Abstract
The migrationbased microseismic event location methods using waveform stacking algorithms are widely used for hydrofracturing monitoring. These methods have the advantage of not requiring the accurate first arrival time around a detected event, which is more suitable for noisy data than classical travel timebased methods. However, accuracy of these methods can be affected under the condition of relatively low signaltonoise ratio (SNR). Therefore, in order to enhance the location accuracy of microseismic events in a borehole system, we have proposed a migrationbased location method using improved waveform stacking with polarity correction based on a masterevent technique, which optimizes the combination way of P and Swave waveform stacking. This method can enhance the convergence of the objective function and the location accuracy for microseismic events as compared to the conventional waveform stacking. The proposed method has been successfully tested by using synthetic data example and field data recorded from one downhole monitoring well. Our study clearly indicates that the presented method is more viable and stable under low SNR.
Introduction
It is vital to accurately and automatically locate the microseismic events for estimating the stimulated reservoir volume. Migrationbased source location methods are more applicable to relatively low signaltonoise ratio (SNR) microseismic data than traditional travel timebased source location methods, because the former methods are far less sensitive to the picking precision than the latter ones (Gharti et al. 2010). During the last two decades, a number of studies have been carried out about the migrationbased location of microseismic events based on nonnegative waveform stacking in order to eliminate the influence of waveform polarity changes due to shear source mechanisms (Kao and Shan 2004; Gajewski et al. 2007; Gharti et al. 2010; Drew et al. 2013; Grigoli et al. 2014; Li et al. 2016; Shi et al. 2019). These approaches can make the location results more reliable at the cost of decreasing the location resolution in the case of high SNR. According to Trojanowski and Eisner (2017), stacking of both the positive and negative values of amplitude can provide more reliable results after the polarization correction as compared to any of absolute valuebased methods. In the past, the polarity was reliably corrected by using source mechanism inversion (Anikiev et al. 2014). However, it dramatically increases the computational cost. Afterward, Kim et al. (2017) proposed the automatic method for the determination of firstmotion polarity which estimates the relative polarities of waveforms at other receivers based on crosscorrelation analysis. Later on, Xu et al. (2019) corrected the changing polarities by using an amplitude trend leastsquares fitting method. These polarization correction methods are effective and comprehensively reduce the computational cost. Therefore, polarization correction methods can be implemented before waveform stacking, which can provide the basic guarantee for obtaining the constructive interference from stacked amplitudes. Moreover, a relative location was also introduced into the migrationbased location methods to mitigate the negative effect of an inaccurate velocity model on the location results, which provides the foundation for accurate waveform stacking (Grigoli et al. 2016; Li et al. 2016). In addition, characteristic function can be calculated within P and Swave corridors by selecting an approximate P or S arrival time instead of scanning the whole time period of seismic records, which can significantly accelerate the scanning efficiency (Eaton et al. 2011).
On the basis of a predefined time window centered on the arrival time of signals (namely P and/or Swave corridors) (Eaton et al. 2011), polarization correction algorithm (Kim et al. 2017) and masterevent technique (Grigoli et al. 2016), we present a new migrationbased location method via improving the combination way of P and Swave waveform stacking in order to increase the resolution of the objective function in the study. Thereafter, a twodimensional (2D) model is used to prove the feasibility of the presented method. Finally, we assess the performance of this method on real data.
Method
This section briefly introduces the masterevent technique and mainly describes the objective functions formulated by using the conventional and improved waveform stacking, as well as the location flow for the migrationbased method to locate a selected microseismic event.
Masterevent technique
The masterevent technique, proposed by Grigoli et al. (2016), can reduce the dependency of the location results on the precision of the adopted velocity model, which inherits the main features of relative location algorithms. Here a master event should have the characteristics of high SNR waveform and reliable source location. The perforation shot event or high SNR events may be selected as master events. Through this masterevent technique, we can calculate the masterevent time corrections of all receivers for P and S waves, respectively. Then, these corrections can be applied to Eq. (1) as discussed in “Conventional waveform stacking function” section in order to reduce the influence of an inaccurate velocity model on the location results.
Formulation of the objective function
The objective function for the migrationbased location method is generally constructed by the way of waveform stacking. The waveform stacking function can be broadly classified into two main categories: the first, which only stacks the positive values of seismograms (such as absolute values, STA/LTA ratio, envelopes and phase square) and the second, which stacks both the positive and negative values of seismograms. Although the former methods, namely absolutevaluebased approaches, can avoid the influence of changing polarities due to source radiation pattern, the imaging resolution of their objective functions may be reduced for microseismic data with relatively low SNR. However, a simple stacking can yield better results than the former methods when the signal polarization correction is applied to the latter methods (Trojanowski and Eisner 2017). So, in this study, we only discuss that method which can stack both the positive and negative values of seismograms with polarization correction. In addition, the waveform stacking function based on the combination of P and S waves is applied to migration algorithms in order to enhance the accuracy of event location as recommended by Gharti et al. (2010).
Conventional waveform stacking function
The waveform stacking function can be calculated within P and Swave corridors by selecting an approximate arrival time instead of scanning the whole time period of seismic records (Eaton et al. 2011). We take the selection of an approximate Swave arrival time because the weaker Pwave energy is more easily submerged in noise.
By assuming the P or Swave calculated travel times at the ith receiver (\(t_{i}^{k}\)) and the Swave calculated travel time at the mth receiver (\(t_{m}^{S}\)), we can obtain their corresponding corrected travel times (\({\text{tc}}_{i}^{k}\) and \({\text{tc}}_{m}^{S}\)) after applying the masterevent time corrections calculated through the masterevent technique (Grigoli et al. 2016). Then, the calculated travel time difference between the ith receiver for P/Swave and the mth receiver for Swave is given by Eq. (1):
For the purpose of discussions, the basic unit of waveform stacking function (\(L_{k} (j)\)) can be defined by Eq. (2):
where n and j denote the number of receivers and an index of the discretetime signal, respectively. \(u_{i}\) represents the signal amplitude at the ith receiver. \({\text{sgn}}_{{_{i} }}^{k}\) is the corresponding polarity correction sign of the raw amplitude \(u_{i}\) at the ith receiver for P or Swave, which is automatically determined using the method proposed by Kim et al. (2017). \(L_{k} (j)\) represents the waveform stacking with polarity correction at time index j from all receivers for P or Swave after we eliminate the moveout (\(\Delta t_{i}^{{\text{k}}}\)) of the corresponding trace. Subsequently, the conventional waveform stacking function with a predefined time window centered on the Swave arrival of this event is constructed based on P and Swave stacking basic unit information as expressed by Eq. (3):
where w_{1} represents the size of the inner window and it controls the SNR of the waveform stacking function. j is centered on the index of time t and its range is from t − w_{1} to t + w_{1}. \(t_{{{\text{mFA}}}}^{S}\) is an approximate estimate for the Swave first arrival at the mth receiver for this event. w_{2} represents the size of the outer time window. And it is a sliding window range centered on the \(t_{{{\text{mFA}}}}^{S}\) mentioned above, which is used to scan through this event in order to avoid searching through the entire time.
Improved waveform stacking function
For enhancing the convergence and resolution of the objective function, we build the objective function by improving the combination way of P and Swave waveform stacking, which calculates the multiplication of the basic units of P and Swave waveform stacking functions before summing within the inner time window [t − w_{1}, t + w_{1}]. Thus, the improved waveform stacking function with the time window range from \(t_{mFA}^{S}  w_{2}\) to \(t_{mFA}^{S} + w_{2}\) can be expressed by the following Eq. (4):
where L_{P}, L_{S}, \(t_{{{\text{mFA}}}}^{{\text{S}}}\), w_{1} and w_{2} are the same as those described previously in “Conventional waveform stacking function” Section.
Location flow
Belowmentioned procedure is adopted to calculate the location of a selected microseismic event.

1.
Input an adjusted velocity model and create a lookup table by calculating the travel times from every potential event location to all of the receivers based on the raytracing technique (Moser 1991).

2.
Calculate the masterevent time corrections by using the masterevent technique (Grigoli et al. 2016) and apply these corrections to Eq. (1).

3.
Only input a single approximate Swave first arrival time for this event.

4.
Calculate the objective function by using the method discussed in “Conventional waveform stacking function” or “Improved waveform stacking function” section.

5.
Output the corresponding location when we determine the global maximum value of the corresponding objective function by utilizing the grid search method (Mao et al. 2019).
Synthetic data example
In this study, we focus on the accuracy of the conventional and improved waveform stacking functions. For simplicity, we used a 2D homogeneous medium model with Pwave velocity 2000 m/s, Swave velocity 1200 m/s and density 2.0 g/cm^{3} as shown in Fig. 1.
To cover the depth range from 950 to 1050 m, eleven receivers were placed at 10m spacing intervals along a vertical observation well. The wellhead was located at x = 200 m. A Ricker wavelet having dominant frequency of 60 Hz was used as the microseismic source time function. Time interval was 0.5 ms. The master event and target event were set at (x, z) = (400, 1050) m and (x, z) = (420, 1030) m, respectively. Twodimensional elastic microseismic records were simulated using staggeredgrid finite differences (Graves 1996). The vertical component records of the synthetic noisefree data for the master event and target event are shown in Fig. 2a, b, respectively. Here, we defined the grid search area which was 200 m both in x and z directions centered on the location of the true event. Meanwhile, the search step length was 1 m both in x and z directions. Then, we calculated the values of different objective functions for all discrete points in the search area using the grid search method.
To analyze the global convergence and resolution of the objective functions based on the conventional and improved waveform stacking constructions mentioned by Eqs. (3) and (4), we specially discussed the distribution of the waveform stacking functions from the conventional and improved methods without noise and velocity model errors. Figure 3 clearly shows the distribution of the conventional and improved waveform stacking functions calculated by using Eqs. (3) and (4) based on the noisefree target event record in Fig. 2b, respectively. As we can see from Fig. 3, the deep red zone denotes the potential microseismic event location area most possibly. From Fig. 3a, b, it can be easily observed that the value in red area, calculated through the improved waveform stacking method, is obviously compressed as compared to that of the conventional waveform stacking method. As a result, the convergence and resolution of the improved waveform stacking function are far better than those of the conventional waveform stacking function.
To test the noise immunity of the conventional and improved methods, we applied Monte Carlo relocation with 100 realizations of random noise for different SNR. Figure 4 shows one separate noisy data of the target event for SNR = 0.5, 1 and 2, which is only an input data for one realization mentioned in Fig. 5.
It is clear from Fig. 5 that the relocation results based on the conventional and improved methods gradually converge to the true event position as the SNR increases. What is more, the relocation results based on the improved method are more convergent to the true event position than those of the conventional method for all SNR (0.5, 1 and 2). In addition, Fig. 6 shows the comparison with absolute location errors through the use of the same corresponding 100 realizations as in Fig. 5. From Fig. 6, it is obvious that the accuracy of the improved method is much higher than that of the conventional method because it estimates less absolute location error compared to the conventional method for the same corresponding SNR as in Fig. 5.
As we know, the accuracy of many traditional location methods greatly depends upon the precision of the velocity model. But relative location methods can generally mitigate the negative effect of an inaccurate velocity model. Hence, the conventional and improved methods in this paper were further extended by using the masterevent technique (Grigoli et al. 2016).
To test the sensitivity of the conventional and improved methods with the masterevent technique to the velocity model errors, we conducted a Monte Carlo relocation with 100 realizations of random velocity perturbation. Both the P and Swave velocity values were perturbed by (− 3%, 3%), respectively. In order to isolate the effect of velocity method errors, we used the noisefree data.
The upper row of Fig. 7a, b shows the relocation results based on the conventional and improved methods without applying the masterevent time corrections calculated through the masterevent technique, which are greatly divergent. However, after applying the masterevent time corrections, the location results become more convergent (Fig. 7c, d). Thus, with the addition of masterevent time corrections, the location accuracy has been dramatically improved under the velocity model errors. Consequently, the masterevent technique can make our waveform stacking location method more reliable under velocity model inaccuracies.
Field data application
For verifying the feasibility of the presented method in field data processing, we performed one real data test with microseismic data obtained during the hydraulic fracturing of tight sandstone from a Chinese oil field. An array of ten threecomponent (3C) receivers was placed in an inclined monitoring well whose wellhead was located at x = 415.9 m and y = 608.1 m. The depth of the placed array ranged from 2455.1 to 2545.1 m with 10m spacing intervals. Afterward, the midpoint location of the perforation interval was (360.6, 281.9, 2538.0) m. To calibrate the initial velocity model and the orientation of 3C receivers, we used the known perforation information. For determining the global maximum value of the waveform stacking function, we implemented the global grid search algorithm based on backazimuth constraint. The volume set for the threedimensional (3D) grid search was 400 m in the x, y and z directions centered on the midpoint of the perforation interval. Then, we chose the search step size 1 m in all three directions (x, y and z directions) and set the acceptable backazimuth error 4° for the conventional and improved methods, respectively. The perforation event and high SNR events were selected as master events for this study.
According to the location flow described in “Location flow” section, more than 170 microseismic events were located by utilizing the conventional and improved methods, respectively. The location results of the conventional and improved methods are shown in Fig. 8a–f in the form of 3D space, top view of xyplane and side view of xzplane.
As we can observe from 3D space (Fig. 8a, b), although the location results based on the methods mentioned above are near to the perforation interval, the inverted results determined by the improved method are more spatially clustering compared with those found through the conventional method. We can clearly find that the location results based on the improved method (Fig. 8d) are significantly more clustering than those of the conventional method (Fig. 8c) from top view in xyplane. Moreover, as we can notice from side view in xzplane (Fig. 8e, f), the inverted results obtained through the use of the improved method are clustered very well than those determined by the conventional method. The real data test suggests that the location results obtained through the improved method are more acceptable.
Discussion
Our results indicate that the proposed migrationbased location method through improving the combination way of P and Swave waveform stacking can significantly increase the resolution and convergence of the objective function on the basis of a predefined time window centered on the arrival time of signals (Eaton et al. 2011), polarization correction algorithm (Kim et al. 2017) and masterevent technique (Grigoli et al. 2016).
In the synthetic data example, the distributions of the conventional and improved waveform stacking functions without noise and velocity model errors clearly indicate that the global convergence and resolution of the improved waveform stacking function (Fig. 3b) are much better than those of the conventional waveform stacking function (Fig. 3a). Subsequently, under different SNR (0.5, 1 and 2) tests, the improved method has achieved more convergent relocation results compared with the conventional method (Fig. 5) and the former has also obtained higher precision results than the latter (Fig. 6). Therefore, the improved method can be more resistant to noise than the conventional method. Furthermore, the former method can lead to better stability than the latter under varying noise levels. Moreover, even under relatively low SNR, the synthetic data results confirm the accuracy of this proposed method. Hence, it is clear that the above two methods can mitigate the dependency upon the precision of the velocity model after the application of masterevent time corrections, which is in agreement with the conclusion gained by Grigoli et al. (2016). For simplicity and reducing the computational cost, we chose 2D model in the synthetic test. Once the azimuth information is estimated, these conclusions may easily be confirmed in 3D synthetic model test.
In the field data application, the location results obtained by the improved method are more clustered than those based on the conventional method both from top view in xyplane (Fig. 8c, d) and side view in xzplane (Fig. 8e, f). Thus, our inverted results also indicate that the improved method can more accurately locate the microseismic events than the conventional method, which is almost consistent with the above conclusion from the synthetic test.
To sum up, the proposed method can obviously enhance the location precision compared with the conventional method under varying noise levels. What is more, the former method seems to be more applicable to process low SNR microseismic data than the latter method. This may provide the reliable foundation for precisely implementing the location procedure even in the presence of low SNR.
Conclusion
This study presents a migrationbased location method using improved waveform stacking with polarity correction based on a masterevent technique. Compared with the conventional waveform stacking location method, the proposed method can improve the convergence of the objective function. Furthermore, this new method may effectively provide more reliable and accurate location results even in low SNR circumstances. Thus, this method may be completely robust and practicable for relatively low SNR microseismic data in the hydrofracturing monitoring. Applications to synthetic and field data have validated the feasibility and reliability of the new proposed method.
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Acknowledgments
This study was cosponsored by Hubei Provincial Department of Education (Grant No. Q20191307) and Open Fund of Key Laboratory of Exploration Technologies for Oil and Gas Resources (Yangtze University), Ministry of Education (Grant No. K201814). The authors gratefully thank the associate editor Prof. Junlun Li and two anonymous reviewers for their constructive comments and suggestions that have significantly improved this manuscript.
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Mao, Q., Azeem, T., Zhang, X. et al. A migrationbased location method using improved waveform stacking for microseismic events in a borehole system. Acta Geophys. 68, 1609–1618 (2020). https://doi.org/10.1007/s1160002000488z
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Keywords
 Microseismic event
 Migrationbased location
 Improved waveform stacking
 Hydraulic fracturing
 SNR