# Hydraulic Fracturing Shear/Tensile/Compressive Crack Investigation Using Microseismic Data

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## Abstract

**:**

## 1. Introduction

## 2. Method

## 3. Data

## 4. Results

^{−3}m/s and 2.4 × 10

^{−3}m/s, respectively. Therefore, P and S waves are fitted separately during the focal mechanism inversions to ensure that both of these waveforms are equally considered and constrained. For event A11 (Figure 5), the VR values of the DC, GD, and MT inversions are 51%, 73%, and 77%, respectively. From the waveform fitting in Figure 5a–c, the polarities of the synthetic and recorded data are consistent with each other for all three models. For the GD and MT models, the amplitudes of the synthetic and recorded data are relatively close, whereas for the DC model, the amplitudes of the synthetic Z-component S waves are significantly larger than those of the observed data. Moreover, for the three models, the inverted moment magnitudes, the strike, dip, and rake angles of nodal plane F1 and the dip and rake angles of nodal plane F2 are similar (with angle differences of less than 25°), whereas the strike angle of GD nodal plane F2 (256°) is very different from that of the DC and MT results (312° and 293°, respectively). The largest difference between the DC, GD, and MT results is the DC percentages, with values of 100%, 19%, and 39%, respectively. For event C03 (Figure 6), all the VR values of the DC, GD, and MT inversions are larger than 60% (70%, 78%, and 82%, respectively).

- (1)
- The inverted DC or GD fault plane results of different events are similar, the nodal lines of the GD results are very close (along the northeast or southwest direction), and the consistency between MT results is worse than the DC and GD results;
- (2)
- The non-DC mechanisms (represented by the relative proportion of shadow areas in the focal mechanism plots) and DC percentages of the GD and MT results show similar tendencies over time;
- (3)

## 5. Discussion

- The inversion quality (i.e., the goodness of fit between the observed data and synthetic seismograms, represented by the VR value) increases from DC → GD → MT (Figure 4), which is certain because the number of the model parameters increases from DC → GD → MT [46,47]. All the GD and MT results have VR values of ≥60%, whereas only 6 of 32 DC results have VR values in this range. Although the VR values of the MT results are better than those of the GD results, this does not mean that the MT results are certainly better. This is because: (1) the full MT inversion is not as stable as the GD inversions in our numerical tests with the same observation geometry [28] and in previous studies on acoustic emission events [26,48,49]; (2) for most of the 32 events, the difference between the VR values of the GD and MT results is not very large (see Figure 4d–f); and (3) from the GD to MT results in Figure 5 and Figure 6, the main improvement in the synthetic and observed waveform fitting (represented by the VR values) is related to the S/P amplitude ratio, which may be affected by the noise in the data.
- In Figure 5, Figure 6, and Figure 10, the difference between the strike angle of nodal plane F2 (or II) from the GD results and that from the DC and MT results is quite large (>25°), whereas the other inverted parameters using these three models are similar. This may be because most of the inverted slope angles are non-zero (with –36° and –30° for events A11 and C03, respectively), and for a GD source with slope angle $\alpha \ne 0\xb0$, the angle between its two possible nodal lines is not 90° (equal to $90\xb0-\left|\alpha \right|$, where $\left|\alpha \right|$ is the absolute value of $\alpha $; refer to Li et al. [9]). Similar observations can also be found in the nodal lines shown in Figure 7, Figure 8 and Figure 9. Taking event A06 in Figure 7b as an example, we see that its two possible nodal lines are nearly the same. From Table S1, for event A06, the inverted slope angle is –87°, then the angle between its two possible nodal lines is $90\xb0-\left|-87\xb0\right|=3\xb0$, and the inverted strike, dip, and rake angles of the two nodal lines are (214°, 73°, 22°) and (217°, 75°, 25°), respectively. Considering that the GD inversion is stable compared to the MT inversion in numerical tests using the same geometry [28] and the DC inversion quality for event A06 is very poor (with a VR of only –37%), we may draw the conclusion that event A06 is nearly a pure compressive crack occurring on a strike-slip fault with strike, dip, and rake angles of 214°–217°, 73°–75°, and 22°–25°, respectively. During the GD inversion, the non-zero slope angle can help to reduce the inversion uncertainty. The larger the inverted slope angle is, the smaller the angle between the two possible nodal lines (if the slope angle is nearly ±90°, the two possible nodal lines for a GD source are nearly the same [9]). According to the GD results in Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11, the fracture geometry for most of the 32 events corresponds to shear/tensile/compressive strike-slip faulting, with strike angles of 195°–240° and dip angles of 75°–90°. These strike ranges are approximately perpendicular to the direction of the horizontal fracturing well. This is reasonable because during HF stimulations, the fracturing well is usually designed and set to be approximately perpendicular to the direction of the regional minimum principal stress. The inverted strike-slip fault type is also consistent with previous studies showing that strike-slip and dip-slip failures are two representative HF microseismic focal mechanisms [15,50,51].
- From the DC percentage curves in Figure 7, Figure 8 and Figure 9, we see that the maximum difference between the GD and MT results is >60% (in Figure 8d). This is consistent with previous numerical tests using the same geometry, in which the MT inversion shows a maximum deviation of ~60% in terms of DC percentages [28]. According to the GD results, most of the HF cracks have non-negligible tensile/compressive mechanisms, especially in HF stage 1; all the microseismic events occur in the order of opening cracks first and then closing cracks. In this study, we use 32 events (with signal-to-noise ratio ≥ 4) to perform focal mechanism inversion. Future work involving this study will be related to data processing of the microseismic events with signal-to-noise ratio values of 2–4, in order to study the spatial-temporal distribution of shear/tensile/compressive HF cracks and the non-DC fracture growth in detail.

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Illustrations of the (

**a**) double-couple (DC) and (

**b**) general dislocation (GD) models.

**n**and

**[u]**are the fault normal and slip vectors, respectively.

**u**is the shear slip component of the slip vector

_{DC}**[u]**. α is the slope angle [8], i.e., the angle between

**[u]**and

**u**.

_{DC}**Figure 2.**Map showing the locations of the HF site and the monitoring well in the Ordos Basin, China. The squares denote the locations of nearby cities.

**Figure 3.**Geometry of the injection and monitoring wells, locations of the microseismic events, and velocity models. There are three HF stages, each with two fluid injection points (shown as crosses). The monitoring system consists of 12 three-component receivers (shown as grey triangles). Selected events in HF stages 1, 2, and 3 are shown as squares, inverted triangles, and circles, respectively. The total event number is 32, with 11, 11, and 10 events in HF stages 1, 2, and 3, respectively. (

**a**–

**c**) Map and side views. (

**d**) P- and S-wave well log data (dotted lines) and velocities (solid lines).

**Figure 4.**Histograms (

**a**–

**c**) and distributions (

**d**–

**f**) of the VR values for the microseismic focal mechanism inversions in three HF stages with the DC, GD, and MT models. Note that only VR values greater than 50% are shown.

**Figure 5.**Waveform fitting and focal mechanism inversion results for event A11 (location shown in Figure 3a–c). Rows (

**a**–

**c**) indicate the results using the DC, GD, and MT models, respectively. The black and blue lines indicate the observed P and S waveforms (filtered and normalized with respect to those at receiver 5, whose amplitudes are listed in the panels), respectively. The red lines indicate the synthetic data. F1 and F2 (with parameters listed in the order of strike/dip/rake angles) are two fault planes corresponding to the same seismograms.

**Figure 6.**Waveform fitting and focal mechanism inversion results for event C03 (location shown in Figure 3a–c). Rows (

**a**–

**c**) indicate the results using the DC, GD, and MT models, respectively. The black and blue lines indicate the observed P and S waveforms (normalized with respect to those at receiver 8, whose amplitudes are listed in the panels), respectively. The red lines indicate the synthetic data. F1 and F2 (with parameters listed in the order of strike/dip/rake angles) are two fault planes corresponding to the same seismograms.

**Figure 7.**Inverted focal mechanism plots of the 11 events in HF stage 1 (marked as A01–A11) using the (

**a**) DC, (

**b**) GD, and (

**c**) MT models. (

**d**) Variations in the fluid discharge rate and the inverted DC percentages using the GD and MT models.

**Figure 8.**Inverted focal mechanism plots of the 11 events in HF stage 2 (marked as B01–B11) using the (

**a**) DC, (

**b**) GD, and (

**c**) MT models. (

**d**) Variations in the fluid discharge rate and the inverted DC percentages using the GD and MT models.

**Figure 9.**Inverted focal mechanism plots of the 10 events in HF stage 3 (marked as C01–C10) using the (

**a**) DC, (

**b**) GD, and (

**c**) MT models. (

**d**) Variations in the fluid discharge rate and the inverted DC percentages using the GD and MT models.

**Figure 10.**Rose diagrams of the strike, dip, and rake angles of the two inverted nodal planes for the 32 microseismic events. (

**a**–

**c**) Results using the DC, GD, and MT models (blue for the directions and red for the counts of angle values in certain ranges).

**Figure 12.**Distribution of all the GD and MT inversion results in two different source-type plots. The red triangles indicate the GD results (with fixed $\nu $ of 0.25) and the gray dots denote the MT results. (

**a**) The 2-D equal-area projection plot of the fundamental lune [24]. The upper left and lower right boundaries indicate pure tensile and pure compressive mechanisms, respectively. The pure shear (DC) mechanism is located in the center. The coordinates of the boundaries are in the order of $\left(\gamma ,\text{}\delta \right)$, where $\gamma $ and $\delta $ are the longitude ($\gamma \in [-30\xb0,\text{}30\xb0]$) and latitude ($\delta \in [-90\xb0,\text{}90\xb0]$) on the eigenvalue lune that determine the source pattern [44]. (

**b**) The diamond CLVD-ISO percentage plot [45]. The upper right and lower left boundaries indicate pure tensile and pure compressive mechanisms, respectively. The pure shear (DC) mechanism locates in the center.

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**MDPI and ACS Style**

Li, H.; Chang, X.; Hao, J.
Hydraulic Fracturing Shear/Tensile/Compressive Crack Investigation Using Microseismic Data. *Remote Sens.* **2024**, *16*, 1902.
https://0-doi-org.brum.beds.ac.uk/10.3390/rs16111902

**AMA Style**

Li H, Chang X, Hao J.
Hydraulic Fracturing Shear/Tensile/Compressive Crack Investigation Using Microseismic Data. *Remote Sensing*. 2024; 16(11):1902.
https://0-doi-org.brum.beds.ac.uk/10.3390/rs16111902

**Chicago/Turabian Style**

Li, Han, Xu Chang, and Jinlai Hao.
2024. "Hydraulic Fracturing Shear/Tensile/Compressive Crack Investigation Using Microseismic Data" *Remote Sensing* 16, no. 11: 1902.
https://0-doi-org.brum.beds.ac.uk/10.3390/rs16111902