Quantification of Topography Effect on Seismic Ground ... · Yi-Ching Lo 1, Li Zhao2, and Shu-Huei Hung 1 1. Department of Geosciences, National Taiwan University, Taiwan 2. Institute

Yi-Ching Lo1, Li Zhao2, and Shu-Huei Hung1

1. Department of Geosciences, National Taiwan University, Taiwan2. Institute of Earth Sciences, Academia Sinica, Taiwan

August 15, 2016

Quantification of Topography Effect on Seismic Ground Motion:

A Case Study in Northern Taiwan

The Earth is not flat. Some regions have drastic variation in surface relief, e.g. ±4 km in Taiwan region over ~100-km distance.

Topography affects wave propagation and therefore arrival times and amplitudes of seismic waves

Neglecting topography:

• Topography-induced travel time anomalies introduce biases in seismic tomography models

• Topography-induced amplitude anomalies lead to unrealistic ground motion predictions

Motivations for Studying Topography Effect

• Surface topography influences the intensity of ground motion by focusing, defocusing and scattering of seismic waves.

• Topography has been ignored in most ground motion studies, leading to biases in PGV and PGA predictions.

Studying Topography Effects on Ground Motion by Numerical Simulations

Numerical simulations show that the effect of topography on PGV predictions can be up to ±50% for ground motion of ~0.5 Hz (Ma et al., 2007; Lee et al., 2009).

Lee et al. (2009)Ma et al. (2007)

Southern CaliforniaNorthern TaiwanSAF

SAF

SAF

SGM

SGM

SGM

• FDM code by Zhang et al. (2012)• Grid spacing: 300 m horizontally and

variable vertically (171.4 m near surface and increasing to 782.6 m at ~ 60-km).

• Accurate waveforms up to 0.8 Hz• FD simulations on the IES HPC cluster

• Newton’s second law:

• Hooke’s Law:

• Surface topography : curvilinear grids transformed to Cartesian grids

Finite-difference Method (FDM)

,t

ρ ∂= ∇⋅ +

∂v σ f

1: [ ( ) ] ,2

T

t∂ ′= ∇ + ∇ −∂σ C v v m

,t ξ η ζ

∂ ∂ ∂ ∂= + + +

∂ ∂ ∂ ∂U U U UA B C F

Zhang et al. (2012)

• Regional model from travel time tomography (Kuo-Chen et al., 2012).

• ETOPO1 topography: 1 arc-minute (~1.85 km). Up to ~6 km topography contrast over 100-km distance in northern Taiwan.

Taiwan: 3D Model and Topography

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

ETOPO1

VP

2

3

4

5

6

7

8

0

2010

3040D

epth

(km

)

(km/s)

VS

2

3

4

5

1.5

2.5

3.5

4.5

0

2010

3040D

epth

(km

)

(km/s)

• Use 54 x 3 sources (at depths 7, 15 and 23km) to examine P and S waves coming from a variety of directions.

• Compute waveforms from the 162 sources to all 38 stations with and without topography and measure the differences in their P- and S-wave travel times and amplitudes.

Sources and Stations38 Stations (BATS and TAIGER)

Comparison of Waveforms (Z component)

Black: “record” (with topography) Red: “Synthetics” (flat surface)

0 10 20 30 40 50 60 70 80 09)ces(emiT

BPNA187/89

10NSN612/45 20NSN632/35 30NSN98/15 40NSN73/1550NSN437/3560NSN431/55 70NSN111/55 80NSN721/65

90NSN572/16

01NSN604/96

11NSN976/4721NSN718/6731NSN729/97

41NSN4302/09

51NSN8961/69

BCBS17/621

OTAT321/58

10NGT8/821

20NGT74/121

30NGT842/211

40NGT812/401

50NGT129/69

60NGT9771/08

80NGT9181/06

90NGT383/84

11NGT617/66 21NGT492/46

31NGT17/35

41NGT322/04

51NGT248/11161NGT997/701

71NGT

81NGT7231/48

91NGT22NGT6401/29

BSFW534/27

BNHY539/58

8961/69

729/97

distance (km)/station elevation (m)

P S

Measuring Time and Amplitude Anomalies

• “Record” and “synthetics” with and without topography

• Compute synthetic autocorrelation CA and record-synthetic crosscorrelation CC

• Bandpass filter the correlations around 3 frequencies: 0.1Hz, 0.2Hz and 0.5Hz

• Time anomaly: lag time of

Amplitude anomaly:

P wave S wave

Broadband CC Broadband CC

0.1 Hz CC 0.1 Hz CC

0.2 Hz CC 0.2 Hz CC

0.5 Hz CC 0.5 Hz CC

Z-comp. P (broadband) Z-comp. P (0.1Hz/10sec)

Frequency-dependence of Topography Effect

P-wave arrival time is more delayed at higher elevation and longer period, up to 0.4 sec.

Z-comp. P (0.2Hz/5sec) Z-comp. P (0.5Hz/2sec)

N-comp. S (broadband) N-comp. S (0.1Hz/10sec) N-comp. S (0.2Hz/5sec) N-comp. S (0.5Hz/2sec)

δt

δt

δlnA

S-wave arrival time is more delayed at higher elevation and longer period, up to 0.7 s.

Topography effect on S-wave amplitude has a complex pattern.

N-comp. S (broadband) N-comp. S (0.1Hz/10sec) N-comp. S (0.2Hz/5sec) N-comp. S (0.5Hz/2sec)

• P-wave delay times due to topography can be up to ~0.4 s.

• Delay times from topography have no clear relationship with epicentral distance; increase with elevation.

• Delay times have larger variation at longer periods (red and green symbols) due to finite-frequency effect.

P-wave Travel Time Anomalies due to Topography

Epicentral distance (km)

δt (s

ec)

Station elevation (m)

δt (s

ec)

broadband0.1 Hz0.2 Hz0.5 Hz

δt vs. epicentral distance

δt vs. station elevation

broadband0.1 Hz0.2 Hz0.5 Hz

• S-wave delay times due to topography can be up to ~0.7 s.

• Delay times from topography have no clear relationship with epicentral distance; increase with elevation.

• Delay times have larger variation at longer periods (red and green symbols) due to finite-frequency effect.

S-wave Travel Time Anomalies due to Topography

δt vs. epicentral distance

Epicentral distance (km)

δt (s

ec)

broadband0.1 Hz0.2 Hz0.5 Hz

Station elevation (m)

δt vs. station elevation

δt (s

ec)

broadband0.1 Hz0.2 Hz0.5 Hz

• S-wave amplitude anomalies due to topography have slightly negative mean, i.e. amplitude reduction.

• Topography effect on amplitudes has no clear relation with either distance or station elevation.

S-wave Amplitude Anomalies due to Topography

δlnA vs. epicentral distanceδl

nA

Epicentral distance (km)

broadband0.1 Hz0.2 Hz0.5 Hz

δlnA vs. station elevation

δlnA

Station elevation (m)

broadband0.1 Hz0.2 Hz0.5 Hz

• In northern Taiwan, topography induces up to 0.4 s and 0.7 s in P- and S-wave delay times, respectively, and up to 80%in S-wave amplitude anomaly.

• P- and S-wave delay times have positive means and no dependence on distance

• Amplitude anomalies for S wave have slightly negative mean and no dependence on distance.

Topography Effects vs. DistanceP wave travel time anomaly S wave travel time anomaly

S wave amplitude anomaly

Source Depths: 7 km 15 km 23 km

Topography Effects vs. Station Elevation

P wave travel time anomaly S wave travel time anomaly

S wave amplitude anomaly

• Delay times for P and S waves increase with station elevation.

• Increase of S-wave delay times with station elevation is nearly twice as fast as P wave delay times.

• Amplitude anomalies for S wave have no dependence on station elevation.

Source Depths: 7 km 15 km 23 km

Topography-induced delay times δt :• No clear variation in the topography-induced P-wave delay times with back azimuth.• Clearly positive with larger values at high-elevation YHNB and smaller values at low-

elevation SBCB.

SBCB : Western Foothills with a low elevation of ~70.6 mTATO : Taipei Basin with an elevation of ~123.0 mYHNB : Central Range with a relatively high elevation of 934.9 m.

Variation with Back Azimuth: P-wave Travel Times

Source Depths 7 km 15 km 23 km

Topography-induced amplitude anomalies δlnA: • Amplitude anomalies show complex variation with azimuth.• A majority of amplitude anomalies are negative (reduction).

Variation with Back Azimuth: S-wave Amplitudes

Source Depths 7 km 15 km 23 km

In northern Taiwan, topography induces up to 0.4 s and 0.7 s in P-and S-wave delay times, respectively, and up to 80% in S-waveamplitude anomaly.

Topography effect leads to positive anomalies in P- and S-wavetravel times (delays), and slightly negative anomalies in S-waveamplitudes (reduction).

Delay times increase with station elevation but have no dependenceon epicentral distance. Amplitude anomalies do not depend on eitherstation elevation or epicentral distance.

Topography-induced travel time delays do not vary with azimuth;whereas topography effect on amplitude varies with azimuth in acomplex fashion.

Summary