The Magic of LaméBill Goodway

Location: Geophysical Society of Alaska, Anchorage.

Date: September 10th 2009

Acknowledgements

Society of Exploration Geophysicists

Shell Sponsorship

EnCana Corporation

SEG MembershipTechnical Journals in Print and Online

Networking Opportunities

Receive Membership Discounts on:

Continuing Education Courses

Publications

Workshops and Meetings Free 

Bookmark

Join Online http://seg.org/join

SEG materials are available today!

Gabriel Lamé (1795-1870): French engineer, mathematician and elastician.Introduced λ and μ in 1828, named after himself, in a series of lectures titled:

“Mémoire sur l’éqiuilibre intérieur des corpssolides homogènes”

Lamé formulated the modern version of Hooke’s law relating stress to strain in general tensor form, creating the basis for the science of materials, including rocks.Interestingly and most notably, only Lamé’smoduli λ and μ appear in Hooke’s law and not Young’s modulus, the bulk modulus, or any other modulus or modulus ratio.

Who was Lamé and what is the physical significance of his parameters Lambda (λ) and Mu (μ) ?Who was Lamé and what is the physical significance of his parameters Lambda (λ) and Mu (μ) ?

Any apparent likeness to myself is purely coincidental!

Assertions

Lamé moduli of rigidity μ and incompressibility λ allow the fundamental parameterization of seismic waves used to extract information about rocks in the Earth.

These parameters link many fields of Earth Science at different scales, from Petroleum Exploration to Earthquake Seismology.

Other common formulations result in contradictions which are removed by restating equations using Lamé parameters.

Disclaimer for use of numerous equations that follow: “If geophysics requires mathematics for its treatment itis the Earth that is responsible not the geophysicist.”

from Sir Harold Jeffreys, University of Cambridge

OutlineP-wave, S-wave propagation, Hooke’s Law and Lamé moduli

Motivation from logs

AVO equations and methods to invert for Lamé moduli

Examples of AVO inversion for elastic parameters from 3D data

Rock Mechanical Properties and Closure Stress

Relating stress (fracture) intensity and orientation to Passive Microseismology and Earthquake Seismology

Conclusions

CompressionalCompressional VelocityVelocity(Sonic Log)(Sonic Log)

UndeformedUndeformed crosscross--sectionsectionof porous sandstoneof porous sandstone

UniUni--axial axial CompressionalCompressionalP Wave P Wave

Modes of Seismic Wave PropagationModes of Seismic Wave Propagation

Shear VelocityShear Velocity(Dipole Log)(Dipole Log)

Shear S Wave Shear S Wave shear

resistanceshea

r re

sist

ance com

pressive resistance

Note λ+2μ, the unnamed P-wave modulus is a direct consequence of bound rocks in the Earth

μμρρ

Vs = λ+2μλ+2μρρ

Vp =

Basic relations: Hooke’s law, moduli and wave equationsHooke’s law as formulated by Lamé:

ijvijij e2e μ+λδ=σ

for shear stress σxz in x direction on the z normal face (i ≠ j) so δij = 0:

xzxz e2μ=σ

Wave equations for P-wave and S-wave propagation “sense” attributes of the medium by equating Newton’s 2nd law (F = Ma) to Hooke’s law.

S-wave propagation of the shear strain exz term in Hooke’s law :

XZ2

2XZ

2

edted

∇μ=ρ

( ) V2

2V

2

e2dt

ed∇μ+λ=ρ

P-wave propagation of the volume strain eV term in Hooke’s law

for normal axial stress in z direction (i = j) so δij = 1:

( ) yyxxzzzz eee2 λ+λ+μ+λ=σ

Lamé parameters: Rigidity Mu (μ) and “Pure Incompressibility” Lambda (λ)

Common moduli resulting from medium’s measurement condition: “Compressional P-wave Modulus” M = λ + 2μ(Bound uni-axial compression)

Young’s Modulus E = μ(3λ+2μ)/(λ+μ) E = M – 2λν(Unbound uni-axial compression)

Bulk Modulus K = λ + (2/3)μ K = M – (4/3)μ

Poisson’s ratio ν = λ /(2 λ + 2μ)

Vp/Vs ratio √(2 + λ/μ)

A given material has various moduli that are purely a function of measurement conditionsLamé parameters λ and μ are invariant and form the basic elements within moduli, giving a simpler physical meaning

Static Moduli and Moduli Ratio Definitions in Lamé terms

Confusing implication of –ve Lambda from Bulk Modulus

μ+λ=Κ

⎟⎠⎞

⎜⎝⎛ μ+λ=−⇒μ+λ=−⇒

++=μ+λδ=σ=−

32 :modulusbulk herew

e32Pe)23(P3

directions stress z y, x,3 themsu

eeee :strain volume wheree2eP

VV

yyxxzzVijVijij σzz

σxx

σyy

Hydrostatic pressure P or tri-axial stress σ in Cartesian coordinates

Lower limits: as μ≥0 and Κ>0 gives a negative Lambda limit as λ> −2/3 μ

Kappa, Mu and Lambda Moduli vs Porosity for 100% BRINE saturation

0

5000

10000

15000

20000

25000

30000

35000

40000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Porosity

Mod

uli [

MPA

]

Log Kappa: BrineLayer 2 Kappa: BrineLog MuKappa Sw 1.0MuLambda Sw 1.0

Kappa, Mu and Lambda Moduli vs Porosity for 100% GAS saturation

0

5000

10000

15000

20000

25000

30000

35000

40000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Porosity

Mod

uli [

MPA

]

Log Kappa: GasLayer 2: GasLog MuKappa gasMuLambda Gas

Saturated moduli vs porosity: Gassmann fluid substitution, Lower Hashin-Shtrikman bound porosity

From theoretical rock physics based on log data Lambda is never negative (dry or wet)

P, S Impedance vs. LambdaRho, MuRho Worldwide Log Data Gas Sand discrimination Castagna mudrock Line and LambdaRho,MuRho threshold cutoff

Gas Sand Brine Sand or Shale

0

2

4

6

8

10

0 2 4 6 8 10 12 14P Impedance km/s.gm/cc

S Im

peda

nce

km/s

.gm

/cc

Vp/Vs = 1.5

Vp/Vs = 2

0

60

-10 0 10 20 30 40 50

MuR

hoG

.Pa.

gm/c

c

20

40

-ve Poisson’s+ve Bulk Mod

Vp/V

s =

1.5

Positive Poisson’s RatioPositive Bulk Modulus

+ve Poisson’s-ve Bulk Mod

Vp/Vs = 2

LambdaRho G.Pa.gm/cc

(Castagna & Smith 1994)

MuR

hoG

.Pa.

gm/c

c

wet sand cloud

In-situ wet sand log

lowlow

porosityporosityhighhigh

LambdaRhoLambdaRho G.Pa.gmG.Pa.gm/cc/cc

background shales

0

LambdaRho vs.MuRho cross-plots for in-situ wet and gas substituted logs

+ve κ, -ve or zero λ

Gas substituted log

gas sand cloud

MuR

hoG

.Pa.

gm/c

c

lowlow

porosityporosityhighhigh

LambdaRhoLambdaRho G.Pa.gmG.Pa.gm/cc/cc

background shales

0

Negative LambdaRhovalues reveal log errors

Histograms of Histograms of VpVp/Vs ratios/Vs ratios(wet sand zones) (wet sand zones)

1.51.5 2.02.01.751.75

LambdaRho vs.MuRho cross-plots for in-situ wet and gas substituted logs

comparable log

log for fluid substitution

Motivation from well logs

Ostracod shale has negative Lambda and Poisson ratio but positive Bulk modulusThis is an error and indicates a log problem

Alberta Cretaceous Clastics/Carbonate facies(Glauconite) Vp m/s Vs m/s

Rho gm/cc

P Impedance m/s. gm/cc

(Rayls)

S Impedance m/s. gm/cc

(Rayls)

LambdaRhoG.Pa. gm/cc

(Rayls2)

MuRhoG.Pa. gm/cc

(Rayls2)

Bulk modulus

G.Pa. Vp/Vs Poisson Lambda/Mu Ostracod Limestone 5464 2186 2.70 14753 5902 147.97 34.84 63.41 2.50 0.40 4.25

Ostracod Shale 2851 2115 2.30 6557 4865 -4.33 23.66 4.98 1.35 -0.11 -0.18Channel Shale Plug 4372 2342 2.60 11367 6089 55.06 37.08 30.68 1.87 0.30 1.48Regional Shale/Silt 4098 2186 2.55 10450 5574 47.05 31.07 26.58 1.87 0.30 1.51

Porous Channel Sand 4098 2342 2.35 9630 5504 32.16 30.29 22.28 1.75 0.26 1.06Tight Channel Sand 4684 2623 2.55 11944 6689 53.19 44.74 32.55 1.79 0.27 1.19

AVG. % CHANGE POROUS/TIGHT SAND 21% 19% 49% 39% 37% 2% 5% 11%

Motivation from well logs

VVpp/V/Vss (V(Vpp/V/Vss))22νν μμ

Gas SandGas SandShaleShale

% change% change

2.252.251.711.712727

5.15.12.92.95555

0.380.380.240.244545

λ+2μλ+2μ20.3720.3718.5318.539.29.2

4.0354.0356.3146.314

4444

λλ12.312.35.95.97070

λ/μλ/μ3.13.10.90.9110110

Vs Vp ρ

1290 m/s 2898 m/s 2.425 gm/ccShale

2.275 gm/cc2857 m/s1666 m/sGas Sand

Averaged log values for Shales, Carbonates and Gas Sands from Alberta

λ = Vp2*ρ - 2 Vs

2*ρ

μ = Vs2*ρ

Relations to transform velocities, density to Lamé parameters λ and μ

Towed streamer P-wave data

Converted wave Converted wave PP--S OBC dataS OBC data

From MacLeod et al 1999 Chevron/WEGCOFrom MacLeod et al 1999 Chevron/WEGCO

OWC

Shale

Shale

Sand

Shear waveVs

OWCSand

Shale

Shale

P-wave Vp

North Sea P-wave and Shear wave Logs Alba Field Seismic P-P and P-S comparison

P-, S-impedance

S ImpedanceP Impedance

metres1240

1260

1280

1300

1320

2000

6000

1000

0

1400

0

1800

0Shale

Carbonates

(m/s.gm/cc)

LambdaRho, MuRho

MuRhoLambdaRho

0 8040 120

160

Silt

ShaleGas Sand BTight Streak

Gas Sand ACarbonates

(GPa.gm/cc)

metres1240

1260

1280

1300

1320

Petroleum industry log tracks for Sands, Shales and Carbonates showing improved LambdaRho, MuRho crossover discrimination of gas zones and lithologies compared to P-, S-impedance

Relations to transform impedances to Lamé parameters λρ, μρ

Impedance = Velocity*DensityP-impedance = Vp*ρS-impedance = Vs*ρ

λρ = (Vp*ρ)2 - 2 (Vs*ρ)2

μρ = (Vs*ρ)2

Fluid, Porosity & Lithology directions in LambdaRho (λρ), MuRho (μρ) spaceFluid, Porosity & Lithology directions in LambdaRho (λρ), MuRho (μρ) space

5%

10%

15%

20%

5%

10%

15%

20%

5%

10%

15%

20% Shale

Poro

sity

Lithology

Carbonates

Sands

FluidWaterOilGas

Dolomite

Shale

QuartzLimestone

λρ (GPa.gm/cm3 or Rayls2)

μρ(G

Pa.g

m/c

m3

or R

ayls

2 )

cons

tant

Poi

sson

ratio

constant P-impedance

Porosity % bubble

20%

15 300

150

125

100

75

25

50

45 60 75 90 105

(Adapted from Hoffe, Perez and GoodwayCSEG convention 2008)

Gas Sand Zone

Wet Sand Zone

Marine Shale above Gas Zone

Tight Sandy Shale between Gas & Wet Sand Zones

Calcareous Shale/Silt

Sensitivity of Vp/Vs, Poisson’s ratio vs. Lambda/Mu ratio

0.000.250.500.751.001.251.501.752.002.252.502.753.003.253.503.754.004.254.50

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

4.8

5.2

5.6

6.0

6.4

6.8

7.2

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Vp/Vs Poisson ratio

Lambda/Mu ratio

Vp/

Vs

ratio

Poisson’s ratio

( )1

VsVp5.0

/d)Vs/Vp(d −

⎟⎠⎞

⎜⎝⎛=

μλ

2)21(5.0)/(d

dν−=

μλν

Comparison to Vp/Vs

Comparison to Poisson’s ratio

0%10%20%30%40%50%60%70%80%90%

100%110%120%130%140%150%160%170%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water Saturation (Sw)

Nor

mal

ized

avg

. % c

hang

e“Fizz Water” (Low Gas Saturation) Discrimination

(data points from Han et al 2001)

LambdaRhoLambda/Mu ratioPoisson ratioIp/Is ratioFluid Factor Smith&Gidlow

Relative sensitivity to water saturation:Ip/Is, Poisson’s, Lambda/Mu ratios and LambdaRho, “Fluid Factor”

0.0

2.0

4.0

6.0

8.0

10.0

-10 -6 -2 2 6 10 14 18 22 26 30 34

LambdaRho-MuRho Difference

Lam

bda/

Mu

Rat

io

Gas Sands

Shales

Brine Sands

Lam

bda/

Mu

ratio

LambdaRho-MuRho difference

slope ∝1/μρ

decreasing Ip

λ/μ ratio vs. λρ−μρ difference with lines of constant P- and Shear Impedance

Lambda/Mu Ratio vs. LambdaRho-MuRho difference crossplotsWorldwide Log Data (Castagna and Smith 1994)

Lam

bda/

Mu

ratio

LambdaRho-MuRho difference

(Dave MacKidd 1996)

linear trend

Fluid discriminationLambda/Mu ratio vs Lambda-Mu difference crossplot templates:

Lithology and Porosity discrimination

-10 0 10-15 -5 50.40

0.60

0.80

1.00

1.20

Glauconitic Gas SandGlauconitic Wet Sand

-10 0 10-15 -5 50.40

0.60

0.80

1.00

1.20

Glauconitic Gas SandGlauconitic Wet Sand

λ−μ (GPa.)

λ/μ

(from T. Chen et al 1998)

-20 0 20 40 600.00

0.80

1.60

2.40

3.20

Porous Sand

Carbonates

Shale

Sandstone line

-20 0 20 40 600.00

0.80

1.60

2.40

3.20

Porous Sand

Carbonates

Shale

Sandstone line

λ−μ (GPa.)

λ/μ

Alberta Glauconitic Gas Sand Log

2 4 6 8 100

2

4

6

λ (GPa)

Hydrocarbons(in yellow)

TargetSand Lines

0 11 - Water SaturationWet Oil

λ/μ

GOM log data

AVO Reflectivity MethodsAVO Reflectivity Methods

Common Reflection PointMultiple Shots and Receivers

Offset Gather with Reflection Amplitude Variation with Offset

Seismic Ray Paths

Far Offset Near Offset

Increasing Offset

ShotsGeophones

WalkawayWalkaway VSP Geometry VSP Geometry Direct proof of AVODirect proof of AVO

AVO AVO ““GathersGathers”” from VSPfrom VSP3C

Geo

phon

es

Source Positions

FarOffset

Near Offset

PPii PPjj

PPii~ ~ PPjj

RRpp--pp==PP--PPr r /P/Pii

P-Pr

Reflector

PP--P reflectionP reflection

OffsetOffset0.50.5

0.60.6

0.70.7

0.80.8

0.90.9

1.11.1

Near FarNear Far200m 1700m200m 1700m

Gas Sand Gas Sand AVO AVO

responseresponse1.01.0

Linear P-P AVO three term reflectivity equations and approximations following Aki & Richards 1980

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+

Δ==

Δρρ

VpVp

21)0(Rpp

Ip2Ip

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+

Δ==

Δρρ

VsVs

21)0(Rss

Is2Is

where the link is:

( )ρρθθθθ Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

Δ−

Δ+= 2

2

22

2

22 sin

VpVs41

21

VsVssin

VpVs4

VpVptan1

21)(Rpp Aki & Richards

1980

Rpp(θ) = f1(θ)∗(Vp change) - f2(Vp/Vs,θ)∗(Vs change)+ f3(Vp/Vs,θ)∗(density change)

Gidlow,Smith,Fatti 1992 ignore Δρ/ρ 3rd term

ρρθθθθθ Δ

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−−

Δ⎟⎟⎠

⎞⎜⎜⎝

⎛−

Δ+= 2

222

22 sin

VpVs2tan

21

Is2Issin

VpVs8

Ip2Ip)tan1()(Rpp

Rpp(θ) = f1(θ)∗(Ip change) - f2(Vp/Vs,θ)∗(Is change)+ [f(Vp/Vs,θ)∼0]∗(density change)

Other P-P reflectivity AVO equations and approximations

( )Δθ−θ+θ⎟⎟

⎠

⎞⎜⎜⎝

⎛ν−νΔ

++=θVp2Vpsintansin

)1()0(ARpp)0(Rpp)(Rpp 222

2

Shuey 1985 ignore ΔVp/Vp term

Note ΔVp/Vp ~ 4Δρ/ρ Gardner 1974

Vp2Vp)tan1(

2)(Rpp 2 Δ++Δ= θ

ρρθ −

μμθ

2sin

VpVs4 2

2 Δ⎟⎟⎠

⎞⎜⎜⎝

⎛Wang 1999 (Goodway 1998)

ignore Δρ/ρ term wide angle gradient approximationintroduced Mu reflectivity into AVO

General form: Rpp(θ) ≈ A + B sin2(θ) A= intercept, B=gradient

NI = Rpp(0) normal incidence reflectivity, PR = Δν/(1−ν)2 Poisson reflectivity

Hilterman & Verm 1995 ignore ΔVp/Vp term( )

θν−νΔ

+θ=θ 22

2 sin1

cos)0(Rpp)(Rpp

Wiggins 1984 ignore Δρ/ρ termθθ 2

2sin)0(Rss

VpVs8)0(Rpp)0(Rpp)(Rpp ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65

Comparison of 3 term Aki & Richards to 2 term approximations

00.010.020.030.040.050.060.070.080.09

0.10.110.120.130.140.150.160.170.180.19

0.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Angle

P-P

refle

ctio

n co

effic

ient

Aki & Richards 3 termGidlow, Smith FattiShueyWang

P re

flec t

ion

coef

ficie

n t

Angle

30° 45°

-0.038-0.036-0.034-0.032-0.030-0.028-0.026-0.024-0.022-0.020-0.018-0.016-0.014-0.012-0.010-0.008-0.006-0.004-0.0020.0000.0020.0040.0060.0080.0100.0120.0140.016

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Angle

Ref

lect

ivity

Rμ(θ)

Rρ(θ)

Rλ(θ)

Rfull(θ)

Aki & Richards AVO reflectivity curve with separate Lambda, Mu and Rho termsR(lambda)= -0.1 R(mu)=0.1 R(rho)=-0.03

Decomposition of AVO reflectivity equations into Lambda,Mu,Rho(Gray et al 1999, Goodway 1997, 2002)

30° 45°

( ) ( ) ( ) tan125.0V

Vsin2

22tan125.0)(R 2

2P

2S22

ρρΔ

θ−+μμΔ

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛θ−

μ+λμ+λΔ

θ+=θ

( ) cos4

2cos

V

V

cos2

2cos

V

V21

cos4

1)(R22

P

2S

2

2

2P

2S

2 ρρΔ

θ

θ+

μμΔ

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

θ

θ+

λλΔ

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

θ=θ

Note behavior at 45ºΔρ/ρ term disappears

with “polarity” flipΔμ/μ term has an

inflection and is zeroΔλ/λ alone remains

Log track Low frequency background model

Inversion result

AVO gather log model

AVO gather inversion

AVO gather error

Base of zone

45ºpolarity flip

P-impedance S-impedance Density

Log based AVO model inversion for density (Gidlow method with error term retained in constrained AVO inversion)

45º angle requirement and polarity flip

Density term is rejected in the error plot as seen in the polarity flip at 45º

( )

KK

KK

1

KK

1 KK

fluid

1solid

solid

dry

2

solid

dry

drysat

⎟⎟⎠

⎞⎜⎜⎝

⎛ φ+⎟⎟

⎠

⎞⎜⎜⎝

⎛−φ−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=−

Biot-Gassmann fluid replacement equation in Lamé terms and relation to “Pore Space Modulus” (Hedlin, Russell, Hilterman and Lines 2003)

Biot-Gassmann Equation:K is bulk modulus, “sat” is saturated rock, φ is porosity

o45at AVO fromdirectly obtained becan Remember K

K

KK K and ngsubstituti and romF

sat2solid

2fluid

drysoliddrysatsatdry

λφ

Δλ≈λΔ⇒

−=Δλ−λ=λΔμ=μBiot-Gassmann Equation in Lamé terms

( ) ( )

K

Kf

above from equating so )(f

2VV

C whereC2ICIf modulus space Pore

sat2solid

2fluid

satdrysat

dry2

)dry(S

)dry(Psatsatsat

2S

2P

ρφ

Δλ≈ρ⇒

λΔρλ−λ=ρ⇒

μ

μ+λ=⎟

⎟⎠

⎞⎜⎜⎝

⎛=μρ−ρμ+λ=−=ρ

Relating “Pore Space Modulus” ρf to Biot-Gassmann Equation in Lamé terms

AVO Classes in Rp, Rs Reflectivity Space(Goodway, Hoffe, Perez 2002, 2008)

III

II

θ

0.20

ΔI p/

I p(θ)

0.10

0.00

-0.10

-0.20

IVV

Rutherford&WilliamsCastagnaYoung&LoPiccoloI

100% φ intercepts: gas sand (Vp≈0) wet sand (Vp≈1500m/s) Vp=A+BVs where Vs=0

gas sands

Mudrock

line

P-wave velocity (km/s)1 2 3 4 5

1

2

3

S-w

ave

velo

city

(km

/s)

shale

swet sa

nd

Linear dry

sand relation

6

Grinsburg and Castagna:Vp(sand)=1065 +1.25 Vs Vp(shale)=1126 +1.3 Vs(velocities in m/s)

background mudrock line relations (Vp=A+BVs)

III

II I

False Type 1

-0.3 0.3

-0.3

+0.3

+ΔIp/Ip = Rp

+ΔIs/Is = Rs

reference pt

V

Increase in Vp/Vs

Zero Gradient Line(ΔIp/Ip=2ΔIs/Is)

Decrease in Vp/Vs

IIIIV

BackgroundRs = 1.43 Rp

-ΔIp/Ip

-Δ Is/Is

Rotation of gas sands away from background

Backg

roun

d wet

sand

/shale

Top gas sand anomaly

Basegas sand anomaly

Backg

roun

d wet

sand

/shale

mud

rock

trend

GAS

BRINE

Rp Rs

TagluT-C11

Rp Rs

Brine (in-situ)

Gas (substituted)

Well: 300F486930134017-Nov-2002 01:44:38

2900.0

2900

3000

3100

3200

3300

3400

3500

DepthMetres

TWTIME_GAS.DT_1US/M500 100

TWTIME_GAS.DTSM_1US/M1200 200

AEC.APPLY_30 10

AEC.VSH_3V/V0 1

TWTIME_GAS.RHOB_1K/M31950 2950

TGLU

T-C8A

T-C11T-C9

T-C11

Rs vs. Rp xplots: angle range 5-40o

Substituted T-C11 gas sand zone identified from blue (top) and orange

(base) x-plot polygons of AVO anomaly

Mac Delta gas discovery: pre-drill AVO model reflectivity prediction Rp,Rs synthetic: Brine (in-situ) vs Gas (substituted)

AVO Inversion Methods

Gidlow, Smith, Fatti methodAVO extraction of Rp, Rs

Goodway methodRp,Rs inversion to Ip,Is

λρ = Ip2 - 2Is2

μρ = Is2

λρ, μρλρ, μρ

P & S ImpedanceP & S Impedance

AngleAngleGathersGathers

P & S P & S ““ReflectivityReflectivity””

Connolly methodRp(θ) inversion to Ip(θ)

AngleAngleGathersGathers

λ, μ, ρ

ElasticElastic ImpedanceImpedanceAI, EIAI, EI

Elastic Impedance extended in Laméparameter terms

Elastic Impedance in Lamé (LMR) terms following Connolly 1999

Density is present in all EI(θ°) Density and Vs always functions of a power of γ = Vs2/Vp2

At 30° and 45° the EI (θ°) values are:

EIVsVpIpIplnpR )psin41(psin8)ptan1( 222

=ρ=⇒= θγ−θγ−θ+θθθ∫

)21(42

)1(23/4

VsVp)45(EI

VsVp)30(EIγ−γ−

γ−γ−

ρ=

ρ=

Formulated in Lamé and density terms:

At 0°, 30°, 45° and 60° the LMRI (θ °) values are:

( )

( )

( ) 1212

21

3/13/3/212

2/12/)21(

)60(LMRI

)45(LMRI

LMRI(30)

LMRI(0)

−γγ−

γ−

γγ−

γγ−

ρμλ=

λ=

ρμλ=

ρμλ= Density independent of γ in all LMRI(θ°)and changes sign at 45°Density and Mu absent in LMRI (45°)At 45° only Lambda “Pore Space Fluid Modulus”(scaled to power of γ)

( ) ( ) (LMRI) Impedance LaméIp2222 cos22coscos2coscos221 =ρμλ= θθθθγθγ−

θ

( ) μρλγ

γ =⎥⎥⎦

⎤

⎢⎢⎣

⎡==−

3/1

3

2321/1

)45(LMRI

LMRI(60))0(LMRI ,

)60(LMRI LMRI(30)

,)45(LMRI

Assuming meaningful LMRI(45°) LMRI(60°) following elastic parameters are extractable:

AVO Classes in Reflectivity and LMR Space(Goodway, Hoffe, Perez 2002, 2008)

Zero Gradient Line(ΔIp/Ip=2ΔIs/Is)

μμ ··ρρ

((Pa·

kg/m

3 )) I

IIIII

λλ··ρρ ((Pa·kg/m3))

5%

10%

20%

5%

10%

15%

20%

5%

10%

15%

reference ptreference pt

Dolomite

Limestone

Shale

Quartz

15%20%

VIV

III

II

θ

0.20

ΔI p/

I p(θ)

0.10

0.00

-0.10

-0.20

IVV

Rutherford&WilliamsCastagnaYoung&LoPiccoloI

Constant P-impedance Ip

Cons

tant

Po

isson

s rat

io

LMR space adds insight to AVO classes Fluid shift

LihologyPo

rosi

ty

IIIII I

False Type 1

-0.3 0.3

-0.3

+0.3

+ΔIs/Is=Rs

reference pt

V

Increase in Vp/Vs

Decrease in Vp/Vs

IIIIV

BackgroundRs = 1.43 Rp

-ΔIp/Ip

-Δ Is/Is

+ΔIp/Ip=Rp

MacKenzieMacKenzie Delta gas discoveryDelta gas discoveryPre-drill Fluid Replacement Log Model of Rp,Rs and LambdaRho vs. MuRhocrossplots of original wet zone in legacy well.Note improved separation and fluid/porosity discrimination in λρ vs. μρ that is not possible with Rp vs. Rs

Rs

Gas sand anomalyAll AVO classes 1,2,3Fluid, porosity confusion?

Back

grou

nd w

et-s

and/

shal

e

mud

rock

trend

Rp

Rp vs. Rs

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

55.0

60.0

0 0

10 10

20 20

30 30

40 40

50 50

60 60

70 70

80 80

90 90

100 100

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

55.0

60.0

0 0

10 10

20 20

30 30

40 40

50 50

60 60

70 70

80 80

90 90

100 100

Incr

easin

g φ

Tight streaks

• Shale• Brine Sand• Gas Sand

-1101

Colo

r: V

olu

me S

hale

Large consistent fluid separationdiscriminates oil (green oval) from gas

λρ

μρ

LambdaRho vs MuRho

Walkaway VSP AVO gather

Zone ofZone ofInterestInterest

R1R1R2R2 4040ºº

3535ºº

3030ºº

2525ºº

200m 1700mFar Offset Near OffsetCMP Gather with Offset Balancing

P vs. S Impedance

LambdaRho (GPa. gm/cc)P Impedance (m/s. gm/cc)

CementedTight SandGas Sand

S Im

peda

nce

(m/s

. gm

/cc)

Shale

Threshold cutoff forIp/Is “Fluid Factor” Stack

SiltShalyGasSand

ShalyGasSand

MuR

ho(G

pa. g

m/c

c) CementedTight Sand

ShaleCluster

Threshold cutoff forLambda/Mu Stack

GasSand

ShalyGasSand

Silt

LambdaRho vs. MuRhoSeismic LambdaRho,MuRho vs. P-,S-impedance crossplots and “fluid factor” stacks

P-, S-impedance “fluid factor” LambdaRho, MuRho “fluid factor”

1.11.1

Ambiguous Gas Sand Zone Isolated Gas Sand channel zone

secsec0.80.8

0.90.9

1.01.0

Alberta Gas Sand Channel

Low High

A B C

Migrated stackamplitude ambiguity

(white boxes)

LambdaRho stackclear gas sand

anomalies (white boxes) at wells

well A wet, wells B,C gas

MuRho stackclear sand channel layer

above unconformity (green zones) at gas wells unconformity

unconformity

unconformity

Alberta Upper/Lower Basal Quartz Sand Channel Discrimination

LMR lithology from crossplot polygons600

700

800

900

Upper BQ

Lower BQ

Tim

em

sec

Upper BQPorosity = 25.6%Permeability = 566 MD

Lower BQPorosity = 13.8%Permeability = 14.6 MD

Core Analysis

1220

LambdaRho G.Pa. g/cc (Incompressibility)

MuR

hoG

.Pa.

g/c

c (R

igid

ity)

22

42

62

50 80 110 140

2.00

2.85

2.42

Upper BQ

Lower BQ

coals

Density OverlayLog Crossplot

15

35

45

40 80 120 1600

Upper BQ

Lower BQ

MuR

ho

LambdaRho

25

Seismic Crossplot

LambdaRho MuRho anomaly (3D Line)LambdaRho MuRho

Low

High

Gas/condensate anomaly

Alberta Deep Basin: Carbonate gas/condensate discovery75 MMCF/day (AAPG Best Paper 2005)

LambdaRho Anomaly MapStrong anomaly delineates gas/condensate discovery

Low λρ

High λρ

Vp/Vs Anomaly MapLimited Vp/Vs attribute response

Low Vp/Vs

High Vp/Vs

Alberta Deep Basin: Carbonate gas/condensate discovery75 MMCF/day (AAPG Best Paper 2005)

100100

8080

4040

2020

00

6060

--2525 00 2525 5050 7575 100100 125125 150150 175175

Porous gas sandPorous gas sand

Silt shaleSilt shale

Mu error = Mu (true) x2Mu error = Mu (true) x2

Mu error = Mu (true) x1/2 Mu error = Mu (true) x1/2 MuR

hoM

uRho

LambdaRhoLambdaRho

LambdaRho/MuRho Crossplot Errors from Mu (S-impedance or velocity) Correlated Error Alone

Gas sand channel seismic LMR crossplot shows clear relative isolation of gas sand points despite inversion error skew (note -ve LambdaRho values)

--2020

6060

5050

4040

3030

2020

00 2020 4040 6060LambdaRho

MuR

ho

λ /μ

rati o

ov e

r lay

00

0.40.4

0.80.8

1.21.2

1.61.6

2.02.0

1313--1616

0909--1717 1212--1616

0505--1616

0101--1717 0404--1616

1414--0909

1111--0808

0808--0808

0101--0808

0909--08081616--0808

0909--0808

1 km1 km

LMR cross-plot gas sandmask on λρ 3D map

Yellow oval in grey cloud mask of known gas sand points, clearly isolates best gas sands from background. Correlated Rp, Rs extraction errors mean gas sand detection in LMR cross-plot space is unaffected

Poison’s ratio decreases with increased Young’s modulus (Grigg SPE 2004)

Geomechanics and Moduliinvolved in fracture prone rocks

Poissons_ratio = - 0.045700 *E + 0.452206

-

0.050

0.100

0.150

0.200

0.250

0.300

0.350

3.00 3.50 4.00 4.50 5.00 5.50

YOUNG'S MODULUS ( MMpsia)

POIS

SON

'S R

ATIO

.

4.753.9 MMpsi=27GPa

0.235

0.27

Poissons_ratio = - 0.045700 *E + 0.452206

-

0.050

0.100

0.150

0.200

0.250

0.300

0.350

3.00 3.50 4.00 4.50 5.00 5.50

YOUNG'S MODULUS ( MMpsia)

POIS

SON

'S R

ATIO

.

4.753.9 MMpsi=27GPa

0.235

0.27

Barnett shale properties (Grigg 2004)

μ=ν+

21

EThis implies a simple increase in a single modulus of rigidity μ.

Lambda vs. Young’s modulus cross-plotoverlaid with: curves of constant Mu lines of constant Poisson's ratioBarnett Shale trend

02468101214161820222426283032343638

Mu (G

.Pa)

Barnett Trend0.10.140.180.220.260.30.340.380.420.46

Poisson’s ratio 05

1015202530354045505560657075

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Lambda (GPa)

Youn

gs m

odul

us (G

Pa)

Brittle

Ductile

Closure Stress Equation (Engineering to Geophysics)Fracture generation and moduli: E,ν,μ and λ

[ ] ( ) ee1

E PBPB 1 yyxx2pHPVzzxx ν+

ν−++−σ

ν−ν

=σ

( ) e and e2strain uniaxialfor law sHooke'

zzxxzzzz λ=σμ+λ=σ

So in λ and μ terms

PBe

e-ePB pHyy

xx2

yyPVzzxx +

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛μ+−σ

μ+λλ

=σ⇒2

22Effective stress

= Overburden – Pore PressureTectonic strain energy% anisotropy = e2

yy - e2xx

σzz - BvPp

σxx, exx

eyyConfining stress

σyy = σmax

σxx=σmin

But horizontal strains are zero exx= eyy = 0Uniaxial strain in ez only, as rock is bound in the earthSo Poisson’s ratio ν = - exx/ezz= 0 !

Whereσxx = min. horizontal closure stress to open an existing fractureσzz = overburden stress Pp = pore pressure acting vertically (Bv) and horizontally (Bh)

Fluid, Porosity, Lithology, Geomechanics and Closure Stress reduction directions in LMR SpaceFluid, Porosity, Lithology, Geomechanics and Closure Stress reduction directions in LMR Space

MuR

ho(G

.Pa.

gm/c

c)

5%

10%

15%

20%

5%

10%5%

10%

15%

20%

Poro

sity

Lithology

FluidWaterOilGas

LambdaRho (G.Pa.gm/cc)15 30 45 60 75 90 1050

Dolomite

25

50

75

125

150

100

QuartzLimestone

Shale constant P-impedance

cons

tant

Poi

sson

’s ra

tio

= 0.

17

20%

15%

Sand

Porosity % bubble

20%

adapted from Hoffe et al CSEG convention 2008

PBe

e-ePB pHyy

xx2

yyPVzzxx +

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛μ+−σ

μ+λλ

=σ2

22

Effective stress= Overburden – Pore Pressure

Tectonic strain energy% anisotropy = e2

yy - e2xx

reduced Effective Stress

amplification

reduced Tectonic

amplification

Barnett shale relative EUR’s30

53

Gas shales W.CanadaCalcareous shales

Ductile shales

Carbonates

3053

Barnett analogue

Good production high EURWeak non-aligned anisotropy (weak 3D attribute-green/blue tick marks) Broad fracture network

Poor production low EURStrong aligned anisotropy (strong 3D attribute-red/orange tick marks)Narrow fracture network

Grey/green overlay of microseismic event monitoring of fracture stimulated perm

From Y. Simon M.Sc. U of H 2005

N. Texas Barnett Shale Fracture Generation and Anisotropy Maps

Lithology and geomechanical attribute mapping using LMR

Sands

Gas shales

3D line with colour overlay from cross-plot polygons (discovery well rate 16 mmcfpd)

Ductile

shale

Brittle

shale

SandsCarbonates

Log guided seismic cross plot poylgons and resulting seismic section(from Eric Keyser)

Higher

poro

sity

gas s

and

Gas shales

LambdaRho

MuR

ho

Gamma log colour overlay

Seismic AVO Gathers, 3D Azimuths and FracturesCommon Reflection Point Multiple Shots (S) and Receivers (R)

Far Offset Near Offset Far Offset

Seismic Record of offset gather with amplitude variation with offset

Seismic Reflection Ray Paths

S S SS R R RR

Increasing Offset

3D seismic acquisition and fractures

Core fracture orientationS

600m

Si, Ri

R

azimuth sectors

Isotropic AVO

AVAZ:Anisotropic AVO

θ = P-wave propagation angle (vertical plane)α, β = P- and S-wave velocityΔα/α = fractional change in P-wave velocityΔμ/μ = fractional change in rigidity Mu

Anisotropy parameters:φ=0: slow (weak) in symmetry axis (across fractures) φ=90: isotropic (parallel to fractures)Δγ = Sh-wave anisotropy ‘velocity splitting’Δε(v) = P-wave anisotropy Δδ(v) = P& Sv-wave anisotropy

P-wavezero offset

Isotropic (in-fracture) AVO terms Anisotropic (cross-fracture) AVO terms

Rp (θ,φ) = Rp(0) + 0.5([ Δα/α − (2β/α)2 Δμ/μ] + [Δδ(v)+ 2(2β/α)2 Δγ]cos2φ) sin2θ

+ 0.5(Δα/α + [Δδ(v) sin2φ cos2φ+ Δε(v)cos4φ]) tan2θ sin2θ

Isotropic layer

Anisotropic layer

3D surface seismic geometry: multi-azimuth offsets

Principal Anisotropy Planes

P

Sv (S2) slow perpendicular

P(slow)

PSv (S1) fast parallel

P(fast)

fract

ure-

para

llel

isotro

pic p

lane

fracture-perpendicular symmetry plane

Anisotropic layerwith vertical fractures

Isotropic layer

Principal Anisotropy Planes

P

Sv (S2) slow perpendicular

P(slow)

PSv (S1) fast parallel

P(fast)

fract

ure-

para

llel

isotro

pic p

lane

fracture-perpendicular symmetry plane

Anisotropic layerwith vertical fractures

Isotropic layer

Principal Anisotropy Planes

P

Sv (S2) slow perpendicular

P(slow)

PSv (S1) fast parallel

P(fast)

fract

ure-

para

llel

isotro

pic p

lane

fracture-perpendicular symmetry plane

Anisotropic layerwith vertical fractures

Isotropic layer

φ=0º

φ=90

º

opposite sign

AVAZ (Amplitude Variation with Azimuth): Ruger et al equation 1997

A better 3 term AVAZ equation: each term has equal significance for robust inversion of Δα/α, Δμ/μ, Δγ, Δδ

Where η∗ = (ε−δ)/(1+2ε) obtained from NMO

P-velocityzero offset

Isotropic (in-fracture) AVO terms

Anisotropic (cross-fracture) AVO terms

Rp (θ,φ) = Δα/α + 0.5(Δα/α + [Δδ(v)+ Δη∗cos2φ]cos2φ) tan2θ

− 0.5((2β/α)2 Δμ/μ − [2(2β/α)2 Δγ − Δη∗cos2φ] cos2φ) sin2θ

Offset vs. Azimuth angle cube

Fracture strike @ N10

1800m offset slice105o 285o

AVO azimuth gradients

strong gradients

perpendicular

Fracture strike @ N10

1800m offset slice105o 285o

AVO azimuth gradients

strong gradients

perpendicular

azimuth angle

t

Azimuthal Anisotropy from 3D seismic AVO over known fractures

III

II I

AVO Classes for Fracture ReflectivityAVO Classes for Fracture ReflectivityAVO Classes for Fracture Reflectivity

-ΔVp/Vp-ΔVp/Vp

-Δμ/μ-Δμ/μ

-0.3-0.3 0.30.3

-0.3-0.3

+0.3+0.3

Zero Gradient Line(assumes ΔIp/Ip=2ΔIs/Is)

Zero Gradient Line(assumes ΔIp/Ip=2ΔIs/Is)

+ΔVp/Vp+ΔVp/Vp

+Δμ/μ+Δμ/μ

V IIIIII

IIII

II

(Hoffe, Perez, Goodway, 2002, 2008)(Hoffe, Perez, Goodway, 2002, 2008)θθ

0.200.20

ΔI p/

I p(θ)

ΔI p/

I p(θ)

0.100.10

0.000.00

-0.10-0.10

-0.20-0.20

IVIVVV

IIIIII

IVIVIIIIII

ΔIp/IpΔIp/Ip ΔIs/IsΔIs/Is Vp/VsVp/VsTypeType

VV

parallel to fractures

perpendicular to fractures

parallel to fractures

perpendicular to fractures

Increase in Vp/Vs

Increase in Vp/Vs

Increase in Vp/Vs

Zero Gradient Line(assumes ΔIp/Ip=2ΔIs/Is)

Zero Gradient Line(assumes ΔIp/Ip=2ΔIs/Is)

Decrease in Vp/Vs

Decrease in Vp/Vs

Decrease in Vp/Vs

IIIIV

False Type 1False Type 1

Colorado B AVAZ fracture intensity and orientation map with well A deviation path

Well A deviation path

Well A deviation path

LOW HIGHINTENSITY

Post-drill well A log tracks confirm 3D seismic attribute predictions

MAXXENE_OVERALL0 150( NONE )

MINXENE_OVERALL0 150( NONE )

XENEDIF0 50( NONE )

0

AVAZ 3D section with Well A gamma logand horizons (Clrd A, Clrd B and SSPK)

FMI images Fracture identification: intensity and orientationfrom FMI from crossed-dipole shear

weak early fast P-wave

strong late slow S-wave

P- and S-wave events recorded across an 8-level 3C geophone array Geometry of treatment and monitor wells

P- and S-waves processed to locate events based on arrival time, azimuth polarization

Potential to characterize fracture plane attributes from magnitude and focal mechanism

Microseismic event frequency ~ 500hz

Microseismic downhole monitoring

Events displayed in cross-section and map view to give quantifiable estimates of Stimulated Reservoir Volume

Surface Microseismic Buried Array Event Mapping

Example of P-wave event 1st arrival polarity reversal

(from Pete Smith and Kevin Smith EnCana & Chris Neale MSI 2009)

100 stations

3000’ grid spacing

Single 3C phone cemented at 250’

~16 sq. mi. grid

Event Map: all 8 stages top 10% of eventsMoment tensor solution suggests normal dip-slip faultingEvents colored by stage and sized relative to all stages

In June a massive Earthquake (magnitude 7.8) twisted South Island NZ. and moved its southern tip 30 cm, toward Australia, a process that usuallytakes ‘hundreds of years‘.Its focus occurred in “soft rocks” between two tectonic plates, muffling its power, as the rocks lurched (ductile) rather than snapped (brittle), causing a low-frequency rolling rather than more damaging high-frequency waves

Moment tensor solution fracture planes

2000’

Frac event trends

Circle size proportional to amplitude(red positive, blue negative) Squares are model amplitude fit to data.

Stage 4A,B(bridge plug flow)

Stage1Stage 2

Stage 6

Stage 7

Stage 8

Stage 2b

Stage 3

Normal dip slip fault

Barnett

Pieance

Barnett shale is more brittle than Pieance silts: High rigidity (Mu), hence lower Closure stress, results in large fracture planes creating high magnitude, low frequency events

Magnitude vs. distance for Barnett and Pieance

length fracture is L whereLD

xue x

xx ≈∂

∂=Strain:

30

xxr2

M

r2De

π=μ≈μ=σΔ

Stress drop Δσ across circular fracture plane

Earthquake moments and stress drop

Stress drop proportional to moment and inversely proportional to area

73.105.1MlogM

radius fracturer slip, averageD where)r(DM

0w

20

−=

==πμ=

rD

Moment magnitude (Mw) related to seismic moment (M0) penny shaped cracks

30

r

M167

=σΔ

Fracture radius inversely proportional to high corner frequency of displacement spectrum frequencycorner f where

f2V

r 00

S =π

∝

Earthquake amplitude displacementspectrum (1995 Chiapas, Mexico)

f0

Fracture surface area vs. moment and stress drop

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1E+2

5

1E+2

6

1E+2

7

1E+2

8

1E+2

9

1E+3

0

1E+3

1

Moment (dyn.cm)

Surfa

ce a

rea

(sq.

km)

1 bar 10 bars 100 bars 1000 bars

y = 0.5655x + 299.36

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 1000 2000 3000 4000 5000 6000 7000 8000

1st Confining Stress2nd Confining Stress3rd Confining Stress4th Confining Stress

Y Intercept = Linear CohesionSlope = Coefficient of Internal Friction

UnstableArea Stable

Area

failure slope=μ (friction)

in-situ stress circle

Mu

x sh

ear s

trai

n, p

si.

(she

ar s

tres

s τ=

μ∗e y

y)

Lambda-Mu log cross-plot (scaled by strain)overlaid on Mohr Coulomb Failure Envelopes

Mohr-Coulomb theory related to seismic LMR

σmin σmax

frac stimulation increases pore pressure

Lambda+2Mu x normal strain, psi. (horizontal normal stress σ=[λ+2μ]∗exx)

brittle gas shales withcritically stressed fractures

carbonates

ductile shales

Barnett shale analogue EUR 5330

3D AVAZ with coherence & 3D AVAZ with coherence & MicroseismicMicroseismic event overlays event overlays

%R

efle

ctio

n A

niso

tropy

LOW

HIGH

1600

m

Coherencelineations

Orientation of AVAZmaxinconsistent with SH max?

areas of relatively high reflection AVAZ anisotropy near horizontal borehole

12

3

4

5

6

7

8

9

10

stages

monitor wellhorizontal treatment well path

Microseimic events with AVAZ overlay

Seismic azimuthal anisotropy (AVAZ) intensity and orientation with microseismic overlay

(courtesy of Keith Young)(courtesy of Keith Young)

Fundamental Lamé parameters of rigidity μ and incompressibility λcontrol seismic wave propagation used to extract information about rocks in the Earth.

These parameters link many fields in Geoscience at different scales, from Petroleum Exploration to Earthquake Seismology.

Common contradictory formulations are simplified by restating equations in Lamé parameters e.g. incompressibility Lambda is less confusing than Bulk Modulus in revealing log errors.

Improved petrophysical discrimination and insight linking rock reservoir properties, pore fluid parameters and their seismic responses.

Insight into angle dependant reflectivity and impedance equations reveals the significance of 45º.

More descriptive sensitivity in AVO crossplotting using inverted λρ, μρseismic attributes to isolate effects of lithology, porosity and fluids.

Conclusions

More intuitive and appropriate for in-situ Geomechanical Closure Stress description of rocks and fractures (brittle vs. ductile deformation) than Young’s modulus and Poisson ratio.

Successful application of seismic attributes in predicting “sweet spots”for unconventional gas shale drilling that intersected predicted fractures and Stimulated Perm as confirmed by Microseismic monitoring.

Moment tensor solution to extract Microseismic event attributes using Earthquake Seismology for stress changes on fracture planes.

Conclusions

AcknowledgementsDave Mackidd, Dave Cooper, John Varsek, Christian AbacoEric Keyser, John Parkin, Taiwen Chen, Weimin Zhang, Keith Young, Pete Smith, Kevin Smith, Dan Potocki (EnCana)

Marco Perez (Apache Canada)

Brian Hoffe (Shell Canada)

Dave Gray, Jon Downton (CGGVeritas)

Peter Duncan, Chris Neale (Microseismic Inc.)

Shawn Maxwell (Schlumberger)