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, Aug 15, 2011

Outline 1.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 (x 1,0, x 3 ) (0,0,x’ 3 ) X 1 (N) X 2 (E) X 3 (D) Previous studies and challenges Assumption: 1)Assume far field 2)Assume homogeneous velocity model, use only direct P and S arrivals Limitation: Can not invert for M 22 from single well data (x 1,0, x 3 ) (0,0,x’ 3 ) X 1 (N) X 2 (E) X 3 (D) Our approach: 1)Full waveform: both near and far field 2)1D layered velocity model, multiple arrivals Goal: Invert for the complete moment tensor from single well data 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 (M 0, r 0, c ISO, c DC, c CLVD, strike, dip, rake) Calculate seismic moment M 0 and component percentages Determine corner frequency f c and source radius r 0 Inverted complete MT Determine (strike, dip, rake) Diagonalize MT into M d Analyze S-wave displacement spectrum Full waveform inversion M d decomposition: M dc, M clvd, M iso

Source receiver configuration: single well vs. multiple well Well azimuth: East of North, B1: 0 0, B2: 45 0, 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 inversion Far field: waveforms not sensitive to M 22, 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 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 True moment tensor: [ ] (c DC, c ISO, c CLVD ): (74%, 11%, 15%) (Strike, Dip, Rake): (108 0, 80 0, 43 0 ) 1D velocity model derived from field study Source time function: smooth ramp with f 0 = 550 Hz Clean synthetic data: mean source-receiver distance: 60 ft (3.5 ) North component in red, East component in blue

Ref: Song et al., 2011 Unconstrained inversion of a non-double-couple source: near field Contribution from near field 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 Input: an approximate velocity model (up to 2% random perturbation) and a mislocated source (up to 20 ft in each direction). 10% Gaussian noise.

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: C ISO ~ 4%, C CLVD ~ 4%, C DC ~ 6%, M 0 ~ 6%, strike ~ 1 0, dip ~ 2 0, rake ~ 1 0 Two wells: C ISO ~ 3%, C CLVD ~ 3%, C DC ~ 4%, M 0 ~ 4%, strike ~ 1 0, dip ~ 2 0, rake ~ 1 0

Ref: Song et al., 2011 Constrained inversion of a non-double-couple source: far field  At far field, M 22 is the least resolvable element  Invert for the rest 5 MT elements and use a-priori information as constraints to determine M 22  Constrained inversion! One well at 0 0 azimuth, mean source-receiver distance: 345 ft (20 ) 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 test Constrained inversion of a non-double-couple source: far field Additional constraints: dip, strike uncertainty range +/ around true values  The cyan strip! Maximize DC percentage within that strip  Green vertical line: M 22 !

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: C ISO ~ 16%, C CLVD ~13%, C DC ~ 13%, M 0 ~ 11%, strike ~ 0 0, dip ~ 4 0, rake ~ 7 0 Two wells: C ISO ~ 6%, C CLVD ~13%, C DC ~ 13%, M 0 ~ 7%, strike ~ 3 0, dip ~ 4 0, rake ~ 5 0  At far field (> 5 S wavelength), by introducing a-priori constraints, complete MTs are invertible using full waveforms from one well

Field test: event horizontal view (Bossier gas play) Ref: Sharma et al., 2004 Select high SNR waveforms from the lower 6 geophones (12835 ~12940 ft) : Average noise level ~ 7% 7 test events: Depth range: ~ ft Average 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 Additional constraints: Dip range: 60 0 ~ 90 0 Strike range: +/ around N87 0 E or N-93 0 E  The cyan strip! Maximize DC percentage within that strip  Green verticals: M 22 !

Field test: full waveform fitting Modeled data in black, observed data in red: a) North component, b) East component 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: +/ around the average fracture trend Dip range: 60 0 ~ 90 0

Field test: corner frequency determined from S-wave Ref: Madariaga, 1976 Madariaga source model

Observations: 1)Strike values are generally consistent with average fracture trend (N87 0 E / N-93 0 E) 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 m 2. Field test: source parameter estimates from constrained inversion Event M w f c r 0 DC% ISO% CLVD% Strike Dip Rake Hz m % % % o o o

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, ft), Fluid net pressure: 6.9 Mpa (1000 psi), Shear strength: 7.4 MPa, Tensile strength: 4.58 MPa >0, Shearing Ref: Zhao et al., 2009

Griffith’s 2D crack model: shear stress distribution Overburden pressure: 89.8 MPa (1 psi/ft, ft), Fluid net pressure: 6.9 Mpa (1000 psi), Shear strength: 7.4 MPa, Tensile strength: 4.58 MPa >0, Shearing Ref: Zhao et al., 2009

Griffith’s 2D crack model: normal stress distribution Overburden pressure: 89.8 MPa (1 psi/ft, 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, 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

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 C ISO (%) C CLVD (%) C DC (%) M 0 (%) Strike ( o )Dip ( o ) Rake ( o ) 2 well well with range constraint well with strike constraint

Observations: 1)Strike estimates are generally consistent with event trends (N87 0 E or N-93 0 E) 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 m 2. Field test: source parameter estimates from constrained inversion Event M 0 M w f c r 0 DC% ISO% CLVD% Strike Dip Rake 10 4 N∙m Hz m % % % o o o

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 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: Ref: Finck, Analyze rock failure mechanism: 3. Determine induced fracture plane orientation: fracture strike, dip, rake Multiple event locationMoment tensor inversion of a single event 4. Estimate stress state: SH min, SH max,

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, +/ around true value Mean absolute errors: One well: C ISO ~ 23%, C CLVD ~11%, C DC ~ 10%, M 0 ~ 25%, strike ~ 12 0, dip ~ 9 0, rake ~ 9 0 Two wells: C ISO ~ 6%, C CLVD ~13%, C DC ~ 13%, M 0 ~ 7%, strike ~ 3 0, dip ~ 4 0, rake ~ 5 0  At far field (~ 20 S wavelength), by introducing a-priori constraints, complete MTs are invertible using full waveforms from one well

Velocity model and perturbation

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: [ ] (c DC, c ISO, c CLVD ): (74%, 11%, 15%) (Strike, Dip, Rake): (108 0, 80 0, 43 0 ) 1D velocity model derived from field study Source function: smooth ramp with f 0 = 550 Hz

Ref: Song et al., 2011 Unconstrained inversion of a non-double-couple source: near field Zooming factor: 30 a) After adding 10% Gaussian noise Reference signal level: maximum absolute amplitude averaged across receivers (max over components) b) After [ ] Hz band-pass filtering

Summary of estimated source parameters 1) Seismic moment, moment magnitude, isotropic component percentage and strike estimate 2) Source radius according to Madariaga ‘s source model

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, ) Vavrycuk, Geophysical Prospecting ) Baig & Urbancic, The Leading Edge, 2010 (0,x 2,x 3 ) (0,0,x 3 ) X 1 (N) X 2 (E) X 3 (D) Why M22 not invertible at far field? Far field P-wave Far field S-wave

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: 1. Infer fracture size from event size: 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: