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A Preliminary Study of Ground Water A Preliminary Study of Ground Water Level Change due to Earthquake using Time Frequency Analysis Time-Frequency Analysis Yetmen Wang Yetmen Wang President/CEO, AnCAD, Inc. Data Source: Water Resource

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A Preliminary Study of Ground Water A Preliminary Study of Ground Water Level Change due to Earthquake using Time Frequency Analysis Time-Frequency Analysis

Yetmen Wang Yetmen Wang President/CEO, AnCAD, Inc. Data Source: Water Resource Agency, MOEA. 2007/9/27 2007/9/27

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SLIDE 2

Contents Contents

  • Time-Frequency Analysis
  • Single Frequency and Harmonics

Single Frequency and Harmonics

  • Diurnal/Semi-Diurnal Tide
  • Precursor to Earthquake
  • Summary
  • Summary
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SLIDE 3

What is Time-Frequency What is Time-Frequency Analysis? y

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SLIDE 4

TF Plot: Single frequency TF Plot: Single frequency

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TF Plot: Change of frequency TF Plot: Change of frequency

  • Signal with abrupt

change of frequency.

⎨ ⎧ < ≤ × 1 , ) 10 2 cos( 30 . ) ( t t π ⎩ ⎨ ⎧ < ≤ × = 2 1 , ) 20 2 cos( 30 . , ) ( ) ( t t t x π

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SLIDE 6

TF Plot: Change of frequency and amplitude

  • Signal with abrupt

change of frequency and amplitude

⎩ ⎨ ⎧ < ≤ π × < ≤ π × = 2 1 ) 20 2 cos( 15 1 , ) 10 2 cos( 30 . ) ( t t t t t x ⎩ < ≤ π × 2 1 , ) 20 2 cos( 15 . t t

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SLIDE 7

TF Plot of 美濃(1) TF Plot of 美濃(1)

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Time-Frequency Analysis in Visual Signal Time Frequency Analysis in Visual Signal

Fourier Transform STFT Morlet / Enhanced Morlet* Hilbert Transform HHT* Instantane

  • us

f n/a distribution distributio n Single value Discrete values frequency Frequency change ith ti no yes yes yes yes with time Frequency resolution good

  • k
  • k/good

good good Adaptive base no no no n/a yes Handling n/a no no yes yes non-linear effect

*Algorithm used in this study

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SLIDE 9

Suggested Criteria for Doing Time- Frequency Analysis

  • recorded length: over 10000 points in total.
  • Bit rate: more than 8 bits

Bit rate: more than 8 bits.

  • Sampling rate/Data Length:

– Once per day => 24 years – Once per hour => 1 year p y – Once per minute => 1 week Once per second => 3 hours – Once per second => 3 hours – Vice versa…

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SLIDE 10

Single Frequency and Harmonics Single Frequency and Harmonics

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SLIDE 11

Average Daily Variation of GWL in A i i Agriculture Region

0.2 0.25 well12200211 0.2 0.25 well12200221 0.05 0.1 0.15 er 0.05 0.1 0.15 er 0 1

  • 0.05

mete

  • 0.1
  • 0.05

mete 5 10 15 20 25

  • 0.2
  • 0.15
  • 0.1

time(hr) 5 10 15 20 25

  • 0.25
  • 0.2
  • 0.15

time(hr) time(hr) time(hr)

美濃(1) 美濃(2)

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Average Daily Variation of GWL in Industrial Region

0.04 0.05 well07140121 0.01 0.02 0.03 er

  • 0.02
  • 0.01

met 5 10 15 20 25

  • 0.04
  • 0.03

time(hr) ( )

彰化．好修 (2)

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SLIDE 13

Average Daily Variation of GWL in Mixed Region

0.2 well03120121 0 025 0.03 well03120111 0.1 0.15 0 01 0.015 0.02 0.025 0 05 0.05 meter

  • 0 005

0.005 0.01 meter

  • 0.15
  • 0.1
  • 0.05
  • 0 02
  • 0.015
  • 0.01
  • 0.005

5 10 15 20 25 0.15 time(hr) 5 10 15 20 25 0.02 time(hr)

桃園樹林 (1) 桃園樹林 (2)

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SLIDE 14

Average Daily Variation of GWL in Recharge Abundant Region

8 x 10

  • 3

well02100121 6 x 10

  • 3

well12200321 2 4 6 ter

吉洋工作站

2 4 er

  • 4
  • 2

met

  • 4
  • 2

met 6 x 10

  • 3

well12200111 5 10 15 20 25

  • 6

time(hr) 5 10 15 20 25

  • 6

time(hr) 2 3 4 5

吉洋人工湖

  • 2
  • 1

1 meter

吉洋人工湖 宜蘭．大隱

5 10 15 20 25

  • 4
  • 3

time(hr)

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Average Daily Variation of GWL in Region without Pumping

8 10 x 10

  • 3

well010311R2 4 6 2 meter

  • 6
  • 4
  • 2

5 10 15 20 25 6 time(hr)

中和 Well, Taipei

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Single Frequency and Harmonics Single Frequency and Harmonics

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Spectrum of 美濃(1) Spectrum of 美濃(1)

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美濃(1) 美濃(1)

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樹林(1) 樹林(1)

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Spectrum of Ground Water Level (樹林1)

0.35 0.25 0.3

X: 377.1 Y: 0.2775

0.15 0.2

X: 145 Y 0 0951

Amp 0.05 0.1

Y: 0.0951 X: 7.001 Y: 0.05168 X: 3.501 Y: 0.02184

10

  • 1

10 10

1

10

2

10

3

10

4

days

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SLIDE 21

TF Plot of GWL (樹林1) TF Plot of GWL (樹林1)

well 03120111- IGaussFilter-Morlet _

1 5849 1.9953 2.5119 0.79433 1 1.2589 1.5849 0.39811 0.50119 0.63096

1/day

0.19953 0.25119 0.31623 1998 2000 2002 0.1 0.12589 0.15849

year

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樹林(2) 樹林(2)

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Spectrum of Ground Water Level (樹林2)

1.4

X 369 3

1 1.2

X: 369.3 Y: 1.378 X: 177.8 Y: 0.9191 X: 121 7 X: 7.012 Y: 1.177

0.6 0.8

X: 121.7 Y: 0.7545 X: 72.11 Y: 0.5178 X: 13.92 Y: 0.476 X: 3.494 Y: 0.4851 X: 2.332 Y : 0 3821

Amp 0.2 0.4

Y : 0.3821 X: 1.75 Y: 0.2435

10

  • 1

10 10

1

10

2

10

3

10

4

days

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SLIDE 24

TF Plot of GWL (樹林2) TF Plot of GWL (樹林2)

well 03120121- IGaussFilter-Morlet well_03120121- IGaussFilter-Morlet

1 5849 1.9953 2.5119 0 79433 1 1.2589 1.5849 0.39811 0.50119 0.63096 0.79433

1/day

0.19953 0.25119 0.31623 1998 2000 2002 0.1 0.12589 0.15849 1998 2000 2002

year

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SLIDE 25

彰化好修 彰化好修

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SLIDE 26

彰化好修 彰化好修

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Abnormal Pumping Abnormal Pumping

後安

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Diurnal/Semi-Diurnal Tide

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SLIDE 29

宜蘭大隱 宜蘭大隱

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SLIDE 30

宜蘭大隱 宜蘭大隱

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宜蘭大隱(EMD) 宜蘭大隱(EMD)

V ie w e r 3

3 5 4 0 3 0 2 0 2 5 1 0 1 5 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 5 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4

d a y

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SLIDE 32

IMF2 (semi diurnal tide) IMF2 (semi-diurnal tide)

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IMF2 (semi diurnal tide) IMF2 (semi-diurnal tide)

Beat wave occurs twice per month.

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IMF2 (semi diurnal tide) IMF2 (semi-diurnal tide)

Channel 2-Morlet

2.8 3 2.4 2.6

1/day

2 2.2 2001 2002 2003 2004

year

1.8

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SLIDE 35

IMF3 (once per day) IMF3 (once per day)

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IMF3 (cont’d) IMF3 (cont d)

Channel 3-Morlet

5 3.5 4 4.5 2.5 3

1/day

1 1.5 2 2001 2002 2003 2004 0.5 1

year

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SLIDE 37

吉洋人工湖(2) 吉洋人工湖(2)

Non-periodical signal is separated via EMD. The periodical part is shown in the middle plot. Its spectrums follows.

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SLIDE 38

TF Plot of 吉洋人工湖(2) TF Plot of 吉洋人工湖(2)

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SLIDE 39

TF Plot TF Plot

Mixer-Morlet

4 3 3.5 2 2.5

1/day

1 1.5 1999 2000 2001 2002 2003

year

0.5

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SLIDE 40

Empirical Mode Decomposition Empirical Mode Decomposition

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IMF1 IMF1

The first IMF is mostly high frequency noise. Though semi-diurnal Frequency appears, its amplitude is small.

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IMF2 IMF2

The component is relatively small compared to other IMFs.

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IMF3 IMF3

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IMF4: Semi diurnal tide IMF4: Semi-diurnal tide

The frequency does not change seasonally. It appears nothing to do with precipitation. The frequency does not change seasonally. It appears nothing to do with precipitation. The centrifugal and centripetal forces from the Sun cause the semi-diurnal variation. Gravitational force from the Moon results in the monthly beat wave phenomena.

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IMF5+IMF6: diurnal period IMF5+IMF6: diurnal period

Note that in TF plot diurnal intensity varies with precipitation. It might suggest diurnal frequency is caused by precipitate injection to the reservoir.

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IMF7: precipitation IMF7: precipitation

Volatility of IMF7 coincides with the one of periodical GWL signal. Increase of volatility correlates with the increase of GWL. This suggests IMF7 is related to precipitation which in this case is the major contribution to the raise of GWL.

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Precursor to Earthquake?

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Well around Chi-Chi Earthquake (南投新光) Well around Chi-Chi Earthquake (南投新光)

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Well around Chi-Chi Earthquake (南投新光) Well around Chi-Chi Earthquake (南投新光)

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Well around Chi-Chi Earthquake (南投竹山(1)) Well around Chi-Chi Earthquake (南投竹山(1))

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SLIDE 51

Well around Chi-Chi Earthquake (南投竹山(1)) Well around Chi-Chi Earthquake (南投竹山(1))

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SLIDE 52

Well away from Chi-Chi Earthquake 雲林觸口(1) Well away from Chi-Chi Earthquake 雲林觸口(1)

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Summary Summary

Ti f l i id i i htf l i f ti

  • Time-frequency analysis provides insightful information

related to recharge, precipitation, earth tide, and event anomaly. y

  • In some cases, EMD (Empirical Mode Decomposition)

can be used to separate earth tide. The strength of earth tid i ht i di t t th i f d tide might serve as an indicator to the size of ground water reservoir.

  • The abrupt rise of GWL without recharge nor daily
  • The abrupt rise of GWL without recharge nor daily

pumping harmonics suggests abnormal water injection to

  • reservoir. It is worthy of further investigation to see if it is

t th k a precursor to earthquake.

  • All the analysis is done using Visual Signal of AnCAD.
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SLIDE 54

Thank You!!

Visual Signal http://www.ancad.com/VisualSignal/downloadform.php yetmen@ancad.com

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SLIDE 55

Thank You!!

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頻譜分析 頻譜分析

南投．新光 桃園．樹林

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海潮(Tide Signal)與海水入侵 海潮(Tide Signal)與海水入侵

海水入侵–台南安平 海潮(Tide Signal)

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SLIDE 58

時頻分析結果—地潮分析 時頻分析結果 地潮分析

吉洋人工湖

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SLIDE 59

時頻分析結果—雨季、旱季 時頻分析結果 雨季 旱季

美濃

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SLIDE 60

時頻分析結果—地震與資料補遺 時頻分析結果 地震與資料補遺

彰化．好修

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美濃(1) 美濃(1)

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美濃(1) 美濃(1)

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IMF1 IMF1

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IMF2 IMF2

Frequency 3 (times a day) and 4 always come together in the same IMF. It is interesting to note that the intensities of these two frequency components comprise each other.

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IMF3 IMF3

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IMF4 IMF4

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Precipitate Injection Precipitate Injection

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IMF5 IMF5

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IMF6 IMF6