Modelling electromagnetic responses from seismic dataModelling electromagnetic responses from...
Transcript of Modelling electromagnetic responses from seismic dataModelling electromagnetic responses from...
Modelling electromagnetic responses from seismic dataDieter Werthmüller [[email protected]], Anton Ziolkowski, and David Wright
IntroductionGood estimates of background resistivit-ies are often crucial in controlled-source elec-tromagnetic (CSEM) feasibility studies and in-versions. Seismic data and well logs are of-ten available prior to CSEM acquisition, butelastic waves and electromagnetic wavesshare no physical parameter.
Contributions• We present a methodology to estimate res-istivities from seismic velocities.
• We apply known methods, including rockphysics, depth trends, structural in-formation, and uncertainty analysis.
• We show an example of the methodologywith data from the North Sea Harding field.
Rock PhysicsWe use a Gassmann-based relation (fG) forthe transformation from P-wave velocity v toporosity φ, and the self-similar model (fs) forthe transformation from porosity φ to resistiv-ity ρ (e.g. Carcione et al., 2007):
ρ = fs(ρs, ρf,m, φ) , where
φ = fG(Ks,Kf, Gs, %s, %f, κ, v) ,
m is the cementation exponent, K and G arebulk and shear moduli, % is density, κ is theKrief exponent, and subscripts s and f standfor solid and fluid fraction (see Fig. 5).
EM-Line
b-7a-3
b-11
b-A01
b-86570000
6575000
412500
417500
4
0.0 0.1 0.2 0.3 0.4
Porosity (-)
1.5
2.5
3.5
4.5
Vel
oci
ty(k
m/s)
Gassmann
10−1
100
101
Res
isti
vit
y(Ω
m)
self-similar
5
The transform is done in three steps:1) Calibrate transform (incl. depth trend,box below) with a well log nearby (b-8).2) Apply to seismic velocity in area of in-terest (including uncertainty, box left).3) Check transform with well log in area ofinterest (if available).
1 10
1
2
3
Dep
th(k
m)
b-8
1 10
b-7
1 10
Resistivity (Ωm)
b-11
1 10
b-A01
1 10
a-3
ρs
mode
±2σ
6
Start – EM-Line – End
1
2
3
Dep
th(k
m)
Grid Sandstone
Seabed
Balder Formation
Base Cretaceous
Background resistivity model [Mode (Ωm)]
0.4
0.7
1.3
2.3
4.17
1D Modelling
1200 1300 1400 1500CMP Position
0
0.2
0.4
0.6Dep
th(k
m)
Start model ρm (Ωm)
1
2
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4
59a
1200 1300 1400 1500CMP Position
0
0.2
0.4
0.6 Dep
th(k
m)
Final model ρm (Ωm)9b
This resistivity model (box left) has two weak-nesses:1) anisotropy (λ =
√ρv/ρh, ρm =
√ρvρh),
2) resistivities outside well control.CSEM impulse (IR) and step (SR) responseshave different sensitivities to anisotropy(Fig. 10). Only if the anisotropy factor is cor-
rect, inversion of IR and SR yield the same res-ult (Fig. 11). Short offset 1D inversions ofmeasured CSEM data, with correct aniso-tropy factor, improve the background resistivitymodel in the shallow section, were we have nowell control (Fig. 9); the resulting resistivitiesare in this case lower.
0.0 0.5 1.0 1.5 2.0 2.5
Time (s)
0.0
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1.0
1.2
1.4
Am
pli
tud
e(Ω/(m
2s)
)
×10−10
ρm = 1.0
ρm = 2.0
ρm = 3.0
λ = 1.0
λ = 1.5
λ = 2.0
10a
0.0 0.5 1.0 1.5 2.0 2.5
Time (s)
0
1
2
3
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Am
plitu
de
(Ω/m
2)
×10−11
10b
1.0 1.5 2.0 2.5
Anisotropy (−)
0
2
4
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NR
MSD
(%)
NRMSD IR
NRMSD SR
Model (SR - IR)
0
2
4
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∆M
odel
IR-S
R(Ω
m)
11
Uncertainty Analysis
0.4 0.6 0.8 1.0
2
6
10
14
Pro
b.
den
sity
(-) Parameter
0.4 0.6 0.8 1.0
Resistivity (Ωm)
Model
0.4 0.6 0.8 1.0
2
6
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Pro
b.
den
sity
(-)Parameter & Model
1a 1b 1c
-1 0 1∆v : v(z)−vs (z)
data
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1
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Pro
b.
den
sity
(-)
2 3 4Vel. (km/s)
0.6
1.0
1.4
1.8D
ep
th (
km
)
v
vs
2
Data, rock physics model, and rock phys-ics parameter have errors. Chen and Dick-ens (2009) describe a methodology to accountfor the uncertainties related to rock physicsparameters and the rock physics model it-self. They describe the rock physics model asgamma distribution in a Bayesian frame-work, with a defined error E, and the rockphysics parameters as distributions,
f(ρ|θ) =βαxα−1
Γ(α)exp (−βx) ,
where θ is a vector containing all model para-meter distributions, α = 1/E2, and β = (α −1)/ρrp. Here, ρrp is one realization of the rockphysics model with a random set of model para-meters.
We define the distribution of the velo-city from the data themselves (see Fig. 2).The distribution is defined as the differencebetween the measured log values and the val-ues of the smoothed log, v(z) − vs(z). Thisyields resistivity as a probability densityfunction, instead of a deterministic resistivityvalue (Fig. 3c).
1 10
Resistivity (Ωm)
0.6
1.0
1.4
1.8
Dep
th(k
m)
Grid Sandstone
ρs
mode
±σ±2σ3a
vf 2.0 3.0 4.0 vs
Velocity (km/s)
ρf
1
10
ρs
Res
isti
vit
y(Ω
m) deterministic
0.6 0.8 1.0 1.2
Resistivity (Ωm)
1
3
5
Pro
b.
den
sity
(-)
3b
3c
Depth TrendRock parameters are a function of, e.g., litho-logy and depth. We include the followingdependences in our model:• Depth: Ks, Gs, κ, ρs
• Temperature: ρf• Porosity: m• Lithology: Grid Sandstones(delineated with seismic horizons)
1 10
Resistivity (Ωm)
ρ
ρs
ρ(φ[v])
2 3 4
Vel. (km/s)
0.6
1.0
1.4
1.8
Dep
th(k
m)
v
vs
10 30
(GPa)
Ks
Gs
1 10
(GPa)
ρf
ρs
2 3
(-)
m
κ
Grid Sandstone
8
AcknowledgmentWe thank PGS for funding the research andthe Harding partners, BP and Maersk, for per-mission to use the data.
ReferencesCarcione, J. M., B. Ursin, and J. I. Nordskag, 2007, Cross-property
relations between electrical conductivity and the seismic velocityof rocks: Geophysics, 72, E193–E204, doi: 10.1190/1.2762224.
Chen, J., and T. A. Dickens, 2009, Effects of uncertainty inrock-physics models on reservoir parameter estimation usingseismic amplitude variation with angle and controlled-sourceelectromagnetics data: Geophysical Prospecting, 57, 61–74,doi: 10.1111/j.1365-2478.2008.00721.x.
Werthmüller, D., A. Ziolkowski, and D. Wright, 2012, Backgroundresistivity model from seismic velocities: SEG Technical ProgramExpanded Abstracts, 31, doi: 10.1190/segam2012-0696.1.
Conclusions• This method yields the range of back-ground resistivity models, consistentwith the known seismic velocities.• This model provides an additional dataset, which can be used for integrated ana-lysis, or as a starting point for a detailedCSEM feasibility study or inversion.• We will use this background resistivity model
for 3D CSEM modelling for comparison withmeasured data.