed from the Taipei Basin are generally smaller than 2.0 sec. Further, the various patterns are likely a result of different distributions of the soil velocity structure as well as different depths of the surface soil layer. As a consequence, the dominant period inducing by both of the basin topology effect and local site effect should be taken into considerations of seismic demands, such as the Taipei Basin. 32

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ACKNOWLEDGMENTS

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Immense gratitude is conveyed to the Central Weather Bureau (CWB) and the Institute

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the TSMIP network and down-hole arrays for this study.

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of Earth Sciences (IES) in Taiwan for their great support in providing rich earthquake data in

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ACCEPTED MANUSCRIPT Research Highlights

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 Multivariate singular spectrum analysis was used to extract long period seismic waves Basin topology effect was identified from the basin earthquake response data Site response in the basin include both the local site effect and the topography effect  Seismic response data of Taipei Basin were used to examine the topography effect Topography effect cannot be ignored for design of structures in the basin

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