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NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF PETROLEUM ENGINEERING
AND APPLIED GEOPHYSICS
Contact person during exam:
Name: Tommy Toverud
Tel.: 94928/94925
90882952 (mobil)
EXAM IN COURSE SIG4047 RESERVOIR SEISMICS
Saturday, May 26, 2001
Time: 0900 - 1300
Date for censorship: June 18, 2001
Examination support:
B1:
- Approved pocket calculator, with empty memory, in accordance with NTNU’s list
allowed.
- No printed or handwritten material allowed.
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PROBLEM 1
a)
Explain what is meant by AVO-analysis.
(AVO = amplitude-versus-offset)
b)
Discuss different amplitude corrections which have to be done in AVO.
c)
How can the influence of the seismic source and the hydrophone cable be modelled in
marine seismics.
d)
Discuss the influence of anelastic attenuation. What kind of problems may occur in
AVO-analysis when attenuation is to be taken into account?
e)
Explain how the plane wave reflection and transmission coefficients between two
homogeneous, isotropic elastic media are defined, and what are the conditions which
lead to the Zoeppritz equations.
f)
For an incoming P-wave, which reflected and transmitted waves will occur? Indicate
the direction of the particle movement for all waves.
g)
The PP-reflection coefficient can be approximated by
2
V 
V p
1 Z p
 1
R pp   
 2 s  sin 2 
 tan 2 
V 
2 Zp
 2
Vp
 p
Explain the meaning of the different terms and give the range of validity for this
approximation of the reflection coefficient.
PROBLEM 2
An exploration team have identified a prospect based on a geological model and
interpretation of seismic data. An AVO analysis were a key element in the interpretation
analysis of the seismic amplitudes at a horizon assumed to represent a shale-sand contrast.
The task is now, on the basis of the mapped amplitude variation with angle (offset) at this
contrast, to predict the reservoir quality and fluid type in the sandstone layer. This is to be
done using different rock models which relate rock and seismic properties. Both the overlying
layer, assumed to be a shale (layer 1), and the underlying layer, assumed to be a sandstone
(layer 2) are assumed to be thicker than the seismic wavelength.
In a wellbore log analysis made in a well which penetrates the same shale layer as assumed to
be present as layer 1 in the prospect, it was found that the ”mudrock” equation represented
favourably the relation between the observed P and S-wave velocities in the well. In addition,
it was observed that a simple linear relation could be applied to represent the relation between
density and P-wave velocity.
a)
Explain in short why the ”mudrock” equation, in general, approximates the conditions
in shales. Calculate the P-wave impedance in the assumed shale (layer 1) in the
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prospect by applying the ”mudrock” equation and a ratio of 2.25 between the P and Swave impedance (as observed in the well). The ”mudrock” equation is given by:
V p  1360  1.16 Vs
where VP and VS are respectively the P and S-wave velocity (in units of m/s). Assume
that the simple linear relation between the P-wave velocity and density is given by:
  2.0  0.5 V p  2.0,
V p  1.75, 3.25 km / s 
where  is the density (in units of g/cm3). The velocity unit in this case is km/s.
Calculate then the P-wave impedance in the assumed sandstone layer (layer 2), when
the zero-offset seismic amplitude is estimated to be:
R pp 0  0.09
b)
In the Gassman equations, we assume that the relation between the bulk modulus of the
skeleton and the particles (matrix material) is much less than 1. Show that by using this
approximation, we obtain the simplified Gassmann equations:
k  k skel 
1  2k skel k S 
,
 k F  1    k S
   skel
Here are kskel and skel respectively the bulk and shear modulus of the skeleton (”dry
moduli”), and kS and kF the bulk modulus of the solid (particles) and the fluid phase.
c)
The prediction of reservoir quality (essentially the porosity) and fluid type in layer 2 is
to be made by calculation of the P-wave impedance in the following 6 cases, and then
compare them to the estimated one in 2.a. The cases which compare favourably to the
estimated one, are assumed to be possible scenarios. Calculate therefore the P-wave
impedance in layer 2 for all the following cases:
a :   0.35, Vsh  0 and full water saturation,
 :   0.35, Vsh  0 and full gas saturation,
y :   0.245, Vsh  0 and full water saturation,
 :   0.245, Vsh  0 and full gas saturation,
 :   0.175, Vsh  0.25 and full water saturation, and
 :   0.175, Vsh  0.25 and full gas saturation.
Here is  the porosity. Vsh is the volumetric clay content, normalized to the volume of
the solid phase in the rock.
Apply the following formulas for the calculation of the skeleton moduli:
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k skel 
kS
,
1  15
 skel 
S
1  25
Use Voigt’s model for the calculation of the effective moduli of the solid phase (as a
mix of quartz and clay particles). The following component values of moduli and
density are used:
Bulk modulus of quartz: 35 GPa
Shear modulus for quartz: 40 GPa
Density of quartz and dry clay: 2.65 g/cm3
Bulk modulus of water: 2.5 GPa
Bulk modulus of gas: 0.25 GPa
Density of water: 1.0 g/cm3
Density of gas: 0.25 g/cm3
Bulk and shear modulus of clay particles must be calculated by applying the empirical
set of equations valid in water saturated clastic rocks (where the velocities is in units of
km/s):
VP  5.5  6.95  2.15 Vsh , and
VS  3.4  4.75  1.80 Vsh .
Use the formulas which relate velocities and moduli in an isotropic medium:


k   VP2  4 3 VS2 og   VS2 .
Assume the uncertainty in the P-wave impedance in layer 2 estimated from observed
near-offset amplitudes to be +/- 250 AI (1 AI is 1 m/s g/cm3). Which one of the 6
modelled cases compares favourably to the calculated P-wave impedance in layer 2,
when we honour the assumed uncertainty?
d)
After an analysis of the seismic amplitude at 30 degrees angle of incidence at the
assumed shale-sand contrast discussed above, it was found that the reflection
coefficient was equal to –0.10, coupled to an uncertainty of +/- 0.01. Apply the
approximation given in Problem 1 to evaluate those of the modelled cases which
compares favourably to the calculated P-wave impedance in layer 2. Does this
additional information (at 30 degrees angle of incidence) contribute positively to the
prospect evaluation?
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