Computational Challenges for Finding Big Oil by Seismic Inversion

JackBuckskin KaskidaTiber 35,055 Feet Motivation for Better Seismic Imaging Strategy ¼ billion $$$ well

Motivation for Better Seismic Imaging Strategy Oil Well Blowouts

Overpressure Zone Motivation for Better Seismic Imaging Strategy Oil Well Blowouts = Low Seismic Velocity Zone

Motivation for Better Seismic Imaging Strategy Mud Volcanoes 6.3 km 2 13 people killed30,000 people displaced May 29, 2006

Computational Challenge Seismic InversionComputational Challenge Seismic Inversion Outline Full waveform InversionFull waveform Inversion Multisource InversionMultisource Inversion

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

Given: d = Lm Computational Challenges Find: Find: m = [L L] L d T T 20x20x10 km 3 dx=1 m # time steps ~ 10 4 # shots > 10 4 m > 10 unknown velocity values Total = d > words

Computational Challenge Seismic InversionComputational Challenge Seismic Inversion Outline Full waveform InversionFull waveform Inversion Multisource InversionMultisource Inversion

Multisource Migration: m mig =L T d Forward Model: m =[L T L] -1 L T d Multisrc-Least FWI: Multisource Encoded FWI m’ = m - L T [Lm - d] f ~ [L T L] -1 f Steepest Descent Preconditioned d +Nd =[N L +NL ]m Nd +Nd =[N L +NL ]m multisource preconditioner

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 To prevent getting stuck in local minima: a). Invert early arrivals initially a). Invert early arrivals initially mute 7 b). Use multiscale: low freq. high freq. b). Use multiscale: low freq. high freq.

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

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

Low-pass Filtering 18 (b) 0-15 Hz CSG (c) 0-25 Hz CSG

Dynamic Early-Arrival Muting Window Hz CSG 0-25 Hz CSG Window = 1 s

Hz CSG 0-25 Hz CSG Window = 2 s Dynamic Early-Arrival Muting Window

Depth (km) X (km) Traveltime Tomogram Velocity (m/s) Waveform Tomogram Depth (km) Results

Depth (km) X (km) Waveform Tomogram Velocity (m/s) Depth (km) Vertical Derivative of Waveform Tomogram

Kirchhoff Migration Images 22

Kirchhoff Migration Images 22

Computational Challenge Seismic InversionComputational Challenge Seismic Inversion Outline Full waveform InversionFull waveform Inversion Multisource InversionMultisource Inversion

1980 Multisource Seismic Imaging vs copper VLIW Superscalar RISC Aluminum Year CPU Speed vs Year

FWI Problem & Possible Soln. Problem: FWI computationally costlyProblem: FWI computationally costly Solution: Multisource Encoded FWISolution: Multisource Encoded FWI Preconditioning speeds up by factor 2-3 Iterative encoding reduces crosstalk

Multisource Migration: m mig =L T d Forward Model: Multisource Phase Encoded Imaging d +d =[ L +L ]m 1221 L {d { =[ L +L ](d + d ) TT = L d +L d TT L d +L d L d +L d212 1 Crosstalk noise Standard migration TT m = m + (k+1)(k)

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

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

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

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

Multisource FWI Summary (We need faster migration algorithms & better velocity models) Future: Multisource MVA, Interpolation, Field Data, Migration Filtering, LSM

Research Goals G.T. Schuster (Columbia Univ., 1984) Seismic Interferometry: VSP, SSP, OBS Multisource+Preconditioned RTM+MVA+Inversion+Modeling: TTI 3D RTM, GPU: Stoffa+CSIM, UUtah K. Johnson SCI, PSU, KAUST Shaheen Cornea

Multisource S/N Ratio # geophones/CSG # CSGs L [d + d +.. ] d + d T d, d 2 1 L [d + d + … ] 1 2 T, …. +….

Multisrc. Migration vs Standard Migration # iterations Iterative Multisrc. Migration vs Standard Migration vs MS S-1 M ~ ~ # geophones/CSG # CSGs MS MI

Crosstalk Term Time Statics Time+Amplitude Statics QM Statics L d +L d L d +L d212 1 TT

Summary Time Statics Time+Amplitude Statics QM Statics 1. Multisource crosstalk term analyzed analytically 2. Crosstalk decreases with increasing w, randomness, dimension, iteration #, and decreasing depth dimension, iteration #, and decreasing depth 3. Crosstalk decrease can now be tuned 4. Some detailed analysis and testing needed to refine predictions. predictions. L d +L d L d +L d212 1 TT

Fast Multisource Least Squares Kirchhoff Mig.Fast Multisource Least Squares Kirchhoff Mig. Multisource Waveform Inversion (Ge Zhan)Multisource Waveform Inversion (Ge Zhan) Multisource Technology

0 Z k(m) 3 0X (km)16 The Marmousi2 Model The area in the white box is used for S/N calculation.

0X (km)16 0 Z k(m) 3 0 Z (km) 3 0X (km)16 Conventional Source: KM vs LSM (50 iterations) LSM (100x) KM (1x)

0X (km)16 0 Z k(m) 3 0 Z (km) 3 0X (km) source Supergather: KM vs LSM (300 its.) LSM (33x) KM (1/200x)

S/N 0 1 I 300 S/N = 7 The S/N of MLSM image grows as the square root of the number of iterations. MI

Fast Multisource Least Squares Migration ( Dai)Fast Multisource Least Squares Migration ( Dai) Multisource Waveform Inversion (Boonyasiriwat)Multisource Waveform Inversion (Boonyasiriwat) Multisource Technology

Comparing CIGs 23

Comparing CIGs 24 CIG from Traveltime Tomogram CIG from Waveform Tomogram

Comparing CIGs 25

Comparing CIGs 26 CIG from Traveltime Tomogram CIG from Waveform Tomogram

Comparing CIGs 27

Comparing CIGs 28 CIG from Traveltime Tomogram CIG from Waveform Tomogram

17 Data Pre-Processing 3D-to-2D conversion Attenuation compensation Random noise removal

17 Source Wavelet Estimation Pick the water-bottom Stack along the water-bottom to obtain an estimate of source wavelet Generate a stacked section In some cases, source wavelet inversion can be used.

17 Gradient Computation and Inversion Multiscale inversion: low to high frequency Dynamic early-arrival muting window Normalize both observed and calculated data within the same shot Quadratic line search method (Nocedal and Wright, 2006) A cubic line search can also be used.