The Boom and Bust Cycles of Full Waveform Inversion: Is FWI a Bust, a Boom, or Becoming a Commodity? Gerard Schuster KAUST Dow Jones Index Avg/decade 1.0 Normalized DJI 0.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016

Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d 3. FWI, History, Examples L 1 2 d m = 4. Summary

Medical vs Seismic Imaging CAT Scan MRI Full Waveform Inversion Tomogram

Traveltime Tomogram & Migration Images Vshallow = L/t Vdeep = L/t

Traveltime Tomogram & Migration Images Vshallow = L/t Intersection of down & up rays Vdeep = L/t

Traveltime Tomogram & Migration Images Vshallow = L/t Vdeep = L/t

Traveltime Tomogram & Migration Images Problems: Hi-Freq. ray tracing, picking traveltimes, tedious, low resolution, fails in complex earth models Shot gather = d(x,t) time Vshallow = L/t migration image Vdeep = L/t

Full Waveform Inversion Given: d(x,t) = predicted traces Find: v(x,y,z) minimizes e=S[d(x,t)-d(x,t)obs]2 x,t - = observed predicted residual Time Problems: Hi-Freq. ray tracing, picking traveltimes, tedious, low resolution, fails in complex earth models

Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d 3. FWI, History, Examples L 1 2 d m = 4. Summary 4. Summary and Road Ahead

Gulf of Mexico Seismic Survey L m = d L m = d 1 2 . N Predicted data Observed data Goal: Solve overdetermined System of equations for m Time (s) 6 X (km) 4 1 d m

Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d 3. FWI, History, Examples L 1 2 d m = 4. Summary 4. Summary and Road Ahead

Details of Ldm = d-dobs dm(k) = LT(d-dobs)(k) c2 dt2 1 d2 [ ] 2 - -1 d(g|s) = Reflectivity or velocity model Time (s) 6 X (km) dobs – 1 d2 d(g|s) = F c2 dt2 2 [ ] Predicted data Observed data m

Conventional FWI Solution L is too big for IO bound hardware L= & d = L d 1 1 L d Given: Lm=d 2 2 In general, huge dimension matrix Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d T -1 or if L is too big m = m – a L (Lm - d) My talk is organized in the following way: 1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges. 2. The second part is theory for a deblurring filter, which is an alternative method to LSM. 3. In the third part, I will show a numerical result of a deblurring filter. 4. The fourth is the main part of my talk. Deblurred LSM (DLSM) is a fast LSM with a deblurring filter. I will explain how to use the filter in LSM algorithm. 5. Then I will show numerical results of the DLSM. 6. Then I will conclude my presentation. Each figure has a slide number is shown at the footer. (k+1) (k) (k) T (k) = m – a L (L m - d ) (k) [ ] T + L (L m - d ) T 1 1 1 2 2 2 Problem: L is too big for IO bound hardware 13

Outline . 1. Inversion Overview: 2. Seismic Experiment: L m = d 3. FWI, History, Examples L 1 2 d m = 4. Summary 4. Summary and Road Ahead

Dow Jones Index vs FWI Index Dow Jones Industrial Avg/decade FWI Index Avg/decade 18.0 0.0 Tarantola + French School 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 Bunks Multiscale Exxon+ BP+Pratt Mora

Dow Jones Index vs FWI Index 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade

What Caused the 1st FWI Boom? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade True v(x,z) FWI v(x,z) 2 Z (km) 0 X (km) 4

What Caused the 1st FWI Bust? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade True v(x,z) FWI v(x,z) 2 Z (km) 0 X (km) 24 0 X (km) 24

What Caused the 1st FWI Bust? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade predicted observed residual = Waveform Misfit V Vtrue Vstart 1 Time (s) 5.0 0.0 x -

What Caused the 1st FWI Bust? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade observed predicted residual 1 = = Time (s) 5.0 0.0 x Waveform Misfit V Vtrue Vstart -

What Caused the 1st FWI Bust? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade observed predicted residual 1 Gradient opt. gets stuck local minima = = Time (s) 5.0 0.0 x Waveform Misfit V Vtrue Vstart -

How to Cure the 1st FWI Bust? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade observed predicted residual 1 = = Time (s) 5.0 0.0 x Waveform Misfit V Vtrue Vstart Low-pass filter - Gradient opt  global minima

How to Cure the 1st FWI Bust? 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade observed predicted residual 1 = Multiscale FWI v(x,z) = Time (s) 5.0 0.0 x Waveform Misfit V Vtrue Vstart Window early events -

How to Cure the 1st FWI Bust? 2004 EAGE Meeting Started New Boom 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade True v(x,z) FWI v(x,z) 2 Z (km) 0 X (km) 24 0 X (km) 24 Multiscale FWI v(x,z)

3. FWI, History, Examples: Transmission FWI Norway Outline 1. Inversion Overview: 2. Seismic Experiment: L m = d L m = d 1 2 . N 3. FWI, History, Examples: Transmission FWI Norway L 1 2 d m = 4. Summary 4. Summary and Road Ahead

Transmission 3D FWI Norway Marine Data 2300 buried hydrophones, 50,000 shots, sea bottom 70 m 16 km 8 km 4.5 gas Gas cloud 1.5 km/s 3.5 km/s  Small dimensions of structures such as sandy outwash channels to 175m depth (Figure 1c) and the scars left on the sea paleo-bottom by drifting icebergs to 500m depth (Figure 1d). A wide low speed region defines the geometry of the gas cloud (Figure 1a, e) the periphery of which a fracture network is identified (Figure 1b, e). The image of a deep reflector, defining the base of the Cretaceous chalk under the tank (Figure 1a, b, white arrows), is uniquely identifiable despite the screen formed by the overlying gas cloud that opposes penetration seismic wave.  S. Operto, A. Miniussi, R. Brossier, L. Combe, L. Metivier, V. Monteiller, Ribodetti A., and J. Virieux,  2015, GJI.

Transmission 3D FWI Norway Marine Data 2300 buried hydrophones, 50,000 shots, sea bottom 70 m 16 km 8 km 4.5 gas 1.5 km/s 3.5 km/s

2D FWI R+T Gulf of Mexico Marine Data Transmission 3D FWI Norway Marine Data 2300 buried hydrophones, 50,000 shots, sea bottom 70 m Transmissions 10x stronger than reflections Therefore gradients will spend greater effort updating shallow v(x,y,z) Vshallow Vshallow Vshallow Vdeep ??????

3. FWI, History, Examples: R+T FWI Gulf of Mexico Outline 1. Inversion Overview: 2. Seismic Experiment: L m = d L m = d 1 2 . N 3. FWI, History, Examples: R+T FWI Gulf of Mexico L 1 2 d m = 4. Summary 4. Summary and Road Ahead

2D FWI R+T Gulf of Mexico Marine Data Reflection Rabbit Ears Transmission Cigars observed predicted predicted Abdullah AlTheyab (2015)

2D FWI R+T Gulf of Mexico Marine Data Transmission Cigars 0.0 observed predicted Z (km) 3.6 0.0 X (km) 19 Migration Image with Initial V(x,z) Migration Image with FWI V(x,z) Migration Image with FWI V(x,z) Abdullah AlTheyab (2015)

3. FWI, History, Examples: Phase FWI Surface Waves Outline 1. Inversion Overview: 2. Seismic Experiment: L m = d L m = d 1 2 . N 3. FWI, History, Examples: Phase FWI Surface Waves L 1 2 d m = 4. Summary 4. Summary and Road Ahead

2D KSA Potash Model Test 10 m surface waves 1D Vs Tomogram m/s True Model m/s 0 60 120 x(m) 30 800 600 400 z (m) Start Model m/s 0 60 120 x(m) 30 800 600 400 z (m) WD Vs Tomogram m/s 0 60 120 x(m) 30 800 600 400 z (m) 1D Vs Tomogram m/s 0 60 120 x(m) 30 800 600 400 z (m)

Problem & Solution Problem: 1D Dispersion inversion assumes layered medium (Xia et al. 1999). Solution: v(x,y,z) minimizes e=S[c(k,w)-c(k,w)obs]2 (Li & Schuster, 2016) FWI: e=S[d(x,t)-d(x,t)obs]2 x (m) t(s) CSGs w(Hz) C (m/s) Dispersion Curves Radon (Radon Transform) v (m/s) Z (m) 1D Inversion 1D Vs Tomogram 0 60 120 x(m) 30 Z (m) True model 0 60 120 x(m) 30 Z (m) WD Vs Tomogram 0 60 120 x(m) 30 Z (m) 2D WD t(s) x (m) CSGs w(Hz) Dispersion Curves C (m/s) Radon Z (m) v (m/s) 1D Inversion

Seismic Imaging of Olduvai Basin Kai Lu, Sherif Hanafy, Ian Stanistreet, Jackson Njau, Kathy Schick ,Nicholas Toth and Gerard Schuster

Olduvai, Tanzania Seismic Data The Fifth Fault COG 0 500 1000 1500 2000 2500 3000 3500 0.6 z (m) 0 500 1000 1500 2000 2500 3000 3500 0.6 S-wave Velocity Tomogram (WD) 1000 800 600 m/s z (m) P-wave Velocity Tomogram Tomogram 0 500 1000 1500 2000 2500 3000 3500 0.6 3500 2000 1500 m/s z (m)

Summary Multiscale+Skeletonized FWI: e =S |di –di pred |2  v(x,y,z), r(x,y,z) i 2. History 1930s 1980 1990 2010-2016 3. Is FWI a commodity? Almost according to 2 industry experts Is FWI a black box? Not yet, works ~80% time (2 experts) Challenges? Deeper imaging, CPU cost, multiparameter

Summary 4. Road Ahead 3D Elastic Inversion & Adaptive Grid. Worth it? 3D Viscoelastic Inversion. Worth it? Clever Skeletonized FWI Anisotropic Inversion Multiples???? Inversion Deeper than src-rec offset/depth<2

(We need faster migration algorithms & better velocity models) Summary (We need faster migration algorithms & better velocity models) Stnd. FWI Multsrc. FWI IO 1 vs 1/20 or better Cost 1 vs 1/20 or better Sig/MultsSig ? Resolution dx 1 vs 1

Qademah Fault, Saudi Arabia Field Data P-wave Tomogram 2D WD S-wave Tomogram 1D S-wave Tomogram

Comparison of 2D WD Inversion with FWI Start Model FWI of Surface Waves Easy to get stuck in a local minimum (Solano, et al., 2014). x (m) z (m) Vs True Model x (m) t (s) A shot gather FD x (m) z (m) Vs Tomogram FWI 2D WD of Surface Waves Avoid local minimum and apply in 2D/3D model. x (m) z (m) Vs Tomogram WD Dispersion curve f (Hz) v (m/s) x (m) t (s)

How to Cure the 1st FWI Bust? 2004 EAGE Meeting Started New Boom 0.0 18.0 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010-2016 FWI Index Avg/decade True v(x,z) FWI v(x,z) 2 Z (km) 0 X (km) 24 0 X (km) 24 Multiscale FWI v(x,z)

Full Waveform Inversion Given: d(x,t) = Find: v(x,y,z) minimizes e=S[d(x,t)-d(x,t)obs]2 x,t time Vshallow = L/t migration image Vdeep = L/t

Transmission 3D FWI Norway Marine Data 2300 buried hydrophones, 50,000 shots, sea bottom 70 m 16 km 8 km 4.5 gas Gas cloud 1.5 km/s 3.5 km/s  Small dimensions of structures such as sandy outwash channels to 175m depth (Figure 1c) and the scars left on the sea paleo-bottom by drifting icebergs to 500m depth (Figure 1d). A wide low speed region defines the geometry of the gas cloud (Figure 1a, e) the periphery of which a fracture network is identified (Figure 1b, e). The image of a deep reflector, defining the base of the Cretaceous chalk under the tank (Figure 1a, b, white arrows), is uniquely identifiable despite the screen formed by the overlying gas cloud that opposes penetration seismic wave.  S. Operto, A. Miniussi, R. Brossier, L. Combe, L. Metivier, V. Monteiller, Ribodetti A., and J. Virieux,  2015, GJI.