Lecture 2: Seismic Inversion and Imaging

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1 Lecture 2: Seismic Inversion and Imaging Youzuo Lin 1 Joint work with: Lianjie Huang 1 Monica Maceira 2 Ellen M. Syracuse 1 Carene Larmat 1 1: Los Alamos National Laboratory 2: Oak Ridge National Laboratory Graduate Student Workshop on Inverse Problem, 216

2 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 1 / 77

3 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 2 / 77

Enhanced Geothermal System Geothermal is a sustainable energy because it is clean and reliable, however the exploration and drilling remain expensive and risky.

4 Enhanced Geothermal System Geothermal is a sustainable energy because it is clean and reliable, however the exploration and drilling remain expensive and risky. Quantitative monitoring for enhanced geothermal systems can help optimize the geothermal production and the placement of new wells. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 2 / 77

Enhanced Geothermal System According to US Energy Information Administration (EIA), 9 western states together have the geothermal potential to provide over 2% of electricity

5 Enhanced Geothermal System According to US Energy Information Administration (EIA), 9 western states together have the geothermal potential to provide over 2% of electricity needs DOE aims a ten-fold increase of US electricity production from geothermal reservoirs within the next 1 years Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 3 / 77

Enhanced Geothermal System However, the reality is that High Risk: Two to five out of every 1 geothermal wells prospected end up dry Expensive to Drill: Wells cost between $2 million and $5 million,

6 Enhanced Geothermal System However, the reality is that High Risk: Two to five out of every 1 geothermal wells prospected end up dry Expensive to Drill: Wells cost between $2 million and $5 million, meaning geothermal investors risk losing millions on poor odds An accurate characterization of the subsurface structure is the key to a successful drilling schemes Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 4 / 77

Quantitative Monitoring for CO 2 Storage Quantifying changes in CO 2 reservoirs is a key element for assessing the performance of geologic carbon sequestration.

7 Quantitative Monitoring for CO 2 Storage Quantifying changes in CO 2 reservoirs is a key element for assessing the performance of geologic carbon sequestration. Reliably monitoring of potential CO 2 leakage through fault zones is crucial for ensuring safe CO 2 storage. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 5 / 77

8 Global Seismology Seismic wave is currently the only effective tool that can penetrate the entire Earth Seismic inversion (tomography) is used to obtain the structural information of the Earth Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 6 / 77

9 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 7 / 77

10 Problem Description - Data Measurement Data Measurement Media & Velocity 1 Media & Velocity 2 Media & Velocity 1 Media & Velocity 2 1 Receiver 1 1 Receiver 1 Source Source Reflection Data Transmission Data Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 7 / 77

11 Problem Description - Data Usage 2 x 16 1 Displacement Time First Arrival Time First Arrival Time Pros: Simplify the nonlinear problem to be linear; Efficient to solve. Cons: Low-resolution imaging. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 8 / 77

12 Problem Description - Data Usage 2 x 16 1 Displacement Time Whole Waveform The Whole Waveform Pros: High-resolution imaging. Cons: Problem stays nonlinear; Computation load is expensive. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 8 / 77

13 Problem Description - Inversion Data Inversion A Model to Get Started (Initial Model) Initial Model Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 9 / 77

14 Problem Description - Inversion Data Inversion A Model to Get Started (Initial Model) Generate The Simulated Data (Forward Modeling) 2 x 16 1 Displacement.5.5 Initial Model Time Forward Modeling Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 9 / 77

15 Problem Description - Inversion Data Inversion A Model to Get Started (Initial Model) Generate The Simulated Data (Forward Modeling) Match The Simulated Data to Measurement (Data Matching) 2 x 16 Measurement Simulating Data 1 Displacement.5.5 Initial Model Time Data Matching Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 9 / 77

16 Problem Description - Inversion Data Inversion A Model to Get Started (Initial Model) Generate The Simulated Data (Forward Modeling) Match The Simulated Data to Measurement (Data Matching) Use The Difference to Update The Initial Model (Model Update) +? Initial Model Model Update Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 9 / 77

17 Problem Description - Regularization & Prior Information Inversion for ill-posed nonlinear problems can be much more challenging to solve Ill-posedness (cause of limited data coverage) Local minima (cause of nonlinearity and non-convex optimization) Include prior information to constrain the inversion To avoid the instability during the inversion of data. To obtain more accurate reconstructions and a faster convergent rate. What can be prior information? Good initial guess (starting models) Smoothness of the models Locations of the regions of interests Shapes of the reconstructions etc. Regularization technique is a method to introduce prior information to the inversion. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 1 / 77

18 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 11 / 77

19 Travel-Time Tomography The tomography is given as an over-determined linear systems: w 1 G Tp h w 1 G Tp v p w w 2 G Ts h w 2 G Ts 1 d Tp v s w h L h w 2 d Ts δh w p L vp δm p = w s L vs, δm λ h I s λ p I λ s I where G Tp h, GTs h, GTp v p, Gv Ts s are the sensitivity matrices of the P- and S-arrivals, L h, L vp, and L vs are the first-order smoothing matrices for h, m p, and m s with weights of w h, w p, and w s ; I is the identity matrix weighted by λ h, λ p, and λ s. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 11 / 77

20 Forward Waveform Modeling Forward Modeling Acoustic-wave equation in the time-domain [ ( )] 1 2 K (r) 1 t 2 ρ(r) p(r, t) = s(t), where ρ(r) is density, K (r) is bulk modulus, s(t) is source, and p(r, t) is pressure field. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 12 / 77

21 Seismic Inversion Inverse Problem Waveform Inversion { } min d f (m) 2 2, m where d f (m) 2 2 is the misfit function, d is recorded waveform data, and 2 stands for the l 2 norm. Difficulties and Solution Ill-posedness, multiple minima, computational costly, slow convergence Regularization Techniques Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 13 / 77

22 Inverse Problem & Regularization Techniques General Regularization Methodology Full-waveform inversion (FWI) with regularization { min d f (m) λ R(m) }, where d f (m) 2 2 m is data fidelity term, R(m) is the regularization term and λ is the regularization parameter. Specific Regularization and Its Characteristics Total-Variation (TV): R(m) = m 1 = i (δm) i, (1-D) Best suited for reconstructing piecewise-constant functions, computationally expensive Tikhonov (TK): R(m) = L m 2 = i (δm)2 i, (1-D) Best suited for reconstructing smooth functions, computationally cheap 1 TV step = 5; TV smooth = = TK step = 5 2 = 25; TK smooth = = 9. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 14 / 77

23 A New Travel-Time Tomography What does this application tell us? Sharp velocity contrast (total-variation might be a better choice) Geologic data are available in the shallow layers (some kind of a priori information) Travel-Time Tomography with a Modified Total-Variation (MTV) Regularization (TomoMTV, Lin et. al., GJI (21) 215): { } E( m, ũ) = min G m d 2 + λ 1 m ũ λ 2 w ũ 1 m,ũ 2 G m d 2 is the data misfit term; 2 m ũ 2 2 and w ũ 1 are the regularization terms; λ 1 and λ 2 are the regularization parameters; w incorporates the a priori information from geologic data. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 15 / 77

24 A Closer Look at the TomoMTV What does w ũ 1 do to the inversion? Avoid the smoothing of the inversion due to the TV term Further encourage the inversion at the sharp velocity contrast inferred from the geologic data { if point (i, j) is on the interface w i,j = 1 if point (i, j) is off the interface. How to pick the two regularization parameters, λ 1 and λ 2? We use L-curve method to pick λ 1 due to its simplicity. We use UPRE method to pick the λ 2. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 16 / 77

25 A Modified Total-Variation Regularization Scheme FWI with Modified Total-Variation (MTV) Regularization (Lin & Huang, GJI (2) 215): } E(m, u) = min { d f (m) 2 m,u 2 + λ 1 m u λ 2 u TV, where λ 1 and λ 2 are both positive regularization parameters. The MTV regularization term contains a new variable u and an additional term m u 2 2 compared to the conventional TV regularization term. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 17 / 77

26 FWI with Modified Total-Variation Regularization FWI with Modified Total-Variation (MTV) Regularization (Lin & Huang, GJI (2) 215): { { } } E(m, u) = min min d f (m) 2 u m 2 + λ 1 m u λ 2 u TV, where λ 1 and λ 2 are both positive regularization parameters. The regularization parameter λ 1 controls the trade-off between the data misfit term and the Tikhonov regularization term, and λ 2 balances the amount of interface-preservation in FWI. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 18 / 77

27 FWI with MTV Regularization (A Closer Look) FWI with Modified Total-Variation (MTV) Regularization (Lin & Huang, GJI (2) 215): { { } } E(m, u) = min min d f (m) 2 u m 2 + λ 1 m u λ 2 u TV, where λ 1 and λ 2 are both positive regularization parameters. The inner problem is to solve for m using a conventional FWI with the Tikhonov regularization and prior model u. The outer subproblem is to solve for u using a standard L 2 -TV minimization method to preserve the sharpness of interfaces in inversion result m. The interleaving of solving these two subproblems leads to an inversion that not only improves the minimization of the data misfit, but also enhances the sharpness of interfaces. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 19 / 77

28 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 2 / 77

29 Computation Methods We employ the Alternating Direction Method of Multipliers (ADMM) to solve our new FWI with the modified total-variation regularization term Alternating Direction Method of Multipliers (ADMM) m (k) = argmin m = argmin m u (k) = argmin u = argmin u {E 1 (m)} { } d f (m) λ 1 m u (k 1) 2 {E 2 (u)} { m } (k) u 2 + λ 2 u TV 2 2 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 2 / 77

30 Selection of the Regularization Parameter: λ 1 The subproblem of m (k) is a classical FWI with Tikhonov regularization. Various parameter estimation method has been developed: L-Curve, GCV, etc. We employ the following formula: Selection of λ 1 : λ 1 = d f (m) 2 2 k m u (k 1) 2, 2 where k is a dimensionless number, which is approximately 1. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 21 / 77

31 Selection of the Regularization Parameter: λ 2 The subproblem of u (k) is a classical L 2 -TV minimization. Surprisingly, not many effective methods in existing references. We employ the unbiased predictive risk estimator (UPRE): Selection of λ 2, (Lin et. al., SP (9) 21): λ 2 = argmin{ 1 λ 2 n r λ σ2 n trace(a TV,λ 2 ) σ 2 }. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 22 / 77

32 Solving for m (k) : Nonlinear Conjugate Gradients CG direction at each iteration is used as search direction of d k. * The search direction d k needs to be a descent direction cos θ = E T k d k E k d k <. Line search for β k, the Armijo condition is used { E(m (k) + β (k) d (k) ) E(m (k) ) + c 1 β (k) (d (k) ) T E(m (k) ) (d (k) ) T E(m (k) + β (k) d (k) ) c 2 (d (k) ) T E(m (k) ). Updating scheme m (k+1) = m (k) + β (k) d (k). Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 23 / 77

33 Gradients The gradient of the data misfit can be obtained by the adjoint-state method m d f (m) 2 2 = 2 m 3 shots 2 f (k) t t 2 r (k), where f (k) is the forward propagated wavefield, and r (k) is the backward propagated residual at iteration k, which is further defined as r (k) = d f (m (k) ). The gradient of L 2 -norm term can be simply derived as, m m u (k 1) 2 = 2(m 2 u(i 1) ). Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 24 / 77

34 Solving for u (k) The subproblem of solving u (k) is a L 2 TV denoising problem. Any TV-solver can be used: Iteratively Reweighted Norm Algorithm, Lagged Diffusivity Fixed Point Iteration Algorithm, Split-Bregman Method, etc. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 25 / 77

35 Solving for u (k) : Split-Bregman Method Reformulate the minimization of u (k) as an equivalent problem based on the Bregman distance: u E(u, d x, d z ) = min m (k) 2 + λ 2 u TV u,d x,d z 2 + µ d x x u b (k) 2 + µ dz z u b (k) An alternating minimization algorithm can be employed, where two subproblems need to be further minimized: min u u m (k) 2 d +µ (k) x u b (k) 2 d +µ (k) z u b (k) 2, x and minλ 2 u TV + µ d x x u b (k) x 2 + µ dz z u b (k) z 2. d x,d z 2 2 x x z z z Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 26 / 77

36 Computational Cost Analysis Suppose that the size of the model is m R m ñ and the data p R q ñ, where m is the depth, ñ is the offset, and q is the time steps. We assume there are s shots and the finite-difference calculation employs a scheme of o(δt 2, δh 4 ). The cost of solving for m (k) : COST 1 k 1 (l + 3) O(s m ñ q) + (l + 5) O( m ñ), where l is the number of trials in the line search for β (k) and k 1 is the total iteration steps. The cost of solving for u (k) : COST 2 18 O( m ñ). Therefore, the cost of solving for u (k) is trivial compared to the cost of solving for m (k). Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 27 / 77

37 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 28 / 77

38 Results - True Model km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 28 / 77

39 Results - Tikhonov Inversion km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 29 / 77

40 Results - Total Variation Inversion km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 3 / 77

41 Numerical Results - Edge-Guided Inversion km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 31 / 77

42 Results - Tikhonov Inversion Difference km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 32 / 77

43 Results - Total Variation Inversion Difference km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 33 / 77

44 Results - Edge-Guided Inversion Difference km 7 km km 9 km km km Vp, km/s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 34 / 77

45 Results - Robustness Tests on the Sparse Data Randomly eliminate 5% of the earthquake events and stations (Left: Tikhonov, Middle: TV, Right: Edge-Guided TV) km 3 km 5 km 7 km 9 km 11 km km 3 km 5 km 7 km 9 km 11 km Vp, km/s 1 km km km km km km Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 35 / 77

46 Results - Robustness Tests on the Sparse Data Randomly eliminate 5% of the earthquake events and stations (Left: Tikhonov, Middle: TV, Right: Edge-Guided TV) km 3 km 5 km 7 km 9 km 11 km km 3 km 5 km 7 km 9 km 11 km dvp, km/s 1 km km km km km km Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 36 / 77

47 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 37 / 77

48 Reservoir Monitoring with Time-Lapse Data Conventional Inversions δm conv = f 1 (d time 2 ) f 1 (d time 1 ), where d time 1 and d time 2 are data collected at two different times. Baseline data Inversion Baseline Image Time lapse data Inversion Time lapse Image Difference Image Figure: Conventional Inversion Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 37 / 77

49 Reservoir Monitoring with Time-Lapse Data Double-Difference FWI The method jointly inverts time-lapse data for reservoir changes. δm DDFWI = f 1 (d sim time 2 ) f 1 (d sim time 1 ), Baseline Time lapse Data Data Inversion Baseline Image Modeling Simulated Baseline Data Difference where d sim time 1 = f (m baseline ) and d sim time 2 = d sim time 1 + (d time 2 d time 1 ) Initial Model Simulated Time lapse Data Inversion Difference Image Time lapse Image Figure: Double-Difference FWI Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 38 / 77

50 Reservoir Monitoring with Time-Lapse Data Double-Difference FWI V.S. Conventional Inversions Computational Cost: There are 2 FWIs involved in both approaches. Similar cost to the conventional inversions Noise and Artifacts: Noises common to data are removed by data differentiation. Less noise and artifacts generated comparing to the conventional inversions Stability: The inversion of the simulated time-lapse data focuses to image the changes of physical properties. Easier to apply different priory information to stabilize the inversion The baseline model is the KEY for a successful implementation of double-difference FWI Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 39 / 77

51 Double-Difference FWI with MTV Regularization Double-Difference FWI with MTV Regularization (Lin & Huang,GJI (23) 215): { } m baseline = m 1 = argmin d time1 f (m 1 ) m 1 MTV, m 1 { m time-lapse = m 2 = argmin d sim time2 f (m 2 ) δm MTV m 2 where δm = m 2 m 1 and m MTV = λ 1 m ũ λ 2 ũ TV. Our FWI with the MTV regularization improves inversion of the baseline dataset to obtain an accurate baseline model. }, we focus our inversion on the regions where time-lapse changes occur using the regularization term δm MTV to constrain the time-lapse model differences. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 4 / 77

Reservoir Monitoring for EGS.5 1. 2. 5.5 1. 2. 5 45 45.5 4.5 4 1.

35 3 Velocity (m/s) 25 25 2 2 Baseline V p Model Baseline V s Model Models are

52 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) Baseline V p Model Baseline V s Model Models are built based on the Brady s enhanced geothermal system (EGS) field (Lin & Huang, SGW 212) Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 41 / 77

53 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model After Stimulation V s Model After Stimulation Models are built based on the Brady s enhanced geothermal system (EGS) field Stimulation leads to decreases in V p and V s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 42 / 77

54 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) Time-lapse Difference of V p Time-lapse Difference of V s Monitoring regions with time-lapse difference of V p abd V s Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 43 / 77

Reservoir Monitoring for EGS.5 1. 2. 5.5 1. 2. 5 45 45.5 4.5 4 1. 35 3 Velocity (m/s) 1. 35 3 Velocity (m/s) 25 25 2 2 V p Initial Model V s Initial Model The initial V p and V s models for inversion.

55 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Initial Model V s Initial Model The initial V p and V s models for inversion. 96 sources and 5 receivers on the top surfaces of the models. Ricker s wavelet with a center frequency of 25 Hz is used as the source function. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 44 / 77

Reservoir Monitoring for EGS.5 1. 2. 5.5 1. 2. 5 45 45.5 4.5 4 1. 35 3 Velocity (m/s) 1.

56 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model V s Model FWI without Regularization Interfaces of the reconstruction are degraded. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 45 / 77

57 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model V s Model FWI with TV Regularization Lots of noise and artifacts are generated. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 46 / 77

58 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model V s Model FWI with MTV Regularization Interfaces of the reconstruction are well preserved. Noise and artifacts are eliminated. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 47 / 77

59 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model V s Model FWI without Regularization Reconstructed values are still off the true values. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 48 / 77

60 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model V s Model FWI with TV Regularization Reconstructed values are highly oscillated. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 49 / 77

61 Reservoir Monitoring for EGS Velocity (m/s) Velocity (m/s) V p Model V s Model FWI with MTV Regularization Reconstructed values are very close to the true values. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 5 / 77

Reservoir Monitoring for EGS.5 1. 2. 25.5 1. 2. 25 2 2 15 15.5 1. 1 5-5 -1 Velocity Perturbation (m/s).5 1. 1 5-5 -1 Velocity Perturbation (m/s) -15-15 -2-2 V p Model Conventional Inversions Hard to identify the location of the reservoir.

62 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model Conventional Inversions Hard to identify the location of the reservoir. Artifacts are significant. -25 V s Model -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 51 / 77

Reservoir Monitoring for EGS.5 1. 2. 25.5 1. 2. 25 2 2 15 15.5 1. 1 5-5 -1 Velocity Perturbation (m/s).5 1. 1 5-5 -1 Velocity Perturbation (m/s) -15-15 -2-2 -25 V p Model V s Model Double-Difference FWI without Regularization Results are significantly improved.

63 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Double-Difference FWI without Regularization Results are significantly improved. The results still contain some artifacts. -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 52 / 77

64 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Double-Difference FWI with MTV Regularization The monitoring regions are very easy to visualize. Background noise and artifacts are significantly reduced. -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 53 / 77

65 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model Conventional Inversions V s Model The magnitudes of the inversion artifacts are almost the same level to those of the inversion results. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 54 / 77

66 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Double-Difference FWI without Regularization The inversion results have been improved. The artifacts above and below the reservoir are still strong. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 55 / 77

67 Reservoir Monitoring for EGS Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Double-Difference FWI with MTV Regularization Reconstructed values are very close to its true values. The profiles are much less oscillated than all the other results. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 56 / 77

68 Reservoir Monitoring for EGS Data Misfit Model Misfit Conventional DD AEWI DD AEWI with Prior DD AEWI with MTV Iterations Data Misfit Convergence Plots.1 Conventional DD AEWI DD AEWI with Prior DD AEWI with MTV Iterations Model Misfit Reference methods: conventional DD-FWI (in blue), the method developed in Zhang & Huang (214) (in green) Our method converges fastest for both data misfit and model misfit Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 57 / 77

69 Robustness Tests FWI can be very easily trapped in the local minima. Using noisy measurements; Using inaccurate initial guess far away from the true model; Total-variation regularization can create those stair-casing artifacts Smooth changes at the monitoring regions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 58 / 77

Robustness Test - Noisy Measurement 5 Receiver number 5 1 15 2 25 3 35 4 45 2 5 x 1 Clean Noisy.25 1.5 Amplitude Time (s).5.75.5 1 1 1.25 2.25.5.75 Common-Shot Gather 1 Time (s) 1.

70 Robustness Test - Noisy Measurement 5 Receiver number x 1 Clean Noisy Amplitude Time (s) Common-Shot Gather 1 Time (s) Seismogram at Recv. Num. 25 Noisy Measurement (Baseline) Baseline measurement 2 db of white noise is added Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 59 / 77

Robustness Test - Noisy Measurement 5 Receiver number 5 1 15 2 25 3 35 4 45 2 5 x 1 Clean Noisy.25 1.5 Amplitude Time (s).5.75.5 1 1 1.25 2.25 Common-Shot Gather.5.75 1 Time (s) 1.25.25 Seismogram at Recv.

71 Robustness Test - Noisy Measurement 5 Receiver number x 1 Clean Noisy Amplitude Time (s) Common-Shot Gather Time (s) Seismogram at Recv. Num. 25 Noisy Measurement (Repeat-survey) Repeat-survey measurement 2 db of different white noise is added Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 6 / 77

Robustness Test - Noisy Measurement.5 1. 2. 5.5 1. 2. 5 45 45.5 4.5 4 1. 35 3 Velocity (m/s) 1.

72 Robustness Test - Noisy Measurement Velocity (m/s) Velocity (m/s) V p Model Noisy Measurement V s Model Some additional artifacts in the deep layers of the velocity inversion results. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 61 / 77

73 Robustness Test - Noisy Measurement Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model -25 Noisy Measurement V s Model Those artifacts do not effect the accuracy of the inverted time-lapse changes in the monitoring region -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 62 / 77

Robustness Test - Initial Guess.5 1. 2. 5.5 1. 2. 5 45 45.5 4.5 4 1.

35 3 Velocity (m/s) 25 25 2 2 V p Initial Model Smoothed by 3

74 Robustness Test - Initial Guess Velocity (m/s) Velocity (m/s) V p Initial Model Smoothed by 3 wavelength Initial Guess V s Initial Model Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 63 / 77

35 3 Velocity (m/s) 25 25 2 2 V p Initial Model Smoothed by 4

75 Robustness Test - Initial Guess Velocity (m/s) Velocity (m/s) V p Initial Model Smoothed by 4 wavelength Initial Guess V s Initial Model Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 64 / 77

35 3 Velocity (m/s) 25 25 2 2 V p Initial Model Smoothed by 5

76 Robustness Test - Initial Guess Velocity (m/s) Velocity (m/s) V p Initial Model Smoothed by 5 wavelength Initial Guess V s Initial Model Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 65 / 77

77 Robustness Test - Initial Guess Velocity (m/s) Velocity (m/s) V p Model V s Model Inversion Results (Baseline) Using initial guess smoothed by 3 WL Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 66 / 77

78 Robustness Test - Initial Guess Velocity (m/s) Velocity (m/s) V p Model V s Model Inversion Results (Baseline) Using initial guess smoothed by 4 WL Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 67 / 77

79 Robustness Test - Initial Guess Velocity (m/s) Velocity (m/s) V p Model V s Model Inversion Results (Baseline) Using initial guess smoothed by 5 WL Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 68 / 77

80 Robustness Test - Initial Guess Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Inversion Results (Time-Lapse) Using initial guess smoothed by 3 WL -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 69 / 77

81 Robustness Test - Initial Guess Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Inversion Results (Time-Lapse) Using initial guess smoothed by 4 WL -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 7 / 77

82 Robustness Test - Initial Guess Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model V s Model Inversion Results (Time-Lapse) Using initial guess smoothed by 5 WL -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 71 / 77

83 Robustness Test - Smoothly Distributed Changes Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model -25 Smoothly Distributed Changes V s Model For some practical applications, a spatial region with time-lapse changes can be smoothly distributed other than piece-wise constant. -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 72 / 77

84 Robustness Test - Smoothly Distributed Changes Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model -25 Smoothly Distributed Changes V s Model Our inversion results preserve sharp edges and the smoothly distributed changes. -25 Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 73 / 77

85 Robustness Test - Smoothly Distributed Changes Velocity Perturbation (m/s) Velocity Perturbation (m/s) V p Model Smoothly Distributed Changes V s Model Our inversion results preserve sharp edges and the smoothly distributed changes. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 74 / 77

86 Outline 1 Subsurface Applications 2 Schematic Description of Seismic imaging 3 Travel-Time Tomography and Full-Waveform Inversion Travel-Time Tomography Full-Waveform Inversion Regularization Techniques A Modified Total-Variation Regularization Scheme 4 Computation Methods 5 Application to Global Seismology 6 Application to Enhanced Geothermal Systems Reservoir Monitoring with Time-Lapse Data Brady s EGS Site Robustness Tests 7 Conclusions Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 75 / 77

87 Conclusions We have developed new travel-time tomography and full-waveform inversion method using a modified total-variation regularization scheme. Our new seismic inversion methods not only preserve sharp interfaces in inversion results, but also greatly reduce inversion artifacts. Our new methods employs the modified total-variation regularization to improve the inversion accuracy and enhance the robustness of our methods for noisy data to some extent. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 75 / 77

88 Related References Lin et. al., GJI (21) 215 : Youzuo Lin, Ellen M. Syracuse, Monica Maceira, Haijiang Zhang and Carene Larmat, Double-difference traveltime tomography with edge-preserving regularization and a priori interfaces, Geophysical Journal International, 21 (2): , 215. Lin & Huang,GJI (23) 215 : Youzuo Lin and Lianjie Huang, Quantifying Subsurface Geophysical Properties Changes Using Double-difference Seismic-Waveform Inversion with a Modified Total-Variation Regularization Scheme, Geophysical Journal International, 23 (3): , 215. Lin & Huang, GJI (2) 215 : Youzuo Lin and Lianjie Huang, Acoustic- and Elastic-Waveform Inversion Using a Modified Total-Variation Regularization Scheme, Geophysical Journal International, 2 (1): , 215. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 76 / 77

89 Acknowledgement The research was supported by (1). the Geothermal Technologies Program of the U.S. Department of Energy, and (2). LANL, Laboratory Directed Research and Development (LDRD) program. We thank Dr. John Queen of Hi-Q Geophysical Inc. for providing us with a velocity model of Brady s EGS field. Youzuo Lin (LANL) Seismic Inversion Inverse Problems Workshop 77 / 77

SUMMARY. min. m f (m) s.t. m C 1

SUMMARY. min. m f (m) s.t. m C 1 Regularizing waveform inversion by projections onto convex sets application to the D Chevron synthetic blind-test dataset Bas Peters *, Zhilong Fang *, Brendan Smithyman #, Felix J. Herrmann * * Seismic