FREQUENCY DEPENDENCE OF SEISMIC DATA
FROM NIGERIA: PRELIMINARY RESULTS
Mary L. Krasovec, Daniel R. Burns, and M. Nafi Toksoz
Earth Resources Laboratory
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT
Seismic data from the Niger Delta is used to test processing sequences involved in
prestack and poststack amplitude and frequency analysis of marine seismic data. Water
bottom reverberations are found to present a formidable challenge in poststack frequency
and amplitude analysis. However, reflectors with anomalously high amplitudes show low
frequency content both in deconvolved poststack data and in the near offsets of prestack
data with no deconvolution, which agrees with results in the literature. Lack of detailed
knowledge of the lithology prevents investigation of the physical nature of the amplitude
and frequency variations.
INTRODUCTION
Recent research suggests the usefulness of frequency content analysis of seismic data.
For example, Eastwood et at. (1994) found a correlation between the attenuation of
high frequencies and the presence of gas in a shallow bitumen reservoir undergoing
steam injection. Schmitt (1998) found instantaneous frequencies to be 20-30 Hertz
lower near well bores during steam injection, coinciding with anomalously high reflection
amplitudes. Radovich and Oliveros (1998) use instantaneous amplitudes and frequencies
to map deep sand channels, finding high amplitudes and low frequencies in the clean,
coarse sands. In this case, the low frequency content is attributed to the geometry of the
sands. Shen (1998) finds correlation between the presence of fractures and the scattering
of high frequencies and uses frequency variation with offset (FVO) and azimuth to map
fracture set orientations.
We note that frequency dependence, like amplitude variation with offset (AVO),
can have many different lithological and geometrical causes and is difficult to interpret.
12-1
Krasovec et al.
To date there are relatively few detailed theoretical studies of the rock physics behind
frequency variation. This paper is part of an ongoing project to quantify the causes of
frequency variation.
SEISMIC DATA
Our data is from the Niger Delta off the west coast of Africa. Producing fields in the area
are characterized by marine shales with local sandy and silty beds thought to have been
laid down as turbidites and continental slope channel fills (Ibie, 1997). The structure of
the Niger Delta is predominantly characterized by listric faults with associated rollover
anticlines. The facies consist of interbedded high-energy deltaic sandstones, siltstones
and shales, and the region is known to have large reserves of natural gas.
A stacked section of our data set (Figure 1) shows some of the features mentioned
above. Since well log data has not been released, this data set is being used only as a test
of the processing sequence and frequency calculations. Our knowledge of the regional
geology does allow a basic interpretation of the section: We see listric normal faults
trending upper left to lower right, and we interpret the shallow bright reflector at CDPs
220 through 270 and two-way time 0.6 seconds, to be a gas reservoir. The bright spot
at CDP 300 to 350 and two-way time 1.5 seconds could also be a hydrocarbon reservoir.
Figure 1 shows four reflectors of interest; the shallowest two, reflectors 1 and 2, pass
above and through the shallow bright spot. Reflectors 3 and 4 are deeper horizons
that appear to terminate at the fault. Reflector 3 shows an increase in amplitude near
the fault, suggesting an accumulation of hydrocarbons sealed by the fault. We will
concentrate on these reflectors in our analysis, with reflectors 1 and 4 assumed to be
background, and the brighter parts of reflectors 2 and 3 being anomalies.
Our processing sequence attempts to preserve the amplitude and spectrum of the
data as much as possible. We use spheri~al divergence amplitude corrections and apply
an FK filter to minimize the water bottom reverberations. Figure 2a shows the shot
gather with only gain corrections and a band pass filter to remove low frequency noise,
Figure 2b shows the same shot gather after FK filtering. To pick the horizons of interest,
we apply deconvolution and do a velocity analysis, then stack the data as shown in
Figure 1. From the stack we choose the zero offset times and stacking velocities of
the events of interest. We use these to define a moveout curve in the prestack domain
(with no deconvolution), such as the solid line shown for synthetic data in Figure 3. A
window of constant width is taken at each offset, shown as dashed lines. The traces in
each window are then analyzed for amplitude and frequency content, shown in Figure 4.
We use two methods of frequency analysis: Instantaneous properties derived from
complex trace analysis (Taner et ai., 1979) and the multiple signal classification (MUSIC) method (Schmidt, 1986), which is useful for power spectrum estimation of short
traces (Shen, 1998).
Following the method of Shen (1998) we describe the frequency dependence of the
poststack data by doing a linear least square fit of peak frequency versus offset, re12-2
Frequency Dependence of Seismic Data From Nigeria
suIting in values for FVO slope and FVO intercept at each point along the poststack
reflector. Similarly, for the amplitude variation, we estimate the incidence angle e for
each poststack trace and find AVO slope and AVO intercept from a plot of amplitude
versus sin 2 e.
RESULTS
Figures 5 and 6 are the frequency and amplitude analysis results for two CMP locations
along horizon 3, at about 1,550 ms. Figure 5 is taken at CMP 315, where the stack
shows a bright spot. Figure 6 is at CMP 425 further along the horizon, where the
reflection is not so bright.
We note that the plot of frequency versus offset has a great deal of scatter. In fact,
no clear correlation between peak frequency and offset is found conclusively. This is
obvious from the lack of coherent peaks in the traces, shown in the top subplot.
The amplitude versus angle plot shows similar problems. We note the sudden
changes in amplitude at middle offsets, part of which we attribute to an artifact of
the FK filtering of the linear arrivals. Figures 2a and 2b show the unevenness of reflectors amplitudes in shot gathers, with and without FK filtering.
Figure 7 shows the FVO slope for the four horizons. We see that the values are
all extremely small and show no correlation with the bright amplitude regions. On the
other hand, the FVO intercept shown in Figure 8 shows low frequencies in the regions
with bright reflections.
Figure 9 shows the instantaneous frequency for the four horizons of interest in the
deconvolved poststack data. The bright reflectors show low frequencies in agreement
with the poststack FVO intercepts shown in Figure 8.
CONCLUSIONS
Preliminary results show, both in the poststack domain and at near offsets, a correlation between low frequency content and large amplitude reflections in areas thought to
contain hydrocarbon reservoirs. However, linear arrivals in the raw data due to direct
waves and water bottom reverberations severely limit our ability to analyze the data in
the prestack domain. Future processing schemes need to address this issue.
ACKNOWLEDGMENTS
This work was supported by the Borehole Acoustics and Logging/Reservoir Delineation
Consortia at the Massachusetts Institute of Technology.
12-3
Krasovec et al.
REFERENCES
Eastwood, J., Lebel, P., Dilay, A., and Blakeslee, S., 1994, Seismic monitoring of steambased recovery of bitumen, The Leading Edge, 13, 242-25l.
Ibie, E., 1997, Seismic stratigraphic analysis in the Niger Delta: A case study of the
Benin River 3-D seismic cube, M.S. thesis, Massachusetts Institute of Technology.
Radovich, B.J., and RB. Oliveros, 1998, 3-D sequence interpretation of seismic instantaneous attributes from the Gorgan field, The Leading Edge, 11, 1286-1293.
Schmidt, R, 1986, Multiple emitter location and signal parameter estimation, IEEE
Transaction on Antennas and Propagation, AP-34, 276-280.
Schmitt, D.R., 1998, Seismic Attributes for monitoring of a shallow heated heavy oil
reservoir: A case study, Geophysics, 63, 368-377.
Shen, F., 1998, Seismic characterization of fractured reservoirs (Part I); Crustal deformation in the Tibetan plateau (Part II), Ph.D. thesis, Massachusetts Institute of
Technology.
Taner, M.T., Koehler, F., and Sheriff, RE., 1979, Complex seismic trace analysis, Geophysics, 44, 1041-1063.
12-4
Frequency Dependence of Seismic Data From Nigeria
Figure 1: The stacked section with a possible fault location and horizons of interest
marked. Horizons 1 and 2 pass above and through the shallow bright spot. Reflectors 3 and 4 are deeper horizons that appear to terminate near the fault.
12-5
Krasovec et al.
Relative Offset (ft)
1000
2000
3000
40
Figure 2a: A shot gather with spherical divergence amplitude correction and bandpass
for low frequency noise.
12-6
Frequency Dependence of Seismic Data From Nigeria
Relative Offset (ft)
1000
2000
3000
Figure 2b: The same shot gather as in Figure 2a with FK filtering applied.
12-7
40
Krasovec et al.
two way time
o
. . . r_---------------.-/
'0>
t - - - - - - - - - - - - - -.. . . . .
~r_--------------~
......
0>
.....
(1)
'0
.:c::.
(1)
I\)
..... ......
(1)
~t-----------~--
.....
~t_-------------!--
~
t_-------------"
Figure 3: Synthetic data to illustrate the windowing process. See text for detailed
description.
12-8
Frequency Dependence of Seismic Data From Nigeria
Q)
E 1.56
;j
1ii
~ 1.58
o
o
~ 1.6
1.62 O~-----~~.L-.L--L---=-=~
" -__~~ll....-.llL-L"""LLLLLL
1500
---.l
2000
2500
3000
2000
2500
3000
offset (m)
roo
N
60
E.
;>.
g 40
Q)
::l
0"
~
- 20
1500
0
offset (m)
40
N
!-35
>.
u
~ 30
•
::J
•
~25
-"i
Q)
•
• • •
20
0
• •
500
1000
Gl
'tl
:l
•
1500
•
• •
•
•
•
•
2000
2500
3000
offset (m)
5
x 10
10
•
•
•
Q.
15
• • •
•
•
•
8
~
Q.
•
E 6
tll
c:
tll
Gl
E 4
•
• •
• •
•
• • •
2
0
2
4
6
8
10
12
14
angle
Figure 4: Offset dependent frequency and amplitude calculation for synthetic data
shown in Figure 3. The top plot shows the traces chosen by the windowing. The
second plot is the power spectrum where lighter means more power. The third plot
shows the peak frequency, and the bottom plot shows the amplitude versus incidence
angle.
12-9
Krasovec et al.
0.55
Q)
:§
0.6
Q)
en
15
e
0.65
Q)
NO.7
o
200
400
600
1000
800
1200
1400
1600
1800
2000
offset (m)
30
Ol-_ _- L
o
200
600
...l-_ _-.J.
-L._ _----l
L -_ _-L._ _----I
400
1000
800
1200
1400
1600
..l.-_ _-J
1800
2000
offset (m)
30,-------rT----r-I----r'----,---I-......-'I----,---..,-----,-------.------,
N
-
~25
>.
g 20
-
Q)
:J
I15
.::s:.
~ 10
.•
••
......--..rt.r---.~=-~~ -=-:-::-:::-
~.;e.~.~.~ ~~.,..~.;t.r~.;-1r
5L-_ _..l...-
o
200
--L._ _
-
400
600
-
• •
• ••
_
-L~
I
__l..._ _--I._ _---l
•
800
1000
1200
•
1400
j-
~ ~ ~ ~ ~ ~
••
•
1600
••••••
1800
2000
x 10-5
offset (m)
1.3 r - - - - - r - - - - - - . - - - - , - - - - - - - , r - - - - - - - r - - - , - - - - - r - - - - - - - . - - - - ,
~
1.25
.3
'5. 1.2
E
ttl
c 1.15
ttl
Q)
E
1.1
5
10
15
20
25
30
35
40
angle
Figure 5: Frequency and amplitude analysis results for horizon 3 at CDP 315. See
Figure 4 caption for subplot description.
12-10
45
Frequency Dependence of Seismic Data From Nigeria
~ 1.64
Q)
l/l
15
1.66
:~ 1.68
N
1500
2000
2500
3000
2000
·2500
3000
offset (m)
~60
N
6
>-
g 40
Q)
:l
c:r
~
- 20
500
0
1000
1500
offset (m)
70
N
660
•
•
>~
50
:J
-
~ 40
•
• •
~Q) 30
0
• • •
•
1000
1500
x 10
2000
•
a.
• • • • • •
c:
til
~2
0
3000
2
•
• •
E4
III
•
2500
• •
Ql
"06
.~
0
• •
•
offset (m)
5
8
•
•
•
•
••
500
•
Q.
20
•
•
()
4
•
•
•
• • • • • • • •
8
6
10
•
•
•
•
12
angle
Figure 6: Frequency and amplitude analysis results for horizon 3 at CDP 425. See
Figure 4 caption for subplot description.
12-11
14
0.6
j1rCll[_~c_,,«._c._««,
0.8
c_c«
c.«_«-.'
(_ _
"--.«i«e: _ ..'
·"l.
(C-t'C_C:_~_c-... ....__c
....-.c._.._
...
1.2
(j)
-.. _u
1.4
E
:;::
>.
~
r-'
l'V
ro
~
_3:
1.6
-...__
~
(j)'"i
n.Pl
O(ll
UiO
o~
[rC"l
(l)
&
Pl
..-
1.8
2
_ l ~
2.2
··C:__·~IaJ"'_(CC.
2.4~
150
-0.60
I
I
I
I
I
I
200
250
300
350
400
450
COP
Figure 7: The FVa slope for all four horizons.
500
_u__
~
. ,
06
0.8
_._,
.
«Ul«C_.«C4["-:.«...... _
.
«."CCC
C4[(<C~ ««-c..c.
I
,_.~
.60.00
• . •C• •
~,---_.~._-
c..- . . . . . - _• •
'.C:.". ___.._. ccccc.
._-
~
(1)
,.0
...j
1.2 f-
I
.::(1)
I
i:J
C"l
'<
tj
OJ
(1)
1.4
'i;j
0.(1)
E
+::
(C__. . .
Cll
-'"''''''~-'''-
~ 1.6
0
>-'
~
tv
37.50
.r".._r......"..._,.• ,.......
>-'
i:J
OJ
(1)
i:J
0C g
rn
(1)
1.8
-l
2f-
......<-
2.2f-
,.,---J
...
.-._~-_ _~
2.4 fI
150
p...
>
0
IJ...H,
I
w
OJ
~
>-
200
250
!
I
300
350
COP
Figure 8: The FVO intercept for all four horizons.
400
450
500
-
......
(fJ
S
......
C"l
tj
Pl
c+
Pl
~
0
s
1,500
-
2:
......
()q
(1)
'1
......
Pl
O.6r--
!-.- c..
n.
.,a._c. (
«c<
«<f:
_
60
-----------Cl:;(<<c.
0.8
.-c. l{«<_
_
.'«ITIII
.
1.2
Q)1.4
.,~
E
:;::;
CI:l
>-'
o
I
"""
~
>-
>-'
l--:J
~ 1.6
30
- - - . - . ............ <
~
-+-'
:"
("l
-"__e.
Cli
C"t-
Pl
......
1.8
2
-..
2.2
......~~
_ _J
o
2.4
150
~
200
250
300
350
400
450
CDP
Figure 9: The instantaneous frequency for all four horizons, calculated from the deconvolved poststack data.
500