# Impact of Shale Anisotropy on Seismic Wavefield

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Forward Modeling for 3D TTI Model

#### 2.2. Quantitative Evaluation of the Shale Anisotropy’s Impact

- Set the parametric medium model M
_{0}(without anisotropy) according to the geological characteristics of shale reservoirs or the actual oilfield models. Add three sets of different anisotropic parameters to the shale layer of model M_{0}and establish three different medium models with shale anisotropy, i.e., M_{E}($\epsilon $ = 0.25, $\delta $ = 0), M_{D}($\epsilon $ = 0, $\delta $ = 0.25), and M_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25). The parameters of model M_{ED}are reasonably geologically chosen from several shale anisotropy studies in China ([9,17]), while the other two models (M_{E}and M_{D}) are built based on the variable-controlling approach, for the purpose of exploring the impact of different anisotropy parameters; - Use the forward modeling method to calculate the elastic wavefields of four medium models (${S}_{REF}$ for model M
_{0}, ${S}_{E}$ for model M_{E}, ${S}_{D}$ for model M_{D}, and ${S}_{ED}$ for model M_{ED}); - Compare the seismic wavefields with each other and calculate the envelope misfit EM and the phase misfit PM of the wavefield ${S}_{E}$/${S}_{D}$/${S}_{ED}$ from ${S}_{REF}$. Evaluate the impact of shale anisotropy on elastic seismic wave response.

## 3. Evaluation of Simulation Models

#### 3.1. Horizontal Layered VTI Model

#### 3.1.1. Parameters and Wavefield Data

_{0}(without anisotropy). We added three groups of anisotropic parameters to the shale layer and built up three different anisotropic models, i.e., M

_{E}($\epsilon $ = 0.25, $\delta $ = 0), M

_{D}($\epsilon $ = 0, $\delta $ = 0.25), and M

_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25).

_{0}/M

_{E}/M

_{D}/M

_{ED}, the seismic waveform records of 402 geophones are respectively synthesized (${S}_{REF}/{S}_{E}$/${S}_{D}$/${S}_{ED}$). The three-component waveforms of model M

_{0}, namely ${S}_{REF}$, is shown in Figure 3a–c. Comparing the X-, Y-, and Z-component waveforms of each detector, we can see that the X- and Y-component records of the two survey lines (line 1: No.1~201 and line 2: No.202~402) are different, while the Z-component records are entirely consistent. The reason for this is that the horizontal coordinates of the two survey lines are different (line 1 is arranged along the X direction, and line 2 is along the Y direction). Therefore, for an explosive seismic source, the received X- and Y-waveforms are different, while the Z-component records of two lines are the same, because the symmetry axis of the medium is along the vertical direction (VTI medium).

#### 3.1.2. Effect of Anisotropy on Different Seismic Phases

_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25) and M

_{0}($\epsilon $ = 0, $\delta $ = 0).

- Direct P wave. The first seismic phases (direct P wave) of two models are exactly the same. From its propagation path (Figure 3d), we can see that the direct P wave traveled from the seismic source to the detector through the surface, so it is not affected by the shale anisotropy.
- Transmitted and reflected P-P-P-P wave. The fourth seismic phases (P-P-P-P wave, its propagation path is shown in Figure 3d) are totally different. When adding anisotropy to the shale layer, the velocities of P-waves along different directions propagating in it are changed and not the same. So this seismic wave’s arrival time, amplitude and phase are all influenced by shale anisotropy.
- Reflected P-P wave and P-SV wave. The arrival time of the second and third phases (reflected P-P and P-SV waves, their paths are shown in Figure 3d) is the same, while their amplitudes are different. The reasons for this are probably because:
- Arrival time. These two waves are both reflected at the interface of the first layer and the shale layer. The first layer is isotropic, so we can use the Snell’s law to analyze the reflection:$$\frac{{v}_{P1}}{\mathrm{sin}{\theta}_{1}}=\frac{{v}_{S1}}{\mathrm{sin}{\varphi}_{1}},$$
- Amplitude. The amplitude of reflected P and SV waves can be evaluated using the anisotropic reflectivity and transmissivity calculator code by Malehmir and Schmitt [19]. According to the observation system and source location (Figure 2), the maximum incident angle ${\theta}_{1}$ of P wave between the first and second (shale) layer is about 32°. Then, we set ${\theta}_{1}$ from 0 to 35° and calculate the reflection coefficients of reflected P and SV waves. The differences of reflection coefficients with and without anisotropy are shown in Figure 5b. We can find that when adding anisotropy to the VTI model (Figure 2), the reflection coefficients of reflected P and SV waves are both changed. Considering that the propagation paths of these two waves are unchanged, so the Z-component amplitudes of reflected P-P and P-SV waves are influenced by the shale anisotropy.

#### 3.1.3. Amplitude and Phase Misfit by Anisotropy

_{0}/M

_{E}/M

_{D}/M

_{ED}($\epsilon /\delta $ are 0/0, 0.25/0, 0/0.25, and 0.25/0.25). Based on Equations (4) and (5), we calculated the wavefields’ amplitude deviation EM and phase deviation PM of the anisotropic model M

_{E}/M

_{D}/M

_{ED}from the model M

_{0}(without anisotropy). The results are shown in Figure 6. Here, the normalized epicentral distance (i.e., epicentral distance divided by wavelength) is used. From Figure 6, we can see the following points:

- The amplitude deviation EM and phase deviation PM of the two survey lines in Z-component are significantly larger than their X- and Y-components, which indicates that anisotropy has a more significant influence on the vertical component. It is speculated that the reason may be that the propagation distance of the seismic wave in the vertical direction is larger than that in the horizontal direction and the medium model’s symmetric axis is along the vertical direction.
- The maximum EM of the two survey lines in Z-component is greater than 1, which indicates that the waveform’s amplitude will be significantly affected by the shale anisotropy. In actual seismic exploration, the amplitude is of great importance to the inversion of reservoir parameters, so ignoring anisotropy may lead to errors in reservoir characterization.
- The Z-component phase deviation PM of the two survey lines reaches 0.4. As is mentioned above, if PM is 1, the polarities of the two signals are completely opposite. So this means that the waveforms’ phase morphology is also largely changed due to anisotropy. The inaccurate phase may lead to the low resolution of migration imaging results, which also affects the processing and interpretation of actual exploration seismic data.
- The amplitude deviation EM and phase deviation PM of X/Y/Z components on two sides of the source are symmetrical, which is caused by the symmetry axis’s verticality of the VTI model. Moreover, the EM all increases with the increase of epicentral distance (offset), while the PM increases first and then decreases. This may because the maximum value of the difference in phase is the odd multiples of π. Therefore, if the phase’s difference gradually increases from 0 to 2π, the difference in waveform’s phase will become bigger first and then smaller, and the calculated PM will also increase first and then decrease correspondingly.
- In most of the results, the deviations of the model M
_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25) are relatively larger than the other two models M_{E}($\epsilon $ = 0.25, $\delta $ = 0) and M_{D}($\epsilon $ = 0, $\delta $ = 0.25).

#### 3.2. Curved Layered TTI Model

_{0}($\epsilon $ = 0, $\delta $ = 0), M

_{E}($\epsilon $ = 0.25, $\delta $ = 0), M

_{D}($\epsilon $ = 0, $\delta $ = 0.25), and M

_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25).

_{0}, M

_{E}, M

_{D}, and M

_{ED}. The comparison of Z-component wavefields with and without anisotropy in the first survey line (geophone No.1–No.201) is shown in Figure 8, and the waveforms of eight different epicentral distance detectors (−1000/−600/−200/+200/+400/+1000 m, the positive and the negative sign indicate that the detectors are on left and right sides of the seismic source, respectively) are shown in Figure 9. From Figure 8 and Figure 9, it can be seen that before and after anisotropy is added, except the direct P wave is not affected, the subsequent phases are all affected by different degrees. When adding shale anisotropy, the amplitude of reflected P-P wave (the second phase) is increased. The arrival time, phase, and amplitude of the other phases (P-SV, P-P-P-P, multiple waves, etc.) are all changed due to the shale anisotropy.

_{E}/M

_{D}/M

_{ED}($\epsilon $/$\delta $ are 0.25/0, 0/0.25, 0.25/0.25) from the model M

_{0}(without anisotropy). The results are shown in Figure 10. Here, the deviation results of Z- and X-component are from line 1, while the results of Y-component are from line 2. From Figure 10, we can find that:

- Same as the VTI model, the EM and PM of Z-component are still larger than that of X- and Y- components. The maximum EM is still greater than one, and the maximum PM is about 0.5 (relatively large; if PM is 1, the polarities of all phases of the two signals are entirely opposite).
- Unlike the VTI model, with the increase of epicentral distance, the variation trend of EM and PM are complicated. Moreover, the EM and PM of Y-component are symmetrical, while the X- and Z- components are not. The reasons are probably because the shape and structure of TTI model are complex, and its symmetry axis is not along the vertical direction. These phenomena prove that the impact of shale anisotropy relies heavily on the model.
- In most of the results, the deviations of models M
_{ED}, M_{E}, and M_{D}from M_{0}are close to each other. This indicates that the impact of different anisotropic parameters on the wavefield is complicated in the curved TTI model, and the influence strength of each parameter cannot be determined simply as the horizontal layered VTI model.

## 4. Evaluation of JY Depression Model

_{0}($\epsilon $ = 0, $\delta $ = 0), M

_{E}($\epsilon $ = 0.25, $\delta $ = 0), M

_{D}($\epsilon $ = 0, $\delta $ = 0.25), and M

_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25). The grid number of the model is 201 × 201 × 201 with spatial size 10 × 10 × 10 m and the time sampling interval is 0.5 ms. The explosive source is located in the center of the surface (1000, 1000, 0 m) and the source time function is Ricker wavelet (20 Hz).

_{0}/M

_{E}/M

_{D}/M

_{ED}, with different shale anisotropy), the seismic waveform records of each detector are forward simulated, respectively. Figure 12 shows the comparison of the Z-component wavefield of line 1 (trace numbers No.1–No.201, Figure 11) with and without the shale anisotropy. Figure 13 illustrates the comparison of Z-component waveforms of eight detectors (with different epicentral distances).

_{E}/M

_{D}/M

_{ED}from the model M

_{0}(without anisotropy). Figure 14 illustrates the calculation results. Here, the deviation results of Z- and X- components are still from the first survey line, while the Y-component results are from the second survey line (Figure 11). From Figure 14, we can find that:

- Similar to VTI and TTI model, the EM and PM of Z-component are still significantly larger than those of the X- and Y- horizontal components. The maximum EM is greater than one and the maximum PM reaches up to 0.5, which indicates that the impacts of anisotropy on the amplitude and phase are remarkable.
- Unlike the VTI and TTI model, for the JY model, the variation of EM and PM in the X- and Z-component with the epicentral distance (offset) is complicated, while the EM and PM of Y-component gets bigger with the increase of the epicentral distance.
- Same as TTI model but different from VTI model, for the JY model, the deviations of M
_{ED}($\epsilon $ = 0.25, $\delta $ = 0.25)/M_{E}($\epsilon $ = 0.25, $\delta $ = 0)/M_{D}($\epsilon $ = 0, $\delta $ = 0.25) are close to each other. This illustrates that the impact of different anisotropic parameters on the wavefield is complicated and needs further study.

## 5. Discussion and Conclusions

_{E}/M

_{D}/M

_{ED}, whose $\epsilon /\delta $ are 0.25/0, 0/0.25, and 0.25/0.25, respectively). For the VTI model, the deviations of M

_{ED}from M

_{0}(without anisotropy) are the largest, while for the other two models (TTI and JY model), the deviations of M

_{E}/M

_{D}/M

_{ED}are about at the same level.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Staggered-Grid Finite-Difference Algorithm

**Figure A1.**Schematic diagram of the staggered-grid finite-difference method. (

**a**) Staggered grids in time; (

**b**) staggered grids in space, $v$ is the velocity and $T$ is the stress, subscript 1 and 3 refer to the X and Z direction of space.

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**Figure 1.**The flow chart of the proposed method for the analysis of anisotropy effects. The procedure of this method starts with adding anisotropy to the medium model, followed by the seismic wavefield forward modeling and quantitative evaluation.

**Figure 2.**Multi-layered VTI model, source, and observation system. The red star is the source; the blue dots are the detectors distributed on two survey lines (402 geophones in total, with 10 m spacing).

**Figure 3.**Three-component seismic wavefield of the M

_{0}model and corresponding wave propagation diagrams of four seismic phases. (

**a**)/(

**b**)/(

**c**) are the geophones’ X/Y/Z waveform records, respectively, (

**d**) indicates the seismic wave propagation paths corresponding to each phase, with ➀ direct P wave, ➁ reflected P-P wave, ➂ reflected P-SV wave, and ➃ P-P-P-P wave.

**Figure 4.**Comparison of Z-component waveforms from model M

_{ED}and (with/without anisotropy, VTI). (

**a**)/(

**b**)/(

**c**)/(

**d**) are waveforms of geophones No.1/21/41/61 (with epicentral distance 1000/800/600/400 m), respectively. Red indicates seismic waveforms of M

_{0}(without anisotropy); blue indicates seismic waveforms from M

_{ED}(with anisotropy).

**Figure 5.**Schematic diagram and coefficients’ differences of reflected waves at the interface. (

**a**) Reflection at the interface between first and second (shale) layer in the VTI model (Figure 2). ${\mathsf{\theta}}_{1}$ and ${\mathsf{\varphi}}_{1}$ are the angles of P and SV waves, respectively. (

**b**) Reflection coefficients’ differences of models with and without anisotropy (M

_{ED}and M

_{0}). Solid and dash line indicates reflected P and SV waves, respectively.

**Figure 6.**Envelope and phase misfit of detectors’ three-component waveforms (VTI model). The blue/green/red lines respectively represent the waveforms’ deviation curve of M

_{E}($\epsilon $= 0.25, $\delta $= 0)/M

_{D}($\epsilon $= 0, $\delta $= 0.25)/M

_{ED}($\epsilon $= 0.25, $\delta $ = 0.25) with respect to M

_{0}($\epsilon $= 0, $\delta $ = 0), and the horizontal axis is the normalized epicentral distance (epicentral distance divided by wavelength) of a detector from the seismic source, the sign indicates that the detectors are located on two sides of the source (positive along X/Y axis direction). (

**a**,

**b**) are the envelope and phase misfit recorded by Z-component of line 1, (

**c**,

**d**) are the X-component’s deviations of line 1, (

**e**,

**f**) are the deviations recorded by Y-component of line 2.

**Figure 7.**Curved layered TTI model, source, and observation system. The red star is the source; the blue dots are the detectors distributed on two survey lines (402 detectors in total, with 10 m spacing).

**Figure 8.**Comparison of Z-component waveforms in line 1 with and without the shale anisotropy (TTI model). (

**a**) is the Z-component wavefield of model M

_{0}(without anisotropy), (

**b**) is the Z-component wavefield of model M

_{ED}(with anisotropy), and (

**c**) is the residual wavefield for (

**a**) and (

**b**).

**Figure 9.**Comparison of Z-component waveforms from model M

_{ED}and M

_{0}(with/without anisotropy, TTI). (

**a**)–(

**f**) are waveform records of geophones No.1/41/81/121/161/201 (with epicentral distance −1000/−600/−200/+200/+600/+1000 m, the sign indicates that the detectors are located on two sides of the source, positive along X-axis direction). Red indicates synthetic waveforms from the model M

_{0}(without anisotropy); blue indicates seismic waveforms from the model M

_{ED}(with shale anisotropy).

**Figure 10.**Envelope misfit and phase misfit of detectors’ three-component waveforms (TTI model). The meanings of each line and axis are similar to Figure 6.

**Figure 11.**JY depression model, source, and observation system. The red star is the source; the blue dots are the detectors distributed on two survey lines (402 detectors in total, with 10 m spacing).

**Figure 12.**Comparison of Z-component waveforms in line 1 with and without the shale anisotropy (JY model). (

**a**) is the Z-component wavefield of model M

_{0}(without anisotropy), (

**b**) is the Z-component wavefield of model M

_{ED}(with anisotropy), and (

**c**) is the residual wavefield for (

**a**) and (

**b**).

**Figure 13.**Comparison of Z-component waveforms from model M

_{ED}and M

_{0}(with/without anisotropy, JY depression model). (

**a**)–(

**f**) are waveform records of geophones No.1/41/81/121/161/201 (with epicentral distance −1000/−600/−200/+200/+600/+1000 m, the sign indicates that the detectors are located on two sides of the source, positive along X-axis direction). Red indicates synthetic waveforms from model M

_{0}(without anisotropy); blue indicates seismic waveforms from model M

_{ED}(with shale anisotropy).

**Figure 14.**Envelope misfit and phase misfit of detectors’ three-component waveforms (JY model). The meanings of each line and axis are similar to Figure 6.

Layer | Depth (m) | V_{P} (m/s) | V_{S} (m/s) | Density (g/cm^{3}) |
---|---|---|---|---|

1 | 0~800 | 3000 | 1700 | 2.0 |

2 | 800~1500 | 3500 | 2000 | 2.3 |

3 | 1500~2000 | 4000 | 2300 | 2.4 |

Layer | Depth (m) | Thickness (m) | V_{P} (m/s) | V_{S} (m/s) | Density (g/cm^{3}) |
---|---|---|---|---|---|

1 | 0 | 700–900 | 3000 | 1700 | 2.0 |

2 | 800 | 500 | 3500 | 2000 | 2.3 |

3 | 1500 | 600–800 | 4000 | 2300 | 2.4 |

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## Share and Cite

**MDPI and ACS Style**

Li, H.; Liu, X.; Chang, X.; Wu, R.; Liu, J.
Impact of Shale Anisotropy on Seismic Wavefield. *Energies* **2019**, *12*, 4412.
https://doi.org/10.3390/en12234412

**AMA Style**

Li H, Liu X, Chang X, Wu R, Liu J.
Impact of Shale Anisotropy on Seismic Wavefield. *Energies*. 2019; 12(23):4412.
https://doi.org/10.3390/en12234412

**Chicago/Turabian Style**

Li, Han, Xiwu Liu, Xu Chang, Ruyue Wu, and Jiong Liu.
2019. "Impact of Shale Anisotropy on Seismic Wavefield" *Energies* 12, no. 23: 4412.
https://doi.org/10.3390/en12234412