Overview of Multisource and Multiscale Seismic Inversion Chaiwoot, Boonyasiriwat, Wei Dai, Ge Zhan, Yunsong Huang, Gerard Schuster KAUST

2. Seismic Inversion Problem: Outline L m = d L m = d 1 2 . N Seismic Experiment: -1 2. Seismic Inversion Problem: L m = d -> m = [L L] L d T T 3. Multiscale & Multisource Inversion L 1 2 d m = vs N L + N L [ ]m = [N d + N d ] 4. Summary and Road Ahead

Gulf of Mexico Seismic Survey L m = d L m = d 1 2 . N Predicted data Observed data Time (s) 4 1 d m 6 km

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

S Details of Lm = d G(s|x)G(x|g)m(x)dx = d(g|s) s g x Reflectivity or velocity model 1 s g x G(s|x)G(x|g)m(x)dx = d(g|s) Predicted data = Born approximation Solve wave eqn. to get G’s S m

Seismic Inverse Problem Given: d = Lm Find: m(x,y,z) Soln: min || Lm-d || 2 waveform inversion m = [L L] L d T -1 migration L d T

2. Seismic Inversion Problem: Outline L m = d L m = d 1 2 . N Seismic Experiment: -1 2. Seismic Inversion Problem: L m = d m = [L L] L d T T 3. Multiscale & Multisource Inversion L 1 2 d m = vs N L + N L [ ]m = [N d + N d ] 4. Summary and Road Ahead

Conventional Least Squares Solution: 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 Non-Linear Optimization = Full Waveform Inversion Linear Optimization = Least Squares Migration 8

Multiscale Waveform Tomography 1. Collect data d(x,t) 2. Generate synthetic data d(x,t) by FD method syn. 3. Adjust v(x,z) until ||d(x,t)-d(x,t) || minimized by CG. syn. 2 e=||d-d|| 2 Model Parameter Data misfit function 4. To prevent getting stuck in local minima: a). Invert early arrivals initially mute Time b). Use multiscale: low freq. high freq. e=||d-d|| 2 Model Parameter e=||d-d|| 2 Model Parameter

2. Multiscale Waveform Inversion 3. Multisource Waveform Inversion Numerical Results 1. Land and Marine MLSM 2. Multiscale Waveform Inversion 3. Multisource Waveform Inversion

Boonyasiriwat et al., 2009, TLE 0 km 6 km/s 6 km 3 km/s 0 km 20 km

Waveform Tomograms Initial model 5 Hz 10 Hz 20 Hz 0 km 6 km 0 km 20 km 6 km/s Initial model 6 km 3 km/s 0 km 20 km 0 km 5 Hz 6 km/s 6 km 3 km/s 0 km 6 km/s 10 Hz 6 km 3 km/s 0 km 6 km/s 20 Hz 6 km 3 km/s

Waveform Tomograms Initial model 5 Hz 10 Hz 20 Hz 0 km 6 km 0 km 20 km 6 km/s Initial model 6 km 3 km/s 0 km 20 km 0 km 5 Hz 6 km/s 6 km 3 km/s 0 km 6 km/s 10 Hz 6 km 3 km/s 0 km 6 km/s 20 Hz 6 km 3 km/s

Traveltime Tomogram Depth (km) 3000 2.5 Velocity (m/s) Depth (km) 3000 2.5 Velocity (m/s) Waveform Tomogram 1500 Depth (km) 2.5 X (km) 20 20

Vertical Derivative of Waveform Tomogram 3000 Waveform Tomogram Velocity (m/s) Depth (km) 1500 2.5 Vertical Derivative of Waveform Tomogram Depth (km) 2.5 X (km) 20 21

Kirchhoff Migration Images

2. Multiscale Waveform Inversion 3. Multisource Waveform Inversion Numerical Results 1. Land and Marine MLSM 2. Multiscale Waveform Inversion 3. Multisource Waveform Inversion

Multi-Source Waveform Inversion Strategy Generate multisource field data with known time shift 144 shot gathers Initial velocity model Generate synthetic multisource data with known time shift from estimated velocity model Using multiscale, multisource CG to update the velocity model with regularization Multisource deblurring filter

3D SEG Overthrust Model (1089 CSGs) 15 km 3.5 km 15 km

2. Multiscale Waveform Inversion 3. Xwell Waveform Inversion Numerical Results 1. Land and Marine MLSM 2. Multiscale Waveform Inversion 3. Xwell Waveform Inversion

Dynamic Polarity Tomogram Numerical Results 1000x 300x 3.5 km Dynamic QMC Tomogram (99 CSGs/supergather) Static QMC Tomogram (99 CSGs/supergather) 15 km Dynamic Polarity Tomogram (1089 CSGs/supergather)

Ray Tracing Tomograms S P A C Depth (m) B 210 90 90 Offset (m) A 1150 2300 C Depth (m) B 3650 m/s 1825 m/s 210 90 90 Offset (m) Offset (m)

Elastic Tomograms P S Depth (m) 210 90 90 Offset (m) Offset (m) 1150 1150 2300 Depth (m) 3650 m/s 1825 m/s 210 90 90 Offset (m) Offset (m)

Viscoelastic Tomograms S P A A A A 1150 2300 C C D Depth (m) B B 3650 m/s 1825 m/s 210 90 90 Offset (m) Offset (m)

Elastic Tomograms P S A B Depth (ft) D C 500 184 184 Offset (ft) A 7750 14000 B Depth (ft) D 12700 ft/s 22500 ft/s C 500 184 184 Offset (ft) Offset (ft)

P S A B Depth (ft) D C 500 184 184 Offset (ft) Offset (ft) Viscoelastic Tomograms P S A 7750 14000 B Depth (ft) D 12700 ft/s 22500 ft/s C 500 184 184 Offset (ft) Offset (ft)

Poisson Ratio Visco. D 0.35 Depth (ft) C 0.05 250 184 Offset (ft)

Poisson Ratio Elastic D 0.35 Depth (ft) C 0.05 250 184 Offset (ft)

Seismic Inverse Problem Given: d = Lm Find: m(x,y,z) Soln: min || Lm-d || 2 waveform inversion m = [L L] L d T -1 migration L d T

What is Problem with FWI Given: d = Lm Find: m(x,y,z) Soln: min || Lm-d || 2 Answers: 1). Local minima 2). Non-uniqueness 3). Inconsistency

Local Minima Cycle Skipping obs - pred pred misfit =

Non-Uniqueness Cycle Skipping obs - pred pred misfit =

Physics Inconsistency obs - pred pred misfit =

Soln: Multiscale Freq. obs - pred pred misfit =

Soln: Multiscale X & T. obs - pred pred misfit =

Data Misfit Function e=||D-d||2 = D2 + d2 – 2Re(D*d) Difference between predicted and observed traces. Match phase and amplitudes e=||D-d||2 = D2 + d2 – 2Re(D*d) e=||D*d||2 = 2Re(D*d) = |D||d|cos(F-f) Correlation between predicted and observed traces. Match phase, no need to match amplitudes

Model Misfit Function e=1/2||mLT Lm-mmig||2 e=1/2||mmig m||2 Difference between predicted and observed migration Match phase and amplitudes e=1/2||mLT Lm-mmig||2 e=1/2||mmig m||2 Correlation between predicted and observed traces. Match phase, no need to match amplitudes