Superresolution Imaging with Resonance Scatterring Gerard Schuster, Yunsong Huang, and Abdullah AlTheyab King Abdullah University of Science and Technology

Question:  x << /2? Migration:  x= z/4L LSM:  x= /2 Non-Linear LSM:  x<< /2 7 km

Outline Summary Question:  x << /2? Answer:  x= /(4N+2) Synthetic Tests vs Field Data Testsvs

Primary Resolution and ZO Migration Where is the Scatterer? T /2=  x Where did this come from? Where did this come from? Where did this come from? Q: How thick is primary donut?  /2 (one roundtip)

2 nd -order multiple Primary Resolution and ZO Migration Where is the Scatterer? T Resonance Resolution and ZO Migration Where is the Scatterer? 1 st -order multiple Assume two interfaces, where we know location of one. ? Q: How thick is 1 st order donut?  /4 (two roundtips) Where is the other? Q: How thick is 2 nd order donut?  /6 (three roundtips) Question:  x << /2? Answer:  x= /(2N+2)

Outline Summary Question:  x << /2? Answer:  x= /(4N+2) Synthetic Tests vs Field Data Testsvs

1-Bounce Migration 3-Bounce Migration 1-Scatterer Model Assume perfect natural multiple migration operator, isolated multiples

6-Scatterer Model 1-Bounce Migration 3-Bounce Migration 0.7 km Assume we know locations Of outer ring of scatterers

Outline Summary Question:  x << /2? Answer:  x= /(4N+2) Synthetic Tests vs Field Data Testsvs

Top of Salt P sea floor top of salt Primary Migration M Resonance Migration Advantage: gain in vertical resolution Superresolution by Resonant Multiples Disadvantage: short-offset data only

Summary kxkx k g + k s  Reconstructed Model Spectrum   x= /(2N+2) N-bounce Resonance vs Slight change in scatterer position  amplified arrival time+Superresolution kzkz vs Primary top of salt Resonance top of salt kzkz kxkx kzkz 1 st -order resonant multiples

Summary Limitations Limited range of resonance Limited range of resonance wavenumbers for specular wavenumbers for specular reflections reflections Resonance can be very weak Separation of different orders of resonance resonance

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Advantage: gain in vertical resolution Examples: Superresolution by Resonant Multiples Top of Salt

Outline Traveltime+waveform Inversion Generalized DSO Inversion ε = ½∑[  m  h] 2 ε = ½∑[  d  ] 2 Motivation Numerical Tests Summary

 Limitations  1. No coherent events in CIGs, then unsuccessful  2. Expensive  3. Infancy, still learning how to walk  4. Low+intermediate wavenumber unless LSM or FWI

Thanks Sponsors of the CSIM (csim.kaust.edu.sa) consortium at KAUST & KAUST HPC

Rayleigh Resolution L D x = min. separation & distinguishable DxDxDxDx z z zL 4 DxDxDxDx

data migration kernel s Skinnier donut=Better resolution e -i  (  sx 1 +  x 1 x 0’ +  x 0’ g ) e i  (  sx 1 +  x 1 x 0 +  x 0 g ) X 0 ’ = trial image point o X’ o g e -i  (  x 1 x 0’ +  x 0’ g -  x 1 x 0 -  x 0 g ) m(x) = ∫ [G(g|x) 1 G(x|s) 1 ]*d(g|s) dg ds 1-Bounce Multiple Scattering e -i  (  x 0’ g -  x 0 x’ 0 g ) Assume x 1 known, x o is to be found XoXo X1X1

Resonance Scattering m(x) = ∫ G(g|x)G(x|s) d(g|s) dg ds data migration kernel d(g|s)= r 2N G(x o |s)G(x o |x 1 ) 2N+1 G(x 1 |g) XoXo X1X1 sg

Numerical Examples Suboffset gathers (Initial) Z (km) X (km) Suboffset gathers Z (km) X (km)

Outline Question:  x << /2? Answer:  x= /(4N+2) Numerical Tests Summary Standard Migration Natural Migration of Resonance Scattering   x<< /2

Primary Scattering m(x) = ∫ G(g|x)G(x|s) d(g|s) dg ds migration kernel data XoXo sg  x= /2 Skinnier donut=Better resolution Where?  x= /2 d(g|s) * *

Primary Scattering m(x) = ∫ G(g|x)G(x|s) d(g|s) dg ds migration kernel XoXo s g X e -i  (  sx +  xg ) e i  (  sx 0 +  x 0 g ) x o is to be foundx = trial image pointdata data migration kernel  x= /2 2-way trip = 2-way trip =

Key Idea: System Amplifies Input Small changes Model  Large changes data Wide-offset Multiples highly sensitive to  bulk properties (i.e., gives better low-wavenumber) Slightly  bulk properties. Can we detect it? Can we detect micro-changes?

Key Idea: System Amplifies Input Small changes Model  Large changes data Slightly  bulk properties. Can we detect it? Can we detect micro-changes? Wide-offset Multiples highly sensitive to  bulk properties (i.e., gives better low-wavenumber) Zero-offset Multiples highly sensitive to  micro properties (i.e., gives better high-wavenumber)

Outline Question:  x << /2? Answer:  x= /(4N+2) Numerical Tests Summary Standard Migration Natural Migration of Resonance Scattering   x<< /2 *  x<< /2

Superresolution by Resonant Multiples Problem: migration of primary, or of primary + multiples of primary + multiples  vertical resolution is limited /2 T t Solution: migration of a multiple only /4 T t zz  t = 4  z / v

XoXo sg Key Idea Resonance Superresolution Small changes X scatterer  Large changes data

XoXo sg  x= /2 I need to travel at least  to get T/2 change in data Can I move  to get T/2 change in data? Key Idea Resonance Superresolution Small changes X scatterer  Large changes data

XoXo sg Can I move  to get T/2 change in data?  x= /6 Key Idea Resonance Superresolution Small changes X scatterer  Large changes data I need to travel at least  to get T/2 change in data

Key Idea Resonance Superresolution Small changes X scatterer  Large changes data XoXo sg Can I move  to get T/2 change in data?  x= /(4N+2) I need to travel at least  to get T/2 change in data

Answer:  x < /2 Standard FWI:  x>> Velocity Model Hybrid FWI:  x< /2 5 km

Outline Question:  x << /2? Answer:  x= /(4N+2) Numerical Tests Summary Standard Migration Natural Migration of Resonance Scattering   x<< /2 *  x<< /2

data migration kernel s e -i  (  sx 1 +  x 1 x 0’ +  x 0’ g ) e i  (  sx 1 +  x 1 x 0 +  x 0 g ) X 0 ’ = trial image point o X’ o g e -i  (  x 1 x 0’ +  x 0’ g -  x 1 x 0 -  x 0 g ) m(x) = ∫ [G(g|x’) 1 G(x’|s) 1 ]*d(g|s) dg ds 1-Bounce Multiple Scattering Assume x 1 known, x o is to be found XoXo X1X1 g  x  c xx T/2=

data migration kernel s e -i  (  sx 1 +  x 1 x 0’ +  x 0’ g ) e i  (  sx 1 +  x 1 x 0 +  x 0 g ) X 0 ’ = trial image point o X’ o g e -i  (  x 1 x 0’ +  x 0’ g -  x 1 x 0 -  x 0 g ) m(x) = ∫ [G(g|x) 1 G(x|s) 1 ]*d(g|s) dg ds 1-Bounce Multiple Scattering Assume x 1 known, x o is to be found XoXo X1X1  x= /2  x  c xx T/2=  x= /2

m(x) = ∫ G(g|x)G(x|s) d(g|s) dg ds migration kernel XoXo X1X1 s o X’ o 3-Bounce Resonance Scattering  x= /6 g e -i  (3  x 1 x 0’ +  x 0’ g - 3  x 1 x 0 -  x 0 g )  x  c  x= /6 T/2=

m(x) = ∫ G(g|x)G(x|s) d(g|s) dg ds migration kernel XoXo X1X1 sg o X’ o N-Bounce Resonance Scattering  x= /(4N+2) Slight change in scatterer position leads to amplified arrival time  Superresolution

Outline Question:  x << /2? Answer:  x= /(4N+2) Numerical Tests Summary Standard Migration Natural Migration of Resonance Scattering   x<< /2 *  x<< /2