Download 2D marine controlled-source electromagnetic

GEOPHYSICS, VOL. 72, NO. 2 共MARCH-APRIL 2007兲; P. WA63–WA71, 12 FIGS.
10.1190/1.2430647
Special Section — Marine Control-Source Electromagnetic Methods
2D marine controlled-source electromagnetic modeling:
Part 2 — The effect of bathymetry
Yuguo Li1 and Steven Constable1
ABSTRACT
Marine controlled-source electromagnetic 共CSEM兲 data
are strongly affected by bathymetry because of the conductivity contrast between seawater and the crust below the seafloor. We simulate the marine CSEM response to 2D bathymetry using our new finite element 共FE兲 code, and our numerical modeling shows that all electric and magnetic components are influenced by bathymery, but to different extents.
Bathymetry effects depend upon transmission frequency,
seabed conductivity, seawater depth, transmitter-receiver geometry, and roughness of the seafloor topography. Bathymetry effects clearly have to be take into account to avoid the
misinterpretation of marine CSEM data sets.
INTRODUCTION
The marine controlled source electromagnetic 共CSEM兲 method
was developed more than 20 years ago to study the electric conductivity structure of the deep ocean lithosphere 共Cox, 1981兲, and has
recently found extensive application within the offshore hydrocarbon exploration industry 共e.g., Constable, 2006兲. Most analyses of
marine CSEM data have assumed a flat 共planar兲 seafloor, and this approximation has been sufficient for many of the academic applications where signals from seafloor geology are dominant. Early tests
of the method for hydrocarbon detection also targeted large reservoirs with a dominant CSEM response 共e.g., Eidesmo et al., 2002兲,
but as the commercial application of marine CSEM matures, drilling
targets having a much smaller predicted response are being surveyed. In these cases, bathymetry effects in the CSEM response may
lead to misinterpretation of seafloor structure, resulting in lost opportunities or misplaced wells. Bathymetry effects on the marine
CSEM response have been rarely reported in geophysical literature.
These effects can be simulated by numerical methods. The finitedifference 共FD兲 method is formulated on a rectangular grid, and
therefore bathymetry must be modeled as a series of small steps. Um
共2005兲 simulated the marine CSEM response to a vertical cliff using
a 3D FD code and suggests that high-quality topographic information should be collected for any marine CSEM survey. MacGregor
共1997兲 distorted the structured finite element 共FE兲 mesh to model
seafloor topography, and considered some simple structures, and later MacGregor et al. 共2001兲 incorporated the modified version of the
FE code of Unsworth et al. 共1993兲 in an Occam inversion that included topography over a mid-ocean ridge. Unstructured triangular FE
are more attractive and more flexible than the FD method for simulating bathymetry effects, because the FE method allows precise
representation of bathymetry with the use of a grid that can conform
to any arbitrary surface. In the companion paper 共Li and Key 2007兲,
the theoretical principles and numerical implementation of the FE
algorithm for forward modeling of the frequency domain marine
CSEM response over a 2D conductivity structure excited by a horizontal electric dipole 共HED兲 are presented, and the code is validated
on a few models. In the present paper, we use this code to specifically
study the marine CSEM response to 2D bathymetry.
BATHYMETRY EFFECTS
We consider an upward slope on the seafloor schematically
shown in Figure 1. We use a Cartesian system of coordinates: x is
strike direction, y is the 2D profile direction, and z positive downwards. The ramp has an elevation of 200 m between 0 and 1000 m in
the y-direction, i.e., the gradient of the slope is 11.31°. The seawater
has a depth varying from h at the bottom of the ramp to h-200 m at
the top of the ramp. It is assumed that the seawater has a resistivity of
0.3 ⍀m, and the sediments below the seafloor are homogeneous
with a variable resistivity ␳. The HED is located at 共0, −500, and
h-100 m兲, i.e., at height 100 m above the seafloor.
Manuscript received by the Editor May 2, 2006; revised manuscript received August 29, 2006; published online March 1, 2007.
1
University of California, San Diego, Scripps Institution of Oceanography, La Jolla, California. E-mail: [email protected]; [email protected].
© 2007 Society of Exploration Geophysicists. All rights reserved.
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Li and Constable
Numerical modeling is done for both the broadside and inline geometries. In the broadside geometry, the HED is oriented along the
x-axis 共i.e., strike-direction兲, and the electric and magnetic fields are
recorded on the seabed along the y-direction. By symmetry, there is
no vertical electric field, only an electric component in the strike-direction 共Ex兲. As a result, this leaves two nonzero magnetic components, a vertical one 共Bz兲 and a horizontal one along the y-direction
共By兲. In the inline geometry, the HED is oriented along the y-axis,
and the electric and magnetic fields are recorded on the seabed also
along the y-axis. Thus, there are two components of electric field: a
vertical one 共Ez兲 and a horizontal one along the y-axis 共Ey兲. The re-
0
0
1000
y (m)
h-200
Seawater
h
z (m)
0.3 Ωm
HED
100 m
Ez = E⬜ cos ␾ − E储 sin ␾ , 共1兲
where ␾ is a slope angle with respect to the horizontal axis y. In the
following sections, the horizontal and vertical components of electric and magnetic fields are presented unless otherwise stated.
200 m
1000 m
ρ
Ey = E储 cos ␾ + E⬜ sin ␾,
Hy = H储 cos ␾ + H⬜ sin ␾, Hz = H⬜ cos ␾ − H储 sin ␾ , 共2兲
Air
–500
maining field is the horizontal magnetic field parallel to the strike-direction 共Bx兲.
In the marine CSEM survey, receivers are placed on the seafloor
and hence follow the local slope. If a receiver lies on a flat seafloor, it
measures the horizontal and vertical components of the electric and
magnetic fields. If a receiver lies on a seafloor slope, it measures the
electrical and magnetic components along the slope 共E储 and H储兲 and
perpendicular to the slope 共E⬜ and H⬜兲. The corresponding horizontal and vertical components in the Cartesian coordinate system can
be obtained by
Horizontal electric field responses
Sediment
Log 10 (IEI V/Am2)
Figure 2a and b show the inline and broadside geometry amplitude and phase of the horizontal electric field at a frequency of
Figure 1. Sketch of basic bathymetric model, which has been run for
0.25 Hz on the bathymetry model 共Figure 1兲 with seawater depth of
various water depths 共h兲, frequencies, seafloor resistivity 共␳兲 and
the ramp bottom h = 1200 m and sediment resistivity ␳ = 1 ⍀m.
field components. The ramp has an elevation of 200 m at the range y
= 0–1000 m. The horizontal electric dipole is located at 共0, − 500,
The amplitude and phase response shows two breaks at 0 and
h–100 m兲, i.e., at height 100 m above the seafloor.
1000 m, which are coincident with the breaks of the seafloor topography. The inline geometry tangential electric
field response 共E储兲 is also shown. From Figure 2a,
a)
Horizontal electric field
–7
the difference between the amplitudes of the tanBroadside
gential component 共兩E储兩兲 and of horizontal comInline E
–8
Inline E
ponent
共兩Ey兩兲 is hardly recognizable. One can see,
–9
however, that on the slope 共y = 0 ⬃ 1000 m兲 the
–10
phase of the tangential component is about 3°
–11
smaller than that of the horizontal component.
0.25 Hz
These differences increase with increasing slope
–12
–1000
–500
0
500
1000
1500
angle and hence should be taken into considerb) 50
ation in the interpretation for data sets collected
Broadside
specially in a region with a rugged bathymetry.
Inline E
0
One may transform the measured tangential and
Inline E
–50
perpendicular components to the horizontal and
vertical components by using equations 1 and 2
–100
before running the modeling.
–150
0.25 Hz
To highlight the effect on the response of a tar–200
get,
the observed electric field amplitude is often
–1000
–500
0
500
1000
1500
normalized
by the data from receivers assumed to
c)
be off-target, or by the response of an a priori
Broadside
1.2
Inline E
background electric structure. Here a flat seafloor
Inline E
1.1
with a 1200 m depth seawater layer, underlain by
1
a 1 ⍀m half-space, is used as a reference model.
0.9
The amplitude of the horizontal electric field at
0.8
the seafloor shown in Figure 2a is divided by the
0.25 Hz
0.7
corresponding response at the flat seafloor 共z
–1000
–500
0
500
1000
1500
= 1200 m兲 for the reference model and illustrated
y (m)
in Figure 2c. One can see that far away from the
Figure 2. Broadside 共dashed lines兲 and inline 共solid lines兲 geometry horizontal electric
ramp the normalized fields for both the inline and
field responses at 0.25 Hz for the model in Figure 1 with water depth h = 1200 m and the
broadside geometries overlap each other and apseafloor resistivity ␳ = 1 ⍀m. 共a兲 Amplitude, 共b兲 phase, and 共c兲 the amplitude in 共a兲 norproximate one. That is, there is no difference bemalized by the corresponding values of the flat seafloor reference model. Dotted lines
tween the electric field of the slope bathymetry
show the inline geometry tangential component. The difference between the amplitudes
and that of a flat seafloor, as the influence of the
of the inline horizontal and tangential fields is invisible, but there is a small difference in
phase.
ramp does not yet appear. Because we are close to
y
II
Normalized field
Phase (°)
y
II
y
II
Effects of bathymetry on marine CSEM field
the bathymetry has a vertical elevation of 200 m from 1200
to 1000 m at y = 0 m 共i.e., a vertical cliff兲. In the second model, the
water depth varies smoothly from 1200 to 1000 m with a sinusoidal
dependence between 0 and 1000 m in the y-direction, i.e., the
bathymetry can be expressed by
z=
冦
1200
冉
␲y
␲
1100 − 100 sin
−
1000 2
1000
冊
y ⱕ 0;
0 ⱕ y ⱕ 1000;
y ⱖ 1000.
冧
The other parameters of both models are the same as those of the
bathymetry model shown in Figure 1. For comparison, the response
on the upward slope model 共Figure 1兲 is also shown. From Figure 3,
one can see that cusps in the bathymetry effect increase with the
sharpness of the slope, becoming greatest for the vertical cliff model,
and disappearing in the smoothing ramp model. This demonstrates
once again that the discontinuity in the inline horizontal electric field
responses at both the lower and upper breaks of the slope 共in Figure
2兲 are the result of the bathymetry undulation and not numerical
noise.
The dependence of the horizontal electric field response on both
the transmission frequency and the seafloor resistivity has been investigated. In Figure 4a and b, the inline and broadside normalized
horizontal electric field for different frequencies over the model in
Figure 1 with a fixed seafloor resistivity of 1 ⍀m is illustrated. One
can see that the broadside normalized anomaly depends largely on
frequency. In general, the broadside normalized electric field decreases with increasing frequency. At 0.01 Hz, the maximal and
minimal anomalies over the slope are 7.9% and 5.2%, respectively,
although at 1 Hz they are 4.5% and −4.8%. The inline normalized
response is independent of frequency around the lower break of
slope, and it varies with frequency around the upper break of the
slope and at the right of the slope, in particular for high frequency.
These behaviors suggest that the bathymetry distortion in inline geometry is mainly the result of a galvanic effect at the bottom and an
inductive effect at the top of the ramp, respectively. Figure 4c and d
illustrate the normalized horizontal electric field response for varying seafloor resistivity at 0.25 Hz. The normalized anomaly increases with increasing seafloor resistivity and tends toward saturation
2
Rough ramp
Smoothing ramp
Vertical cliff
0.25 Hz
Normalized field
the ramp, the influence of the ramp starts to appear. The normalized
fields for both geometries start to deviate from a constant value of
one, but in different patterns. The broadside normalized field goes up
from that point up the ramp toward the right and reaches a maximum
of about 1.051 共i.e., 5.1% anomaly兲 at about y = 120 m, then it falls
down, and this downtrend goes on until the point at the top of the
break 共y = 1000 m兲. Beyond this point the broadside normalized
field goes up again toward the right. The inline normalized field has
two cusp-like anomalies, a minimum of about 0.935 共i.e., negative
6.65% anomaly兲 at the lower break of the slope 共y = 0 m兲 and a
maximum of about 1.105 共i.e., 10.5% anomaly兲 at the top break of
the slope 共y = 1000 m兲. One can see that, on most of the slope, the
topographic distortion for the inline geometry is larger than that for
the broadside geometry.
Jiracek 共1990兲 clearly demonstrated that the near-surface and topographic distortions in electromagnetic 共EM兲 induction can be described in terms of a galvanic effect arising from the electric charge
buildup at the boundary of inhomogeneities, and also an inductive
effect. The distorted EM fields can be regarded as a vectorial sum of
primary field caused by a background layered earth and secondary
field caused by inhomogeneity with the anomalous resistivity ⌬␳
= ␳ − ␳n, where ␳ is the resistivity of an inhomogeneity and ␳n is the
resistivity of a background structure. In our case, because the ramp
and 1D three-layer earth 共air layer + 1200 m depth seawater layer
+ 1 ⍀m half-space兲, respectively, are regarded as the inhomogeneity and a reference model, the ramp has an anomalous resistivity of
0.7 ⍀m. Note that the resistivity of seawater is set to be 0.3 ⍀m. Assume that the primary electric field points to the right, downward and
upward, respectively, over the lower and upper part of the ramp.
Boundary charges form at the boundary of the inhomogeneity, resulting in a secondary electric field that is opposite to the primary
field at the lower part of slope and additive to the primary field at the
upper part of slope. Hence the total field obtained by a vectorial sum
of the primary and secondary fields is reduced at the lower part of
slope and enhanced at the upper part of slope. This produces a minimum and a maximum in the normalized field response around the
bottom and the top of the ramp, respectively. The magnitude of the
galvanic effect is frequency independent. In the broadside geometry,
the electric dipole is oriented along the strike-direction, and then the
primary electric field might be pointed to the strike-direction too.
Hence the electric field in broadside geometry is affected by excessive currents because of the x-directed primary electric field. These
currents produce a secondary magnetic field which adds to the primary magnetic field and an anomalous electric field. The amplitude
of the inductive effect depends on the frequency. In general, the
anomalous electromagnetic field is the result of galvanic charge
buildup and of self- and mutual-induction processes 共Menvielle,
1988兲. Note that the normalizing field is the electric field response at
the flat seafloor 共at z = 1200 m兲 calculated for the reference model;
it is different from the primary field that is the electric field along the
slope calculated for the reference model. Hence the normalized
anomaly is also caused by geometry of bathymetry undulation, i.e.,
the leveled height difference between the measured site and the corresponding point at the flat seafloor.
The bathymetry effects depend on the slope and roughness of the
seafloor topography, especially for the inline geometry. In Figure 3
the normalized inline geometry horizontal electric responses for two
other models are shown. In the first model, we simply suppose that
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1.5
1
0.5
–1000
–500
0
500
1000
1500
y (m)
Figure 3. The dependence of the inline normalized horizontal electric field response on the roughness of the seafloor topography. Dotted and dash lines show response for a smoothing bathymetry and a
vertical cliff at y = 0 m, respectively. Solid lines show the response
of the upward slope model in Figure 1.
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Li and Constable
when the seafloor resistivity is larger than 50 ⍀m. This means that
the bathymetry is dominated by a galvanic effect for high resistivity
below the seafloor.
a)
b) 1.3
1.3
Broadside geometry
Inline geometry
1.2
1.2
Normalized field
Normalized field
Figure 4. Dependence of the normalized horizontal
electric field on both the transmission frequency 共a
and b兲 and the seafloor resistivity 共c and d兲 for
the model in Figure 1 with the water depth h
= 1200 m. The broadside normalized anomaly depends on frequency, although the inline one is independent of frequency around the lower break of
slope and dependent on frequency on the upper part
of slope; The normalized anomaly tends toward
saturation when the seafloor resistivity increases.
Figure 5 shows the broadside and inline geometry horizontal electric field responses for three different seawater depths 共h = 400, 800,
and 1200 m兲 in the model in Figure 1. The transmission frequency is
1.1
1
0.9
0.01 Hz
0.05
0.1
0.25
0.5
1
0.8
0.7
–1000
–500
ρ = 1 Ωm
0
500
1
0.9
0.01 Hz
0.05
0.1
0.25
0.5
1
0.8
1000
0.7
–1000
1500
y (m)
c)
1.1
–500
Normalized field
1
0.9
1 Ωm
5
10
50
100
1000
0.25 Hz
–500
0
y (m)
500
1000
0.9
1 Ωm
5
10
50
100
1000
–500
1500
0.25 Hz
0
500
y (m)
–6
1200 m
800
400
–8
–10
–12
–14
–1000 0
0.25 Hz
1000 2000 3000 4000 5000
e)
300
1200 m
800
400
200
100
0
–100
–1000 0
1.5
1200 m
800
400
1000 2000 3000 4000 5000
y (m)
–10
–12
–14
–1000
0.25 Hz
0
1000 2000 3000 4000 5000
100
1200 m
800
400
-100
-200
–1000
f)
0.25 Hz
1200 m
800
400
–8
-300
1000 2000 3000 4000 5000
1
Inline geometry
–6
0
0.25 Hz
2
0.5
–1000 0
Log 10 (E-field magnitude (V/Am2))
d)
Broadside geometry
Phase (°)
Log 10 (E-field magnitude (V/Am2))
1000
1
0.7
–1000
1500
a)
Phase (°)
1500
1.1
0.8
Normalized field
Normalized field
1.1
0.7
–1000
Normalized field
1000
1.2
0.8
c)
500
y (m)
Inline geometry
1.2
b)
0
d) 1.3
1.3
Broadside geometry
Figure 5. The broadside 共left兲 and inline 共right兲 geometry horizontal electric field for three different
water depths 共h = 400, 800, and 1200 m兲 for the
model in Figure 1 with the seafloor resistivity of
1 ⍀m. Amplitude is shown in the top row and
phase in the middle row. The amplitude in 共a兲 and
共d兲 is normalized by the corresponding response of
the flat seafloor model with the water depth of h and
then illustrated in the bottom row.
ρ = 1 Ωm
0.25 Hz
0
1000 2000 3000 4000 5000
2
1.5
1
0.5
–1000
0.25 Hz
0
1200 m
800
400
1000 2000 3000 4000 5000
y (m)
Effects of bathymetry on marine CSEM field
different vertical scales in the normalized response 共Figure 7c and f兲
are used for the inline and broadside transmission. The airwave effects on the horizontal magnetic field are observed. As the seawater
gets shallower, the airwaves become more significant. In the case
with seawater depth of 400 m, the airwaves dominates the horizontal magnetic field response when the horizontal coordinate 共y兲 is
larger than 700 m, and the bathymetry effect can be barely recognized.
In Figure 8a and b, the frequency dependence of the inline and
broadside normalized horizontal magnetic fields for the model in
Figure 1 is illustrated, respectively. The seafloor resistivity is 1 ⍀m
and the water depth on the left side is 1200 m. One can see that the
broadside normalized magnetic fields vary with frequency over the
whole bathymetry 共from the bottom of the slope extending to the
right兲, although the inline normalized responses vary with frequency
only at the range y ⬎ 1000 m and are independent of frequency
along the slope. This means that the broadside horizontal magnetic
responses 共By兲 are mainly caused by induction effects, although the
0.25 Hz and the seafloor has a resistivity of 1 ⍀m. Airwave dominance can be seen as a flattening of the phase curves at ranges 2000,
3500, and 4500 m, respectively. As the seawater gets shallower, the
source-receiver distance where the airwave dominates the seafloor
horizontal electric response gets smaller. One can see that after normalization 共Figure 5c and f兲, the effect of bathymetry is the worst for
shallower water.
Vertical electric field response
Vertical electric field
1200 m
800
400
0.25 Hz
–500
0
500
1000
1500
2000
2500
3000
3500
4000
1200 m
800
400
Phase (°)
Log 10 (E–field magnitude (V/Am2))
The vertical electric field of marine CSEM method has been rarely
studied in the literature, but it is important because it responds to
edges of structure 共Constable and Weiss, 2006兲. As stated in the previous section, the vertical electric field Ez exists only for the inline
geometry. Figure 6 shows the vertical electric field responses for
three different seawater depths 共h = 400, 800, and 1200 m兲 for the
model in Figure 1. The transmission frequency is 0.25 Hz and the
seafloor has a resistivity of 1 ⍀m. These results illustrate that the
vertical component of the electric field is distorted by bathymetry. The amplitude and phase rea)
sponse shows two breaks at 0 and 1000 m, where
the bathymetric slope changes. Note that, as ex–8
pected, the phase has a 180° shift at the location of
the HED source 共y = −500 m兲, where the verti–10
cal electric field changes its direction. The airwave effect is not observed on the vertical electric
–12
field response because the airwave is always horizontal and does not have a vertical component.
–14
However, varying the water depth does have an
–16
effect on the seafloor vertical field. In shallow wa–1000
ter, the image source above the sea surface is closer to the bathymetry, thus a stronger effect can be
b)
observed. In deep water 共1200 m兲, we see a small
600
reduction in the vertical field along the slope fol500
lowed by an increase with range associated with
the shallower seafloor. Because the vertical elec400
trical fields for a 800-m water depth are similar,
300
these effects are associated with the bathymetry
200
and not the water surface. However, for a 400-m
water depth, the effects of bathymetry on the ver100
tical electrical field are greatly magnified by an
0
interaction with the water surface.
–1000
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The magnetic field response presents an additional and useful measurement for the marine
CSEM method. Figure 7 shows the inline and
broadside geometry, horizontal magnetic field response at 0.25 Hz for the bathymetry model 共Figure 1兲 with a seafloor resistivity of 1 ⍀m and the
water depth on the left side h = 400, 800, and
1200 m, respectively. The amplitude of the horizontal magnetic field is normalized by the corresponding value of the flat seafloor model with the
water depth equal to that at the HED location 共i.e.,
h兲 and then is shown in Figure 7c and f. It can be
seen that the normalized horizontal magnetic
field response for the broadside geometry is much
larger than that for the inline geometry. Note that
0
500
1000
1500
2000
2500
3000
3500
4000
c)
1.5
Normalized field
Horizontal magnetic field response
0.25 Hz
–500
1
0.5
0
–1000
1200 m
800
400
0.25 Hz
–500
0
500
1000
1500
2000
2500
3000
3500
4000
y (m)
Figure 6. The vertical electric field response for three different water depths 共h = 400,
800, and 1200 m兲 at 0.25 Hz for the model in Figure 1 with ␳ = 1 ⍀m. 共a兲 Amplitude; 共b兲
phase; 共c兲 the amplitude in 共a兲 normalized by the corresponding data of the flat seafloor
model with the water depth of h. Airwave effect is not observed on the vertical field response.
a)
Log 10 (IBI (nT/Am))
Figure 7. The horizontal magnetic field responses
for three different water depths 共h = 400, 800, and
1200 m兲 for the model in Figure 1 with ␳ = 1 ⍀m.
The bathymetry distortion in broadside geometry
共left兲 is much larger than that in inline geometry
共right兲. Airwave effect dominates the horizontal
magnetic field response for large source-receiver
offset, particularly in the case with 400-m water
depth.
Li and Constable
d)
Broadside geometry
–10
1200 m
800
400
–12
–14
–16
0.25 Hz
–18
–1000 0
1000 2000 3000 4000 5000
b)
Phase (°)
–200
0.25 Hz
–1000 0
c)
1000 2000 3000 4000 5000
–16
0.25 Hz
–18
–1000
0
1000 2000 3000 4000 5000
100
0
–100
–200
–300
–400
–500
–1000
0
1000 2000 3000 4000 5000
0
1000 2000 3000 4000 5000
y (m)
f)
Normalized field
5
4
3
2
1
0.25 Hz
0
–1000 0
0.25 Hz
2
1.5
1
0.5
0
–1000
1000 2000 3000 4000 5000
y (m)
a)
0.25 Hz
b)
Broadside geometry
1.3
Normalized field
1.2
1.1
1
0.9
0.8
0.7
0.6
–1000
Inline geometry
1.3
1.2
Normalized field
–14
Normalized field
Phase (°)
0
–400
0.01 Hz
0.05
0.1
0.25
0.5
1
0
ρ = 1 Ωm
1000
y (m)
1.1
1
0.9
0.8
0.7
2000
0.6
–1000
3000
c)
0.01 Hz
0.05
0.1
0.25
0.5
1
0
ρ = 1 Ωm
1000
y (m)
2000
3000
d)
Broadside geometry
1.3
Normalized field
1.2
1.1
1
0.9
0.8
0.7
0.6
–1000
Inline geometry
1.3
1.2
Normalized field
1200 m
800
400
–12
e)
200
Figure 8. Dependence of the normalized horizontal
magnetic field on both the transmission frequency
共a and b兲 and the seafloor resistivity 共c and d兲. The
broadside normalized response depends on frequency 共a兲, although the inline one is independent
of frequency around the lower break of slope and
dependent of frequency around the upper break of
slope 共b兲. The normalized anomaly tends toward
saturation when the seafloor resistivity is larger
than 50 ⍀m 共c and d兲.
Inline geometry
–10
Log 10 (IBI (nT/Am))
WA68
1 Ωm
5
10
50
100
1000
0
0.25 Hz
1000
y (m)
1.1
1
0.9
0.8
0.7
2000
3000
0.6
–1000
1 Ωm
5
10
50
100
1000
0.25 Hz
0
1000
y (m)
2000
3000
Effects of bathymetry on marine CSEM field
As stated previously, the vertical magnetic
field Bz exists only in the broadside geometry.
Figure 9 shows the vertical magnetic field response for three different seawater depths 共h
= 400, 800, and 1200 m兲 at 0.25 Hz for the model
in Figure 1. The seafloor has a resistivity of
1 ⍀m. As with the vertical electric field, the
phase of the vertical component of the magnetic
field has a 180° shift at the location of the HED
source 共y = −500 m兲, where the vertical magnetic field changes its direction. The airwave effect is
observed on the vertical magnetic field response,
but it is weaker than that of the horizontal magnetic field and dominates at larger source-receiver offset.
RESPONSES OF RESERVOIR
MODELS WITH BATHYMETRY
Log 10 (IBI (nT/Am))
Vertical electric field
–10
–12
–14
1200 m
800
400
–16
–18
–1000
b)
Phase (°)
Vertical magnetic field response
a)
0.25 Hz
0
1000
2000
3000
4000
5000
3000
4000
5000
3000
4000
5000
200
0
–200
1200 m
800
400
–400
–1000
c)
1.5
Normalized field
inline bathymetry distortion in the horizontal
magnetic field response is caused by the galvanic
effect along the slope and by induction effects on
the right side of the slope. Figure 8c and d show
the normalized horizontal magnetic field response for varying seafloor resistivity at 0.25 Hz.
The normalized anomaly tends toward saturation
when the seafloor is larger than 50 ⍀m. The similar phenomenon have been observed in the normalized horizontal electric field response shown
in Figure 4c and d.
WA69
1
0.25 Hz
0
1000
2000
1200 m
800
400
0.5
–1000
0.25 Hz
0
1000
2000
y (m)
Figure 9. The vertical magnetic field response for three different seawater depths 共h
= 400, 800, and 1200 m兲 at 0.25 Hz for the model in Figure 1 with ␳ = 1 ⍀m. Airwave
effect is observed, but it is weaker than that in the horizontal magnetic field.
1D reservoir model
–1000
1200 m
Air
0
b)
1000
1000 m
0.3 Ωm
HED
100 m
1000 m
1000 m
1 Ωm
100 m
100 Ωm
y(m)
200 m
Log 10 (IEI (V/Am2))
a)
400
350
300
250
200
150
100
50
0
–10
0.5 Hz
–5
0
y (km)
Broadside
Inline
5
10
0.5 Hz
–8
Broadside
Inline
–10
–12
–14
d)
60
Normalized field
c)
–6
–16
–10
1 Ωm
Phase (°)
A 1D resistive layer with a thickness of 100 m
and a resistivity of 100 ⍀m is introduced into the
bathymetry model as shown in Figure 10a. The
broadside and inline geometry horizontal electrical field responses of the 1D reservoir model are
computed at a transmission frequency of 0.5 Hz
for a HED location at 共0, −500, 1100 m兲. Figure
10b and c shows the amplitude and phase of the
horizontal electric field, respectively. One can see
that the amplitude and the phase are asymmetric
with respect to the HED location, particularly in
the inline geometry. The amplitude of the horizontal electric field in Figure 10b is divided by the
corresponding values at the flat seafloor for a reference model which consists of the air layer,
1200 m depth seawater layer and 1 ⍀m halfspace, and is shown in Figure 10d. The asymmetry of the normalized responses clearly shows a
bathymetry effect upon the marine CSEM results.
The survey line on the right side yields smaller
normalized response because the seafloor receivers on the right side are further from the 1D resistive layer than those on the left side 共Um, 2005兲.
The bathymetry effect for the inline geometry is
much larger than that for the broadside geometry.
50
–5
0
y (km)
5
0.5 Hz
Broadside
Inline
0
y (km)
5
10
40
30
20
10
0
–10
–5
10
Figure 10. The horizontal electric field response of the 1D reservoir model with bathymetry. 共a兲 Sketch of the model; 共b兲 amplitude; 共c兲 phase; 共d兲 the amplitude in 共b兲 is normalized by the corresponding values at the flat see afloor for a reference model consisting of
air layer, 1200-m depth water layer and 1 ⍀m half-space. The asymmetry of the normalized responses clearly shows effect of the seafloor topography upon the marine CSEM results.
WA70
Li and Constable
a)
2D reservoir model
Air
–1000
1000
0
y (m)
0.3 Ωm
1200 m
HED
1400 m
100 m
1000 m
1 Ωm
800 m
100 Ωm
100 m
5000 m
b)
Air
–1000
1000
0
y (m)
1000 m
1200 m
0.3 Ωm
HED
100 m
1200 m
1000 m
1 Ωm
100 m
100 Ωm
We consider a 2D reservoir model with a finite lateral extent of
5000 m and thickness of 100 m. A simple 2D bathymetry slope is
introduced as schematically shown in Figure 11a and b. The horizontal electric dipole 共HED兲 is located at 共0, −500, 1100 m兲. The
amplitude and phase of the inline geometry horizontal electric field
responses for the 2D reservoir model with both the upward and
downward slopes are shown in Figure 12a and b, respectively. For
comparison, the electric field responses for the 2D model with flat
seafloor topography are also shown. The amplitude of the electric
field response is divided by the corresponding values at the flat seafloor for the reference model which consists of the air layer, 1200 m
depth water layer and 1 ⍀m half-space and illustrated in Figure 12c.
Although the model with the upward slope topography produces
smaller normalized response than that model without topography
change, the model with the downward slope topography produces
the largest normalized response. This is because the seafloor receivers on the model with the upward slope topography are further from
the reservoir body than those on the flat seafloor model. Similarly,
the receivers on the model with downward slope are closer to the reservoir than those without the seafloor topography.
5000 m
CONCLUSIONS
Figure 11. Sketch of the 2D resistive reservoir model with bathymetry topography 共a兲 with downward slope, 共b兲 with upward slope.
a)
Log 10 (IEI (V/Am2))
–6
–10
–12
–14
–16
–2
b)
0.5 Hz
–8
2D reservoir with upward slope
2D reservoir with downward slope
2D reservoir with flat slope
0
2
400
4
6
8
10
4
6
8
10
4
6
8
10
0.5 Hz
Phase (°)
300
200
100
0
–100
–2
Normalized field
c)
2D reservoir with upward slope
2D reservoir with downward slope
2D reservoir with flat slope
0
2
40
0.5 Hz
30
20
10
0
–2
Bathymetry greatly affects the electric and
magnetic field responses measured by the frequency domain marine CSEM method. Model
calculations show that all electric and magnetic
components are influenced by bathymetry, but to
different extents. Bathymetry effects depend on
transmission frequency, sediment resistivity, water depth, trasnmission-receiver geometry, and
roughness of seafloor topography. The broadside
normalized anomaly depends on frequency, although the inline one is independent of frequency
around the lower break of slope and dependent on
frequency at the upper part of slope. The normalized anomaly in both geometries tends toward
saturation when the seafloor resistivity increases.
The inline geometry effect on the horizontal electric field is larger than that for the broadside geometry, whereas the broadside geometry effect
on the horizontal magnetic field is larger than that
for the inline geometry. The vertical electric field
is not affected by airwaves, but because the vertical field disappears at the sea surface, water depth
has an effect on the vertical field. In relatively
shallow water, the image source above the sea
surface is close to the bathymetry, thus can produce large variations in the vertical electric field
response.
2D reservoir with upward slope
2D reservoir with downward slope
2D reservoir with flat slope
ACKNOWLEDGMENTS
0
2
y (m)
Figure 12. The inline horizontal electric field response of the 2D reservoir model 共Figure
11兲 at 0.5 Hz. 共a兲 Amplitude, 共b兲 phase, and 共c兲 normalized response.
Y. Li acknowledges funding support from BP
America. We thank Kerry Key for useful discussions. We also thank Mike Tompkins, David
Alumbaugh, and other, anonymous, reviewers
Effects of bathymetry on marine CSEM field
for constructive comments, in particular an anonymous reviewer
who pointed out that Ez behavior can be explained in terms of image
source.
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