Micro-seismic monitoring using sparse planar array and a weak signal enhancement method

Abstract

Traditional ground micro-seismic monitoring is performed by laying long survey lines. This is expensive and difficult to implement in complex mountainous areas and deep marine shale gas reservoirs in China. To address these challenges, this study proposes a ground micro-seismic monitoring method using a sparse planar array that offers greater flexibility in implementation. This study presents a weak signal enhancement method based on a broadband-array adaptive beamforming algorithm to improve the signal-to-noise ratio (SNR) of micro-seismic data collected by sparse planar arrays and to suppress coherent noise. The proposed method involves establishing a signal model for a broadband planar array, estimating the direction of arrival (DOA) of broadband signals using a grid search method, and setting constraint conditions and objective functions based on the DOA results. The optimal weight vector is then calculated by solving the objective function to obtain the desired signal and suppress noise. This study demonstrates that the proposed method effectively improved the SNR and suppressed coherent noise in synthetic and real data. It also highlights the effectiveness of the sparse planar array as a ground micro-seismic monitoring method and the adaptive broadband beamforming method as a practical weak signal enhancement technology.

1. Introduction

Micro-seismic is a method for evaluating the effectiveness of fracturing modifications. Studies on micro-seismic monitoring methods have been conducted by scholars at home and abroad, mainly including fracture simulation methods (Liu et al.2003; Zhang 2010), intelligent micro-seismic event identification methods (Liu et al.2021; Zhang et al.2022), event localization methods (Anikiev et al.2021), and the influence of formation anisotropy and fracturing processes on formation velocity models, micro-seismic event identification and localization results (Grechka et al.2011; Zhang et al.2013; Wang et al.2022; Zhang et al.2014), and other aspects.

In hydraulic fracturing, micro-seismic waves are emitted by rock fractures with magnitudes that are typically weak, on the order of −3 to −1 on the Richter scale (Maxwell et al.2006). Improving the signal-to-noise ratio (SNR) of micro-seismic data and enhancing event recognition ability are critical goals of micro-seismic monitoring. Deep marine shale gas reservoirs in South China are known for their challenging conditions, such as deep burial and complicated surface, which pose substantial obstacles to ground micro-seismic monitoring. The micro-seismic waves in these reservoirs are too weak to detect because the seismic waves need to travel a relatively long distance from the target stratum to the ground. Implementing a surface acquisition system is challenging because of the poor ground conditions. In addition, the SNR of micro-seismic data is typically relatively low owing to ground noise, making it difficult to accurately detect micro-seismic events and resulting in larger event location errors.

Surface-based seismic arrays have been successfully implemented in numerous fracture-monitoring projects (Lakings et al.2006; Duncan & Lakings 2006; Abbott et al.2007; Eisner et al.2008; Williams-Stroud 2008; Hulsey et al.2009). In geometries such as the star-shaped layout, the array generally extends 4–6 km horizontally (Duncan & Lakings 2006). However, survey lines need to be transformed in the presence of obstacles, such as rivers, roads, valleys, and villages. Micro-seismic data are often affected by noise from fracturing construction because the survey lines are located at the well site. Consequently, crew members face difficulties in implementing these geometries under complex ground conditions, and the SNR of the micro-seismic data remains relatively low.

To address the challenges of micro-seismic monitoring in China's deep marine shale gas reservoirs, a honeycomb-shaped acquisition system has been proposed inspired by phased-array radar receiver systems and the distribution of wireless communication base stations.

In recent years, considerable research effort has been devoted to improving the SNR of micro-seismic data. Zhu (2007) proposed a multichannel cross-correlation filtering method and Eisner et al.2008 introduced a matched filtering method for recognizing micro-seismic data. Zhang & Baan (2019a) proposed micro-seismic signal reconstruction using block matching with a novel matching criterion. Song et al. (2009) applied the Kalman filtering algorithm to suppress noise and Yu (2014) proposed a micro-seismic noise suppression method based on an improved wavelet transform. Liu (2013) proposed an improved adjacent cross-correlation method to suppress ground micro-seismic noise. Jiang et al. (2012) suggested an adaptive threshold denoising method based on a curvelet transform to improve the SNR of ground micro-seismic data. Song et al. (2013) introduced an adaptive algorithm for fourth order cumulants, based on a Bayesian framework, to suppress noise. Hu (2013) and Iqbal et al. (2016) proposed micro-seismic denoising methods based on SVD. Chen et al. (2015), Li et al. (2016, 2016), and Zhou et al. (2018) proposed methods for low-frequency noise suppression based on mathematical morphology and multiscale morphology for weak signal detection in micro-seismic monitoring. Chen et al. (2018) proposed a denoising technique based on a local projection algorithm to enhance the SNR and applied it to field micro-seismic data. Li et al. (2018) presented a new algorithm for micro-seismic denoising based on an empirical wavelet. The application indicated that this method performed more successfully than CEEMD, the db5 wavelet, and SWT in retaining detailed information and improving the SNR of the reconstruction signal. Li et al. (2018) proposed micro-seismic SNR enhancement through a strip-matching shearlet transform. Zhang & Baan (2019b) introduced a method for micro-seismic data noise attenuation using supervised deep learning with noisy images. However, these methods are predominantly based on mathematical manipulation and are mainly designed for ground micro-seismic monitoring data acquired by long survey lines. This makes them unsuitable for ground monitoring of sparse arrays.

Adaptive beamforming is a signal-processing technique commonly used in fields such as sonar, radar, and radio astronomy to enhance the desired signals and suppress noise. The primary objective is to preserve signals arriving from a specific direction and attenuate coherent noise from other directions (Zhang et al.2010; Zhang & Wang 2015).

This technology has also been successfully applied to seismic data processing, in which beamforming is primarily studied for multiple attenuation and SNR enhancement (Hu et al.2002; Hong et al.2003; Panea et al.2005; Panea & Drijkoningen 2006; Ogah & Chinedu 2012). Hu (1995) provided a more accurate and detailed description of the adaptive minimum variance unbiased (MVU) beamforming wave field decomposition. This was used by Hu & White (1998) to introduce a robust multiple-suppression method using MVU beamforming. Hu et al. (2002) demonstrated the application of multiple attenuations onshore and offshore in China. Hong et al. (2003) introduced a 3D beamforming approach to eliminate multiple sets of 3D seismic data effectively. For low-SNR seismic data, Hong et al. (2004) proposed an optimal beamforming method to attenuate multiples, which was more effective than f-k and Radon transformations. Panea & Drijkoningen (2006) proposed a minimum variance distortion-less response beamformer and applied it to events with low apparent velocity. Özbek (2000a, 2000b) proposed an adaptive beamforming noise suppression method similar to an adaptive FK filter to enhance the SNR. Beamforming has been used to extract useful information from noisy seismic refraction data (Ogah & Chinedu 2012), and Bakulin et al. (2017) used a nonlinear beamforming algorithm for pre-stack data enhancement to suppress strong near-surface scattering. Sun et al. (2022) proposed a 2 + 2 + 1 method for estimating local travel time operators using nonlinear beamforming technology.

In this study, we proposed a micro-seismic ground monitoring system specifically designed for deep marine shale reservoirs. To improve the detection ability of weak micro-seismic events, we incorporated adaptive beamforming technology. This was conducted to reduce the complexity of broadband signal processing and develop a signal model and robust DOA estimation algorithm for a broadband planar array. Synthetic and actual data were used to evaluate the performance of the proposed system. Our results have indicated that a micro-seismic monitoring system using a sparse planar array is well-suited for China's deep marine shale gas reservoirs.

2. Methods

2.1. Micro-seismic monitoring using sparse planar array

Three common geometries with different shapes for micro-seismic ground monitoring are shown in Fig. 1. In Fig. 1, the blue and red lines are survey lines and well trajectory, respectively. Both typically involve long survey lines with up to 1500 geophones or more, requiring substantial time and human capacity to implement the geometric layout. Consequently, these geometries are expensive and difficult to implement in complex mountainous areas, particularly in China's deep marine shale gas reservoirs.

The sparse planar-array micro-seismic monitoring system is shown in Fig. 2. As shown in Fig. 2a, the monitoring region consists of 41 independently distributed planar arrays. The red line is the trajectory of Well D to be fractured. Each planar array was hexagonal in shape and consisted of 37 geophones, as shown in Fig. 2b. Planar arrays are typically placed in areas with relatively flat terrain and minimal noise pollution. Therefore, the sparse planar-array monitoring method offers the advantage of a flexible construction. Meanwhile, compared with the traditional monitoring geometry, this method is economical as fewer geophones and manpower are used. This makes it a suitable and more economical option for monitoring China's deep-water shale gas reservoirs, especially in challenging mountainous areas.

2.2. Signal model for the broadband planar array

The signal model is essential for array signal processing, in which the signal received by the array is usually expressed as the product of the direction matrix and signal source matrix. In radar array signal processing, a narrowband signal model is often used, in which a phase shift is usually used instead of a time shift to obtain the array signal model. A narrowband signal is defined as a signal center frequency-to-bandwidth ratio >10 (Zhang et al.2010). However, the seismic records do not follow the narrowband hypothesis. Therefore, it is necessary to establish a broadband-array signal model for seismic processing.

Compared with the deep buried depth of the target layer, each planar array can be approximately regarded as a point. Each effective signal arriving at the detector is approximately perpendicular to the ground. The coordinate system was set up as shown in Fig. 3. Assuming that a signal is incident on a planar array with a fixed inclination angle θ and azimuth angle |$\varphi$|⁠, the arrival time of the signal received by the ith geophone in the planar array is given by Zhang et al. (2010)

where |${t}_i$| is the travel time of the P-wave; x_i, y_i, and z_i are the coordinates of the ith geophone; and v is the velocity of the P-wave.

In Fig. 2b, the origin of the coordinate system was set as the reference geophone. The signal arrival time difference between the reference geophone and the ith geophone was calculated using Equation (1). The direction vector of the kth incident signal of frequency f can be obtained as follows (Harry L. Van Trees 2002):

where |$\omega = 2\pi f$|⁠, and M is the number of detectors in the hexagonal array. Δt_i denotes the travel time difference between the ith and reference geophones. Assuming a total of K incident signals incident into the planar array at inclination θ_k and azimuth φ_k (k = 1,2, … K), the signals observed from a planar array consisting of M (M = 37) detectors are shown in Equation (3) (Hu 1995):

where x_i(f), S_i(f), and n_i(f) denote the received signal, incident signal, and random noise of the ith geophone, respectively. The desired signal, that is, the beamforming output y(f) for the broadband array in the frequency domain, is calculated by multiplying the weighted vector by the observed signal. This shows that the weighted vector w(f) is the key to beamforming:

2.3. Adaptive planar-array beamforming

The P-wave is the desired signal for micro-seismic monitoring, which is approximately vertically incident on the surface array, and the incident angle is set to |${\theta }_d$|⁠. The ground coherent noise was almost horizontally incident on the planar array with an angle of incidence of |${\theta }_{noise}$|⁠. Owing to the pronounced difference between |${\theta }_d$| and |${\theta }_{noise}$|⁠, the constraint conditions were set as follows (Hu 1995):

To facilitate analysis, Equation (5) can be written in matrix form as:

where |$C = [\vec{a}({\theta }_d),\vec{a}({\theta }_{noise})]$|⁠, |$F = [I,0]$|⁠.

Under these constraints, the weighted vector (w) should minimize the beamforming output power.

where R is the covariance matrix of the observed data, and H is the transpose transform. The Lagrange multiplier is used to obtain the optimal weighted vector as follows:

where C^H denotes the transpose transformation of C. The effective signal is finally extracted using Equations (4) and (8). A flowchart of the complete method is presented in Fig. 4.

2.4. Direction of arrival (DOA) estimation for planar arrays

The key to adaptive beamforming technology is the design constraints (Equation (5)). In addition, the incident angle of the coherent noise and desired signal should be known. The accuracy of adaptive beamforming technology predominantly depends on accurate estimation of the DOA, which involves the identification of the incident angles of the coherent noise and desired signals. However, the DOA estimation of planar arrays is complex and unstable, and the calculation results are easily affected by the SNR. Therefore, it is not suitable for micro-seismic data with low SNR acquired by a sparse planar array. To obtain a reliable DOA estimation, we proposed an azimuth and inclination estimation method using lattice search.

In micro-seismic monitoring, the identification of micro-seismic events is typically performed on NMO-corrected gathers, where the P-wave event appears nearly horizontal. Meanwhile, coherent noise is approximately horizontally incident on the planar array, resulting in a non-straight NMO-corrected event. Therefore, the angles of incidence of the P-wave and coherent noise were significantly different. Therefore, angular diversity was used to suppress the coherent noise.

We perform a detailed search over the entire solution space (θ: −180°–180°, φ: −180°–180°) at an 1° × 1° interval to calculate the DOA on NMO-corrected recordings. For each attempted solution, we calculated the time difference between adjacent channels and corrected it to obtain the superposition energy (Equation (9)). The direction spectrum is obtained by traversing the entire solution space, where the local maximum represents the possible DOA of the signal.

where |${x}_m({t}_{mn} - {\tau }_m(\theta ,\varphi ))$| is the time-delayed signal of the mth receiver, |${\tau }_m(\theta ,\varphi )$| is the time delay of the mth receiver calculated using Equation (1), M and N are the number of receivers and time-domain sample points, respectively.

3. Model test

3.1. DOA estimation

To evaluate the effectiveness of DOA estimation for a hexagonal array, we conducted tests using noise-free and noisy models. The geometry and coordinate system in the test are shown in Fig. 2b. The distance between adjacent receivers in the x- and y-directions was 20 m. The sampling interval was 1 ms, and the P-wave velocity was 2000 m s⁻¹. If one effective signal and two coherent noise signals were incident on a planar array, the desired signal was incident perpendicularly to the planar array at an angle of 0°. The azimuth of interference signal is −5° and 10°, respectively, and the inclination is −20° and 20°, respectively, with the normal direction of alignment being positive in the counterclockwise direction. Based on the angular incidence information, the arrival time of each signal was calculated using Equation (1). Based on convolution theory, the synthetic record was calculated and is shown in Fig. 5a. The DOA spectrum obtained using the lattice search algorithm is shown in Fig. 5b. When the desired signal arrives at 0°, it shows a strong energy line in the DOA spectrum, whereas regular interference shows a strong energy cluster in the DOA spectrum. The DOA of the incident signal can be obtained by calculating the extreme values in the region.

In the following section, we evaluated the robustness of the DOA estimation algorithm in the presence of noise. Random noise was added to the synthetic data as shown in Fig. 6a to achieve an SNR of 1. The DOA spectrum for the noisy data was calculated using a lattice search algorithm, and the results are shown in Fig. 6b. The results indicate that when the SNR is one, the lattice search algorithm can accurately estimate the DOA, demonstrating its robustness as a DOA estimation method.

3.2. Adaptive planar-array beamforming

Based on results from the DOA estimation, setting the constraint conditions in equation (5), and solving equation (7), the optimal weight vector was obtained. The spatial response spectrum of the optimal weight vector is shown in Fig. 7. The algorithm produces a high gain in the direction of the desired incidence, while producing a pronounced null response in the direction of the noise incidence.

Using the adaptive beamforming filter described, synthetic data without (Fig. 5a) or with random noise (Fig. 6a) were subjected to adaptive beamforming processing. The results of this process were compared and analyzed using the τ-p transform. Figure 8a shows the synthetic data without random noise. Figure 8b and c are data after applying adaptive beamforming and τ-p transform noise suppression to Fig. 8a, respectively. Figure 8b and c show that both methods effectively suppress regular noise. However, in Fig. 8c, there is a faint indication of the coherent axis of regular noise. Figure 8d shows the single-channel waveform recordings after applying both methods for noise reduction. The graph shows that in the single-channel record after adaptive beamforming processing, the energy of the regular noise around 0.4 and 0.8 s is weaker compared to the τ-p transform method. Figure 8e and f are the τ-p transformation spectra shown in Fig. 8b and d, respectively. In Fig. 8e, only the energy cluster of the desired signal (near 0.2 s) can be observed. Meanwhile, in Fig. 8f, in addition to the energy cluster of the desired signal, two energy clusters can be seen near the regular noise at 0.4 and 0.8 s. Comparative analysis indicates that the residual energy of regular noise in the adaptive beamforming processing is weaker than that of the τ-p transform.

Figure 9a shows the synthetic data with random noise. Figure 9b and c are the seismic records after applying adaptive beamforming and τ-p transform noise suppression to Fig. 9a, respectively. Comparing Fig. 9b to a, it shows that the regular noise was effectively suppressed, and the SNR of the seismic record significantly improved. As shown in Fig. 9c, regular noise was also suppressed. However, some residual random noise remains throughout the profile. Figure 9d shows the single-shot records after applying both methods for noise reduction. The graph shows that the SNR of the record after adaptive beamforming processing is significantly stronger than that of the record after τ-p transform. Figure 9e and f represent the τ-p spectra of Fig. 9b and c, respectively. A comparison of the two shows that the SNR in Fig. 9e is higher than that in Fig. 9f. In Fig. 9f, residual energy clusters of the regular noise can be seen. Comparative analysis shows that adaptive beamforming exhibits better noise resistance, effectively suppressing regular noise in recordings with random noise, and simultaneously improving the SNR of the seismic records.

4. Real data test

4.1. Study area

The study area was located in a deep marine shale gas reservoir block in southern China. The geometry consists of 41 hexagonal arrays, as shown in Fig. 10a. Letters A and B in Fig. 10a represent the heel and toe of the fractured well, respectively. The arrays were distributed on a relatively flat surface at distances between them ranging from 1000 and 2000 m. Within 60 km² of the monitoring area, there were multiple traffic arteries. In Fig. 10a, the yellow, red, and red dotted lines represent the expressway, railway, and tunnel, respectively. Therefore, the seismic data acquired in this area may have been severely damaged by noise. One planar array is zoomed in and displayed in Fig. 10b. The hexagonal array consists of 36 geophones with a space interval of 30 m. In the monitoring test, the time sampling is 1 ms.

4.2. Noise suppression and event detection

A planar array near the highway, marked by a yellow circle in Fig. 10a, was selected to analyze the effectiveness of the beamforming algorithm for noise suppression. Figure 11a shows the seismic records obtained from the array. We found that there was not only an approximate horizontal event but also obvious abnormal noise and random noise in this gather. Pronounced coherent noise was not observed in this record, indicating that there was no noise on the highway at the time. A DOA estimation was performed, and the results are shown in Fig. 11b. The incidence angle was effectively estimated to be 0°, which indicates that the method for DOA estimation introduced here is robust for noisy field data.

When disturbances occur on a highway, the planar array records a seismic gather, as shown in Fig. 12a. The SNR of this gather is relatively low. Furthermore, coherent noise was visible in this gather, and it was difficult to identify the desired signal with an approximately horizontal event. The results of the DOA estimation using the lattice search method are shown in Fig. 12b. The figure shows that in addition to the expected signal with an angle of incidence of 0°, there is a coherent signal with an incident angle of (42°, −74°). Based on the angle of incidence, the travel time of the coherent signal was calculated according to equation (1) and is displayed as red lines in Fig. 12a. The travel time curve was consistent with the event, indicating that the DOA estimation was correct. Based on this, adaptive beamforming was performed to form a null trap in the direction of the coherent noise. The spatial response of the beamforming is shown in Fig. 12c. The spatial response spectrum shows that beamforming has a response of 0 dB in the direction of the desired signal and −800 dB in the direction of the coherent noise incidence. Therefore, beamforming retained the desired signal well and suppresses coherent noise. In addition, the response spectrum of beamforming has a spatial response slightly below 0 dB in the other spaces, indicating that beamforming can suppress some radon noise, although the suppression is weaker than that of coherent interference. In Fig. 12d, after noise suppression, the desired signal indicated by the arrow was significantly enhanced, and the coherent signal was well suppressed in the seismic record. Moreover, the SNR shown in Fig. 12d is higher than that shown in Fig. 12a. The application confirms that the lattice search method is a robust and effective method for DOA estimation. Beamforming not only suppresses coherent noise, but also enhances the SNR and desired signal.

Figure 13 shows the effect of a weak micro-seismic event (enclosed by the yellow rectangular box) received by the 41 hexagonal arrays before and after beamforming. A normal moveout correction (NMO) was applied to each hexagonal array to flatten the desired micro-seismic event. Traditional denoising processing methods, such as filtering, were then used to improve the SNR, and its result is shown in Fig. 13a. In the yellow rectangular box of Fig. 13a, it is difficult to detect the weak micro-seismic event by our eyes. Here, a shot-term/long-term average (STA/LTA) ratio method from earthquake seismology is used to detect a potential micro-seismic event. The detection curve of Fig. 13a is plotted in waveforms as shown in Fig. 13b. Similarly, no strong wave peaks were visible in the event detection curves. Therefore, weak micro-seismic events could not be detected using traditional denoising methods. The seismic gather denoised by adaptive beamforming is shown in Fig. 13c, where a horizontal event can be seen in the yellow rectangular box. What is more, there is a strong peak visible on the detection curve (Fig. 13d). The application result indicated that adaptive beamforming successfully enhanced the amplitude of weak micro-seismic events, thereby improving the ability to detect weak events.

4.3. Micro-seismic event location

Finally, the proposed method was applied to micro-seismic data obtained during the hydraulic fracturing treatment of Stages 1–25. The numbers of micro-seismic events detected before and after beamforming are shown in Fig. 14. As shown in the histogram, the number of micro-seismic events detected in some stages increased significantly after beamforming was applied. Before beamforming, 410 reliable micro-seismic events were detected and after beamforming, 639 micro-seismic events were detected. This indicates that adaptive broadband-array beamforming technology improves the ability to detect weak micro-seismic events.

The locations of the events before and after beamforming were determined using the Geiger algorithm (Geiger 1912) and the results are shown in Fig. 15a and b, respectively. The dots in Fig. 15 represent the estimated hypocenters of event. The colors of dots match the colors of treated stages to which they correspond. The scales of the dots represent the intensity of the hypocenters. A comparison of the two figures shows that the locations are generally similar. However, the distribution of micro-seismic events after beamforming was more concentrated, and the direction of the fracture network was clearer. The enhanced SNR of the micro-seismic data after adaptive beamforming results in improved accuracy of the micro-seismic localization results, such that the fracture patterns represented by the micro-seismic data are more clearly defined, therefore, indirectly improving the location accuracy of micro-seismic events.

5. Discussion

The adaptive beamforming algorithm was validated using synthetic and field data. The denoising process of array data often requires a three-dimensional transformation of seismic records or the use of two-dimensional mathematical transformations applied to each individual profile. The calculation process was relatively complex. These mathematical transformations often rely on regular observational system that are difficult to strictly adhere to during actual field operations. By estimating the incident angle and azimuth of the seismic waves received by the array, adaptive beamforming achieved noise suppression without the need for individual profile processing. It can also improve the SNR of the seismic records. DOA estimation is crucial for adaptive beamforming. Precise DOA estimation is challenging for array data with SNRs of less than 1. A feasible approach is to first perform denoising on the records and then proceed with the DOA estimation. However, the high computational cost of beamforming algorithms limits their real-time monitoring capabilities. Therefore, future studies should focus on improving the computational efficiency of the proposed algorithm.

6. Conclusion

The sparse planar-array system is a flexible and effective method for micro-seismic monitoring in China's deep marine shale gas reservoirs. Its advantageous layout in areas with less noise damage and relative flatness enhances the performance of the system. The adaptive beamforming algorithm effectively suppresses the coherent noise owing to the different angles of incidence of the desired signal and noise. Application to synthetic and field data shows that the beamforming algorithm not only suppresses coherent noise, but also improves the SNR, resulting in improved micro-seismic event detection capability and micro-seismic event location accuracy.

Acknowledgements

The authors gratefully acknowledge the support of the Fund of the National Key Research and Development Program of China (grant no. 2019YFC0604902) and the Joint Funds for Enterprise Innovation and Development of the National Natural Science Foundation of China (grant no. U19B6003).

Conflict of interest statement. None declared.

References