A migration-based location method using improved waveform stacking for microseismic events in a borehole system

Abstract

The migration-based microseismic event location methods using waveform stacking algorithms are widely used for hydro-fracturing 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 time-based methods. However, accuracy of these methods can be affected under the condition of relatively low signal-to-noise ratio (SNR). Therefore, in order to enhance the location accuracy of microseismic events in a borehole system, we have proposed a migration-based location method using improved waveform stacking with polarity correction based on a master-event technique, which optimizes the combination way of P- and S-wave 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. Migration-based source location methods are more applicable to relatively low signal-to-noise ratio (SNR) microseismic data than traditional travel time-based 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 migration-based 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 value-based 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 first-motion polarity which estimates the relative polarities of waveforms at other receivers based on cross-correlation analysis. Later on, Xu et al. (2019) corrected the changing polarities by using an amplitude trend least-squares 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 migration-based 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 S-wave 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 S-wave corridors) (Eaton et al. 2011), polarization correction algorithm (Kim et al. 2017) and master-event technique (Grigoli et al. 2016), we present a new migration-based location method via improving the combination way of P- and S-wave waveform stacking in order to increase the resolution of the objective function in the study. Thereafter, a two-dimensional (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 master-event technique and mainly describes the objective functions formulated by using the conventional and improved waveform stacking, as well as the location flow for the migration-based method to locate a selected microseismic event.

Master-event technique

The master-event 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 master-event technique, we can calculate the master-event 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 migration-based 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 absolute-value-based 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 S-wave 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 S-wave arrival time because the weaker P-wave energy is more easily submerged in noise.

By assuming the P- or S-wave calculated travel times at the ith receiver (\(t_{i}^{k}\)) and the S-wave 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 master-event time corrections calculated through the master-event technique (Grigoli et al. 2016). Then, the calculated travel time difference between the ith receiver for P/S-wave and the mth receiver for S-wave is given by Eq. (1):

$$\Delta t_{i}^{k} = \left\{ {\begin{array}{*{20}l} {t_{i}^{k} - t_{m}^{S} } \hfill & {\text{if not applying the master }-\text{ event time corrections}} \hfill \\ {{\text{tc}}_{i}^{k} - {\text{tc}}_{m}^{S} } \hfill & {\text{if applying the master }-\text{ event time corrections}} \hfill \\ \end{array} } \right.\quad k \in \left\{ {P,S} \right\}$$
(1)

For the purpose of discussions, the basic unit of waveform stacking function (\(L_{k} (j)\)) can be defined by Eq. (2):

$$L_{k} (j) = \sum\limits_{i = 1}^{n} {\left( {{\text{sgn}}_{{_{i} }}^{k} u_{i} (\Delta t_{i}^{k} + j)} \right)} \quad k \in \left\{ {P,S} \right\}$$
(2)

where n and j denote the number of receivers and an index of the discrete-time 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 S-wave, 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 S-wave 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 S-wave arrival of this event is constructed based on P- and S-wave stacking basic unit information as expressed by Eq. (3):

$${\text{CWS}}(t) = \sum\limits_{{j = t - w_{1} }}^{{t + w_{1} }} {L_{P} (j)} \times \sum\limits_{{j = t - w_{1} }}^{{t + w_{1} }} {L_{S} (j)} \;\left( {t = (t_{{{\text{mFA}}}}^{S} - w_{2} ), \ldots (t_{{{\text{mFA}}}}^{S} + w_{2} )} \right)$$
(3)

where w1 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 − w1 to t + w1. \(t_{{{\text{mFA}}}}^{S}\) is an approximate estimate for the S-wave first arrival at the mth receiver for this event. w2 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 S-wave waveform stacking, which calculates the multiplication of the basic units of P- and S-wave waveform stacking functions before summing within the inner time window [t − w1, t + w1]. 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):

$${\text{IWS}}(t) = \sum\limits_{{j = t - w_{1} }}^{{t + w_{1} }} {L_{P} (j) \times L_{S} (j)} \,\left( {t = (t_{{{\text{mFA}}}}^{S} - w_{2} ), \ldots (t_{{{\text{mFA}}}}^{S} + w_{2} )} \right)$$
(4)

where LP, LS, \(t_{{{\text{mFA}}}}^{{\text{S}}}\), w1 and w2 are the same as those described previously in “Conventional waveform stacking function” Section.

Location flow

Below-mentioned procedure is adopted to calculate the location of a selected microseismic event.

  1. 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 ray-tracing technique (Moser 1991).

  2. 2.

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

  3. 3.

    Only input a single approximate S-wave first arrival time for this event.

  4. 4.

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

  5. 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 P-wave velocity 2000 m/s, S-wave velocity 1200 m/s and density 2.0 g/cm3 as shown in Fig. 1.

Fig. 1
figure1

Acquisition geometry for the 2D model with the target event (red pentagram) to be located, the master event (green pentagram) to be known and receivers (blue triangles). The x- and z-axes denote the offset and depth directions, respectively

To cover the depth range from 950 to 1050 m, eleven receivers were placed at 10-m 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. Two-dimensional elastic microseismic records were simulated using staggered-grid finite differences (Graves 1996). The vertical component records of the synthetic noise-free 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.

Fig. 2
figure2

Record section of the synthetic noise-free microseismic data (vertical component) for the a master and b target events

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 noise-free 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.

Fig. 3
figure3

Waveform stacking function distribution based on the a conventional and b improved methods. The color scale indicates the waveform stacking function value (deep red for the maximum values and deep blue for the minimum values). In each subplot, the white pentagrams denote the true location of synthetic event (target event) and the intersections of black dashed lines, namely the positions of the maximum waveform stacking function values, represent the calculated locations

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.

Fig. 4
figure4

Record section of one separate noisy data of the target event with the SNR = a 0.5, b 1 and c 2 as one realization mentioned in Fig. 5. The record section of the different SNR data is generated by adding random noise with different amplitudes to noise-free data of the target event as in Fig. 2b

Fig. 5
figure5

One hundred realizations from Monte Carlo relocation using the conventional [left column (a, c, and e)] and improved [right column (b, d, and f)] methods, under random noise for different SNR. The SNR = (a, b) 0.5, (c, d) 1 and (e, f) 2. The red pentagram and black dots represent the true event (target event) and inverted results (calculated locations), respectively

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.

Fig. 6
figure6

Comparison with absolute location errors based on the same corresponding 100 realizations as in Fig. 5. The SNR is a 0.5, b 1 and c 2

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 master-event technique (Grigoli et al. 2016).

To test the sensitivity of the conventional and improved methods with the master-event technique to the velocity model errors, we conducted a Monte Carlo relocation with 100 realizations of random velocity perturbation. Both the P- and S-wave velocity values were perturbed by (− 3%, 3%), respectively. In order to isolate the effect of velocity method errors, we used the noise-free data.

The upper row of Fig. 7a, b shows the relocation results based on the conventional and improved methods without applying the master-event time corrections calculated through the master-event technique, which are greatly divergent. However, after applying the master-event time corrections, the location results become more convergent (Fig. 7c, d). Thus, with the addition of master-event time corrections, the location accuracy has been dramatically improved under the velocity model errors. Consequently, the master-event technique can make our waveform stacking location method more reliable under velocity model inaccuracies.

Fig. 7
figure7

One hundred realizations from Monte Carlo relocation under random velocity perturbation. a and b show the relocation results using the conventional and improved methods without applying the master-event time corrections. c and d show the relocation results using the conventional and improved methods applying the master-event time corrections

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 three-component (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 10-m 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 back-azimuth constraint. The volume set for the three-dimensional (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 back-azimuth 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 xy-plane and side view of xz-plane.

Fig. 8
figure8

Location results based on the conventional [left column (a, c, and e)] and improved [right column (b, d and f)] methods. Three-dimensional space view for using the a conventional and b improved methods, respectively. Top view in xy-plane for the corresponding methods mentioned above is observed in c and d, respectively. Side view in xz-plane for the corresponding methods mentioned above is observed in e and f, respectively. The red pentagram and blue triangles indicate the perforation shot and receivers, respectively. The blue and red curves denote the monitoring and fracturing wells, respectively. The black dots represent inverted locations determined by the conventional and improved methods. The x-, y- and z-axes denote the east, north and depth directions, respectively

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 xy-plane. Moreover, as we can notice from side view in xz-plane (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 migration-based location method through improving the combination way of P- and S-wave 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 master-event 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 master-event 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 xy-plane (Fig. 8c, d) and side view in xz-plane (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 migration-based location method using improved waveform stacking with polarity correction based on a master-event 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 hydro-fracturing 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 co-sponsored 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. K2018-14). 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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Correspondence to Qinghui Mao.

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Mao, Q., Azeem, T., Zhang, X. et al. A migration-based location method using improved waveform stacking for microseismic events in a borehole system. Acta Geophys. 68, 1609–1618 (2020). https://doi.org/10.1007/s11600-020-00488-z

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Keywords

  • Microseismic event
  • Migration-based location
  • Improved waveform stacking
  • Hydraulic fracturing
  • SNR