C~“NnAH
“lx
JOURNAL
OF EXPLORATION
GEOP”YSlc*
26, NO.5 1 8 2 iDECEMBER
1990,. P. 94.103
EFFECTS OF LITHOLOGY, POROSITY AND SHALINESS
P AND SWAVE VELOCITIES FROM SONIC LOGS
SUSAN L.M.
MILLER’
ON
AND ROBERT R. STEWART~
geometry,
pore fluid, bulk density, effective
stress, depth of
burial, type and degree of cementation
and degree and ori-
ABSTRACT
entation
complex
Full-waveformsoniclogsfromfour wells in Ihe MedicineRiver
field of Alberta are analyred far relationships betweenP-wave
velocity(V,). S-wavevelocity (KS).VP/V,andlihology, shaliness and
porosity.V,IVsin conjunchmwith VPeffectivelyidentifies mnistone,
limestone andshalelithologiesin the sampled
intervals.VPincreases
quasi-linearly with V.7in sandstone
and limestone. AverageVpiVs
valuesof I .h" for sandstone
a"* 1.89for limestonearef"""d. In formationrwith mixedcarbonate,clastic
silicatelithologies(6x Nodegg,
ShundaandDetrital), V, increases approximatelylinearly with Vs.
The VP/h ratiosin the mixedlirhologies arehoundedby the VpiVs
Ya,"es‘or tile componenr
litholagies.
I" tile san*s,onesconsideredhere,b&7 v, an* vi decreaseas
porosityincreases but K dependence
on porosityis very weak.The
V,d%ratio decrcssesas purusity increases. An increasein shale
COntent
lowersVPand"r but increases"DIVX.Pomity hasa greater
influence on velocitythanshalincss by aboutanorderof magnitude.
Both VPandVr decrease
asporosityincreasesin the limeslone data
but the correlationis poorberweenVP/Kandporosity.The linear
regressionintercepts from the limestone velocity versusporosity
plots accuratelypredictcalcite matrix velocities.In the Nordegg.
ShundaandDetrital Fornations m increase in porosity is accompanied by a decrease
in bothPi andS-Wavevelocities.No VpiV,trend
is observedin either theNordeggor the Shun&,hut VpM decreases
asporosityincreasesin theDetritalFormation.
ties influence
factors
the elastic-wave
velocities
including
velocity
S-wave
well logs
response to known
of shear seismic
multicomponent
are affected
rock
matrix
by numerous
mineralogy,
tools
are crucial
in tying
geology
and guiding
sections.
seismic
analyze full-waveform
basin and search for
these field
waves
addi-
provide
a number
but in the
available.
observed
elastic
the interpretation
Ultimately,
the goal
data for petrophysical
is to invert
informa-
sonic logs in the western Canadian
trends which provide
information
on
porosity
and pore fluid. The approach has been to
several of the factors which have been studied by
workers
and determine
if trends
are present
in
data.
REVIEW
Work
that has been
data in conjunction
at the well
geologic
porosity,
a variety
tion.
This paper considers four wells in the Medicine
River oil
field of central Alberta.
The objective
of this study is to
previous
response
have employed
of measurements
which describe the subsurface,
seismic realm VP and VS are the main descriptors
the litbologic
information
inherent in seismic elastic-wave
velocities
requires
an understanding
of the relationship
between geology and velocity.
To this end, we are interested
bore.
Seismic
researchers
1983; McCormack
et al., 1984).
In the well bore various logging
tional information
about the subsurface
(Nations,
1974;
Gregory, 1977; Tatbarn, 1982; Robertson,
1987). Deciphering
in studying
velocity,
of approaches
such as core analysis,
seismic and well log
interpretation
and numerical
modelling
(e.g., Kuster and
ToksGz,
1974; Gregory,
1977; Eastwood
and Castagna,
INTRODUCTION
as well as compressional
and well logging provides
1985). The
complicates
the task of inverting
seismic velocities
to obtain petrophysical information.
In order to understand
how rock proper-
lithology,
examine
Recording
shear waves
during seismic acquisition
of fracturing
(McCormack
et al.,
interaction
of these and other factors
pore
with
done
to date suggests
P-wave
that S-wave
data can provide
informa-
tion on lithology,
porosity,
among other things (e.g.,
Domenico,
1984).
pore geometry
Gregory,
1977;
Compressional
lithology
indicator
velocity
alone is not a good
of the overlap in Vp for various
seismic
because
and pore fluid,
Tatham,
1982;
Manuscript received by the Editor July 1.5. 1990: revised manuscript received October 16, 1990.
1Depanment of Geology and Geophysics. The University of Calgary, Calgary, Alberta T2N IN4
We are grateful to David Byler. Manager of khnical
Services a* Suncar Inc., for the donation of well log and lithology infommtion for this study. We
would also like to acknowledge helpful suggestions from Dr. John Hapkim and Dr. Terry Gordon of the Universiry Of Calgary and Douglas Bayd of
Hallihurton Lagging Services. This work was supponed by the Consonium for Research in Elastic Wave Exploration Seismology (CREWES) Project at the
university Of Calgary.
94
EFFECTS OF LITHOLOGY, P”R”SlTY AND SHALINESS ON P- AND S-WAVE“ELOC,TIES
rock
types.
The additional
information
provided
by shear
velocity
can reduce the ambiguity
involved
in interpretation. Pickett (1963) demonstrated
the potential
of VB/Vs as a
lithology
indicator
through
his laboratory
research.
Using
he determined
VplVs values of 1.9 for
dolomite,
I.1 for calcareous
sandstone
core measurements,
limestone,
1.8 for
and 1.6 for clean
erally
sandstone.
Subsequent
research
has gen-
confirmed
these values and has also indicated
that
in mixed lithologies
vary linearly
between the
of the end members
(Nations,
1974; Kithas,
carbonates
and sand/shale
sequences
9s
(McCormack
et al.,
1984; Anno, 1985; Garotta et al., 1985; Robertson,
and well logging studies of elastic silicates (Castagna
1987)
et al.,
1985). The increase in V,iV, with shaliness has been used
in seismic
field
studies
to outline
sandstone
channels
encased
1985).
in shales
Eastwood
(McCormack
and Castagna
et al., 1984;
(1983)
Garotta
examined
et al.,
full-waveform
constant
l/,/l/~ with increasing
limestone
and increasing
V,/V,
V,dVs values
V,A4 ratios
sonic logs and observed
porosity
in an Appalachian
1976; Eastwood
and Castagna,
1983; Rafavich
et al., 1984;
Wilkens,
1984: Castagna et al., 1985).
Various approaches
have been taken to analyze the effect
with increasing
porosity
in the Frio Formation
sandstones
and shales.
VpiV, is sensitive to gas in most elastics and will often
of porosity
show a marked
Gregory,
1977;
on velocity.
These
include
the time-average
equation
(Wyllie
et al., 1956). the Pickett empirical
tion (Pickett,
1963) and the transit-time-to-porosity
form of Raymer
et al. (1980).
Domenico
(1984)
Pickett’s
data to demonstrate
that I& in sandstones
equatransused
is 2 to 5
than V, in
was found
times more sensitive
to variations
in porosity
sandstones
or Vs in limestones.
VP in limestone
to be the least sensitive porosity
indicator.
The model of Kuster
and Tokssz
indicates
that pore-
aspect ratio has a strong
influence
on how Vp and VA
respond to porosity
(Kuster and ToksBr, 1974; Toksi% et al.,
1976). The actual Vp/Vs ratio appears to be independent
of
pore geometry
unless the aspect ratio
Robertson
(1987)
used this
model
to interpret
carbonate
porosity
from seismic
data and correlated
an
increase in VpiVs with an increase in porosity due to elongate
POES.
A number of workers have included a clay term in empirical linear regression
equations developed
from core-analysis
data (Tosaya and Nur, 1982; Castagna et al., 1985; Han et
al., 1986; King et al., 1988; Eberhart-Phillips
et al., 1989).
When both porosity
and clay effects were studied, porosity
was shown to be the dominant
effect by a factor of about 3
or 4 (Tosaya
1988).
Minear
and Nur,
1982;
(I 982) examined
Ensley,
1984, 1985;
of carbonate
Han et al., 1986; King
the importance
et al.,
of clay on veloc-
in its presence
1982; Eastwood
(Kithas,
1976;
and Castagna,
McCormack
et al., 1985). The
rocks to gas is variable,
a dis-
crepancy
which
may be attributable
to pore
V,dV, reduction has been observed in carbonates
gate pores
carbonates
gas effect
penetration
(Anna,
1985;
Robertson,
with rounder
pores (Georgi
may not be observed on well
does not exceed
the invaded
1987)
geometry.
with elon-
and absent
in
et al., 1989). The
logs if the depth of
zone.
STUDY AREA
is low, less than about
0.01 to 0.05 (Minear,
1982; Tatham,
1982; Eastwood
and
Castagna,
1983). Modelling
suggests that for small-aspect
ratio pores such as cracks, Vp/Vs will increase as porosity
increases.
1983;
Vp/V.r response
decrease
Tatham,
The Medicine
River field
(Figure
I) which
produces
Cretaceous,
formations
chart
is an oil field in central Alberta
from a number
of zones in
Jurassic and Mississippian
of interest
are indicated
in Figure
2. The locations
rocks. The ages and
in the stratigraphic
of the wells
examined
in this
paper are 9.5.39.3W5,
9.I-39-3W5,
15.18.39.3W5
and
9-13.39.4W5.
These are development
wells drilled
by
Suncor Inc. between 1987 and 1989 which are or have been
oil producers.
The 9-7 and 9.13 wells produce
out of the
Nordegg
Formation.
the 15.18 well produces from an interval in the Basal Quartz (Ellerslie)
and the 9-5 well produces oil from both the Basal Quartz
and the Pekisko
Formations.
fluid filling
It is difficult
to accurately
determine
the porein some of the zones as there are no drill stem
test data available
The sandstones
for any of these wells.
sampled
in this study
are the Basal
ties using the Kuster-ToksGz
model. Results suggested that
dispersed clay has a negligible
effect on velocity:
however,
Quartz sandstone
(9.15, 15.18) and the Glauconitic
sandstone (all four wells).
Watkins
(1966) describes
the Basal
laminated
and structural
shale have a similar and significant effect in reducing
velocities.
Since clay tends to lower
the shear modulus
of the rock matrix,
K decreases more
Quartz
sorted,
than VP, resulting
in an overall
increase in V&S. Tosaya
and Nur (1982) concluded
that neither clay mineralogy
nor
location
of clay grains
were significant
factors
in the
P-wave response
Because
to clay content.
shear velocity
is thought
than compressional
1984) and to clay
to be more
sensitive
velocity
both to porosity
(Domenico,
content (Minear,
1982), an increase in
either
result
component
should
has been observed
(Han
et al., 1986:
King
result in an increase in V,AG. This
in core studies of elastic silicates
et al., 1988),
seismic
surveys
over
in this field as a very fine to fine-grained,
wellsubangular,
quartritic
sandstone.
The Glauconitic
sandstone
is a fine-grained,
gular, quartzose
sandstone
(Watkins,
1966).
well-sorted,
angular to subanwith siliceous
cementation
The only limestone
sampled
in this study is from the
Pekisko with data from the 9-5 and 15.18 wells. The well
site geologist’s
cuttings
log identifies
Formation
as a slightly
dolomitic,
slightly
the Pekisko
argillaceous,
crypto to microcrystalline
limestone
with pinpoint porosity.
The shale points are from the Femie shale only, with data
fmm the 9-7, 9.13 and 15.18 wells. The Femie shale is medium to dark grey, platy, tissile,
cakareous
and micaceous.
s. L.M. MILLER and R. R. STEWART
metres
through
the zones
of interest.
Readings
tool may be suspect in regions of horehole
wave curve cannot he used in formations
5
n
z
wave velocity
mud as there
:
from
washout.
in which
is slower than the P-wave
will be no S-wave refraction.
the
The Sthe S-
velocity
of the
In these wells,
ALBERTA
this occurs in some shales and in all coals and is indicated
by warning
flags on the log and either off-scale
or straightline S-wave transit times.
. PEACE
RWER
were judged to be reliable were examined
for zones which
either represent a particular
lithology
or are of exploration
:
Those
portions
of the log where
the elastic
transit
times
interest. Intervals were chosen which could be clearly identified using well log curves (e.g.. gamma-ray
curve) and
geological
infomution
(e.g., well site geologist’s
cuttings
report).
Only
intervals
which
were
a minimum
of five
mctrcs thick were selected for sampling.
Date points were
[not taken from the top and base of the formations
where
. EDMONTOI
the well log curves were deflecting
rapidly.
The well log curves were digit&d
with readings recorded every metre. Transit times were used to calculate
VP, Vv
. REDOEER
and !I,,/\/,,~. V,, and Vs are directly
used in seismic
processing
and conventional
rock characterization;
thus, WC prefer to
USC V,dK instead ol’introducing
the related Poisson‘s ratio.
The gamma-ray
curve was used to compute the gammaray index
STUDY
AREA
(G) as follows:
c; =
GRI~,,-GL,,
GR,~dNm,
MEDICINE
RIVER
GR is the gamma-ray
response in GAPI units and
CR,,,,, and GR,,,,,, values are based on the interpreted
sand
where
FIELD
and shale
Fig. 1. Location map showing the Medicine River oil field of central
Alberta.
Several mixed lithologies
were also chosen for analysis.
The Nordegg
Formation
is of Lower
Jurassic
age and is
described
by Ter Berg
(1966)
medium-sorted,
fine-to-medium
which is cemented by dolomitic
the 9.1 and Y-13 wells,
Shunda is sampled from
well site geologist’s
limestone
and shale.
Shunda as dolomite
are available
which
can he
ray response
and clay volume
as determined
by x-raydiffraction
data from core samples. Kukal and Hill (1986)
volume could be calculated
from the expression
above by
multiplying
G by 0.60. Since we do not have available
the
both of which are oil-filled.
the 9-S well and, according
The
to the
production
data and the well logs,
in the Jurassic
and Mississippian
data from
relationship
between
shale
and clay
these well
logs was
limited
by several factors.
The full-waveform
sonic logs
analysed
in this study were only run over several hundred
content
for this area,
we have chosen to use a simple linear relationship
between
gamma-ray
deflection
and shale content. In this study we
have used the gamma-ray
index (x 100) as a measure of
percentage
shaliness.
Porosities
were calculated
using neutron-density
crossplots and, when the data were available,
hulk density and
photoelectric
absorption
crossplots.
Porosity
values were
corrcctcd
for shale content in the sandstone data. Gammaray readings
formations
are most likely due to shale content in these
(J. Hopkins,
1990, pen. comm.)
and were
therefore
used as a mcasure
porosity
and density
porosity
shales were used tc~ determine
METHODS
of S-wave
curves
grained
quartz and chert
limestone.
It is sampled in
are oil and water.
The availability
Various
confirmed
the linear relationship
and noted that most sheles
contain about 60 percent clay. Based on their analysis. clay
consisting
refers to rock detritus on top of the Mississippian
unconformity and consists mainly of dolomite
in the 9-13 well from
which the data is taken.
formations
lines.
used to convert the gamma-ray
index to clay content, each
of which will give significantly
different
estimates (Heslop,
1974). Heslop observed a linear correlation
between gamma-
of
as a sandstonc
cuttings
log, consists of intcrhedded
The core-analysis
report describes the
with interbedded
shale. The Detrital
Based on the available
the pore fluids present
(1)
of shale volume.
Neutron
values
lrom surrounding
the shale point on the cross-
plot. This point was used to crcnte a scale from 0 to 100
percrnt
shale so that the required
correction
for a given
percentage
of shale could be determined.
The neutron-
97
EFFECTS OF LrrHDLOGY, POROSrrY AND SHALLNESSON P- AND S-WAVE “ELOCrrlES
AGE
- - I
I
I
’ !I
’ E
: 2
, ii
I 5
’ f5
FORMATION
T
LEGEND
SH
I,,,
GLAUCONITIC
: 5
I
I
I
I- - j ij
DOL, SH, SS
1 5
I -)
- - ’ 5
I
E
-
Conformity
M
Unconformity
j 1
I g
I- - (afler ERCB, 1976)
Fig. 2. Stratigraphic chart of the ages and formations
dolomite (DOL) and complex mixtures af these.
of inter&
density porosity
values were then shifted toward the clean
lithology
lines by the corresponding
correction
factor.
Porosity values from the Nordegg and Dehital Formations
The lithologies
studied are shale (SH), sandstone
bility. The values for all formations
(within
1 or 2 porosity
percentage
(SS), limestOne (LS).
are the same as or close
units) to those deter-
were not corrected
for shaliness
as the radioactivity
in
these units may he due to rock fragments
rather than shale
mined by a computer-processed
interpretation
which incorporates
a suite of environmentally
corrected
log cwves.
Core reports from the 9-5 and 15.18 wells were examined
(I. Hopkins,
1990, pus. comm.). The uncorxcted
crossplot
porosities
agreed with other porosity
measurements
as
described
below. Although
the Shunda has shale interbeds,
although
core porosity
values were not available
for the
exact depths
studied
in this analysis.
Neutron-density
crossplot porosities
from nearby units were generally
within
uncorrected
crossplot
porosity
values tracked
core measurements in the vicinity
closely.
Neutron-density
crossplot porosity
values were compared
to porosity
data from two other sources to check their relia-
l or 2 porosity percentage
At two depths the FDC
units of available
core porosities.
values
were closer to the core
porosity
than the crossplot
corresponded
most closely
values, but overall the crossplot
to core measurements.
Porosity
s. L.M. MILLER an* R. R. STEWART
98
values were not taken in shales
obtaining
meaningful
values.
The effect
of pressure
due to the difficulty
on velocity
of
and VS are consistent
in
gators.
Shale does not show a strong linear correlation
between V, and VT (I = 0.29) but has an average Vp/Vs ratio
has been examined
with
the observations
of other
investi-
laboratory
work (Pickett,
1963; Gregory,
1977: Domenico,
1984; Han et al., 1986; King, 1988; Eherhart-Phillips
et ill.,
1989). Velocities
generally
increase
rapidly
initially
but
of I .X9. VPIVS is quite variable
for shales; however,
the
average value observed here falls within the range used by
Minear
(1982) and is comparable
to the value of I.936
stabilire
at higher pressures.
The formations
examined
in
this paper are all at depths between 2OCO and 22uO metres,
used by Eastwood
giving
an effective
stress
of about
25 MPa
(3600
psi).
At
and Castagna
(1983)
for modelling.
The data have been replotted
in Figure 4 to demonstrate
the effectiveness
of using Vp/Vs and VP to differentiate
the
pure lithologies
in this data set. Although
the Vp values for
this depth, pressure effects have levelled off and should he
similar for all the formations.
Analysis
involved
crossplotting
of velocity,
slowness,
sandstone
and shale compressional
velocities
about 4200 m/s and sandstone
and limestone
velocity
about
ratio,
porosity
and percentage
shale for the selected
units in each of the four wells. These plots were examined
for trends. We have used single and multivariate
linear
regression
analysis
various parameters.
to assess the relationship
between
the
In regression
analysis the independent
variable
is assumed to be error-free.
This is not the case for
porosity
or shale data obtained
from well logs: however,
the analysis
is conventionally
held to be a valid means of
studying
velocity
dependence
and Williams,
1987).
Well cuttings log depths
line
log depths
geologic
referred
Lithology
Figure
and required
on these variables
sometimes
differed
adjustment
marker,
such as coal, for
to in this paper are sonic-log
using
reference.
depths.
5200
m/s, the lithology
the addition of V&4 values.
Several
complex
lithologies
Nordegg,
Shunda and Detrital
from
with correlation
coefficients
respectively
(Figure 6).
All
by
are also examined.
The
are mixtures
of carbonates
and limestone
1.75, 1.76 and
of the Nordegg,
linear relationships
Drtrital
and Shunda
between Vp und V.7
of 0.84,
0.91,
and 0.92,
depths
effects
3 is a plot
of Vp vs VT for
sandstone,
0 ss
limestone
and shale for all four wells. The superimposed
lines have
slopes of I .9 and 1.6, the conventional
Vp/K ratios for
limestone
and sandstone,
respectively.
The sandstone
data
points are scattered around the V,/Vs value of I.6 and have
an average VpIK ratio of I .60. The limestone
data have an
average
at
at
1.76, respectively
(Figure
5). Clearly,
complex
lithologies
can cuuse ambiguities
in the interpretation
of velocity
data.
The mixrd lithologies
show approximately
wire-
are differentiated
and clestics and plot between the sandstone
end members with average VplK values of
(Troutman
a suitable
types
overlap
overlap
CD/!/, ratio
of 1.89. Within
the range
related
coeffi-
cients (r) are 0.8X and 0.89, respectively.
The I/,/V, values
for both lithologies
and the good correlations
between
VP
VP
(mls)
2~1
2.0
1
1.9
D
q
SH
a
LS
1.8
2
>”
1.7
1.5
1.5
l.4
3000
s
Fig. 3. VP vs Vi for sandstone (SS), limestone (LS) and shale (SH)
lithologies. The data are from full-waveform
sonic logs from the
Medicine River field. Lines of constant Ifp/Vr are superimposed on
the data points.
LS
Fig. 4. v&Q vs v,, for sandstone, limestone and shale. The data
from Figure 3 are replotted to demonstrate
the separation
of
6
0 ss
SH
A
%Moo
of data repre-
linearly
sented here, VP appears to be approximately
to VT for both sandstone and limestone.
Correlation
q
4000
5000
W
6000
0Nord
q
“emal
A
Shunda
1
7000
(m/s)
Fig. 5. vplV, vs vJ, for complex lithologies. The Nordegg, Shunda
and Detrital are formations with mixed carbonateiclastic
silicate
lithologies. The superimposed Outlines from Figure 4 show that the
V,dvs ratios for mixed rock types plot between the ratios of the
component lithologies.
EFFECTS OF LITHOLCZY,
VD
The functional
relationship
between
and Vs for different rock types is still open to question.
We have considered
the VP/V, ratio, which is an average value, and the linear
correlation
between
VD and VS. The significance
slope and intercept
values obtained from regression
of the
analy-
sis and how they relate to physical
rock properties
is a subject for further investigation.
Ikwuakor
(1988) suggests that
the slopes and intercept
values derived from linear velocity
relationships
are better indicators
of lithology
than VplVs
and may also contain other geologic
information.
However,
for
small
data
sets with
surements,
accurate
ues may be difficult
inherent
uncertainty
and repeatable
to obtain.
slope
in the mea-
and intercept
val-
Porosity and shale effects
The highest
obtained
when
correlation
coefficients
for these data are
velocity
(rather than slowness
or traveltime
difference)
is plotted
stone data are shown
weak
value
against porosity.
Results for the sandin Figure 7. P-wave velocity
shows a
dependence
on porosity.
The extracted
Vp intercept
indicates
a sandstone matrix velocity
of 5028 m/s -
somewhat
lower
than the range
of 5486 to 5944 m/s given
by Gregory
(1977).
An unexpected
observation
is in the
S-wave velocity,
which shows a very weak dependence
on
porosity.
This differs from the previous
studies cited which
found S-wave
velocities
in sandstones
to be highly
sensitive to variations
in porosity.
Residual analysis on both data
sets suggests that there may be a higher order dependence.
However,
the number
of data points
rant extensive
statistical
manipulation.
ity of V, results in an overall decrease
is too limited
to war-
The greater sensitivin VplVs (Figure X), a
result which also differs
from research
previously
cited.
The large scatter and relatively
low correlation
coefficient
of 0.65 indicate caution in interpreting
these results.
In an attempt
to improve
multivariate
linear
tion as independent
regression
variables.
99
POROSITY AND SHALINESS ON P- AND S-WAVE VELOCITIES
the fit to the data we have used
with porosity
and shale fracThe data suggests that poros-
best fit was obtained by plotting
velocity,
rather than slow
ness, as the dependent
variable.
Multivariate
linear regrcssion with linear terms produced the following
relationships:
V, (km/s) = 5.30
7.120 - 0.44~
!A (km/s) = 3.16 - 2.620 - 0.38~
V/A’s = I .68 0.99~ + 0.056~
where
B = frdctional
K = fractional
(2)
r = 0.32, and
r = 0.66,
(4)
(3)
porosity,
shale, and
I = correlation
These
i-=0.51,
relationships
coefficient.
are calculated
over
a porosity
range
of 0.04 to 0.14 and a shale range from 0.01 to 0.44. The
standard error is about 5 percent for V, and ttr and 2 percent for V,lV,. The standard
error of the porosity
coefficients is almost 40 percent in the expressions
for Vp and
V,,lL and 56 percent in the equation
for V.v. The large
uncertainty
in the coefficients
suggests that these expressions are more useful for describing
trends in the data
rather than predicting
values.
shale coefficient
is sometimes
itself. However,
so that the effect
The
intercepts
The standard
error in the
as high as the coefficient
the magnitude
of the coefficient
is small,
on predicted velocities
is also small.
in equations
(2)
and (3) are similar
those obtained
by Tosaya and Nur (1982). Castagna
(1985).
Han et al. (19X6)
and Eberhart-Phillips
to
et al.
et al.
(1989). The coefficient
for the porosity
term in equation (2)
is also similar in magnitude
to those quoted by these workers, but the porosity
coefficient
in equation
(3) is 40 to 60
percent
lower,
emphasizing
again
the lack of !A sensitivity
to porosity
in these data. We see this effect in equation (4),
which shows that V,d!A will increase as porosity
decreases.
These equations
also differ from those of the investigators referred
to above in that the shale coefficient
is lower
than the porosity
coefficient
by about an order of magnitude rather
somewhat
of velocity
than by a factor
of 3 or 4. Although
dependent
on shale content
and shale content indicate
porosity
is
in these data, plots
a minor effect from
ity is weakly dependent
on shale content, so that the results
should again be viewed
with caution.
Addition
of a shale
term improves
the correlation
somewhat
and also increases
shale. If we use clay fraction
rather than shale fraction
(where
shale is assumed
to be composed
of 60 percent
clay), the coefficient
for K increases by about 67 percent in
the intercepts,
each of these equations.
or predicted
sandstone
matrix
velocities.
The
Fig. 5. V, vs KY for complex lithologies. Approximately linear relationships exist between VP and v,, for the Nordegg, Shunda and
Detrital Formations.
Fig. 7. VjJ and Vr vs percent porosity for sandstone. Data are from
the Glauconitic and Basal Quartz sandstones. VP shows a weak
dependence on porosity in sandstone, decreasing by 15 to 20% as
porosity increases from 4 to 14%. V,Tis fairly insensitive to porosity
variations.
5. L.M. MLLER
100
The relative magnitudes
that Vs is more sensitive
of the shale coefficients
to the addition
of shale
indicate
than &I.
and R. K. STEWART
porous,
velocity
oil-saturated
and a lower
9-5
well
V,d!A ratio
has both a lower
than the shalier,
P-wave
tighter,
This results in an apparent increase in Vp/V.t with increasing
shaliness (Figure 9). This trend is consistent
with the obser-
water-saturated
interval
in the 15.18 well. This separation
could be due to a differcnce
in porosity,
shale, pore fluid,
vations
or some combination
thereof. The production
GOR (gas/oil
ratio) for the 9-5 well is about 150 which is quite high for
this formation.
This suggests that gas might be a factor in
of the other researchers
cited.
Eberhart-Phillips
et al. (1989) found that using the square
root of clay content improved
the fit as it accounted
for the
large change
in velocity
observed
when only a small
amount
of clay was present.
improved
the correlation
contain too much scatter
Use of the square root term here
marginally:
however,
the data
to support a more complex
term.
The data were also analyzed
for the response
ular formation
from well to well.
Variations
response
within
to changes
the same formation
in porosity,
pore
should
fluid
of a particin Vp/V.s
The
Basal
Quartz
sandstone
is sampled
from the 9-5 well (2144 to
214X m) and the 15-1X well (2170 to 2174 m). The portion
of the Basal Quartz sampled in the 9-S well averages about
13 percent
the 15.18
sampled
porosity,
4 percent shale and is oil-saturated.
well, the Lower Basal Quartz section which
averages
about
6 percent
shale and is water-saturated.
wells
separate
distinctly
(Figure
::
;
>
interval
1.Y)
35 percent
from
the relatively
clean,
0
0
vs porosity
for the Pekisko
V, and I4 are dependent
limestone
on porosity
(Figure 11). The intercepts represent limestone matrix velocities and are very close to the V, (6259 m/s) and V, (3243
m/s)
values
for calcite
quoted by Domenico
(1984). The
matrix is about I .9 as predicted
but shows little change as porosity
increases
(Figure
12).
This is consistent
with findings
by Eastwood
and Castagna
(1983). It is also the response predicted
by Kuster-Toksbz
modelling
in a saturated limestone
in which the majority
of
pores are round, i.e.. have high-aspect
ratios (Robertson,
1987). This
is likely
has pinpoint
porosity
to be the cast with
(secondary
the Pekisko
porosity
with
voids
which
<l/l6
mm).
Velocity
and porosity
data from the Nordegg,
Shun&
and Detrital
Formations
are plotted in Figures
I3 through
15, respectively.
In each case, both Vp and V, show a
0
In the case of the Shunda, V, appears to be slightly
more
sensitive
than VS to the rise in porosity,
but the porosity
0
000
y = 1.71 1.208-a
1.45 .,.,.,.,.,.,.
2
4
6
of velocity
that both
dependence
on porosity.
Both Vp and VS show a similar
decrease as porosity
increases
in the Nordegg
Formation.
0
0 0
1~65
/1___1
1.60
1%
In
is
The data points from the two
on a crossplot
of VplVs vs Vp
10). The siimpled
‘.=1
1~70
porosity,
Plots
indicate
V,Z/VAratio for the limestone
be attributable
or fxies.
VD and, thus, VIA4 in this well.
reducing
08
range is very limited.
In the Detrital
Formation,
P-wave
velocity
decreases more rapidly
than S-wave velocity
for
0
0
8 o.
an overall
R = 0.65
8 10 12
% Porosity
14
I
16
Fig. 8. ViiVs v* percent poro*ity for sandstone. The data are scattered but the velocity
ratio shows an apparent
tendency
to
decrease as porosity increases in sand*tone.
1
1.65
cm ‘-;I 0
0 a
0
1.60
0
2” 1.55
me
Oc.
008 00 o
00
0
1.50o y=1.55
+*me-3x
R=0.55
1.45
0 10 20 30 40
%SHALE
Fig. 9. V,dVf vs percent shale for sandstone. “,JV., may exhibit a
slight trend of increasing V~IC’,Ias the shale content Of the sandstone increases.
decrease
is consistent
researchers.
C”NCLUSI0NS
Data
that
obtained
Vn with
from
full-waveform
l’~y successfully
stone, limestone
::::i
in V,dVs. This
decrease
with the observations
for the sandstones
but differs from
the previously
cited
results
by a number
of other
sonic
discriminate
and shale lithologies.
..
.
.
0
.
a
.
.
.
logs
between
Average
.
indicate
sand-
Vd!A ratios
.
l
1.451
4200 4400 4600 4800 5000 5200 :
vp
(m/r)
Fig. 10. VP,“, vs “p for the Basal C)uartz sandstone. The data
points from the 9-5 well, which averages about 13% porosity, 4%
shale and is oil-saturated. are separated lrom the IS-18 well which
averages about 6% porosity, 35% shale and is water-saturated.
EFFECTS OF LtT’HclLOGY, POROSfTY AND SHALINESS ON P- AND SWAVE “ELOCITIES
are 1.60 for sandstones
and 1.89 for limestone
and shale.
Complex
lithologies
have V&T ratios which plot between
the values
ambiguities
of their component
in interpretation.
rock
types.
This
may cause
linearly
Vp is approximately
correlated
with Vs in the lithologies
studied here.
Seismic velocities
in sandstone are affected by variations
in porosity
and sheliness,
with porosity
having a stronger
effect. Multivariate
linear regression
results in three relationships
which describe
the trends observed
in the data.
These relationships
indicate
that Vp decreases as porosity
is relatively
insensitive
to
increases. I/S in these sandstones
changes in porosity,
showing
only a slight reduction.
As a
result, the V,l!A ratio decreases
with increasing
porosity.
This observation
differs from that quoted by several other
investigators,
who observed an increase in VDIVTwith rising
porosity.
Porosity
has a greater influence
on velocity
than shaliness by
suggest
Vs and
agrees
about an order of magnitude,
but our correlations
that an increase in shale content will lower V, and
cause the Vp04 ratio to rise. The increase in V,d!A
with observations
by other workers;
however.
in
these data the effect of the shale is substantially
smaller.
Data from the Pekisko
limestone
indicate
that both V,
and Vs decrease as porosity
increases
but the VW, ratio
exhibits
little
trend
with
rising
porosity.
This
R = 0.79
I
101
response predicted
by Kuster-Toksoz
modelling
for limestones in which the pores tend to be round, which is probably the case for the pinpoint
porosity
of the Pekisko.
The
linear regression
intercepts
from the limestone
velocity-vsporosity
plots accurately
predict calcite matrix velocities.
P-wave and S-wave
velocities
decrease
as porosity
increases in the carbonate/elastic
lithologies
of the Nordegg,
Shunda and Detrital
Formations.
VP/K decreases as porosity
increases in the Detrital
but does not demonstrate
a porosity
trend
in either
A number
gesting that
the Nordegg
or the Shunda.
of trends were visible in these field data, sugP- and S-wave data can contribute valuable infor-
mation about tbe subsurface.
In particular,
velocities
contain
information
on lithology,
porosity and the degree of shaliness.
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APPENDIX
-.
Lithology
Formation
Sandstone
Sandstone
S.WldEfO”e
limestooe
Limestone
Limestone
Limestone
%%
ShWdil
Sh,
Oeha,
Lmrita,
Detrifal
Detrital
well bzition
Depthjm,