Wave Equation Dispersion Inversion of Guided P-Waves (WDG) Jing Li, Sherif Hanafy, and Gerard Schuster King Abdullah University of Science and Technology (KAUST)

Outline Motivation Guided-waves Inversion Theory Results GW Shot Gather Motivation Guided-waves Inversion Theory Results Synthetic and Field Data Conclusions and Limitation WDG Tomogram WDG P-velocity Tomogram 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. 2

(LVL: low velocity layer) Motivation Guided-waves Snapshots of wavefield (LVL: low velocity layer) Shot Gather If there is great velocity difference, P-wave will be trapped in the low velocity layer (Grant and West, 1965) Guided-waves P-wave reverberations

Different kinds of Guided-waves (Boiero, TLE, 2013). Motivation Different kinds of Guided-waves (Boiero, TLE, 2013). Land Seismic data OBC data Towed-streamer f (Hz) k (1/m) f (Hz) k (1/m) f (Hz) k (1/m)

Problem & Solution Problem: Wave-equation traveltime inversion (WT) Low-mid Res.Vp Solution: Wave-equation dispersion inversion for Guided-waves (WDG) Mid-high Res. Vp Shot Gather t (s) x (m) Traveltime map Receiver Source Pick WT WT P-velocity Tomogram Z (m) x (m) Shot Gather t (s) x (m) Dispersion Curve V (m/s) f (Hz) Radon Transform WDG WDG P-velocity Tomogram Z (m) x (m) GW

Outline Motivations Guided-waves Inversion Theory Results Synthetic and Field Data Conclusions and Limitation Predicted Observed Frequency (Hz) Dispersion Curves v (m/s) 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. 6

Guided-waves Inversion Theory (WDG) Dispersion Curves f (Hz) c (m/s) 1) Misfit Function 2) Gradient Backpropagated field 3) Velocity Update Source field

Wave-equation Traveltime Inversion (WT) vs Wave-equation Dispersion Inversion for Guided-waves (WDG) Properties: Wave-equation traveltime tomography (Luo and Schuster, 1991) Wave-equation dispersion tomography (Li and Schuster, 2016) Misfit function: Δ𝜏 Predicted Observed Frequency (Hz) Wavenumber (m-1) Frechet derivative Gradient:

WDG Workflow CG Update RTM True Vp Model Obs. Dispersion Residual Dispersion f (Hz) k (m-1) True Vp Model 0 x (m) 120 10 z (m) Obs. Dispersion f (Hz) v (m/s) Pred. Dispersion Radon Transform Backpropagated Data 0 x (m) 120 0.5 t (s) Weighted Initial Vp Model 0 x (m) 120 10 z (m) Update 0 x (m) 120 10 z (m) Gradient RTM CG Inverted Vp 0 x (m) 120 10 z (m)

Outline Motivation Guided-waves Inversion Theory Results WDG P-velocity Tomogram WDG Tomogram Motivation Guided-waves Inversion Theory Results Synthetic and Field Data Conclusions and Limitation 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. 10

WT vs WDG True P-velocity Model WT Tomogram WDG Tomogram Parameter: 5 10 15 20 0 x (m) 120 z (m) 2500 2000 1500 1000 m/s WT Tomogram V1=1000 m/s V2=1400 m/s WDG Tomogram Initial P-velocity Model λ/2=12.5m Parameter:  V1=1000 m/s V2=2500 m/s.  f=40 Hz,  λ=25 m  Sr=30, Re=60;

Synthetic Model Test 1 Parameter: True P-velocity Model 10 20 True P-velocity Model z (m) Parameter:  V1=1000 m/s V2=2500 m/s.  f=40 Hz,  λ=25 m  Sr=60, Re=120; Initial P-velocity Model λ/2=12.5m 2500 2000 1500 1000 10 20 z (m) m/s WDG P-velocity Tomogram 10 20 0 60 120 180 240 z (m)

Synthetic Model Test 2 True P-velocity Model WDG Tomogram Initial Model Parameter:  V1=900 m/s V2=1100 m/s, 1800 m/s.  f=30 Hz, λ=33 m  Sr=30, Re=30 45 True P-velocity Model 0 x (m) 200 z (m) m/s 1800 1500 1300 1100 900 λ/4=8m 45 WDG Tomogram 0 x (m) 200 z (m)

Qademah Field Data Test Seismic - Parameter Equipment: Geometrics No of Profiles: 2 No. of shots: 120 Shot Interval: 5 m No. of Receivers: 240 Receiver Interval: 2.5 m Profile Length: 600 m (Sherif, et al, 2012)

Qademah Field Data Test Dispersion Curves V (m/s) f (Hz) Raw Shot Gather t (s) x (m) Window Guided-waves t (s) x (m) Adaptive window mute Radon Transform

P-velocity Tomogram WT Tomogram WDG Tomogram 40 z (m) 40 z (m) 0 600 40 WT Tomogram z (m) 3.0 2.2 1.6 1.0 km/s 40 z (m) WDG Tomogram 3.0 2.2 1.6 1.0 km/s 0 600 x (m)

WDG and WT COG (Offset=40 m) T (s) x (m) Raw COG WDG COG WT COG

Trace Comparison 0.25 0 200 t (s) Offset (m) Raw Data WT Data

Trace Comparison 0.25 0 200 t (s) Offset (m) Raw Data WDG Data

Outline Motivation Guided-waves Inversion Theory Results Synthetic and Field Data Conclusions and Limitation 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. 20

Conclusions 1. Guided-waves dispersion inversion (WDG) can accurately reconstruct the P-velocity in near surface structure. Shot Gather t (s) x (m) Traveltime map Rec. Source Pick WT WT Tomogram Z (m) x (m) Shot Gather t (s) x (m) Dispersion Curve V (m/s) f (Hz) Radon Transform WDG WDG Tomogram Z (m) x (m) GW

Conclusions 2. WDG tomogram has higher (?) resolution than WT. WT Tomogram WDG Tomogram True P-velocity Model 20 0 120 z (m) x (m) 2500 2000 1500 1000 m/s

Conclusions 3. Improvement P-wave statics in near surface. Stack without applying static correction Stack with static from high resolution P-velocity (CGG, Florian Duret, et al, 2016, TLE}

Limitations WDG resolution decreases as the velocity contrast between the two-layers becomes smaller x (m) z (m) V1=1000 m/s V2=1400 m/s True Vp Model Shot Gather V1=1000 m/s V2=2500 m/s z (m) WDG Tomogram z (m)

Acknowledgements Sponsors of the CSIM (csim.kaust.edu.sa) consortium. KAUST Supercomputing Laboratory (KSL) and IT research computing group.

Thank you