Microseismic Event Estimation Via Full Waveform Inversion

Transcription

1 Microseismic Event Estimation Via Full Waveform Inversion Susan E. Minkoff 1, Jordan Kaderli 1, Matt McChesney 2, and George McMechan 2 1 Department of Mathematical Sciences, University of Texas at Dallas 2 Department of Geosciences, University of Texas at Dallas Richardson, TX 758, USA IMA Hot Topics Workshop Hydraulic Fracturing: From Modeling and Simulation to Reconstruction and Characterization May 13, 215

2 Exploration Seismology Exploration is the search for commercial deposits of useful minerals, including hydrocarbons, geothermal resources, etc. Source generates a disturbance (wave). Wave reflects when it encounters a change in material properties. Returning wave is recorded using seismometers at the earth s surface. We can analyze the recorded data to image the earth s interior. Source can be intentional or active (e.g. explosion) or unintentional or passive (e.g. earthquake). Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 2 / 31

3 Hydraulic Fracturing (a) Hydraulic Fracturing Fracking is used to extract oil and gas from materials with low permeability such as shale. High pressure liquid is injected into the well to create fracture openings that allow oil and gas to flow more freely. Buildup of pressure and stress may result in a microseismic event (small earthquake), thus generating a passive source for imaging. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 3 / 31

4 Hydraulic Fracturing Simulation and Elastic Response (the Big Picture) Processing Workflow: Using the Complex Fracture Research Code (CFRAC) (courtesy of Marc McClure, UT Austin, CPGE), model coupled flow and deformation to synthesize microseismic events produced by hydraulic fracturing. The code models hydraulic injection of a single phase fluid into an impermeable isotropic medium with discrete fractures. Deformation is modeled in a 2D plane assuming quasistatic equilibrium. Extract synthesized microseismic events from the flow/deformation code and inject the microseisms into an 3D (visco)elastic wave modeling code (courtesy of George McMechan, UTD, Geosciences). Model the elastic wave response resulting from these microseismic sources. Result could be used as forward model for inversion. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 4 / 31

5 Numerical Example: Problem Setup 4 Fracture Geometry 8 Well Stimulation Treatment Curves Y (m) Injection Rate (kg/s) Injection Pressure (MPa) X (m) (b) Fracture Geometry: black line is well; blue line is natural fracture; red lines are (potential) hydraulic fractures Time (sec) (c) Well Treatment Curve Student Version of MATLAB Student Version of MATLAB Model contains a single natural fracture transecting an open wellbore. Strike of natural fracture is 6. Two potentially forming hydraulic fractures at ends of natural fracture (strike is 9 ). Injection pressure held constant at 6 MPa. Injection rate varies with time as failures occur along the fracture(s). Note: additional injection rate variation after about 5 s due to failure on hydraulic fracture. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 5 / 31

6 Numerical Example: Microseismic Event Generation 4 Fracture Geometry with Microseismic Hypocenters 8 Well Stimulation Treatment Curves with Microseismic Events Y (m) Injection Rate (kg/s) Microseismic Moment Magnitude X (m) Time (sec) (d) Fracture Geometry with microseisms (e) Well Treatment Curve with microseisms Microseismic events defined to occur when sliding velocity reaches.5 m/s. Student Version of MATLAB One event has occurred Student along Version of MATLAB the potentially forming hydraulic fracture. Microseismic events correlate with changes in flow rate. Microseismic event at 525 s corresponds to failure on hydraulic fracture. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 6 / 31

7 Microseism 13 Well Natural Fractures Hydraulic Fractures Microseismic Hypocenters Geophone Locations Numerical Example: Elastic Wave Modeling from Microseismic Event 13 4 v x snapshot 8 ms x y cordianate [m] Seismic Amplitude (m/s) x coordinate [m] (f) Fracture Geometry with microseismic hypocenters (g) X-component of particle velocity modeled using microseismic event 13 Student Version of MATLAB 4 v y snapshot 8 ms x v z snapshot 8 ms x y cordianate [m] Seismic Amplitude (m/s) y cordianate [m] Seismic Amplitude (m/s) x coordinate [m] x coordinate [m] (h) Particle velocity (y) (i) Particle velocity (z) Student Version of MATLAB Student Version of MATLAB Microseismic source has dip of 9, strike of 9, and rake of. Small microseismic event occurred along potentially forming hydraulic fracture. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 7 / 31

8 Microseism 14 Well Natural Fractures Hydraulic Fractures Microseismic Hypocenters Geophone Locations Numerical Example: Elastic Wave Modeling from Microseismic Event 14 4 v x snapshot 8 ms y cordianate [m] Seismic Amplitude (m/s) x coordinate [m] (j) Fracture Geometry with microseismic hypocenters 4 35 v y snapshot 8 ms.1.8 (k) X-component of particle velocity modeled using microseismic event v z snapshot 8 ms Student Version of MATLAB y cordianate [m] Seismic Amplitude (m/s) y cordianate [m] Seismic Amplitude (m/s) x coordinate [m] x coordinate [m] (l) Particle velocity (y) (m) Particle velocity (z) Microseismic source has dip of 9, strike of 6, and rake of. Student Version of MATLAB Student Version of MATLAB Microseismic event occurred along natural fracture. Note the directional polarity of the emitted wavefield. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 8 / 31

9 Numerical Example: Receiver Data for Microseismic Event 13 X-component of particle velocity as recorded at the receiver locations. Note the existence of both P and S-wave arrivals in the recorded seismograms. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 9 / 31

10 Outline Goal is to estimate the microseismic source using full waveform inversion. I. Description of Problem and Approach II. Overview of Full Waveform Inversion III. Numerical Experiments for Source Location and Onset Time IV. Discussion of Future Work Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 1 / 31

11 Traditional Methods for Microseismic Event Detection Figure: Traditional Methods rely on traveltime picking of first arrivals. (a) Event estimation using clean data (b) Event estimation using noisy data Reference (courtesy of Pioneer Natural Resources): 1. Han L., J. Wong, and J. C. Bancroft, Hypocenter location using hodogram analysis of noisy 3C microseismograms, CREWES Research Report - Vol. 21, University of Calgary, (29), pp Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 11 / 31

12 Seismic Full Waveform Inversion 1 2 u c 2 t 2 2 u = s (c) Forward Problem (d) Velocity Inversion (e) Source Inversion Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 12 / 31

13 Assumptions We model wave propagation through a constant density medium using the acoustic wave equation: m(x, z) 2 u(x, z, t) 2 u(x, z, t) = f (x, z)w(t) t 2 where m(x, z) is the known squared slowness, i.e. the reciprocal of the sound velocity squared, f (x, z) is the spatial component of the source of acoustic energy, w(t) is a Ricker wavelet, and u(x, z, t) is the acoustic pressure. In the typical inverse problem, we know f (x, z)w(t), and we want to determine the sound velocity, i.e. we want to find m(x, z). In our source inversion problem, we know m(x, z), and we want to find f (x, z)w(t). Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 13 / 31

14 Overview of Full Waveform Inversion 1 1 Choose initial guess f. 2 Given the correct sound velocity and the current source estimate f n, solve the wave equation u n = F [f n]. 3 Compute the residual u n d obs, where d obs is the recorded data. 4 Solve the adjoint equation backwards in time using the residual as the source F (u n d obs ). 5 Compute the gradient to find a descent direction for the least squares objective function J(f ) = 1 2 F (f ) d obs 2. 6 Update the model f n+1 = f n α gradient. 7 Increment n and loop back to Step 2. 1 Note: all experiments shown were implemented using a modified version of PySIT, a seismic inversion toolbox developed originally by the Imaging and Computing Group at MIT. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 14 / 31

15 Comparison of gradient for velocity inversion vs. source inversion In the typical velocity inversion problem, J(m) = 1 2 In our source inversion problem, J(f ) = 1 2 P In the typical velocity inversion problem, δ mj = P s s,r P s,r h R i T (Ss,r u ds,r )2 dt. h R i T (Ss,r u ds,r )2 dt. h R i T ( m 2 u, λ)dt. t 2 In our source inversion problem, δ f J = P s h R T (w, λ)dt i. We do not need to store the forward model data for all time steps. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 15 / 31

16 Overview of Full Waveform Inversion Step 1: Given the correct sound velocity and an initial guess for the source f, solve the wave equation u = F [f ]. (f) Experimental Setup (g) Receiver Data for Initial Source Note that F is the forward operator, i.e. the wave equation operator, and maps from the x-z domain to the t-x domain. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 16 / 31

17 Overview of Full Waveform Inversion Step 2: Compute the residual u n d obs. (h) Receiver Data for Initial Source (i) Recorded Data (j) Residual Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 17 / 31

18 Overview of Full Waveform Inversion Step 3: Solve the adjoint equation backwards in time using the residual as the source F (u n d obs ). (k) Residual (l) Adjoint Field at time t = 1.5 (m) Adjoint Field at time t = Note that F (the adjoint operator) maps from the t-x domain to the x-z domain. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 18 / 31

19 Overview of Full Waveform Inversion Step 4: Compute the gradient to find a descent direction for the least squares objective function J(f ) = 1 2 F (f ) d obs 2. (n) Gradient Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 19 / 31

20 Overview of Full Waveform Inversion Step 5: Update the model f n+1 = f n α gradient. (o) f n (p) α gradient (q) f n+1 Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 2 / 31

21 Overview of Full Waveform Inversion Step 6: Increment n and loop back to Step 1: Given the correct sound velocity and the current source estimate f n, solve the wave equation u n = F [f n]. (r) Receiver Data after 1 Iteration (s) Recorded Data Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 21 / 31

22 Numerical Experiments: inverting for spatial component of the source (f ) Note: for all the experiments shown, Domain is size 181 x 141. Velocity is assumed constant and known. For this experiment Time-dependent component of source is 2 Hz Ricker wavelet (known). Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 22 / 31

23 Inverting for spatial component of the source using noisy data Initial source estimate is zero everywhere. Data has a.8 signal-to-noise ratio!! Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 23 / 31

24 Inverting for time-dependent part of the source (w) Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 24 / 31

25 Inverting for time-dependent part of the source using noisy data Data has.83 signal-to-noise ratio!! Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 25 / 31

26 Joint inversion for both the time and space components of the source Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 26 / 31

27 Joint inversion for both the time and space components of the source Problem: source is too spread out in space which has a corresponding impact on the time dependence. Need to focus the source. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 27 / 31

28 Adding L 1 Regularization With regularization our new objective function for the spatial component of the source is J(f ) = 1 2 F (f ) d obs λ f 1 where λ is a penalty parameter. Anywhere in the domain where the source is zero (in our case, almost everywhere), the second term above is not differentiable. Several L 1 minimization algorithms attempt to handle this problem. We focus on Iteratively Reweighted Least Squares (IRLS 12 ): Away from f i =, gradient of the regularization term f 1 contains components f i / f i. Defining a diagonal matrix W with elements W i,i = 1/ f i we can handle the non-differentiability at f i = by j 1/ fi f i ɛ W i,i = 1/ɛ f i < ɛ or by where ɛ is a tolerance, and f 1 = Wf. q W i,i = 1/ (fi 2 + ɛ 2 ) 1 Daubechies, Devore, Fornasier, Gunturk, Iteratively reweighted least squares minimization for sparse recovery. Communications on Pure and Applied Mathematics, v.63, no.1., Aster, Borchers, and Thurber. Parameter Estimation and Inverse Problems. Elsevier, 25. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 28 / 31

29 Numerical Experiment: inverting for spatial component of the source (f ) with L 1 Regularization. Domain is size 181 x 141. Velocity is assumed constant and known. Time-dependent component of source is 2 Hz Ricker wavelet (known). ɛ = Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 29 / 31

30 Numerical Experiment: inverting for spatial component of the source (f ) with L 1 Regularization. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 3 / 31

31 Conclusions and Future Work Hydraulic fracturing of low permeability shale rock creates fractures. Buildup of pressure and mechanical stress may lead to small releases of elastic energy (earthquakes) which are called microseismic events. These passive sources can be used to further refine our images of the earth s subsurface (e.g., estimates of the velocity). To estimate these sources traditional methods have relied on picking first arrivals of seismic energy in the data. Unfortunately, first arrival picking is very difficult in the presence of noise. By using full waveform inversion, we have successfully found the spatial location of the microseismic event as well as the onset time even in the presence of substantial noise and with poor initial guesses. Joint inversion for both the space and time component of the source may require additional information from well logs, etc. Our future work will include Extending the work to more realistic problems, including more realistic representations of the source. Coupling the big picture with the source inversion via FWI. Adding uncertainty quantification in the context of joint inversion for velocity and the source. Susan E. Minkoff (UTD) Microseismic Source Estimation using FWI 5/13/15 31 / 31