(China Youshi University (East China) College of Earth Science and Technology, Qingdao 266555)
Fund projects: National 973 Project (No.2065438+201CB 202402), Innovation Fund of Petroleum University (No.27R 100 1046A) and (Y090/KLOC-0).
About the author: Li Na, female, Ph.D. candidate, is now engaged in the forward modeling of seismic waves. E-mail: Lina19202 @163.com.
Abstract: shear-wave splitting is an important index to identify the anisotropy of wave propagation media. Fast and slow shear-wave splitting time difference and fast shear wave polarization direction are two main parameters for evaluating shear-wave splitting. In anisotropic media with directional parallel arrangement, fast shear-wave splitting time difference and polarization direction can reflect fracture information such as fracture density, width, volume, strike and media properties. In order to detect the azimuth attribute characteristics of shear-wave splitting in directional fractured media and analyze the variation law of splitting time difference with polarization angle and Thomson weak anisotropy parameters, this paper uses staggered grid high-order finite difference method and PML absorption boundary method to obtain three-component records of counterclockwise rotation of VTI media around X axis at different angles. The main conclusions are as follows: (1) From the energy point of view, when polarization angle is 45, the energy contrast between fast and slow shear waves is the strongest. (2) At the same time, the single channel waveforms are compared and quantitatively analyzed, and it is found that the split time difference decreases with the increase of the anisotropic strength parameter ε of qP wave, increases with the increase of the anisotropic strength parameter γ of qS wave, and increases with the increase of the transition parameter δ connecting P wave and P wave velocity. (3) Under the same intensity, the anisotropic intensity parameter γ of qS wave has the greatest influence on shear-wave splitting time difference, while δ has the least influence. The velocity of fast shear wave is only determined by γ, so the value range of γ can be judged by the velocity of fast shear wave, while the velocity of qP wave is determined by ε, so the value range of ε can be judged by the velocity of qP wave. In addition, when ε approaches δ, the shear-wave splitting time difference does not change obviously with the angle, on the contrary, the shear-wave splitting time difference increases or decreases with the polarization angle, which further deepens the understanding of the split time difference representing shear-wave splitting.
Keywords: shear-wave splitting; Anisotropy; VTI media; Split time difference
Quantitative study on shear-wave splitting of carbonate karst reservoir
Li Na, Li Zhenchun, Huang Jianping, Tian Kun, Kong Xue and Liu Yujin.
(School of Earth Sciences, China Shiyou University (East China), Qingdao 266555)
Abstract: The biggest diagnostic effect of anisotropy is shear-wave splitting. The conventional measurement of shear-wave splitting is the delay time between fast and slow waves and the polarization of fast shear waves. Two measures of shear-wave splitting in seismic anisotropy of stress arrangement reflect the density, width, size, strike and the nature of anisotropic system of cracks. In order to detect the azimuth property of stress-oriented cracks and analyze the variation law of time delay with polarization angle and anisotropic parameters, three-component records of VTI media rotating counterclockwise at different angles are obtained by using staggered grid high-order finite difference combined with PML absorption layer method. The results show that: (1) from the energy point of view, when the polarization angle reaches 45, both fast and slow shear waves have strong energy, which can be used as the best angle to observe shear splitting; (2) At the same time, through the comparative analysis of single waveform and qualitative research, it is found that the delay time decreases with the increase of ε, γ and δ related to qP and qS wave velocities. (3) Under the same intensity, γ has the greatest influence on the delay time and δ is the smallest. The velocity of fast shear wave is only controlled by γ, so we can measure γ by the velocity of fast shear wave, and the velocity of qP wave is only controlled by ε, so we can measure ε by the velocity of qP wave. In addition, when the difference between ε and δ is small, the delay time has no obvious change, on the contrary, the delay time tends to increase or decrease. All these are helpful for us to understand the time delay in shear-wave splitting.
Keywords: shear-wave splitting; Anisotropy; VTI media; time delay
1 Introduction
Anisotropy of the earth's medium is universal. It is a frontier subject in seismology and exploration seismology to study the propagation law and imaging method of seismic waves in anisotropic media. There are many factors and complicated reasons for earthquake anisotropy caused by the actual earth medium. Many geophysicists and seismologists have done a lot of research on the propagation law and formation mechanism of seismic waves in anisotropic media by observing the propagation phenomenon of seismic waves in the earth medium [1 ~ 10], and realized that the earth medium is anisotropic; Shear-wave splitting is the most effective method to diagnose anisotropy. Generally speaking, the causes of seismic anisotropy of underground rocks mainly come from three aspects: inherent anisotropy, fracture-induced anisotropy and long-wave anisotropy.
The mechanism of fracture-induced anisotropy is very complicated. Due to the stress field, cracks, fissures and pores with preferential orientation are formed in rocks, and these cracks, fissures and pores may be filled with fillers such as gas or fluid. The propagation of seismic wave in fractured rock is equivalent to that in homogeneous elastic anisotropic solid. Through theoretical and laboratory research, it is confirmed that most rocks in the earth's crust have directional liquid-filled cracks, which can cause shear-wave splitting widely.
With the fractured carbonate reservoirs in the west gradually becoming the focus of oil exploration, the forward modeling method based on anisotropy has also been greatly developed in recent years. Byun( 1984), Tanimoto( 1987), Chapman( 1989) and others studied ray tracing technology on the basis of Cerveny( 1972), on the premise of high-frequency approximation of wave equation. Mora( 1989), Tsingas et al. (1990) and Igel et al. (1995) studied the forward modeling of seismic waves in anisotropic media by finite difference method. Kosloff( 1989) and Carcione et al. (1992) studied the forward modeling of pseudo-spectral seismic wave field. In China, Professor He and others have studied the forward modeling of anisotropy by using finite difference method, finite element method and Fourier transform method [1; Niu (1994, 1995, 1998) studied the seismic wave field, shear-wave splitting phenomenon and P-wave anisotropy in EDA media by finite element method. (1998) and Dong (1999) have done in-depth research on the physical simulation of anisotropic elastic waves.
Figure 1 Comparison of Wave Propagation in Isotropic and Anisotropic 3D Graphics [1]
For shear-wave splitting's research, Pei [16] used the staggered grid high-order finite difference method to study the shear-wave splitting phenomenon in layered anisotropic media; Wu Songhan et al. [20] designed an anisotropic medium logistics model with vertically oriented cracks, and studied the relationship between the propagation speed and propagation time of split shear waves and the orientation of cracks. Guo Guihong et al. [9] analyzed the relationship between shear-wave splitting time difference, polarization direction and fracture density and orientation by pseudo-spectral method.
The so-called shear-wave splitting means that the shear wave will split into two waves with vertical polarization direction and different ray path speeds in different directions in anisotropic media. The polarization of fast shear wave is consistent with the crack direction, and the polarization of slow shear wave is parallel to the crack arrangement direction. Shear-wave splitting time difference is one of the main parameters to characterize shear-wave splitting.
In this paper, the variation of splitting time difference with polarization angle is studied from the angle of energy. At the same time, different models are established by changing Thomson weak anisotropy parameters, and single channel waveforms are obtained, from which the peak times of fast and slow shear waves are picked up and compared, and the relationship between shear-wave splitting time difference and Thomson parameters is obtained.
Two-dimensional three-component elastic wave equation of 2 TTI medium
X and y are horizontal (parallel to the surface) and z is vertical, along the depth. The VTI (transverse anisotropy) medium with vertical symmetry axis rotates around the X axis to obtain TTI medium (called polarization anisotropy), and the angle between the symmetry axis of TTI medium and the Z axis of the coordinate axis is called polarization angle.
It is necessary to rotate the observation coordinate system to observe the change of shear-wave splitting phenomenon with polarization angle, but the conventional two-dimensional elastic wave numerical simulation method can not observe it after rotation, because the fracture trend simulated by VTI medium is parallel to the Y direction, and the polarization direction of fast shear wave is consistent with the fracture trend; Therefore, in this paper, the two-dimensional three-component method is used to increase the partial derivative of Y direction to X and Z, and simulate the spatial wave field more truly. The two-dimensional three-component uses all elastic parameters except the second row and the second column in the three-dimensional anisotropic elastic constant tensor matrix, and considers the elastic constant c66 of the anisotropic strength of shear waves, which more accurately reflects the shear-wave splitting phenomenon.
Let the velocity vector be v = (VX, vy, vz)', the physical force vector be f = (FX, fy, fz)', the stress vector be (σxx, σzz, σyz, σxz, σxy)', and ρ be the medium density, then the two-dimensional three-component stress-velocity elastic wave equation of TTI medium can be expressed as
Proceedings of the International Conference on Unconventional Oil and Gas Exploration and Development (Qingdao)
Proceedings of the International Conference on Unconventional Oil and Gas Exploration and Development (Qingdao)
In the formula, cij represents the spatial differential operator and the elements in the elastic constant matrix Cx, and the calculation method is as follows. The moment matrix of elastic constant of three-dimensional VTI medium is
Proceedings of the International Conference on Unconventional Oil and Gas Exploration and Development (Qingdao)
The coordinate transformation matrix of rotating θ counterclockwise around the X axis is
Proceedings of the International Conference on Unconventional Oil and Gas Exploration and Development (Qingdao)
Then the tensor matrix expression of the elastic constant after rotation is
Proceedings of the International Conference on Unconventional Oil and Gas Exploration and Development (Qingdao)
3 model trial calculation
Quantitative observation of the influence of polarization angle change from 0 to 90 on shear-wave splitting time difference and energy. Parameter of uniform lateral anisotropy model (azimuth 90): ρ =1000kg/m3.
The number of grid points is 300×300, the grid size DX = DZ = 10m, the focal frequency is 20Hz, the X-direction shear wave source, the focal position (150, 150), and the receiving line: z =1/kloc-0.
3. 1 Study on the variation of shear-wave splitting time difference with polarization angle under different models.
(1) Thomson parameters: VP = 2449.49m/s, vs =1414.214m/s, ε =13, δ = 0./kloc-0.
Figures 2 ~ 4 show the shot records and 500ms wave field snapshots of the X, Y and Z components when the VTI medium rotates 20, 45 and 70 around the X axis in the opposite direction.
Fig. 2 gun record (rotated by 20); Top: X component; Lower left: y component; Bottom right: Z component
Fig. 3 gun record (rotated by 70); Left: x component; Medium: y component; Right: z component
As can be seen from figs. 2 to 4; (1) When the polarization direction of the seismic source forms a certain angle with the symmetry axis of the medium, shear-wave splitting phenomenon will occur, and the fast shear wave (qS 1 wave) along the rupture direction can be clearly seen from the wave field snapshot; (2) From the gun records, we can see the change of energy: with the polarization angle changing from 0 to 90, the fast shear wave gradually increases and the slow shear wave (qS2 wave) gradually decreases, so about 45 is the best angle to observe shear-wave splitting, and the energy of fast and slow shear waves is equivalent; (3) In addition, as can be seen from the gun records, there is little difference in shear-wave splitting time difference at all angles, and there is no obvious increase or decrease.
Fig. 5 is a single channel waveform with x = 250 grid lines, and the peak times of fast and slow shear waves are obtained to quantitatively observe the time difference of shear wave splitting.
It can be seen that with the increase of polarization angle, the first arrival of fast shear wave decreases and the first arrival of slow shear wave increases, which makes the shear-wave splitting time difference increase, and the time difference changes by 39ms, showing an increasing trend; It can be seen from single channel recording that the first break of qP wave decreases with the increase of polarization angle.
Fig. 4 shot point record (top) and wave field snapshot (bottom, t = 500 ms) when rotating 45; Left: x component; Medium: y component; Right: z component
Figure 5
(2) Thomson parameters: VP = 2449.49m/s, VS =1414.214m/s, ε = 0. 1, δ = 0.2, γ = 0.25.
It can be seen from the gun records and 500ms gun records that the energy contrast between fast and slow shear waves is the strongest when the polarization is still around 45.
As can be seen from Figure 6, the first arrivals of fast and slow shear waves are decreasing, and the split time difference tends to decrease as a whole, with the maximum change of 6ms, which is much smaller than that of the previous model. This is because although the anisotropic strength parameters of shear waves have not changed, the parameters connecting longitudinal waves and shear waves have changed, thus affecting the split time difference of shear waves; It can be clearly observed from the single channel waveform that the variation amplitude of the first break with the angle decreases because the anisotropic strength parameter of qP wave becomes smaller.
(3) Thomson parameters: VP = 2449.49m/s, VS =1414.214m/s, ε = 0.05, δ = 0.2, γ = 0.25.
As can be seen from Figure 7, with the increase of the angle, the split time difference gradually decreases; Because γ has not changed, the changing trend of fast shear wave is the same as that in Figure 5(a) and Figure 6(a). The peak time of slow shear wave decreases with the change of polarization angle; In addition, it can be seen from single channel recording that the first break of qP wave decreases with the increase of angle.
Figure 6
Figure 7
By comparing Figure 5(b), Figure 6(b) and Figure 7(b), it can be seen that the first arrival of the fast shear wave is determined by γ, and when γ is constant, the change of the peak time of the fast shear wave is basically unchanged; The first break of qP wave is determined by ε, the first break of slow shear wave is determined by ε and δ * *, and its change with polarization angle depends on ε and δ. When the two parameters are close, the first break of slow shear wave changes slowly; However, when the difference between the two parameters is large, the first arrival of slow shear wave changes obviously, which further affects the trend of split time difference with the increase or decrease of angle. Therefore, the relationship between ε and δ can be measured by the change trend of splitting time difference with polarization angle, and the range of γ can be judged by the first arrival or peak time of fast shear wave.
3.2 When the polarization angle is 45, observe the influence of ε, γ and δ on shear-wave splitting time difference.
Thomson parameters: ρ = 1000kg/m3, VP = 2450m/s, VS = 14 14m/s, ε = 1/3, δ = 1/6.
ε and γ change from 0 to 0.3, and δ changes from -0.3 to 0.3, respectively, and the variation trend of shear-wave splitting time difference with each parameter is observed.
As can be seen from Figure 8, ε increases, shear-wave splitting time difference decreases, and the total amplitude is 38ms；; The change of ε basically does not affect the first arrival of fast shear wave, but the first arrival of slow shear wave decreases gradually. In addition, it can be seen from the single channel waveform diagram that the first arrival of qP wave also decreases gradually, and the change is slow, and the shear wave is large, which verifies that ε is a parameter to characterize the anisotropic strength of qP wave.
As can be seen from Figure 9, with the increase of δ, the splitting time difference increases, and the increasing amplitude is 13ms within 0.3ms, which is far less than the influence of ε on splitting time difference. In addition, from the single channel waveform, it can be seen that δ mainly affects slow shear waves, and the first arrival of fast and slow shear waves increases, while the first arrival of qP wave decreases, but the first arrival of qP wave and fast shear wave changes very little, within 3 ms ..
Figure 8
Figure 9
It can be seen from figure 10 that with the increase of γ, the splitting time difference increases, and the splitting time difference changes to138 ms within 0.3ms; ; In addition, it can be seen from the single channel that the change of γ has a great influence on fast shear waves, while the first break of slow shear waves has little change. It has no effect on qP wave and does not cause the change of first arrival of qP wave.
Figure 10
Figure 1 1 shows the relationship between ε, δ and γ and shear-wave splitting time difference under the same intensity (all 0.1).
Fig. 1 1 The relationship between ε, δ and γ and shear-wave splitting time difference under the same intensity.
From the above figure, it can be found that under the same intensity, γ has the greatest influence on the splitting time difference, because γ represents the anisotropic intensity of shear waves, and the splitting time difference changes gently with ε and δ.
4 conclusion
In this paper, the shear-wave splitting time difference of transversely anisotropic media under different polarization angles is studied by using the two-dimensional three-component staggered grid high-order finite difference method, and the following main understandings are obtained: (1)ε increases and shear-wave splitting time difference decreases; The first arrival of qP wave and shear wave decreases, ε only affects the first arrival of qP wave and slow shear wave, but has little effect on fast shear wave, and its peak time changes within 2ms; (2) shear-wave splitting time difference increases with δ; The first arrival of slow shear wave increases, δ only affects the first arrival of slow shear wave, but has little effect on qP wave and fast shear wave, and its peak value changes within 3ms; (3) shear-wave splitting time difference increases with the increase of γ; The first arrival of fast shear wave increases, γ only affects the first arrival of fast shear wave, and qP wave is not affected. Combining (1) and (2) at the same time, we know that fast shear wave is only affected by γ, so γ can be judged by the velocity of fast shear wave, and qP wave is only controlled by ε, so the value range of ε can be judged by the velocity of qP wave, and the final value range of δ can be determined by the velocity of qP wave and slow shear wave. (4) According to Figure 1 1, under the same intensity, γ has the greatest influence on shear-wave splitting time difference, while ε and δ have a gentle influence on it. When the two values are close, the splitting time difference does not change much with the polarization angle, and may not increase or decrease. When the numerical difference between them is large, it plays a leading role in the change of splitting time difference with polarization angle, affecting the changing trend of splitting time difference, ε decreases splitting time difference with angle and δ increases splitting time difference; (5) From the point of view of energy, the energy contrast between slow and fast shear waves observed around 45 is the strongest, which is the best angle to study shear-wave splitting; The energy of fast shear wave and slow shear wave of X and Z components changes regularly with the change of angle. At 0, only the wave equivalent to slow shear wave is observed, and at 90, only the wave equivalent to fast shear wave is observed. Because the shear wave does not split at 0 and 90, the two waves have the same speed, which is called SV wave and SH wave.
Crampin [3 ~ 5] After years of theoretical research and practice, it has been proved that azimuthal anisotropy is universal, which is often related to cracks and accompanied by shear-wave splitting. For carbonate areas, fractures are closely related to permeability, oil and gas accumulation and migration. Therefore, it is of great significance to study carbonate fractures by using shear-wave splitting. However, because the thickness of the stratum where underground fractures develop is usually small, and the fast and slow shear waves often overlap, it is difficult to extract the split time difference and fracture orientation. In this paper, we only discuss the relationship between split time difference and fracture orientation in homogeneous anisotropic media. For more complex fractured media, it is necessary to combine energy ratio method, waveform feature most similarity method and minimum entropy rotation method [1 1] to determine the fracture time difference, so as to obtain better research results.
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