Full-waveform approach for complete moment tensor inversion using downhole microseismic data during...

$: Full-waveform approach for complete moment tensor inversion using downhole microseismic data during hydraulic fracturing Fuxian Song, M. Nafi Toksöz Earth.$
Full-waveform approach for complete moment tensor inversion using downhole microseismic data during

hydraulic fracturing

Fuxian Song, M. Nafi Toksöz

Earth Resources Laboratory, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, 02139

Aug 15, 2011

Outline1. Objective

2. Introduction• Microseismic monitoring for hydraulic fracturing

• Microseismic moment tensor

• Downhole microseismic moment tensor inversion: previous work and challenges

• Introduction to full waveform based moment tensor inversion and source estimation

3. Test with synthetic data • Condition number of the sensitivity matrix A

• Unconstrained inversion of a non-double-couple source: near field

• Constrained inversion of a non-double-couple source: far field

4. Field test

5. Conclusion

Objective

• Study the feasibility of inverting complete seismic moment tensor and stress regime from one single monitoring well by matching full waveforms

• Fracture plane geometry, together with shear and volumetric components derived from complete moment tensors contain important information on fracturing dynamics. A better understanding of fracturing mechanism and growth eventually leads to a better hydraulic fracturing treatment.

Conclusion

1. Understanding the dynamics of fracture growth requires knowledge of complete moment tensors

2. At near field (< 5 S-wavelengths), a complete moment tensor solution can be obtained from one well data without a priori constraints.

3. At far field (> 5 S-wavelengths), a priori constraints are needed for complete moment tensor inversion using one well data.

4. Two wells are sufficient to resolve complete moment tensors, even at far field.

5. Initial field results show a dominant double-couple component in hydrofrac events, while a non-negligible volumetric component is also seen in some events.

Microseismic monitoring for hydraulic fracturing

1) Event locations to map fractures

2) Source studies to determine fracture orientation, size, rock failure mechanism and stress state

Ref: Stein & Wysession, 2003

Seismic moment tensor

Complete moment tensor:

6 independent components of this symmetric matrix

Ref: Vavrycuk, 2007; Baig & Urbancic, 2010

(x1,0, x3)

(0,0,x’3)

X1(N)

X2(E)

X3(D)

Previous studies and challenges

Assumption:1) Assume far field2) Assume homogeneous velocity model,

use only direct P and S arrivals

Limitation: Can not invert for M22 from single well data

(x1,0, x3)

(0,0,x’3)

X1(N)

X2(E)

X3(D)

Our approach: 1) Full waveform: both near and far field2) 1D layered velocity model, multiple arrivals

Goal: Invert for the complete moment tensor from single welldata and estimate source parameters

Ref: Song et al., 2010, 2011

Ref: Song et al., 2011

Full waveform based moment tensor inversion

Grid search over event location and origin time

Determine the best MT (with the smallest fitting error)

Evaluate the inverted MT (for source parameters)

Pre-calculate Green’s function(for each said event location)

Linear inversion to obtain the complete MT(for each said event location and origin time)

Multi-component microseismic data

Preprocessing (noise filter)

Methodology for source parameter estimation

Ref: Jost & Herrmann, 1989; Vavrycuk, 2001; Song et al., 2010, 2011

Source parameters(M0 , r0 , cISO, cDC, cCLVD, strike, dip, rake)

Calculate seismic moment M0 and component percentages

Determine corner frequency fc

and source radius r0

Inverted complete MT

Determine (strike, dip, rake)Diagonalize MT into Md

Analyze S-wave displacement spectrum

Full waveform inversion

Md decomposition: Mdc, Mclvd, Miso

Source receiver configuration: single well vs. multiple well

Well azimuth: East of North, B1: 00, B2: 450 , etc.

Sensitivity matrix A: elementary seismograms derived from Green’s function

Complete moment tensor:6 independent elements

Observed data: velocity data

Condition number of matrix A: 1) Provides an upper bound on errors of the inverted moment tensor due to noise in the data; 2) The least resolvable MT element determined by the eigenvector of the smallest eigenvalue.


Influence of well coverage and mean source receiver distance

• Condition number increases with increased source receiver distance Near field: waveforms sensitive to all 6 components; unconstrained inversionFar field: waveforms not sensitive to M22, additional constraints needed; constrained inversion

• Condition number doesn’t improve much when comparing 2 wells with 8 wells 2 wells sufficient to recover all 6 components

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

140

160

180

200

Mean source receiver distance (S)

Con

d(A

)

8 wells2 wells@azimuth 0,45 degrees1 well@azimuth 45 degrees1 well@azimuth 0 degree

a)

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

140

160

180

200

Mean source receiver distance (S)

Con

d(A

)

3C@azimuth 0 degrees2C@azimuth 0 degrees

b)

• Condition number only increases slightly when using only horizontal components


Unconstrained inversion of a non-double-couple source: near field

0 0.005 0.01 0.015 0.02 0.025

0

1

2

3

4

5

6

7

8

506s

505s

504s

303s

302s

101s

Time (s)

Geo

phon

e in

dex

P S

True moment tensor:[0.43 -0.72 0.78 -0.72 -0.37 0.02 0.78 0.02 0.39]

(cDC, cISO, cCLVD ): (74%, 11%, 15%)

(Strike, Dip, Rake):(1080, 800, 430)

1D velocity model derived from field study

Source time function: smooth ramp with f0 = 550 Hz

Clean synthetic data:mean source-receiver distance: 60 ft (3.5 )North component in red, East component in blue

s



Contribution from near field

0 0.005 0.01 0.015 0.02 0.025

0

1

2

3

4

5

6

7

8

506s

505s

504s

303s

302s

101s

Time (s)G

eoph

one

inde

x

b)

0 0.005 0.01 0.015 0.02 0.025

0

1

2

3

4

5

6

7

8

506s

505s

504s

303s

302s

101s

Time (s)

Geo

ph

one

ind

ex

P Sa)

Near field terms onlyTotal wave-fields

Average peak amplitude ratios (near-field terms/total wave-fields):

9%, 11%, 14%, 18%, 22% and 60% for geophones 1 to 6



a) waveform fitting: North component

b) waveform fitting: East component

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

Time (s)

Geo

phon

e in

dex

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

8

Time (s)

Geo

phon

e in

dex

a)

b)

Input: an approximate velocity model (up to 2% random perturbation) and a mislocated source (up to 20 ft in each direction). 10% Gaussian noise.

-20 -15 -10 -5 0 5 10 15 200

20

40

ISO error (%)

Freq

uenc

y

-20 -15 -10 -5 0 5 10 15 200

20

40

CLVD error (%)

Freq

uenc

y

-20 -15 -10 -5 0 5 10 15 200

20

40

DC error (%)

Freq

uenc

y

-20 -15 -10 -5 0 5 10 15 200

20

40

Seismic moment error (%)

Freq

uenc

y

-6 -4 -2 0 2 4 60

10

20

30

Strike error (degrees)

Freq

uenc

y

-6 -4 -2 0 2 4 60

10

20

30

Dip error (degrees)

Freq

uenc

y

-6 -4 -2 0 2 4 60

10

20

30

Rake error (degrees)

Freq

uenc

y



At near field (<5 S wavelength), complete MTs are invertible using full waveforms from one well without constraints.

Mean absolute errors: One well: CISO ~ 4%, CCLVD ~ 4%, CDC ~ 6%, M0~ 6%, strike ~ 10, dip ~ 20, rake ~ 10

Two wells: CISO ~ 3%, CCLVD ~ 3%, CDC ~ 4%, M0~ 4%, strike ~ 10, dip ~ 20, rake ~ 10


Constrained inversion of a non-double-couple source: far field

At far field, M22 is the least resolvable element

Invert for the rest 5 MT elements and use a-priori information as constraints to determine M22

Constrained inversion!

One well at 00 azimuth, mean source-receiver distance: 345 ft (20 )s

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

140

160

180

200

Mean event receiver distance (S)

Con

d(A

)

M22 excluded, Layered mediumM22 excluded, Homogeneous mediumM22 included, Layered medium

Both near field information and additional refracted/reflected rays from layered structure contributes to the decrease of the condition number


Synthetic testConstrained inversion of a non-double-couple source: far field

Additional constraints: dip, strike uncertainty range +/- 150 around true values The cyan strip!

Maximize DC percentage within that strip Green vertical line: M22!


Input: 10% Gaussian noise, up to 2% velocity model errors, up to 20 ft location errors in each direction; Constraints: known strike value

Mean absolute errors: One well: CISO ~ 16%, CCLVD~13%, CDC ~ 13%, M0~ 11%, strike ~ 00, dip ~ 40, rake ~ 70

Two wells: CISO ~ 6%, CCLVD~13%, CDC ~ 13%, M0~ 7%, strike ~ 30, dip ~ 40, rake ~ 50

At far field (> 5 S wavelength), by introducing a-priori constraints, complete MTs are invertible using full waveforms from one well

-10 -8 -6 -4 -2 0 2 4 6 8 100

50

100


Fre

quen

cy

-15 -10 -5 0 5 10 150

10

20

Dip error (degrees)

Fre

quen

cy-25 -20 -15 -10 -5 0 5 10 15 20 250

10

20

Rake error (degrees)

Fre

quen

cy

-60 -40 -20 0 20 40 600

10

20

ISO error (%)

Fre

quen

cy

-50 -40 -30 -20 -10 0 10 20 30 40 500

10

20

CLVD error (%)

Fre

quen

cy

-60 -40 -20 0 20 40 600

10

20

DC error (%)

Fre

quen

cy

-60 -40 -20 0 20 40 600

10

20


Fre

quen

cy

Field test: event horizontal view (Bossier gas play)

Ref: Sharma et al., 2004

-250 -200 -150 -100 -50 0 50

-50

0

50

100

150

200

Easting (m)

Nor

thin

g (m

)

Monitoring well

Injection well

Bonner Azimuth = N870E or N(-930)E

Select high SNR waveforms from the lower 6 geophones (12835 ~12940 ft) :Average noise level ~ 7%

7 test events:Depth range: 13040 ~ 13100 ftAverage distance from center receiver: 350 ft

Only horizontal components used in inversion:noisy vertical component due to poor clamping

Field test: constrained inversion

Ref: Song et al., 2011; Warpinski et al. 2010

Additional constraints: Dip range: 600 ~ 900

Strike range: +/- 600 around N870E or N-930E The cyan strip!

Maximize DC percentage within that strip Green verticals: M22!

Field test: full waveform fitting

Modeled data in black, observed data in red: a) North component, b) East component

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

0

2

4

6

Time (s)

Geo

phon

e in

dex

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

0

2

4

6

Time (s)

Geo

phon

e in

dex

a)

b)

Good fit in both major P and S wave trains

Un-modeled wave packages probably due to un-modeled lateral heterogeneity

Constraints (one well data):Strike range: +/- 600 around the average fracture trend

Dip range: 600 ~ 900

Field test: corner frequency determined from S-wave

Ref: Madariaga, 1976

101

102

103

104

10-16

10-14

10-12

10-10

Frequency: Hz

Dis

plac

emen

t spe

ctra

l den

sity

: m*s

2)(1

0)(

cff

sQ

sVfR

efU

Hz 481 cf m 2.12

32.10r

cf

sV

Madariaga source model

Observations: 1) Strike values are generally consistent with average fracture trend (N870E / N-930E)

2) Double-couple component is dominant for most events, but for some events, the isotropic component is non-negligible.

3) Event moment magnitude ranges from -4 to -2. Rupture area of these events are also small, only a few m2.

Field test: source parameter estimates from constrained inversion

Event Mw fc r0 DC% ISO% CLVD% Strike Dip Rake

Hz m % % % o o o

1 -3.22 481 1.2 96 1 -3 108 81 43 2 -3.36 561 1.0 68 3 -29 107 62 8 3 -3.06 547 1.1 52 48 0 -122 65 -168 4 -2.89 564 1.0 69 31 0 -128 66 0 5 -3.30 714 0.8 87 -13 0 -124 73 -151 6 -3.05 736 0.8 45 55 0 83 63 -158 7 -3.05 744 0.8 82 18 0 138 73 -43

Conclusion

1. Understanding the dynamics of fracture growth requires knowledge of complete moment tensors

2. At near field (< 5 S-wavelengths), a complete moment tensor solution can be obtained from one well data without a priori constraints.

3. At far field (> 5 S-wavelengths), proper a priori constraints are needed for complete moment tensor inversion using one well data.

4. Two wells are generally sufficient to resolve complete moment tensors, even at far field.

5. Initial field results show a dominant double-couple component in hydrofrac events, while a non-negligible volumetric component is also seen in some events.

6. Future work includes more field tests and some geo-mechanical modeling to understand the observed source mechanisms.

Acknowledgement

• Dr. Norm Warpinski, Dr. Jing Du, and Dr. Qinggang Ma from Pinnacle/Halliburton

• Dr. Bill Rodi, Dr. Mike Fehler, and Dr. H. Sadi Kuleli from MIT

Thanks for your attention!

Questions or comments?

-----Backup----

Discussion: Open questions about dynamics of hydrofractures

1) Why a dominant double-couple component? Why hydrofracture propagates as shearing instead of tensile growth?

Griffith’s crack model to calculate stress distribution

2) What is the influence of pre-existing fractures on hydraulic fracture growth?

3) In the far field, does the hydraulic fracture propagate along the pre-existing fracture or along the maximum horizontal stress direction?

Griffith’s 2D crack model: shear stress distribution

Overburden pressure: 89.8 MPa (1 psi/ft, 13040 ft), Fluid net pressure: 6.9 Mpa (1000 psi), Shear strength: 7.4 MPa, Tensile strength: 4.58 MPa

x/c: fracture length direction

y/c

: fr

actu

re w

idth

dire

ctio

n

Maximum Shear Stress after deducting the shear strength: 2D crack

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0

10

20

30

40

50

60

>0, Shearing

Ref: Zhao et al., 2009

Griffith’s 2D crack model: shear stress distribution


>0, Shearing


y/c

: fr

actu

re w

idth

dire

ctio

n

Maximum Shear Stress after deducting the shear strength: 2D crack

0.5 1 1.5

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0

10

20

30

40

50

60


Griffith’s 2D crack model: normal stress distribution


y/c

: fr

actu

re w

idth

dire

ctio

n

Normal Stress after deducting overburden pressure and the tensile strength: 2D crack

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 -50

0

50

100


<0,tensile

>0, compressive


Griffith’s 2D crack model: normal stress distribution


<0,tensile

>0, compressive


y/c

: fr

actu

re w

idth

dire

ctio

n

Normal Stress after deducting overburden pressure and the tensile strength: 2D crack

0.96 0.97 0.98 0.99 1 1.01 1.02 1.03

-0.03

-0.02

-0.01

0

0.01

0.02

-50

0

50

100



Comparison of mean absolute errors in the inverted source parameters from the one-well case and two-well case

CISO

(%)CCLVD (%)

CDC (%)

M0

(%)Strike (o) Dip

(o)Rake

(o)

2 well 6 13 13 7 3 4 5

1 well with range constraint

23 11 10 25 12 9 9

1 well with strikeconstraint

16 13 13 11 0 4 7

Observations:

1) Strike estimates are generally consistent with event trends (N870E or N-930E)

2) Double-couple component is dominant for most events, but for some events, the isotropic component is non-negligible.

3) Event moment magnitude ranges from -4 to -2. Rupture area of these events are also small, only a few m2.

Field test: source parameter estimates from constrained inversion

Event M0 Mw fc r0 DC% ISO% CLVD% Strike Dip Rake

104N∙m Hz m % % % o o o

1 1.8 -3.22 481 1.2 96 1 -3 108 81 43 2 1.1 -3.36 561 1.0 68 3 -29 107 62 8 3 3.1 -3.06 547 1.1 52 48 0 -122 65 -168 4 5.8 -2.89 564 1.0 69 31 0 -128 66 0 5 1.4 -3.30 714 0.8 87 -13 0 -124 73 -151 6 3.2 -3.05 736 0.8 45 55 0 83 63 -158 7 3.3 -3.05 744 0.8 82 18 0 138 73 -43



a) waveform fitting: North component

b) waveform fitting: East component

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

Time (s)

Geo

phon

e in

dex

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

8

Time (s)

Geo

phon

e in

dex

a)

b)

Input: an approximate velocity model (up to 2% random perturbation) and a mislocated source (up to 20 ft in each direction). 10% Gaussian noise. Grid search range, space 15*15*11, origin time: 2 dominant periods, space: 5ft; origin time: 0.25 ms (Sampling frequency: 4KHz)

Source studies from seismic moment tensor

1. Infer fracture size from event size: g(M)))max(abs(ei 0

M

Ref: Finck, 2004

2. Analyze rock failure mechanism:

DCMCLVDMISOM dM M

3. Determine induced fracture plane orientation: fracture strike, dip, rake

Multiple event locationMoment tensor inversion of a single event

4. Estimate stress state: SHmin , SHmax ,


Input: 10% Gaussian noise, up to 2% velocity model errors, up to 20 ft location errors in each direction, Constraints: dip, strike range, +/- 150 around true value

-20 -15 -10 -5 0 5 10 15 200

50

100


Fre

quen

cy

-20 -15 -10 -5 0 5 10 15 200

20

40

Dip error (degrees)

Fre

quen

cy-30 -20 -10 0 10 20 300

10

20

Rake error (degrees)F

requ

ency

-60 -40 -20 0 20 400

2040

ISO error (%)

Fre

quen

cy

-60 -40 -20 0 20 400

2040

CLVD error (%)

Fre

quen

cy

-60 -40 -20 0 20 400

1020

DC error (%)

Fre

quen

cy

-40 -20 0 20 40 60 80 1000

1020


Fre

quen

cy

Mean absolute errors: One well: CISO ~ 23%, CCLVD~11%, CDC ~ 10%, M0~ 25%, strike ~ 120, dip ~ 90, rake ~ 90

Two wells: CISO ~ 6%, CCLVD~13%, CDC ~ 13%, M0~ 7%, strike ~ 30, dip ~ 40, rake ~ 50

At far field (~ 20 S wavelength), by introducing a-priori constraints, complete MTs are invertible using full waveforms from one well

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

8

10

Geo

phon

e in

dex

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

8

10

Time (s)

Geo

phon

e in

dex

a)

b)

Velocity model and perturbation

4200 4300 4400 4500 4600 4700 4800 4900 5000 5100

3800

3900

4000

4100

Dep

th (

m)

Vp perturbedVp reference

2300 2400 2500 2600 2700 2800 2900

3800

3900

4000

4100

Velocity (m/s)

Dep

th (

m)

Vs perturbedVs reference

Field test: Bonner gas play in East Texas

Ref: Griffin et al., 2003; Sharma et al., 2004



True moment tensor:[0.43 -0.72 0.78 -0.72 -0.37 0.02 0.78 0.02 0.39]

(cDC, cISO, cCLVD ): (74%, 11%, 15%)

(Strike, Dip, Rake):(1080, 800, 430)

1D velocity model derived from field study

Source function: smooth ramp with f0 = 550 Hz

0 0.005 0.01 0.015 0.02 0.025

0

1

2

3

4

5

6

7

8

506s

505s

504s

303s

302s

101s

Time (s)

Geo

phon

e in

dex

P S



Zooming factor: 30

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

8

10

Geo

phon

e in

dex

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

8

10

Time (s)

Geo

phon

e in

dex

a)

b)

a) After adding 10% Gaussian noise

Reference signal level: maximum absoluteamplitude averaged across receivers (max over components)

b) After [200 900] Hz band-pass filtering

Summary of estimated source parameters

iM max

0

0

)(

3

1

M

jkmtrISOc

067.6)0

(10

log3

2 M

wM

1) Seismic moment, moment magnitude, isotropic component percentage and strike estimate

cf

sV

r2

32.1

0

2) Source radius according to Madariaga ‘s source model

||||1 ISOcCLVDcDCc

ISOcCLVDc 12

*max

*min


Test event 2: a) North component fitting, b) East component fitting


Test event 3: a) North component fitting, b) East component fitting

Ref: 1) Nolen-Hoeksema, & Ruff, Tectonophysics, 20012) Vavrycuk, Geophysical Prospecting 20073) Baig & Urbancic, The Leading Edge, 2010

(0,x2,x3)

(0,0,x3)

X1(N)

X2(E)

X3(D)

Why M22 not invertible at far field?

],,0[],,[ 32321 nn

Far field P-wave Far field S-wave

rtM

r

rtM

r

rtM

r

rtM

r

dtMr

GM

pqqnppn

pqqpn

pqnpqnqppqnqpn

pqnpqnqppqnqpn

r

rpq

npqnqppqnqpnqnppq

1

4

1

4

1

4

26

1

4

6

)(1

4

33315

33

22

22

/

4,

Statement

Hydraulic fracturing has become an important process in the energy industry.

Production of oil, natural gas from unconventional sources (tight sands, gas shales)

and geothermal energy require hydraulic fracturing at some stage of their

development. Even CO2 injection for geologic sequestration produces hydraulic

fracturing.

Understanding the dynamics of fracture initiation, propagation and growth in the earth

is a challenging problem. Mechanisms of microearthquakes generated during

fracturing contain important information for fracture dynamics. Analysis of observed

events is essential for developing a better understanding of fracturing.


2. Analyze rock failure mechanism:

0

)d

M(tr

3

1 ;

dM M

MISOc

DCM

CLVDM

ISOM

1. Infer fracture size from event size: g(M)))max(abs(ei 0

M

Ref: Finck, 2004


3. Determine induced fracture plane orientation: fracture strike

Multiple event locationMoment tensor inversion of a single event

4. Estimate stress drop:

Full-waveform approach for complete moment tensor inversion using downhole microseismic data during...

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