3D dipole borehole-source wavefieldsimulation

Junxiao Li, Kris Innanen, Laurence R. Lines

Kuo Zhang, and Guo Tao

Dec 3rd 2015

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Outline

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• 1 Introduction

• 2 3D staggered grid finite difference method

• 3 The hybrid perfectly matched layer

• 4 Numerical simulation for dipole source

• 5 Discussion

• 6 Conclusions

Introduction

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• Great potential has been reviewed for acoustic reflection imaging logging todetect unconventional subtle reservoirs like fractures and vugs.

• Dipole source is capable of unveiling azimuth and dip information of structuresoutside borehole.

• 3D staggered-grid finite difference method with hybrid perfectly matched layerabsorbing scheme.

• Based on the convolutional model of received waveforms, the relationshipsbetween the reflection amplitude and the offset as well as the relationshipsbetween the reflection reception response and the azimuth angle areanalyzed.

Staggered-grid finite difference

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xyxx xz x

yx yy yz y

zyzx zz z

V

x y z t

V

x y z t

V

x y z t

11 11 66 13

11 66 11 13

13 13 33

44

44

66

( 2 )

( 2 )

yxx x z

yy yx z

yxzz z

yz y z

xz x z

xy yx

VV Vc c c c

t x y z

VV Vc c c c

t x y z

VV Vc c c

t x y z

V Vc

t z y

V Vc

t z x

VVc

t y x

1

0

1 1, , ( 1, , ) ( , , )

2

Nn n n

x xx x y z m xx x y z xx x y z

m

l l l a l m l l l m l lx

yz

zV

iixV

xy

xz

yV

x

y

z

The perfectly matched layer (PML) (Bérenger, 1994)

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Take x direction as an example

xxi k X t k

s Ae

xx xi

Drawbacks: 1. Requires the use of split fields2. Its efficiency becomes poor at grazing incidence

after discretization.

The convolutional-PML(C-PML) (Kuzuoglu and Mittra, 1996 )

xx x

x

ds

i

Drawbacks: Suffers instability either because of its frequency-dependent term or the convolution operations

C-PML

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M-PML

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i

dmdmds

zyx

x

1

H-PML

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x y z

x x

x

d m d m ds

i

Snapshots in isotropic media

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Borehole wave field reception

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Dip

ole

Rec

eive

rs

Ref

lect

or

X

Z

Y

Unit: m

Borehole

5

5

6

dx=0.01m, dt=1us, f0=3k

(Meredith, 1990)

(Peng et al., 1993)

Received reflections when azimuth is 0 and 90 degrees

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Received reflections when azimuth is 30 and 60 degrees

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0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Reflected waves received by R1 with an offset of 1.5 m

0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Reflected waves received by R1 with an offset of 2.25 m

0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Reflected waves received by R1 with an offset of 3.0 m

0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Reflected waves received by R1 with an offset of 3.75 m

SH

SV

(c)

(a) (b)

(d)

S-SP-P

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0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Full waveforms received by R2 with an offset of 1.5 m

0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Full waveforms received by R2 with an offset of 2.25 m

0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Full waveforms received by R2 with an offset of 3.0 m

0 2000 4000 6000 8000 100000

2

4

6

8

Time(us)

Full waveforms received by R2 with an offset of 3.75 m

SH

SV

(c)

(a) (b)

(d)

S-SP-P

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Simulation for a dipole in VTI media

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dx=0.01m, dt=1us, f0=3k

Receiver spacing: 0.16 m

Offset of receivers: 1 to 5.64 m

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Conclusions

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• A hybrid PML based on the C-PML and M-PML is proposed and used in 3D staggered-grid FD method.

• The wavefield simulation for a directional dipole source in isotropic media isanalyzed. And a transition is detected between the SH-SH reflection and SV-SVreflection with the increase of the offset. Based on the cross-plot of maximumamplitude versus receiver offsets, both the distance between the borehole and thereflector and the critical angle can be calculated.

• For a further discussion, the wavefield simulation for a directional dipole source inVTI media is discussed. The SH-SH reflection coefficient in the VTI medium isintroduced and used to calculate the relationship between the incident angle andreflected amplitude.

Discussion and future work

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SH-SH reflection imaging Coordinate Stretching scheme

Acknowledgement

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• CREWES sponsors

• CREWES staff and students

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Questions & Comments