Source-free Converted-wave RTM using Acoustic...

Source-free Converted-wave RTM

using Acoustic Propagators

Yue Du

Co-Authors: Yunyue Elita Li, Jizhong Yang, Arthur Cheng, Xinding Fang

May 2018

Singapore Geophysics Project

Introduction: What is source-free?

Source Receivers

R(t)p

S(t)p

Reverse Time Migration (RTM)

Backward propagate

Receiver wavefieldI=0𝑇

*Forward propagate

source wavefield

Conventional PP image condition

2

R(t)s

Backward propagate

S Receiver wavefieldI=0𝑇

*Backward propagate

P Receiver wavefield

SFCW image condition

(Shabelansky et al., 2017)

\PS


Motivation: Velocity imprints by elastic propagator !

3

Elastic Propagator Acoustic Propagator

? ? ?

Use a wrong

velocity model to

back propagate


SFCW Image

Outline

❖Theoretical basis• New set of elastic wave equations

• Imaging as an inverse problem

❖Numerical examples• Acoustic propagator v.s. Elastic propagator

• SFCW applications in surface seismic and VSP

❖Summary

4Singapore Geophysics Project

Outline





❖Summary


New set of elastic wave equations

P- and S-

potential

Propagation

Equation:

PP at ΔVp PP at ΔVs SP at ΔVs

SS at ΔVs PS at ΔVs

Converted-wave

5

✓ New set of equations: coupled but separated for P- and S-

propagations in heterogeneous (Lamé) media (constant density).

✓ “In-situ” mode conversion happens at S-wave discontinuities.

Source term

u: particle displacement

(Li et al., 2018)


SFCW imaging condition

✓ The gradients/images for converted-wave:

6

• Match the modeled S-wave data ds with the recorded S-wave data ds0

Backward propagate

Receiver wavefieldI=0

𝑇*

Forward propagate

source wavefield

Conventional PS image condition

Backward propagate

S Receiver wavefieldI=0𝑇

*Backward propagate

P Receiver wavefield

SFCW image condition

and are propagation operators.


≈

Outline





❖Summary


4-layer example

P S

Simulated Elastic Data: i.e. source x = 0m

(Removed direct arrival)

Vp_scatter = 5000 m/s;

Vs_scatter = 2500 m/s

PP1

PP2

PP3 PS2

PS3


4-layer example: RTM images

Receiver spacing: 5m

Source spacing: 50m

Acoustic Propagator

Elastic Propagator

9

PS Image SFCW Image


Degradation of SFCW images

10

Snapshot at early T

PP1PP2

PP3

PS2

PS3

PP1

PP2

PP3

PS2

PS3

Snapshot at late T

SFCW Image for S0

1. Degraded resolution because of the narrow angle range between PP and PS-waves.

2. Strong artifacts due to the cross-talk of PP and PS-waves from different reflectors.

θ


12

? ? ?

Use a wrong velocity model to back propagate


Elastic Propagator Acoustic Propagator

SFCW Image

Motivation: Velocity imprints by elastic propagator !

Velocity imprints by Vs scatter

13

Acoustic

Propagator

PS ImagePP Image

Elastic

Propagator


SFCW Image

Velocity imprints by Vs scatter

14

SS from vertical-scatter

PS from vertical-

scatter

PP from vertical-

scatter

Back propagated P wavefield

Acoustic

Propagator

Back propagated P wavefield

Back propagated S wavefield

Back propagated S wavefield


SFCW Image

Elastic

Propagator

Outline





❖Summary


Mamoursi: Smooth velocity model


Acoustic

Propagator

SFCW Image Conventional PS Image

Elastic

Propagator

17

? ? ?


Acoustic

Propagator

SFCW Image Conventional PS Image

Elastic

Propagator

Mamoursi: Rough velocity model

Application for VSP

18

PP Image

? ? ? ? ? ?

Avoid uncertain overburden structure

S(t)p

PS Image SFCW Image

R(t)s

R(t)p


Application for VSP

19

PP Image

A part of SEAM model


PS Image SFCW Image

20

Avoid

uncertain

overburden

structure

Wrong shallow layer velocity


Application for VSP

PP Image

A part of SEAM model

PS Image SFCW Image

Summary

➢This work provides a rigorous theoretical basis for the SFCW image conditions from the new set of elastic wave equations.

➢Degradation of SFCW images:

• Low resolution & Strong artifacts

➢ Elastic propagator issue:

• Imprints of S-wave velocity model – “in-situ” mode conversions.

➢ The SFCW image may not be beneficial to use in surface seismic. However, we can apply it for VSP to avoid uncertain overburden structure and image the target around wellbore.


22

Thank you!


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