AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH
© 2014, Science Huβ, http://www.scihub.org/AJSIR
ISSN: 2153-649X, doi:10.5251/ajsir.2014.5.1.13.22
Estimation of Shear Wave Velocity for Lithological Variation in the NorthWestern Part of the Niger Delta Basin of Nigeria
Horsfall, O.I, Omubo-Pepple, V.B. and Tamunobereton-ari, I.
Department of Physics, Rivers State University of Science and Technology, 500001, Port
Harcourt, Rivers State, Nigeria
Corresponding e-mail: [email protected]
ABSTRACT
This paper presents the estimation of Shear wave velocity analysis for the prediction of
lithological discrimination of the subsurface geology from two petroleum wells AK-1 and AK-2
located in the North-Western part of the Niger Delta. Gamma ray log was used for the lithological
differentiation. Sonic log was used for computation of compressional wave velocity. Shear wave
velocity was determined from compressional wave velocity. The analysis of shear and
compressional wave velocity shows a general conventional trend of increase in velocity with
depth but varies at some depth due to lithological variation, heterogeneity and anisotropic nature
of the earth. Compressional wave velocity Vp is higher than shear wave velocity Vs in both sandy
and shaly formations for the two wells under consideration. The compressional wave velocity
values of shale beds of well AK-1, and well AK-2 varies from 3485 to 4830m/s, and 2339 to
3167m/s respectively while compressional wave velocity values of sand beds for the same wells
varies from 3304 to 6767m/s, and 2093 to 3932m/s and respectively. The shear wave velocity
values of shale beds of well AK-1, and well AK-2 varies from 2682 to 3717m/s, and 1799 to
2437m/s respectively while shear wave velocity values of sand beds for the same wells varies
from 2656 to 5441m/s, 1682 to 3161m/s and 1826 to 2809m/s respectively. This implies that the
shear wave velocity is slower than the compressional wave velocity.
Keywords: Shear wave, Compressional wave,Velocity, lithology,Well Logs, Transit Time,
INTRODUCTION
Velocity is one of the most important petrophysical
parameters used in oil-field optimization or other
geophysical surveys to easily determine and predict
horizons, faults, facies, unconformities, stratigraphic
boundaries, geologic structures, fluid contents etc
Tamunobereton-ari et al(2010). The knowledge of
velocity at any depth is very important in the
recognition of reflectors and refractors with dip or
plane horizontal beds. Tamunobereton-ari et al
(2011).
The optimization of oil-field operations has proven
successful for the effective imaging of subsurface
geology by characterizing the propagation of waves
that travel through the earth material. When sound
waves impinge on a rock material, the material
undergoes stress, deforms and returns to its original
shape ,the sound waves is then picked by a receiver
from which it is stored and used to measure the
elastic properties of rock material. The elastic
properties of a rock material includes the Bulk
modulus, Lame constant, Poisson’s ratio, Shear
modulus, and Young’s modulus.
As sound waves encounter a medium of different
elastic properties and density, compressional and
shear waves are generated. The compressional
waves travel parallel to its particle displacement, Pwaves propagate through solids, liquids, and
gaseous media. These waves could be produced by
earthquakes and recorded by seismographs. Its
velocity is faster than shear wave velocity. The shear
waves travel perpendicular to its particle
displacement. In practical situations shear wave data
have proven to have little or no information thus, the
rock physicist enhanced the usefulness of shear
wave data by combining it with other rock related
properties such as acoustic impedance, elastic
impedance, Lame elastic constant, shear modulus
etc.
Shear wave velocity can be measured directly from
sonic well logs (prescribed), core data laboratory
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
analysis or predicted from compressional wave
velocity data. Brigaud et al. (1990) has observed that
geophysical well logs provide a better representation
of in-situ conditions in a lithological unit than
laboratory measurements because they sample a
finite volume of rock around the well and provide a
continuous record with depth rather than discrete
sample points. Laboratory measurements have a
number of setbacks. A large number of samples must
be measured to characterize adequately the
stratigraphic section; the rock properties determined
in laboratory measurements must still be modified to
apply to in-situ conditions and; some lithologies,
mostly in shales, may be altered in the drilling and
cutting recovery stage so that laboratory
measurements contain systematic error. Blackwell
and Steel (1986)
and the assign a fraction of this to the total interval
within the sand-shale baselines which is then
expressed as a percentage.
The %(shale/sand) is computed from the gamma ray
log as:
%Shale
(
)
(1)
where
%shale = volume of shale in the formation by
percentage
GRlog
= Gamma Ray Log Reading
GRmax = Gamma Ray Log Reading in Shale Zone
GRmin
=Gamma Ray Log Reading in clean Sand
Zone
from the above equation, %sand =100% - %shale
(2)
Numerous studies have shown that the ratio of
compressional wave velocity (vp) to shear wave
velocity (vs) is indicative of lithology. Pickett (1963) in
a detailed work established the (vp/vs) values of 1.9
for limestone, 1.8 for dolomite and 1.6 for sandstone
thereby differentiating the various lithologies.
Lithological presumptions are made based on which
percentages is greater than or equal to 50%
The
Compressional
wave
velocity(Vp)
was
determined from the inverse of sonic transit time from
the logs. The sonic log is simply a recording of the
time required for a sound wave to traverse one foot of
a formation.
Rafavich et al (1984) in a detailed laboratory study of
velocity relationships with petrographic character in
carbornates concluded that the (vp/vs) ratio
successfully differentiated limestone and dolomite.
The equation below was used to compute for the
compressional wave velocity (Vp):
Eastwood and Castagna (1983) studied fullwaveform sonic logs in Appalachian limestone and
observed that shear wave amplitude was attenuated
in shale zones, and thus it could be used for lithology
discrimination.
(3)
Where
Compressional wave velocity (m/s) and
Transit time (µs/m)
METHODOLOGY
To achieve the goal of this study, data from two
exploratory well logs AK-1 & AK-2 from multinational
oil company operating within the North-Western Delta
region of Nigeria was used to evaluate the
parameters of interest. 30ft (10m) depth interval was
chosen to digitize the records on the log runs through
the logged depth. Delineation of the lithology of the
formation was done using the gamma ray log runs
for the different wells. Basically the gamma ray log is
useful for locating shales and non-shaly beds, it
reflects the shale content of sedimentary formations.
Clean sandstones normally exhibits low level of
natural radioactivity, while shale show higher levels of
radioactivity due to adsorption of heavy radioactive
elements. However, the amount of each lithofacies is
estimated by counting the interval of each lithofacies
The Shear wave velocity (Vs) was computed from the
compressional wave velocity using the Castagna and
Greeberg’s(1993) relations for sand and shale beds
as shown below;
(
)
(Sand beds)
(4)
(
)
(Shale beds)
(5)
RESULTS AND DISCUSSION
The results obtained from the study are presented in
Tables 1 and 2 showing the depth, GR(API)readings,
percentage(%)Shale and Sand of the formation,
interval travel times, Compressional wave velocities
14
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
(Vp) and Shear wave Velocities(VS). Figures 1,2,4
and 5 showed trends of increasing shear and
compressional wave velocities with an increase in
depth; Figures 3 and 6 also showed a linear trend of
the plot of shear wave velocity against compressional
wave velocity.
Transit time decreases with
increasing depths. Compressional velocity is greater
than shear wave velocity in the study area. Increases
in shear and compressional wave velocities can be
used in identification of pore fluids type in porous
reservoir. Also the Vp to Vs ratio which is a key
parameter for lithological and fluid prediction shows
that,Poisson’s ratio (VP/VS) is greater in shaly
formation than in sandy formations, The Poisson’s
ratio (Vp/VS) is nearly constant throughout the
formation which is indicative of dry sandstone. The
computed Poisson’s ratio for sandy and shaly
formations for the two wells are 1.24 and 1.30
respectively.
Table:1 Showing Depth, Interval Transit times, GR(API), %shale and sand, compressional wave
velocities (Vp) and shear wave velocities(Vs) relationship for well AK-1.
Depth
(m)
DT (µs/ft)
GR (API)
Shale %
Sand %
1216
60.23
48
32
68
5062
4070
1.24
1226
76.40
22
14
86
3991
3208
1.24
1235
75.08
22
14
86
4061
3264
1.24
1244
77.47
23
14
86
3936
3164
1.24
1253
66.07
26
17
83
4614
3710
1.24
1262
75.54
73
48
52
4036
3245
1.24
1271
81.24
26
17
83
3753
3017
1.24
1280
77.22
55
36
64
3948
3174
1.24
1290
77.18
26
17
83
3950
3176
1.24
1299
76.97
29
19
81
3961
3184
1.24
1308
76.21
29
19
81
4001
3216
1.24
1317
77.38
26
16
84
3940
3168
1.24
1326
67.79
70
46
54
4498
3616
1.24
1335
87.47
77
51
49
3485
2682
1.30
1345
78.18
24
15
85
3900
3135
1.24
1354
78.81
24
15
85
3868
3110
1.24
1363
78.22
33
21
79
3898
3133
1.24
1372
75.03
21
13
87
4063
3267
1.24
1381
72.51
21
13
87
4205
3380
1.24
1390
75.54
22
14
86
4036
3245
1.24
1399
74.90
19
12
88
4071
3273
1.24
1409
73.14
21
14
86
4168
3351
1.24
1418
74.09
23
15
85
4115
3308
1.24
1427
76.21
28
18
82
4000
3216
1.24
15
(m/s)
(m/s)
()
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
1436
69.75
43
28
72
4371
3514
1.24
1445
74.09
23
15
85
4115
3308
1.24
1454
69.36
20
13
87
4396
3534
1.24
1463
71.33
22
14
86
4274
3436
1.24
1473
71.33
21
13
87
4274
3436
1.24
1482
77.89
29
19
81
3914
3147
1.24
1491
69.52
17
11
89
4386
3526
1.24
1500
69.75
21
13
87
4371
3514
1.24
1509
71.49
31
20
80
4265
3429
1.24
1518
76.45
29
19
81
3988
3206
1.24
1527
72.12
21
14
86
4227
3399
1.24
1537
70.70
24
15
85
4312
3467
1.24
1546
66.37
19
12
88
4594
3693
1.24
1555
69.28
18
11
89
4400
3538
1.24
1564
68.66
32
21
79
4440
3570
1.24
1573
72.93
26
17
83
4180
3361
1.24
1582
68.77
33
21
79
4433
3564
1.24
1591
70.40
27
17
83
4331
3482
1.24
1601
65.76
26
17
83
4636
3728
1.24
1610
71.79
28
18
82
4247
3414
1.24
1619
67.24
24
16
84
4534
3645
1.24
1628
71.03
71
47
53
4292
3451
1.24
1637
72.62
36
23
77
4198
3375
1.24
1646
67.96
21
14
86
4486
3606
1.24
1655
69.49
24
16
84
4387
3527
1.24
1665
68.19
20
13
87
4471
3595
1.24
1674
72.67
39
25
75
4196
3373
1.24
1683
66.36
76
50
50
4594
3694
1.24
1692
63.85
45
29
71
4775
3839
1.24
1701
77.16
53
35
65
3951
3177
1.24
1710
74.09
21
14
86
4115
3308
1.24
1720
70.94
22
14
86
4298
3455
1.24
1729
63.85
29
19
81
4775
3839
1.24
1738
66.14
21
13
87
4609
3706
1.24
1747
69.26
21
14
86
4402
3539
1.24
1756
63.61
20
13
87
4793
3853
1.24
1765
78.81
79
52
48
3868
2977
1.30
16
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
1774
71.33
30
20
80
4274
3436
1.24
1784
65.52
61
40
60
4653
3741
1.24
1793
65.58
91
60
40
4649
3577
1.30
1802
66.52
70
46
54
4583
3685
1.24
1811
73.44
22
14
86
4151
3338
1.24
1820
69.49
83
55
45
4387
3376
1.30
1829
74.36
33
21
79
4100
3296
1.24
1838
45.06
22
14
86
6767
5441
1.24
1848
66.31
24
15
85
4598
3697
1.24
1857
92.28
21
13
87
3304
2656
1.24
1866
72.58
41
27
73
4200
3377
1.24
1875
63.12
87
58
42
4830
3717
1.30
1884
64.45
27
18
82
4731
3803
1.24
1893
69.55
41
27
73
4383
3524
1.24
1902
65.61
87
58
42
4647
3576
1.30
1912
72.26
26
17
83
4219
3392
1.24
1921
64.01
34
22
78
4763
3830
1.24
1930
70.01
58
38
62
4355
3501
1.24
1939
66.21
84
56
44
4605
3543
1.30
1948
80.54
49
32
68
3785
3043
1.24
1957
68.77
62
41
59
4433
3564
1.24
1966
63.06
36
23
77
4835
3887
1.24
1976
67.55
32
21
79
4513
3629
1.24
1985
70.94
19
12
88
4298
3455
1.24
1994
66.42
20
13
87
4590
3690
1.24
2003
61.64
20
13
87
4946
3976
1.24
2012
63.26
46
30
70
4820
3875
1.24
2021
65.90
27
18
82
4627
3720
1.24
2030
65.35
48
32
68
4666
3751
1.24
2040
62.27
69
46
54
4896
3936
1.24
2049
77.45
48
32
68
3937
3165
1.24
2058
66.37
32
21
79
4594
3693
1.24
2067
64.30
18
11
89
4741
3812
1.24
2076
67.94
29
19
81
4488
3608
1.24
2085
71.88
55
36
64
4241
3410
1.24
17
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
2095
46.05
37
24
76
6620
5323
1.24
2104
46.50
25
16
84
6557
5272
1.24
2113
70.31
77
51
49
4336
3486
1.24
2122
69.52
73
48
52
4386
3526
1.24
Table 2: Showing Depth, Interval Transit times, GR(API), %shale and sand, compressional wave
velocities(Vp) and shear wave velocities(Vs) relationship for well AK-2.
Sand
Depth
(m)
DT (µs/ft)
GR (API)
Shale %
1372
141.18
27
17
83
2159
1736
1.24
1381
136.72
27
18
82
2230
1792
1.24
1390
130.36
83
55
45
2339
1799
1.30
1399
123.71
26
17
83
2464
1981
1.24
1409
124.37
25
16
84
2451
1970
1.24
1418
119.11
40
26
74
2560
2057
1.24
1427
118.53
26
17
83
2572
2068
1.24
1436
122.55
26
17
83
2488
2000
1.24
1445
114.98
25
16
84
2652
2131
1.24
1454
128.72
35
23
77
2369
1904
1.24
1463
120.35
30
20
80
2533
2036
1.24
1473
117.92
24
16
84
2585
2078
1.24
1482
120.44
23
15
85
2531
2035
1.24
1491
120.48
24
16
84
2531
2034
1.24
1500
120.28
30
20
80
2535
2037
1.24
1509
125.30
25
16
84
2433
1956
1.24
1518
119.84
20
13
87
2544
2045
1.24
1527
118.82
24
15
85
2566
2063
1.24
1537
107.42
28
18
82
2838
2282
1.24
1546
117.24
24
15
85
2600
2090
1.24
1555
117.10
26
17
83
2604
2093
1.24
1564
109.90
30
19
81
2774
2230
1.24
1573
111.92
23
15
85
2724
2190
1.24
1582
123.67
75
50
50
2465
1982
1.24
1591
116.68
62
41
59
2613
2100
1.24
1601
112.17
33
21
79
2718
2185
1.24
%
18
(m/s)
(m/s)
()
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
1610
118.22
34
22
78
2579
2073
1.24
1619
94.35
21
13
87
3231
2598
1.24
1628
122.36
23
15
85
2492
2003
1.24
1637
110.97
26
17
83
2747
2208
1.24
1646
114.13
106
71
29
2671
2055
1.30
1655
114.28
24
16
84
2668
2144
1.24
1665
113.90
80
53
47
2677
2059
1.30
1674
114.75
27
18
82
2657
2136
1.24
1683
109.43
37
24
76
2786
2240
1.24
1692
120.08
65
43
57
2539
2041
1.24
1701
108.48
79
52
48
2810
2162
1.30
1710
131.31
75
50
50
2322
1866
1.24
1720
122.55
37
24
76
2488
2000
1.24
1729
122.15
27
18
82
2496
2006
1.24
1738
117.90
29
19
81
2586
2079
1.24
1747
119.45
43
28
72
2552
2052
1.24
1756
118.04
61
40
60
2583
2076
1.24
1765
125.04
81
54
46
2438
1960
1.24
1774
116.48
26
17
83
2617
2104
1.24
1784
115.45
30
19
81
2641
2123
1.24
1793
118.72
46
30
70
2568
2064
1.24
1802
106.33
81
54
46
2867
2206
1.30
1811
122.33
63
42
58
2492
2003
1.24
1820
107.81
32
21
79
2828
2273
1.24
1829
119.76
21
13
87
2546
2046
1.24
1838
107.73
37
24
76
2830
2275
1.24
1848
111.49
29
19
81
2735
2198
1.24
1857
118.64
34
22
78
2570
2066
1.24
1866
110.52
87
58
42
2759
2122
1.30
1875
113.16
42
27
73
2694
2166
1.24
1884
110.75
33
22
78
2753
2213
1.24
1893
105.30
32
21
79
2895
2327
1.24
1902
109.26
29
19
81
2790
2243
1.24
1912
77.54
47
31
69
3932
3161
1.24
1921
106.01
81
53
47
2876
2213
1.30
19
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
1930
120.06
83
55
45
2539
1954
1.30
1939
112.12
49
32
68
2719
2186
1.24
1948
109.63
35
23
77
2781
2235
1.24
1957
111.70
31
20
80
2729
2194
1.24
1966
112.38
26
17
83
2713
2181
1.24
1976
110.52
20
13
87
2759
2217
1.24
1985
113.51
27
18
82
2686
2159
1.24
1994
108.31
51
34
66
2815
2263
1.24
2003
110.69
84
56
44
2754
2119
1.30
2012
113.81
32
21
79
2679
2153
1.24
2021
105.97
22
14
86
2877
2313
1.24
2030
111.66
28
18
82
2730
2195
1.24
2040
110.12
40
26
74
2769
2226
1.24
2049
106.95
29
19
81
2851
2292
1.24
2058
107.42
24
15
85
2838
2282
1.24
2067
111.42
34
22
78
2736
2200
1.24
2076
107.18
26
17
83
2845
2287
1.24
2085
111.55
66
44
56
2733
2197
1.24
2095
111.19
81
53
47
2742
2110
1.30
2104
118.18
83
55
45
2580
1985
1.30
2113
122.36
76
50
50
2492
1917
1.30
2122
122.41
78
52
48
2491
1916
1.30
2131
124.59
76
50
50
2447
1883
1.30
2140
120.58
85
56
44
2528
1945
1.30
2149
114.46
82
54
46
2664
2049
1.30
2159
116.57
85
56
44
2616
2012
1.30
2168
120.35
83
55
45
2533
1949
1.30
2177
145.68
26
17
83
2093
1682
1.24
2186
127.98
30
20
80
2382
1915
1.24
2195
107.90
86
57
43
2826
2174
1.30
2204
104.30
83
55
45
2923
2249
1.30
2213
107.58
87
58
42
2834
2180
1.30
2223
116.16
28
18
82
2625
2110
1.24
2232
112.36
24
16
84
2714
2181
1.24
2241
96.27
81
54
46
3167
2437
1.30
20
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
2250
103.03
24
16
84
2959
2379
1.24
2259
97.18
48
31
69
3137
2522
1.24
2268
110.07
42
28
72
2770
2227
1.24
2277
99.54
88
59
41
3063
2357
1.30
Shear velocity (m/s)
2000
4000
0
0
0
500
500
Depth (m)
Depth (m)
0
Compressional velocity (m/s)
2000
4000
6000
8000
1000
1500
6000
1000
1500
2000
2000
2500
2500
6000
5000
4000
3000
2000
1000
0
Fig.2: Depth Vs Shear Wave Velocity(VS) for
Well AK -1
y = 0.8037x - 9.3935
R² = 0.9912
0
2000
4000
6000
0
Compressional velocity (m/s)
2000
4000
6000
0
Depth (m)
Shear velocity (m/s)
Fig.1: Depth Vs Compressional Wave Velocity
(VP) for Well AK -1
8000
500
1000
1500
2000
Compressional velocity (m/s)
2500
Fig.3: Shear WaveVelocity(VS) Vs Compressional
wave Velocity(VP) for well AK-1
Fig. 4: Depth Vs Compressional wave
Velocity(VP) for well AK-2
21
Am. J. Sci. Ind. Res., 2014, 5(1): 13-22
3500
Shear velocity (m/s)
0
Shear velocity (m/s)
1000
2000
3000
4000
0
Depth (m)
500
1000
1500
y = 0.7832x + 33.482
R² = 0.9549
3000
2500
2000
1500
1000
500
0
0
2000
2000
4000
6000
Compressional velocity (m/s)
2500
Fig.5: Depth Vs Shear Wave Velocity(VS) for
Well AK-2
AK-2
Fig.6: Shear Wave Velocity(VS) Vs
Compressional Wave Velocity(VP) for well
CONCLUSION
geophysical well logs: AAPG Bulletin. Vol. 74,
no.9, P, 1459 – 1477.
The knowledge of shear and compressional
wave velocities, and Poisson ratios can provide
valuable information about litholgy differention
and physical properties of rocks, including how
rocks will deform under a given stress. This type
of information can be valuable during recognition
of reservoir fluid contacts, and design and
construction phases of building projects. The
study has provided information on the linearity in
trend of the variation of shear and
compressional wave velocities with depth in a
given lithology.These velocities increases with
depth for both sand and shalebeds. Shear wave
velocity can only be determined for solids or
highly viscous medium. Compressional wave
velocity Vp is higher than shear wave velocity Vs
in both sandy and shaly formations for the two
wells under consideration.
Eastwood, R.L. and Castagna, J.P. (1983); Bases for
interpretation of (VP/VS) ratios in complex
th
lithologies. Soc. Prof. Well Log analysts 24
Annual logging Symposium.
Greenberg, M.L, and Castagna, J.P. (1993); ShearWear Velocity Estimation in porous Rocks.
Theoretical formulation, Preliminary verification
and applications. Geophys. Prosp., 40, 195-209.
Pickett, G. (1963), Acoustic Character Logs and their
applications in formation evaluation. J. Petr.
Tech., 659 – 667.
Rafavich, F., Kendall,C.H. St. C., and Todd, T.P.
(1984). The relationship between acoustic
properties and the petrographic character of
carbonate rock: Geophysics, 49, 1622 – 1636.
Tamunobereton-ari, I., Omubo-Pepple, V.B. and Uko,
E.D. (2010). The Influence of Lithology and
Depth on Acoustic Velocities in South-East Niger
Delta, Nigeria. American Journal of Scientific and
Industrial Research 1.(2), 279 – 292.
REFERENCES
Blackwell, D.D., and Steel, J.L. (1986); Thermal
Conductivity of sedimentary rock-measurement
and significance in thermal history of sedimentary
Basins; Methods and Case Histories. Springer,
New York NY PP.13-36.
Tamunobereton-ari, I., Omubo-Pepple, V.B. and Uko,
E.D. (2011).Determination of the Variability of
Seismic velocity with Lithology in the SouthWestern part of the Niger Delta Basin of Nigeria
using well logs. Journal of Basic and Applied
Scientific Research 1(7), 700 – 705.
Brigaud, F. Chapman, D.S. and Le Douaran, S.
(1990); Estimating thermal conductivity in
Sedimentary Basin using Lithological data and
22