Post on 11-Jan-2016
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.
Ref: Song et al., 2011
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
Ref: Song et al., 2011
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
Ref: Song et al., 2011
Unconstrained inversion of a non-double-couple source: near field
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
Ref: Song et al., 2011
Unconstrained inversion of a non-double-couple source: near field
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
Ref: Song et al., 2011
Unconstrained inversion of a non-double-couple source: near field
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
Ref: Song et al., 2011
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
Ref: Song et al., 2011
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!
Constrained inversion of a non-double-couple source: far field
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
Strike error (degrees)
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
Seismic moment error (%)
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
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
>0, Shearing
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
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
Ref: Zhao et al., 2009
Griffith’s 2D crack model: normal stress distribution
x/c: fracture length direction
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
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
<0,tensile
>0, compressive
Ref: Zhao et al., 2009
Griffith’s 2D crack model: normal 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
<0,tensile
>0, compressive
x/c: fracture length direction
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
Ref: Zhao et al., 2009
Constrained inversion of a non-double-couple source: far field
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
Ref: Song et al., 2011
Unconstrained inversion of a non-double-couple source: near field
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 ,
Constrained inversion of a non-double-couple source: far field
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
Strike error (degrees)
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
Seismic moment error (%)
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
Ref: Song et al., 2011
Unconstrained inversion of a non-double-couple source: near field
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
Ref: Song et al., 2011
Unconstrained inversion of a non-double-couple source: near field
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
Field test: full waveform fitting
Test event 2: a) North component fitting, b) East component fitting
Field test: full waveform 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.
Source studies from seismic moment tensor
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
Source studies from seismic moment tensor
3. Determine induced fracture plane orientation: fracture strike
Multiple event locationMoment tensor inversion of a single event
4. Estimate stress drop: