new waveform-based bayesian full moment tensor inversion and … chen gu.pdf · 2016. 5. 20. ·...

Waveform-based Bayesian Full Moment Tensor Inversion and Uncertainty Quantification for

the Induced Seismicity in Oil/Gas Fields

Chen Gu Graduate Student,

Department of Earth, Atmospheric, and Planetary Sciences

In collabora<on with Prof. Youssef Marzouk and Prof. M. Nafi Toksöz

MIT Earth Resources Laboratory 2016 Annual Founding Members Mee<ng

May 18, 2016

2016 Annual Founding Members Mee<ng

In many oil/gas fields and hydrofracking there are induced earthquakes due to fluid extraction or injection

•  Research motivation – Source mechanisms of induced earthquakes and error bars

•  Method – Waveform-based Bayesian moment tensor inversion

•  Examples – Synthetics and an example from Oman

v1(tb )!

v1(te )!

!

"

#####

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%

&&&&&

=

G11,1(tb ) G11,2 (tb ) G11,3(tb ) G12,2 (tb ) G12,3(tb ) G13,3(tb )! ! ! ! ! !

G11,1(te ) G11,2 (te ) G11,3(te ) G12,2 (te ) G12,3(te ) G13,3(te )! ! ! ! ! !

$

%

&&&&&

!

"

#####

M11

M12

M13

M22

M23

M33

$

%

&&&&&&&&

!

"

########

P T


Motivation: Understand fracturing mechanisms, map microseismicity, and evaluate hydrofracking

•  More high-quality data •  In predictable places

Oil/Gas field


Motivation: Understanding earthquake dynamics, hazard assessment, and damage measurement

Note: Earthquakes occur in the same place of Oil/gas fields

Oil fields in Kuwait Induced earthquakes

4.1

4.5


In many oil/gas fields and hydrofracking there are induced earthquakes due to fluid extraction or injection

•  Research motivation – Source mechanisms of induced earthquakes and error bars

•  Method – Waveform-based Bayesian moment tensor inversion

•  Examples – Synthetics and an example from Oman

v1(tb )!

v1(te )!

!

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#####

$

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=



$

%

&&&&&

!

"

#####

M11

M12

M13

M22

M23

M33

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%

&&&&&&&&

!

"

########

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Moment Tensors of Earthquakes

•  The mechanisms of the greatest majority of tectonic earthquakes can be described by a “Double Couple” – “DC”, corresponding to a shear fracture

•  However some events exhibit more complex source mechanism such as volumetric component (ISO) and “Compensated Linear Vector Dipole” – “CLVD”.

•  A complete moment tensor including all these components can be written as:

MT =M11 M12 M13

M21 M22 M23

M31 M32 M33

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

Aki and Richards (1980)


Moment Tensors of Earthquakes

12

0 1 01 0 00 0 0

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

16

1 0 00 1 00 0 −2

"

#

$$$

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&

'''

13

1 0 00 1 00 0 1

!

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&&&

DC CLVD ISO

−1

−0.5

0

VA11

−0.10

0.10.2

VA21

−0.2−0.1

00.1

VA31

−0.2

0

0.2

VA41

0 1 2 3 4 5 6 7 8−0.2

0

0.2

VA51

Time (s)

0

0.5

1

VA11

−0.10

0.10.20.3

VA21

−0.10

0.10.2

VA31

−0.20

0.2

VA41

0 1 2 3 4 5 6 7 8−0.4−0.2

00.20.4

VA51

Time (s)

−0.4−0.2

00.20.40.6

VA11

−0.10

0.10.2

VA21

−0.10

0.10.2

VA31

−0.20

0.20.4

VA41

0 1 2 3 4 5 6 7 8−0.5

00.5

1

VA51

Time (s)


Least Square vs. Bayesian inversion

•  Least square method: cannot quantify the uncertainty well •  Bayesian inversion method: estimate the probability density

function of moment tensor solutions

Observed Data

Green’s Function: Velocity structure

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M11

M12

M13

M22

M23

M33

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########

Moment Tensor


Waveform-based Bayesian inversion (Adaptive Metropolis MCMC)

Prior

Information we know about the distribution of Mij before we do any inversion Here we use the first P-wave polarity.

Likelihood

How the waveform data are distributed for a given Mij

Posterior

The distribution of Mij solutions given the data

π 0 (Mij )∝1,0,

pol(Mij ) = polobs,

pol(Mij ) ≠ polobs.

⎧⎨⎪

⎩⎪

P(d |Mij )∝Pε (d −G(Mij ),σε2 )

π (Mij | d)∝P(d |Mij )π 0 (Mij )


Waveform-based Bayesian inversion

Polarity

Waveforms

Mij solu<on distribu<on

π 0 (Mij )

P(d |Mij )

π (Mij | d)



Polarity

Waveforms

Mij solu<on distribu<on High

Probability

Low Probability

M1

M2

π 0 (Mij )

P(d |Mij )

π (Mij | d)



Polarity

Waveforms

Mij solu<on distribu<on M1 High

Probability

Low Probability

M2

π 0 (Mij )

P(d |Mij )

π (Mij | d)


Synthetic test: Experiment setup

Step 1: Use a known synthetic source inside a layered structure Step 2: Calculate synthetic seismograms at five stations Step 3: Add 10% Gaussian noise Step 4: Estimate the moment tensor using the “observed” data Step 5: Quantify the uncertainties

05

10

0

5

10

0

1

2

3

4

T1

West to East (km)

T4T5T2

T3

South to North (km)

Depth

(km)

0 1000 2000 3000 4000 5000 6000 7000

0

500

1000

1500

2000

2500

3000

3500

4000Velocity (m/s)

Depth

(m)

VpVs

x = 8.18 km, y = 6.22 km, z = 1.14 km Strike = 305°, Dip = 20°, Rake = 85°DC%: 61, CLVD%: 17, ISO%: 21, α = 10°

NT1

T2

T5T3

T4

0 50 100 150 200 250 300−1

0

1 x 10−5

ST

A1

East Component

0 50 100 150 200 250 300−2

0

2 x 10−5 North Component

0 50 100 150 200 250 300−2

0

2 x 10−5 Vertical Component

0 100 200 300 400−2

0

2 x 10−6

ST

A2

0 100 200 300 400−5

0

5 x 10−6

0 100 200 300 400−5

0

5 x 10−6

0 100 200 300 400−2

0

2 x 10−6

ST

A3

0 100 200 300 400−2

0

2 x 10−6

0 100 200 300 400−2

0

2 x 10−6

0 50 100 150 200 250 300−5

0

5 x 10−6

ST

A4

0 50 100 150 200 250 300−5

0

5 x 10−6

0 50 100 150 200 250 300−1

0

1 x 10−5

0 50 100 150 200 250−5

0

5 x 10−5

ST

A5

Time (Sec)0 50 100 150 200 250

−2

0

2 x 10−5

Time (Sec)0 50 100 150 200 250

−2

0

2 x 10−5

Time (Sec)

Time (s)

Amp. (A

.U.) Blue: Data

Red: Model

Stable calculate uncertainty

P

T

Slide 14 2016 Annual Founding Members Mee<ng

Synthetic test: AM MCMC Bayesian Inversion Parameter M

ij

105 realizations of Mij

M11

M12

M22

M33

M13

M23 Search

Mij


Synthetic test: Uncertainty Quantification

Source Parameters

True Value

Posterior Mean

Standard Deviation

Strike 305° 304° 7°

Dip 20° 19° 3°

Rake 85° 85° 6°

DC% 61.3% 63.4% 7.7%

CLVD% 17.2% 17.7% 5.6%

ISO% 21.5% 18.9% 3.2%

α 10° 10° 4°

P

T


Induced Earthquakes from an Oil/Gas field in Oman


Oman: induced earthquake seismograms

Blue: Data Red: Model

0 1 2 3−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

VA 1

1

0 1 2 3−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

VA 2

1

0 1 2 3−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

VA 3

10 1 2 3 4−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

VA 4

1

0 1 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

VA 5

1Time (s)

Time (s)

Time (s)

Time (s)

Time (s)


Oman: Uncertainty Quantification

Source Parameters

Posterior Mean

Standard Deviation

Strike 53° 5°

Dip 81° 3°

Rake 154° 5°

DC% 70% 6%

CLVD% 7% 6%

ISO% 22% 4%

α (°) 4° 4°

P

T


Summary

Conclusions

•  Waveform-based Bayesian inversion can estimate the full moment tensor of seismicity and quantify the uncertainties of source parameters.

Future work •  Stress triggering analysis and geodynamic modeling •  Hazard assessment and damage measurement


Acknowledgement

•  This research was supported by the Kuwait-MIT Center (CNRE).

•  We thank Petroleum Development Oman for providing seismic data in Oman.

•  We also thank Dr. A. Al-Enezi and Ms. F. Al-Jeri for providing seismic data in Kuwait and assisting in the analysis.

Contact Email: [email protected]

Thank you!


Summary

Conclusions

•  Waveform-based Bayesian inversion can estimate the full moment tensor of induced seismicity and quantify the uncertainties of source mechanisms.

Future work •  Stress triggering analysis and geodynamic modeling •  Hazard assessment and damage measurement

new waveform-based bayesian full moment tensor inversion and … chen gu.pdf · 2016. 5. 20. ·...

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