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
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Full-waveform approach for complete moment tensor inversion using downhole microseismic data during hydraulic fracturing Fuxian Song, M. Nafi Toksöz Earth.
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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
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
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
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
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0 0.005 0.01 0.015 0.02 0.025
0
2
4
6
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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
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