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Forward modeling to improve seismic reflection energy of a protective coal seam based on Zoeppritz equation
JOURNAL OF CHINA UNIVERSITY OF
MINING & TECHNOLOGY J China Univ Mining & Technol 18 (2008) 0046–0049 www.elsevier.com/locate/jcumt
Forward modeling to improve seismic reflection energy of a protective coal seam based on Zoeppritz equation TAO Wen-peng, DONG Shou-hua, LI Yang School of Resource and Geoscience, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China
Abstract: In seismic exploration for coal, seismic waves are very difficult to transmit downward because of high velocity protective layers, making the reflection information very hard to receive above ground. Based on the Snell law and the Zoeppritz equation, we studied the relationship between the incidence angle and reflection seismic wave energy using a forward model of level media. The result shows that the seismic wave energy has a sudden increase at the critical angle. Based on the energy propagation rule, using big offset to receive the seismic wave energy under a protective layer can effectively reduce its protection effect. Key words: high velocity shielding layer; Zoeppritz equation; forward modeling
1
Introduction
Currently, in seismic exploration for coal, a reflection P-wave is mainly used. The condition for forming the reflection wave is the difference in wave impedance between upper and lower strata. However, in some areas several high-speed strata occur which show considerable differences in wave impedance with respect to the surrounding rocks, leading to large reflection coefficients and forming a strong reflection interface. The consequence of this is that it is difficult for the energy of seismic waves to reach the target layer. In addition, seismic waves cannot be transmitted downward because of multiple reflections. This makes for the reception of a low S/N ratio, which greatly affects the result of seismic exploration[1]. Therefore, the study of seismic wave propagation in protective layers is important for improving the accuracy of seismic exploration. Based on the Zoeppritz equation and Snell’s law and given the kinematic characteristics of seismic waves, we have used simulation to perform forward modeling of a horizontal geological model. In particular, we have studied the relationship between the energy reflection of seismic waves and the incidence angle in order to find an effective way to improve seismic energy and obtain a high S/N ratio of seismic data.
2
Method and principle
2.1 Seismic reflection and transmission Seismic wave impinging on a plane interface is partly reflected and partly transmitted. The first part of the energy, returned from the first medium, is the so-called reflection wave; the other part penetrates into the second medium and is called the transmission wave. Both reflection and transmission waves are shown in Fig. 1.
Fig. 1
Incidence waves, reflection waves and transmission waves
Fig. 1 shows an interface whose upper area is the 1st medium and the lower is the 2nd medium, where ρ1 and ρ 2 represent the density of the two media. V1 and V2 are the velocity transmissions of the seismic waves in the two media[2].
Received 05 May 2007; accepted 10 November 2007 Projects 40574058 supported by the National Natural Science Foundation of China, 2005cb221500 by the National Basic Research Program of China and 03(2007) by the Scientific and Technological Project about Geology and Mineral Resources of Henan Land Resources Department Corresponding author. Tel: +86-516-82842826; E-mail address: [email protected]
TAO Wen-peng et al
2.2
Forward modeling to improve seismic reflection energy of a …
Zoeppritz equation
The reflection of the seismic wave and the transmission at the interface is determined by the density of the two media and their elastic parameters. In a general way, when the incident P-wave (or S-wave) reaches the interface, it will form a reflection P-wave and a transmission P-wave, or a reflection S-wave and a transmission S-wave. If we assume two uniform semi-infinite elastic media (Fig. 2), then the reflection and transmission will take place at the interface[3].
Fig. 2
Different types of waves (incident P-wave)
If the density of the 1st medium is ρ1 , the velocity of the P-wave is VP1 and the velocity of the S-wave is VS1 , then that of the 2nd media is ρ 2 , VP 2 and VS 2 ,
the amplitude of the incident P-wave is A0 and the incidence angle is θ1 . The amplitude of the reflection
of the P-wave is A1 and the reflection angle is θ1 . The amplitude of the reflection of the S-wave is B1 and the reflection angle is δ1 . The amplitude of the transmission of the P-wave is A2 and the transmission angle is θ 2 . The amplitude of the reflection of the S-wave is B2 and the reflection angle is δ 2 . Given these conditions, we have, according to Snell’s law: sin δ1 sin θ1 sin δ 2 sin θ 2 = = = VS 1 VP1 VS 2 VP 2
Forward modeling and analysis
In Table 1, there is a shielding stratum model[5–7], the thickness of the 1st coal seam is H 3 = 10 m , that of the 2nd coal seam is H 5 = 3 m , the P-wave’s ve-
(1)
There are four unknown parameters in the Zoeppritz equation. If we divide A1 , A2 , B1 and B2 by incidence amplitude A0 , then we can obtain the reflection coefficient R pp = A1 , R ps = B1 and the transmission A0 A0 B coefficient Tpp = A2 , Tps = 2 . A0 A0 According to Cramer's Rule we can obtain Eq.(2) which expresses the distribution of the energy relationship between reflection coefficient and transmission coefficient[4]. If the elasticity parameters of the stratum and the angle of incidence are known, we can find the reflection coefficient. In other words, we can find the reflection energy of the wave.
cosδ1 cosδ 2 − sinθ 2 ⎤⎡ ⎡ sinθ1 ⎥ ⎢Rpp ⎢− cosθ sinδ1 − cosθ2 − sinδ 2 1 ⎥⎢ ⎢ VP1 ρ2 VP1VS 2 ρ2 VP1 VS22 ⎥ ⎢ Rps ⎢ ⎢ sin2θ1 V cos2δ1 ρ V V 2 sin2θ2 − ρ V 2 cos2δ 2 ⎥ ⎢ T 1 P2 1 S1 S1 S1 ⎥ ⎢ pp ⎢ ρ2 VS 2 ⎢ cos2δ − VS1 sin2δ − ρ2 VP2 cos2δ sin2δ 2 ⎥ ⎢ Tps − 1 1 2 VP1 ρ1 VP1 ρ1 VP1 ⎦⎥ ⎣ ⎣⎢
3
47
⎤ ⎡ − sinθ1 ⎤ ⎥ ⎢ ⎥ ⎥ ⎢− cosθ ⎥ 1 ⎥=⎢ ⎥ ⎥ ⎢ sin2θ ⎥ 1 ⎥ ⎢ ⎥ ⎥ ⎣− cos2δ1 ⎦ ⎦
(2)
We can obtain the curve between reflection P-wave energy and the incidence angle from the Zoeppritz equation (Figs. 3–4). Because the incidence angle varies, the seismic wave energy received is also different.
locity in coal seam is VP 3 = 2100 m/s , the S-wave’s velocity is VS 3 = 1200 m/s . Table 1
Forward shielding model
No.
VP (m/s)
VS (m/s)
Thickness (m)
1
2000
1100
160
2
3600
2100
200
3
2100
1200
10
4
3600
2100
80
5
2100
1200
3
6
3600
2100
100
Fig. 3
Relationship between reflection wave energy and incidence angle (P-wave)
In Fig. 3, the high-speed protective stratum exists, the energy of the reflection P-wave has a minimum
48
Journal of China University of Mining & Technology
value at the incidence angle of 25°, it then increases sharply and reaches its maximum value at the critical angle. Beyond the critical angle after the first decrease, it increases slowly[8]. Otherwise, the energy of the seismic wave initially decreases slowly and when the incident angle increases to a certain degree, it will gradually increase. In other words, we can use a large incidence angle to receive a strong seismic signal.
dence angle. Fig. 5 shows that, because of the protective stratum, the reflection energy at first reduces to a minimum and then gradually increases with the increasing offset.
Fig. 5
4 Fig. 4
Relationship between reflection wave energy and incidence angle (S-wave)
From Fig. 4 we can see that, for the reflection S-wave, when the seismic wave enters the protective stratum, the energy at first increases, then slowly decreases. At the critical angle it suddenly decreases, then rapidly increases to a certain point and after that it rapidly decreases again[9]. Without the protective stratum, the change in energy is relatively stable. We know that the offset increases with an increase in the incidence angle. The relationship between reflection wave energy and offset is similar to the relationship between reflection wave energy and inci-
Relationship between reflection wave energy and offset
Relationship between shot frequency and resolution
In seismic exploration for coal, the thickness of some coal seams is very small, so the seismic wavelet cannot tell the difference of the reflection between roof and floor. The thickness of coal seams is usually 0–20 m. It is smaller than the main wavelength of the seismic wave λ (20–50 m), according to the Ricker rule. If the thickness of one stratum is less than λ 4 , then the stratum is a thin layer and the coal seam is thin in coal seismic exploration[10–11]. We use both low and high frequencies pulses for forward modeling (Fig. 6).
(a) Low frequency
(b) High frequency
Fig. 6
Simulation single shot record
For thin seams, low frequency cannot tell it. Therefore, in seismic exploration for coal, we can use high frequency pulses to enhance the record of seismic resolutions.
5
Vol.18 No.1
Conclusions
Our simulation results show that the reflection energy will suddenly change at the critical angle and we can receive strong reflection signals from below the protective stratum using the big offset. We should be
well aware that the coal seam is relatively thin in seismic exploration for coal. We should use high frequency pulses in order to enhance the resolution of seismic data. Also, if the protection is very shallow, we can consider pulses under the protective stratum to increase the transmission of energy to receive more reflection information of the coal seam. If the protective stratum is relatively deep, we can use a large number of detonators to generate pulses in order to receive reflection signals.
TAO Wen-peng et al
Forward modeling to improve seismic reflection energy of a …
References [1]
[2] [3]
[4]
[5]
Li K E, Xiong X J, Yang J. Seismic acquisition analysis in the area of high velocity shielding layers. Natural Gas Geo-science, 2006, 17(4): 527–531. (In Chinese) Lu J M. Seismic Explorer Elements. Dongying: University of Petroleum Press, 1993: 14–15. (In Chinese) Dong S H. Method to Lateral Prediction and Evaluation of Coal Seams Based on Seismic Data. Xuzhou: China University of Mining and Technology Press, 2004: 46– 47. (In Chinese) Wang Z, He Z H, Huang D J, et al. A seismic survey method for weak reflectors below shielded layer of high velocity: wide angle reflection. Progress in Exploration Geophysics, 2002, 25(5): 23–27. (In Chinese) Dong S H, Ma Y L, Zhou M. Forward modeling of relationship between coal seam thickness and seismic attributes of amplitude and frequency. Journal of China University of Mining and Technology, 2004, 33(1): 29–32. (In Chinese)
[6]
49
Dong S H, Yun J H. Forward modeling of the relationship between reflection coefficient and incident angle of the P-wave in a coal seam. Journal of China University of Mining & Technology, 2006, 16(1): 5–7. [7] Zhang J G, Dong S H, Yun J H. Forward modeling of azimuthally anisotropy to the reflected P-wave of coal seam . Journal of China University of Mining & Technology, 2006, 16(3): 321–324. [8] Liu Y, Wei X C. Fracture detection using the travel time of 3-D reflected compression wave. Oil Geophysical Prospecting, 1999, 34(6): 607–613. (In Chinese) [9] Fruehn J, White R S, Fliedner M, et al. Large-aperture seismic: imaging beneath high-velocity strata. World Oil, 1999, 220(1): 109–113. [10] Brittan J, Warner M. Wide-angle seismic velocities in heterogeneous crust. Geophysics Journal International, 1997, 129(2): 269–280. [11] Zillmer M, Gajewski D, Kashtan B M. Reflection coefficients for weak anisotropic media. Geophysics Journal International, 1997, 129(2): 389–398.
MINING & TECHNOLOGY J China Univ Mining & Technol 18 (2008) 0046–0049 www.elsevier.com/locate/jcumt
Forward modeling to improve seismic reflection energy of a protective coal seam based on Zoeppritz equation TAO Wen-peng, DONG Shou-hua, LI Yang School of Resource and Geoscience, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China
Abstract: In seismic exploration for coal, seismic waves are very difficult to transmit downward because of high velocity protective layers, making the reflection information very hard to receive above ground. Based on the Snell law and the Zoeppritz equation, we studied the relationship between the incidence angle and reflection seismic wave energy using a forward model of level media. The result shows that the seismic wave energy has a sudden increase at the critical angle. Based on the energy propagation rule, using big offset to receive the seismic wave energy under a protective layer can effectively reduce its protection effect. Key words: high velocity shielding layer; Zoeppritz equation; forward modeling
1
Introduction
Currently, in seismic exploration for coal, a reflection P-wave is mainly used. The condition for forming the reflection wave is the difference in wave impedance between upper and lower strata. However, in some areas several high-speed strata occur which show considerable differences in wave impedance with respect to the surrounding rocks, leading to large reflection coefficients and forming a strong reflection interface. The consequence of this is that it is difficult for the energy of seismic waves to reach the target layer. In addition, seismic waves cannot be transmitted downward because of multiple reflections. This makes for the reception of a low S/N ratio, which greatly affects the result of seismic exploration[1]. Therefore, the study of seismic wave propagation in protective layers is important for improving the accuracy of seismic exploration. Based on the Zoeppritz equation and Snell’s law and given the kinematic characteristics of seismic waves, we have used simulation to perform forward modeling of a horizontal geological model. In particular, we have studied the relationship between the energy reflection of seismic waves and the incidence angle in order to find an effective way to improve seismic energy and obtain a high S/N ratio of seismic data.
2
Method and principle
2.1 Seismic reflection and transmission Seismic wave impinging on a plane interface is partly reflected and partly transmitted. The first part of the energy, returned from the first medium, is the so-called reflection wave; the other part penetrates into the second medium and is called the transmission wave. Both reflection and transmission waves are shown in Fig. 1.
Fig. 1
Incidence waves, reflection waves and transmission waves
Fig. 1 shows an interface whose upper area is the 1st medium and the lower is the 2nd medium, where ρ1 and ρ 2 represent the density of the two media. V1 and V2 are the velocity transmissions of the seismic waves in the two media[2].
Received 05 May 2007; accepted 10 November 2007 Projects 40574058 supported by the National Natural Science Foundation of China, 2005cb221500 by the National Basic Research Program of China and 03(2007) by the Scientific and Technological Project about Geology and Mineral Resources of Henan Land Resources Department Corresponding author. Tel: +86-516-82842826; E-mail address: [email protected]
TAO Wen-peng et al
2.2
Forward modeling to improve seismic reflection energy of a …
Zoeppritz equation
The reflection of the seismic wave and the transmission at the interface is determined by the density of the two media and their elastic parameters. In a general way, when the incident P-wave (or S-wave) reaches the interface, it will form a reflection P-wave and a transmission P-wave, or a reflection S-wave and a transmission S-wave. If we assume two uniform semi-infinite elastic media (Fig. 2), then the reflection and transmission will take place at the interface[3].
Fig. 2
Different types of waves (incident P-wave)
If the density of the 1st medium is ρ1 , the velocity of the P-wave is VP1 and the velocity of the S-wave is VS1 , then that of the 2nd media is ρ 2 , VP 2 and VS 2 ,
the amplitude of the incident P-wave is A0 and the incidence angle is θ1 . The amplitude of the reflection
of the P-wave is A1 and the reflection angle is θ1 . The amplitude of the reflection of the S-wave is B1 and the reflection angle is δ1 . The amplitude of the transmission of the P-wave is A2 and the transmission angle is θ 2 . The amplitude of the reflection of the S-wave is B2 and the reflection angle is δ 2 . Given these conditions, we have, according to Snell’s law: sin δ1 sin θ1 sin δ 2 sin θ 2 = = = VS 1 VP1 VS 2 VP 2
Forward modeling and analysis
In Table 1, there is a shielding stratum model[5–7], the thickness of the 1st coal seam is H 3 = 10 m , that of the 2nd coal seam is H 5 = 3 m , the P-wave’s ve-
(1)
There are four unknown parameters in the Zoeppritz equation. If we divide A1 , A2 , B1 and B2 by incidence amplitude A0 , then we can obtain the reflection coefficient R pp = A1 , R ps = B1 and the transmission A0 A0 B coefficient Tpp = A2 , Tps = 2 . A0 A0 According to Cramer's Rule we can obtain Eq.(2) which expresses the distribution of the energy relationship between reflection coefficient and transmission coefficient[4]. If the elasticity parameters of the stratum and the angle of incidence are known, we can find the reflection coefficient. In other words, we can find the reflection energy of the wave.
cosδ1 cosδ 2 − sinθ 2 ⎤⎡ ⎡ sinθ1 ⎥ ⎢Rpp ⎢− cosθ sinδ1 − cosθ2 − sinδ 2 1 ⎥⎢ ⎢ VP1 ρ2 VP1VS 2 ρ2 VP1 VS22 ⎥ ⎢ Rps ⎢ ⎢ sin2θ1 V cos2δ1 ρ V V 2 sin2θ2 − ρ V 2 cos2δ 2 ⎥ ⎢ T 1 P2 1 S1 S1 S1 ⎥ ⎢ pp ⎢ ρ2 VS 2 ⎢ cos2δ − VS1 sin2δ − ρ2 VP2 cos2δ sin2δ 2 ⎥ ⎢ Tps − 1 1 2 VP1 ρ1 VP1 ρ1 VP1 ⎦⎥ ⎣ ⎣⎢
3
47
⎤ ⎡ − sinθ1 ⎤ ⎥ ⎢ ⎥ ⎥ ⎢− cosθ ⎥ 1 ⎥=⎢ ⎥ ⎥ ⎢ sin2θ ⎥ 1 ⎥ ⎢ ⎥ ⎥ ⎣− cos2δ1 ⎦ ⎦
(2)
We can obtain the curve between reflection P-wave energy and the incidence angle from the Zoeppritz equation (Figs. 3–4). Because the incidence angle varies, the seismic wave energy received is also different.
locity in coal seam is VP 3 = 2100 m/s , the S-wave’s velocity is VS 3 = 1200 m/s . Table 1
Forward shielding model
No.
VP (m/s)
VS (m/s)
Thickness (m)
1
2000
1100
160
2
3600
2100
200
3
2100
1200
10
4
3600
2100
80
5
2100
1200
3
6
3600
2100
100
Fig. 3
Relationship between reflection wave energy and incidence angle (P-wave)
In Fig. 3, the high-speed protective stratum exists, the energy of the reflection P-wave has a minimum
48
Journal of China University of Mining & Technology
value at the incidence angle of 25°, it then increases sharply and reaches its maximum value at the critical angle. Beyond the critical angle after the first decrease, it increases slowly[8]. Otherwise, the energy of the seismic wave initially decreases slowly and when the incident angle increases to a certain degree, it will gradually increase. In other words, we can use a large incidence angle to receive a strong seismic signal.
dence angle. Fig. 5 shows that, because of the protective stratum, the reflection energy at first reduces to a minimum and then gradually increases with the increasing offset.
Fig. 5
4 Fig. 4
Relationship between reflection wave energy and incidence angle (S-wave)
From Fig. 4 we can see that, for the reflection S-wave, when the seismic wave enters the protective stratum, the energy at first increases, then slowly decreases. At the critical angle it suddenly decreases, then rapidly increases to a certain point and after that it rapidly decreases again[9]. Without the protective stratum, the change in energy is relatively stable. We know that the offset increases with an increase in the incidence angle. The relationship between reflection wave energy and offset is similar to the relationship between reflection wave energy and inci-
Relationship between reflection wave energy and offset
Relationship between shot frequency and resolution
In seismic exploration for coal, the thickness of some coal seams is very small, so the seismic wavelet cannot tell the difference of the reflection between roof and floor. The thickness of coal seams is usually 0–20 m. It is smaller than the main wavelength of the seismic wave λ (20–50 m), according to the Ricker rule. If the thickness of one stratum is less than λ 4 , then the stratum is a thin layer and the coal seam is thin in coal seismic exploration[10–11]. We use both low and high frequencies pulses for forward modeling (Fig. 6).
(a) Low frequency
(b) High frequency
Fig. 6
Simulation single shot record
For thin seams, low frequency cannot tell it. Therefore, in seismic exploration for coal, we can use high frequency pulses to enhance the record of seismic resolutions.
5
Vol.18 No.1
Conclusions
Our simulation results show that the reflection energy will suddenly change at the critical angle and we can receive strong reflection signals from below the protective stratum using the big offset. We should be
well aware that the coal seam is relatively thin in seismic exploration for coal. We should use high frequency pulses in order to enhance the resolution of seismic data. Also, if the protection is very shallow, we can consider pulses under the protective stratum to increase the transmission of energy to receive more reflection information of the coal seam. If the protective stratum is relatively deep, we can use a large number of detonators to generate pulses in order to receive reflection signals.
TAO Wen-peng et al
Forward modeling to improve seismic reflection energy of a …
References [1]
[2] [3]
[4]
[5]
Li K E, Xiong X J, Yang J. Seismic acquisition analysis in the area of high velocity shielding layers. Natural Gas Geo-science, 2006, 17(4): 527–531. (In Chinese) Lu J M. Seismic Explorer Elements. Dongying: University of Petroleum Press, 1993: 14–15. (In Chinese) Dong S H. Method to Lateral Prediction and Evaluation of Coal Seams Based on Seismic Data. Xuzhou: China University of Mining and Technology Press, 2004: 46– 47. (In Chinese) Wang Z, He Z H, Huang D J, et al. A seismic survey method for weak reflectors below shielded layer of high velocity: wide angle reflection. Progress in Exploration Geophysics, 2002, 25(5): 23–27. (In Chinese) Dong S H, Ma Y L, Zhou M. Forward modeling of relationship between coal seam thickness and seismic attributes of amplitude and frequency. Journal of China University of Mining and Technology, 2004, 33(1): 29–32. (In Chinese)
[6]
49
Dong S H, Yun J H. Forward modeling of the relationship between reflection coefficient and incident angle of the P-wave in a coal seam. Journal of China University of Mining & Technology, 2006, 16(1): 5–7. [7] Zhang J G, Dong S H, Yun J H. Forward modeling of azimuthally anisotropy to the reflected P-wave of coal seam . Journal of China University of Mining & Technology, 2006, 16(3): 321–324. [8] Liu Y, Wei X C. Fracture detection using the travel time of 3-D reflected compression wave. Oil Geophysical Prospecting, 1999, 34(6): 607–613. (In Chinese) [9] Fruehn J, White R S, Fliedner M, et al. Large-aperture seismic: imaging beneath high-velocity strata. World Oil, 1999, 220(1): 109–113. [10] Brittan J, Warner M. Wide-angle seismic velocities in heterogeneous crust. Geophysics Journal International, 1997, 129(2): 269–280. [11] Zillmer M, Gajewski D, Kashtan B M. Reflection coefficients for weak anisotropic media. Geophysics Journal International, 1997, 129(2): 389–398.