Submitted for SEG 2001 by Rock Solid Images
for more papers like this - visit www.rocksolidimages.com
Rock Physics of Marls
Jack Dvorkin (Stanford University), Joel D. Walls (Rock Solid Images), Gary Mavko (Stanford University)
Summary
Rock physics analysis of well log data in marl
intervals shows that distinctive relations exist between the
elastic propagational properties and porosity of this rock
and also between Vs and Vp. In the Vs versus Vp cross
plot, the marl data fall onto an experimental Vs versus Vp
trend originally designed for calcite. As the amount of
shale in marl increases, the data move along the calcite line
and intersects the shale line. Although the impedance of
marls may vary within a large range, depending on the
concentration of calcite, their Poisson's ratio varies only
within a small interval between 0.3 and 0.33.
Introduction
In spite of their common occurrence, very little
detailed rock physics analysis is available for shaly
carbonates known as marls. In this paper, petrophysical
analysis was performed on two well logs from the North
Sea. The lower part of these two wells was identified as
marl by the local oil company geologists. From this log
data, we derived rock physics relations for Vs versus Vp
and also for P wave and S wave velocity and impedance
versus porosity and bulk density. These relations can be
used in seismic forward modeling and interpretation.
Data Analysis
Ip = -4.7 + 5.78 RHOB,
Ip = 10.6 – 9.25 Phi,
where porosity is in fraction (p.u.), density is in g/cm3, and
impedance is in km/s . g/cm3.
Poisson’s ratio is plotted versus density and porosity
in Figure 3. It is cross-plotted versus the P-wave
impedance in the same figure. There are no trends present
in these cross-plots for the marl interval simply because
Poisson’s ratio is essentially constant (between 0.3 and
0.32). This Poisson’s ratio value can be probably used for
Vs prediction and forward seismic modeling.
Well B
Well-log curves in Well B (Figure 4) have the same
character as in Well A. However, the bottom interval in
this well has much lower GR count and is much faster than
the marl interval in Well B. The reason may be smaller
amounts of clay and larger calcite or dolomite presence in
Well B. It remains a question of definition, whether the
very fast bottom interval in Well B is marl or not.
Nevertheless, we include these data in our analysis. Notice
also that Poisson’s ratio in the (questionably) marl interval
in Well B is about 0.31, about the same as in the marl in
Well A.
Well A
The well log curves available in Well A are shown in
Figure 1. This figure shows only the bottom interval with
marl. Pay intervals are higher and not shown. The marl
interval has relatively low GR count, practically constant Swave (~ 2 km/s) and P-wave (~ 3.8 km/s) velocity, and
practically constant Poisson’s ratio (~ 0.31) which gives a
constant Vp/Vs ratio of about 1.91.
The velocity and impedance versus density and
velocity and impedance versus porosity cross-plots with the
marl interval highlighted are given in Figure 2 and 3,
respectively. Trends in these cross-plots are evident,
especially in the impedance-density and impedanceporosity plots. The impedance trends fitted by straight
lines are:
In Figure 5 we plot the P-wave impedance versus the
bulk density and porosity for both wells. The trends are
different from those in the “soft” marl present in Well A.
The linear fits are:
Ip = -30.4 +16.558 RHOB,
Ip = 13.6 – 25.23 Phi.
Poisson’s ratio is plotted versus the P-wave
impedance for both wells in Figure 6. Although the
impedance values differ between the two wells, Poisson’s
ratio remains practically constant, about 0.31.
Conclusions
Poisson’s ratio in the marl intervals is constant and
about 0.31 which corresponds to Vp/Vs ratio 1.91.
Rock Physics of Marls
Depth (m)
In Figure 7, Vs is plotted versus Vp for the marl
intervals together with empirical relations by Castagna et
al. (1993) and Williams (1990). Notice that the marl data
in Well A fall precisely on the empirical limestone curves
close to their intersection with the mudrock (shale) curve
and precisely at the intersection with the Williams shale
line. The Well B data are on the limestone curves but
farther from the mudrock line which confirms our
hypothesis that the Well B marl interval is predominantly
limestone.
References
Mavko et al., 1998, The Rock Physics Handbook,
Cambridge University Press.
Vs
PhiRHO
Vp
MARL
MARL
MARL
10 m
25
50
75 100
2.4
2.6
0
0.1
0.2
Porosity
RHOB
GR
1
2
3
4
Velocity (km/s)
5
6
8
10
P-Impedance
12
0.3
0.4
Poisson's Ratio
Figure 1. Well log curves for the marl interval in Well A.
5
10
Below
Marl
Vs (km/s)
Vp (km/s)
MARL
Pay
MARL
3
MARL
2
4
Below
Marl
12
Well A
)
Well A
Pay
3
1
P-Impedance (km/s g/cm
Below
Marl
Well A
Ip = 10.6 - 9.25 Phi
R = 0.88
8
Pay
6
Shale
Shale
Shale
4
2
0
0.1
0.2
0.3
Total Porosity
0.4
0
0.1
0.2
0.3
Total Porosity
0.4
0
0.1
0.2
0.3
Total Porosity
0.4
Figure 2. Velocity and impedance versus porosity in Well A.
Submitted for SEG 2001 by Rock Solid Images
for more papers like this - visit www.rocksolidimages.com
Rock Physics of Marls
Well A
Well A
Below
Marl
Shale
Shale
Below
Marl
0.4
Poisson's Ratio
Well A
Shale
Below
Marl
Pay
Pay
MARL
0.3
MARL
2.0
2.2
2.4
Bulk Density
MARL
2.6
0
0.1
Pay
0.2
0.3
Bulk Density
0.4
4
6
8
10
P-Impedance
12
PhiRHO
NPHI
Well B
100 m
Depth (m)
Figure 3. Poisson’s ratio versus density, porosity, and P-impedance in Well A.
Vs
Vp
~ 1800 m
MARL?
20
40 60
GR
80
1
10
Resistivity
2.0
2.2 2.4
RHOB
2.6
0
0.2
0.4
0.6
Porosity
1
2
3
4
Velocity (km/s)
5 2 4
6 8 10 12 14
P-Impedance
0.2
0.3
0.4
Poisson's Ratio
Figure 4. Well log curves in Well B.
Submitted for SEG 2001 by Rock Solid Images
for more papers like this - visit www.rocksolidimages.com
Rock Physics of Marls
Well A: RED
14
Well A: RED
MARL B?
Well B: GREEN
Well B: GREEN
MARL B?
P-Impedance (km/s g/cm
3
)
12
Ip = -30.4 + 16.55 RHOB
R = 0.96
Ip = 13.6 - 25.23 Phi
R = 0.98
10
MARL A
MARL A
8
Pay
Pay
6
Shale
Shale
4
1.8
2.0
2.2
Bulk Density
2.4
2.6
0
0.1
0.2
0.3
Total Porosity
0.4
Figure 5. Cross-plots for Well A and Well B with marl intervals (questionable for Well B) highlighted.
.35
Poisson's Ratio
Well B
.30
Well A
.25
8
10
12
P-Impedance
14
Figure 6. Poisson’s ratio versus the P-wave impedance for marl intervals in Well A and Well B.
Williams
Shale
Mudrock
Line
Vs (km/s)
3
Well B
Limestone
Curves
2
Well A
3
4
5
6
Vp (km/s)
Figure 7. Vs versus Vp in marl intervals in Wells A and B plus existing empirical relations.
Submitted for SEG 2001 by Rock Solid Images
for more papers like this - visit www.rocksolidimages.com