Bode Omoboya

Collaborators:

Emrah Pacal

J.J.S de Figueiredo

Nikolay Dyaur

Robert. R Stewart

� Physical Modeling Examples

� Study Objectives

� Sample Description

� Experimental Methods

� Azimuthal P-Wave NMO results

� Travel time and Velocity results

� Stiffness coefficients and Anisotropic parameters

� Conclusion and Future work

Y

Z

Stress

Stress

�

Uniaxial Stress and Ultrasonic Anisotropy in a Layered Orthorhombic Medium

Bode OmoboyaJ.J.S de FigueiredoNikolay DyaurRobert. R. Stewart 0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6

stress stress stress stress ---- strain curvestrain curvestrain curvestrain curve

stress (Mpa)strain (%)

0

5E+09

1E+10

1.5E+10

0 0.1 0.2 0.3 0.4 0.5 0.6

C11

C22

C33

C44

C55

C66

� Stress (MPa)

Sti

ffn

ess

Co

eff

icie

nts

(P

a)

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6

gz

gx

gy

� Stress (MPa)

An

iso

tro

pic

Pa

ram

ete

r γ

Shear wave seismogram in different stress regimes a) 0.16MPa b) 0.36MPa c) 0.56MPa

Model M2Crack Density = 4.5 %

Model M3Crack Density = 4.0 %

Model M1Reference Model

Hudson, 1981

ɛ = �����

�

Effect of source frequency on seismic anisotropy

J.J.S de FigueiredoNikolay DyaurBode OmoboyaRobert. R. Stewart

ϒ �1

2

!"#

!##

− 1

Type equation here.

Thomsen, 1986

� To explore the effect of different fluids on seismic response and consequently anisotropy in an inherently anisotropic medium.

� To compare predictions of various theories of wave propagation in fractured media to lab measurements.

Model Dimensions = (296.9 X 296.7 X 131.6) mm

Constituent Materials:

• Resin• Plexiglass

(polycarbonate)• Copper tubes

(a)Copper tubes(b)Plexiglass/polycarbonate

stack(c)Grooves or scratches

between stacked plexiglass(d)Isotropic background resin

Volume fraction/ratio of fractures plexiglass area to composite model =

0.12 : 0.88

d

� Fractured area is made up of 95 scratched plexiglass sheets each 1.1 mm to 1.3 mm thick

� Grooves or scratches on the sheets are 0.1 mm to 0.2 mm deep (on both sides)

� Fractures/scratches are randomly placed and run in all directions on the sheets

� Source-receiver transducers with dominant frequency 100kHz (dominant λ ~ 30 mm) was used in all experiments

Vp = 2540m/sVs = 1250m/s Density ρ = 1.22 g/ccVp/Vs = 2.032Poisson’s ratio * � 0.340

Physical properties of Isotropic resin (background medium)

Vp (matrix) = 2300m/sVs (matrix) = 1320m/s Density (matrix) ρ = 1.188 g/ccVp/Vs (matrix)= 1.742Poisson’s ratio * (matrix) � 0.254

Physical properties of scratched or fractured plexiglass stacks(cracked medium)

ɛ = 0.35ϒ = 0.39

, � 0.007

Porosity φ = 2.5 %

Crack density ζ = 14 %Crack aspect ratio a = 4.2%

Estimated from travel time and

anisotropic measurements

(Thomsen, 1995)

Physical properties of whole sample/model(composite medium)

ɛ = 0.22ϒ = 0.21, � 0.051Porosity φ = 2.5 %

� Background resin medium was found to be isotropic and homogeneous.

� On close inspection, composite model was found to be slightly orthorhombic� C11 ≠ C22 or C33� C22 ≈ C33 (5% difference but were treated as equal in our

analysis)

� Fractured plexiglass inclusion zone has HTI symmetry � Based on model fabrication setup and inverted parameters

(Thomsen, 1995), we consider our cracks to be somewhat penny-shaped with very low aspect ratio (4.2%)

� In all measurements, source wavelength (λ) was 15 to 20 times greater than fracture aperture (H) {λ >> H}

Azimuth 0o

Azimuth 90oAxis of symmetry

source

receiver

Source transducer

Receiver transducer

• Single source transmission measurements in all axes and directions at dry (Gas saturated), partially saturated (50% water saturation) and wet (100% water saturated) conditions

• Surface scaled CMP measurements at dry (Gas saturated) and wet (100% water saturated) conditions

t=2.5s

t=4s

t=0s

Min offset = 400m, Max offset = 2200m, Offset interval = 30m

15o azimuth 30o azimuth 45o azimuth 60o azimuth

All travel time and distance/offset measurements are scaled by a factor of 10,000

t=2.5s

t=2.5s

Gas saturatedVnmo =2131 m/s

Water saturatedVnmo =2372 m/s

NMO corrected gather at 30o azimuth at gas and water saturated conditions

-20 0 20 40 60 80 100 120 140 160 180 2001400

1600

1800

2000

2200

2400

2600

2800

3000

3200V

nm

o (

m/s

)

Azimuth

Gas Saturated

Water Saturated

2440

2450

2460

2470

2480

2490

100% Water

Saturated50% Water

Saturated

VP

(X

) (m

/s)

Gas

Saturated

1700

1750

1800

1850

1900

1950

2000

100% Water

Saturated50% Water

Saturated

VP

(Z

) (m

/s)

Gas

Saturated

Vs (fast)

Vs (slow)

550

600

650

700

750

800

100% Water

Saturated50% Water

Saturated

Gas

Saturated

Velo

city (

m/s

)

2.6

2.8

3.0

C1

3 (

GP

a)

100% Water

Saturated50% Water

Saturated

Gas

Saturated

7.1

7.2

7.3

7.4

100% Water

Saturated50% Water

Saturated

Gas

Saturated

C1

1 (

GP

a)

3.5

4.0

4.5

100% Water

Saturated50% Water

Saturated

Gas

Saturated

C3

3 (

GP

a)

0.74

0.76

0.78

0.80

100% Water

Saturated50% Water

Saturated

Gas

Saturated

C4

4 (

GP

a)

0.35

0.40

0.45

0.50

C5

5 (

GP

a)

Gas

Saturated

50% Water

Saturated

100% Water

Saturated

Gas Saturated

Water Saturated

Percentage difference from gas to water saturated conditions

0.20

0.25

0.30

Thom

sen's

γ

Gas

Saturated

50% Water

Saturated

100% Water

Saturated

0.10

0.15

0.20

0.25

Thom

sen's

ε

Gas

Saturated50% Water

Saturated

100% Water

Saturated

-0.2

-0.1

0.0

0.1

Thom

sen's

δ

Gas

Saturated

50% Water

Saturated

100% Water

Saturated

• Experimental results show that shear wave splitting is affected by the nature of the saturating fluid.

• Results show a 45% decrease in ɛ and 30% increase in ϒ as a function of water saturation.

• NMO velocities shows different trends with source-receiver azimuth as a function of water saturation.

• Stiffness coefficients C33 and C55 are most affected by change in the saturating fluid.

• Repeat experiment with a different saturating fluid (glycerin)• Quantitative AVAZ analysis on CMP gathers• Anisotropic reflectivity modeling from computed stiffness

coefficients

� Ebrom, D. A., R. H. Tatham, K. K. Sekharan, J. A. McDonald, and G. H. F. Gardner, 1990, Hyperbolic traveltime analysis of first arrivals in an azimuthally anisotropic medium: A physical modeling study: Geophysics, 55, 185–191.

� Ebrom, D., J.A. McDonald, 1994, Seismic physical modeling: Geophysics Reprint Series

� Hudson, J. A., 1981, Wave speeds and attenuation of elastic waves in material containing cracks. Geophysical Journal of the Royal Astronomical Society, 64, 133–150.

� Hudson, J. A., T. Pointer, and E. Liu, 2001, Effective-medium theories for fluid-saturated materials with aligned cracks. Geophysical Prospecting, 49, 509–522.

� Omoboya, B., J. J. S, de Fegueiredo., N, Dyaur., and R. R, Stewart., 2011, Uniaxial stress and ultrasonic anisotropy in a layered orthorhombic medium. SEG Expanded Abstracts 30, 2145-2149

� Thomsen, L.,1986, Weak elastic anisotropy Geophysics, 51, 1954-1966.

� Thomsen, L., 1995, Elastic anisotropy due to aligned cracks in porous rock1. Geophysical Prospecting, 43, 805–829.

� Tsvankin, I., 1997, Reflection moveout and parameter estimation for horizontal transverse isotropy. Geophysics 62, 614-629.