Multicomponent and source-free

converted-wave reverse-time

migration for VSP

Yue Du1, Yunyue Elita Li1, Jizhong Yang1, Arthur Cheng1, Xinding Fang2

Singapore Geophysics Project 1

1 Department of Civil & Environmental Engineering, National University of Singapore2 Department of Earth & Space Sciences, Southern University of Science and Technology, China

88th SEG Annual Meeting

17 October 2018

SOUTHERN UNIVERSITY OF SCIENCE AND TECHNOLOGY

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

\PS

(Du et al., 2018)

(Li et al., 2018)

Outline

❖Theoretical basis• New set of elastic wave equations

• Elastic imaging using acoustic propagators

• SFCW image limitations

❖Numerical examples• Simple model

• A part of SEAM model

❖Conclusions and Discussions

3

Outline

❖Theoretical basis• New set of elastic wave equations

• Elastic imaging using acoustic propagators

• SFCW image limitations

❖Numerical examples• Simple model

• A part of SEAM model

❖Conclusions and Discussions

4

Seismology 101: mode conversion

Incident P Incident S

P SV P

SV P

solidsolid

SV

P

SV

P

SV

solidsolid

Are these mode conversion types unconditional?

✓New set of equations: clear mode conversion and its condition

5

New set of separated P- and S-wave equations

Source term

P-wave interacts with Vp boundary

P-wave interacts with Vs boundary

S-wave interacts with Vs boundary

P-wave propagation

6

(Li et al., 2018)

Source term

P-wave interacts with Vs boundary

S-wave propagation

S-wave interacts with Vs

boundary

New set of separated P- and S-wave equations

7

(Li et al., 2018)

Insights from the equations

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

heterogeneous (Lamé) media (constant density)

✓ Wave-medium interactions can be directly interpreted

✓ Mode-conversion only happens at S-wave discontinuities!

✓ Discontinuities only in Vp are transparent to S-wave

8

P P

P scatter

Elastic imaging using acoustic propagators

9

✓ Wave-equations reduce to fully decoupled P- and S-wave equations (acoustic wave

equations) for their potential fields

✓ They can be efficiently solved using acoustic propagators

✓ The elastic propagators can generate strong “in-situ” mode conversions when using

a rough S-velocity model.P

S scatter

SVSV

Velocity imprints by elastic propagators

10

Elastic Propagator Acoustic Propagator

? ? ?

Use a wrong

velocity model to

back propagate

SFCW Image

(Du et al., 2018)

Velocity imprints

SFCW Image Conventional PS Image

SFCW imaging limitations

11

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

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

1. The SFCW image is a second-order approximation to the S-velocity perturbations.

Outline

❖Theoretical basis• New set of elastic wave equations

• Elastic imaging using acoustic propagators

• SFCW image limitations

❖Numerical examples• Simple model

• A part of SEAM model

❖Conclusions and Discussions

12

Simple Model

13

PP Image

Slow V

Avoid uncertain overburden structure

S(t)p

PS Image SFCW Image

R(t)s

R(t)p

A Part of SEAM Model

14

P velocity model PP Image

Image salt boundary without

salt model

Utilize full wavefields

Different illumination

A Part of SEAM Model

15

S velocity model PS Image

Higher resolution

less defined salt image

Different illumination

A Part of SEAM Model

16

S velocity model SFCW Image

Cannot image

far-offset

Near wellbore imaging

17

PP Image PS Image SFCW Image

18

PP Image PS Image SFCW Image

• The events in PP and PS images are pushed down by faster migration velocities.

• The overburden velocity error has stronger impact on the shallower layers.

Near wellbore imaging: fast overburden velocities

Conclusions and Discussions

• This work utilizes elastic imaging conditions with acoustic wave equations for VSP RTM to image complex structures.

➢Advantages of using acoustic propagators for elastic imaging

✓Lower memory and computational cost

✓Free of the artifacts caused by the unphysical wave mode conversion:

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

➢Limitation: Need a clear P- and S-data separation in the recorded data

19

Conclusions and Discussions

• Joint interpretation of the PP and PS image can provide a better understanding for the subsurface structures due to different illuminations.

• PP image reflect both Vp and Vs perturbations while the PS and SFCW images only show Vs perturbations.

• The SFCW image is target oriented and is robust for the complex overburden velocity uncertainties, while it lacks illumination for the areas further away from the borehole.

20

21

Thank you!

Singapore Geophysics Project