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Arrival-time picking method based on approximate negentropy for microseismic data
Journal of Applied Geophysics 152 (2018) 100–109
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Arrival-time picking method based on approximate negentropy for microseismic data Yue Li, Zhuo Ni, Yanan Tian ⁎ Department of Communication and Engineering, Jilin University, Changchun, China
a r t i c l e
i n f o
Article history: Received 17 January 2017 Received in revised form 28 December 2017 Accepted 16 March 2018 Available online 20 March 2018 Keywords: Arrival-time picking Approximate negentropy Microseismic data Low SNR
a b s t r a c t Accurate and dependable picking of the first arrival time for microseismic data is an important part in microseismic monitoring, which directly affects analysis results of post-processing. This paper presents a new method based on approximate negentropy (AN) theory for microseismic arrival time picking in condition of much lower signal-tonoise ratio (SNR). According to the differences in information characteristics between microseismic data and random noise, an appropriate approximation of negentropy function is selected to minimize the effect of SNR. At the same time, a weighted function of the differences between maximum and minimum value of AN spectrum curve is designed to obtain a proper threshold function. In this way, the region of signal and noise is distinguished to pick the first arrival time accurately. To demonstrate the effectiveness of AN method, we make many experiments on a series of synthetic data with different SNR from −1 dB to −12 dB and compare it with previously published Akaike information criterion (AIC) and short/long time average ratio (STA/LTA) methods. Experimental results indicate that these three methods can achieve well picking effect when SNR is from −1 dB to −8 dB. However, when SNR is as low as −8 dB to −12 dB, the proposed AN method yields more accurate and stable picking result than AIC and STA/LTA methods. Furthermore, the application results of real three-component microseismic data also show that the new method is superior to the other two methods in accuracy and stability. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Exploration of shale gas, coalbed methane or other unconventional oil and gas is the focus of oil and gas industry in the future, which is also the issue that the whole world concerns about. Hydraulic fracturing and microseismic monitoring methods have been widely used in oil and gas exploration. Source location is very important in microseismic data processing (Belayouni et al., 2015; Zhang et al., 2015; Li and Song, 2017). Denoising and picking of microseismic data are the two key steps for events identification and source location (Han and van der Baan, 2015; Velis et al., 2015). However, microseismic data is featured with huge amount of data, widely distributed frequencies and low signal-to-noise ratio (SNR). Accurate and quick arrival-time picking methods remain in urgent need. So far, numerous methods of arrival-time picking both in time and frequency domains have been presented for single-component and three-component records by scholars from various countries. Akaike information criterion (AIC) and short/long time average ratio (STA/LTA) are two representative approaches for microseismic first arrival picking. AIC is often used with auto-regressive method (AR-AIC) to divide the input signal into some locally stationary segments, each of which is ⁎ Corresponding author at: Nanhu Road 5372, Changchun 130012, China. E-mail address: [email protected] (Y. Tian).
https://doi.org/10.1016/j.jappgeo.2018.03.012 0926-9851/© 2017 Elsevier B.V. All rights reserved.
assumed to be represented as an auto-regressive model. Sleeman and van Eck (1999) used an optimal separation of two stationary time series, which can calculate AIC directly without considering the convergence of AR. Meanwhile, the minimum of AIC spectrum is considered to be the first arrival time. St-Onge (2011) indicated that this quick method could be implemented for picking large volumes of microseismic data. However, AIC method can always find a minimum in condition of high SNR. Yet it cannot recognize the microseismic signal buried in highamplitude noise accurately. Thus, AIC method is generally not used alone but combines with other picking methods. STA/LTA is a conventional method for microseismic events identification in time domain. The method divides characteristic function according to the different lengths of short and long time windows. It utilizes the characteristics of absolute amplitude, energy and envelope of microseismic signal. Then the ratio between average values of the new time series is calculated, the maximum of which is considered as the first arrival time. In addition, several other modified methods based on it have been proposed later. Wong et al. (2009) developed a modified energy ratio (MER) method. Akram (2011) used standard deviation in a moving time window to pick P-wave arrival time. Gou et al. (2011) used STA/ LTA method combined with an envelope method to detect the arrival time of local events. However, the disadvantage of STA/LTA method is that it is difficult to select an appropriate length of time window for picking accurately in low SNR. Other feasible picking methods involving
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Fig. 1. a) Actual microseismic data and final picking result (vertical line). b) AN spectral curve and final picking result (dot) at the first sample exceeding the threshold.
polarization proposed to pick the first arrival times by Moriya (2008, 2009). Küperkoch et al. (2010) presented an iterative method for picking onset of seismic events based on higher order statistics (HOS) method. Sheng et al. (2015) used CWT to analysis microseismic signal and applied HOS method to first arrival picking. Liao et al. (2010) used the fractal dimension and polarized method together for automatic P/ S-wave arrivals picking. Zhang et al. (2003) developed an automatic P waves picking method based on wavelet transform combined with AIC analysis. Capilla (2006) used Haar wavelet to identify seismic data. Wavelet transform combined STA/LTA method has been proposed by Rodriguez (2011) and Li et al. (2016). Al-Shuhail (2015) used the super virtual seismic interferometer method to pick up first arrivals in petroleum seismic data. An et al. (2015) developed the extended super-virtual interferometer. Tan et al. (2014) proposed method combined correlation and polarization. Qu et al. (2015) developed a method first-arrival picking that combined cross-correlation and AIC methods. Akram and Eaton (2016a) improved the method based on crosscorrelation. Kim et al. (2016) suggested a fast picking method by combing stacking and cross-correlation approaches. Tan and He (2016) developed a cross-correlation and least-squares-based algorithm to identify microseismic events. In addition, Zhu et al. (2016) proposed a method based on fuzzy C-means clustering for arrival-time picking on
microseismic data. These picking methods above offer the reliability of arrival time picking and have many places worth for our reference. However, the picking accuracy of these methods is limited by strong noise. In other words, weaker amplitudes of microseismic data make arrival-time picking difficult in low SNR (Akram and Eaton, 2016b). In view of the above problems, finding an arrival time picking method with fast calculating speed and high picking precision needs more discussion and studies by experts in this field. Based on the characteristics of microseismic data itself, this paper presents a new picking method based upon approximate negentropy (AN) theory. Compared with the existing picking methods, the new method can achieve accurate arrival picking when SNR is as low as −12 dB. Meanwhile, its calculation process is simple, fast and accurate. This paper is arranged as follows. First, AN theory is introduced briefly and its application process in microseismic signal is described concretely including the selection of approximate function and the design of threshold function. Then, we evaluate the performance of the proposed method using a synthetic seismic record, in which dominant frequency of effective signal is 300 Hz. The SNRs range is from −1 dB to −12 dB. Moreover, we compare its picking result with AIC method and STA/LTA method. Comparison results show that the proposed method performs better in the aspect of first arrival time picking than the other two methods.
Fig. 2. Framework diagrams of first arrival picking by the proposed AN method.
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Besides, experimental results on a real three-component microseismic record also show that the new method can even pick accurately in condition of lower SNR as −12 dB. 2. Basic theory 2.1. Approximate negentropy (AN) Let y = {yi, i = 1, 2, ⋯, n}T be a random vector of n data points. Negentropy of the digital waveform y is defined as follows: 0
J ðyÞ ¼ H ðy Þ−H ðyÞ;
ð1Þ
where y′ is a Gaussian random vector with the same covariance matrix as y, H(y) is entropy of sequence y and H(y′) is entropy of sequence y′. Negentropy is regarded as the amount of structure of the distribution of y. For random variables with the same variance, the distribution concentrated on a certain value has largest negentropy. Namely, the more “random” the distribution of y is, the smaller its negentropy is. Because Gaussian distribution can be considered as the least structured of all distributions. Negentropy does not vary with the amplitudes of signals and can be interpreted as a classical non-Gaussian measuring method. Negentropy value is equal to zero for Gaussian distribution. For nonGaussian distribution, negentropy value is positive. In view of microseismic characteristics of low SNR, weak signal and strong noise, the property of negentropy has good applicability for arrival-time picking.
In practical applications, calculation of negentropy relies on the prior probability of random variables, but exact probability of microseismic data is unknown, which makes the calculation of negentropy extremely complicated and difficult to achieve. Therefore, this paper constructs a proper function of approximate negentropy to apply to arrival-time picking on microseismic data. There are many approximate negentropy methods, the approximate method based on maximum entropy criterion (minimum negative entropy) is widely used and relatively sensitive to signals. The expression is described as follows: J ðxÞ ¼
n X
2
ki fE½Gi ðxÞ−E½Gi ðx0 Þg ;
ð2Þ
i¼1
where operator E represents the calculation of mathematical expectation and each non-quadratic function Gi(.) must be orthogonal in a certain sense. i means the number of comparison equation Gi(.), the higher the value of i is, the more accurate the approximation of negentropy is. Random vector x is a sequence of zero mean and unit variance with n data points, which is generated from sequence y after normalization. The vector x′ has a Gaussian distribution with zero mean and unit variance. Each ki is a positive constant and n is an integer greater than or equal to 1. Generally, n = 2 and k1 = k2 = 1. The selection of a suitable contrast function Gi(.) is an important task, which affects confidence level of picking. In practice, the choice of contrast equation Gi(.) should satisfy at least two conditions: 1) the calculation of the equation should be simple and fast. 2) The equation
Fig. 3. First arrival times picking by three methods for synthetic records. a) Single-channel record (SNR = −3 dB) and picking results by AIC method, STA/LTA method and AN method. b) AIC spectral curve and final picking at the minimum. c) STA/LTA ratio spectral curve and final picking at the maximum. d) AN spectral curve and final picking at the first sample exceeding the threshold.
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can detect the super-Gaussian or the sub-Gaussian component. In order to satisfy the above selection criteria to obtain a more robust estimate, we choose two appropriate non-quadratic contrast equations of Gi(.) for sequence ζ = {ζi, i = 1, 2, …, n}, which are defined as: !
G1 ðζÞ ¼ − exp
G2 ðζÞ ¼
−ζ2 ; 2
1 4 ζ : 4
ð3Þ
ð4Þ
One of the main features of these two different contrast functions is that G1(ζ) and G2(ζ) are piecewise linear approximations. G1(ζ) has good robustness and can be used to detect the super-Gaussian properties of independent components and G2(ζ) is suitable for estimating the subGaussian properties of random variables. It is known that x′ is the stanqffiffi dard normal distribution sequence. So E½G1 ðx0 Þ ¼ 12 and E½G2 ðx0 Þ ¼ 34 are calculated by using mean value formula. Therefore, the new approximate function of negentropy we proposed can be described as: ANðxÞ ¼
( rffiffiffi)2 −x2 1 1 3 2 − þ E x4 − : E − exp 2 4 4 2
ð5Þ
Here, random vector x obtained from normalization of microseismic data is a sequence of zero mean and unit variance. AN(x) represents the approximate negentropy of random sequence x. It can be seen that the
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proposed AN method is not only be easily defined, rapidly calculating, but also has good statistical properties. 2.2. Arrival-time picking based on AN When a Gaussian random sequence passes through a linear filter, the output result is still subject to Gaussian distribution. According to the central limit theorem, microseismic random noise can be seen as an infinite number of independent identically distributed noise sources that work together in ideal conditions. So in ideal conditions, microseismic random noise can be regarded as Gaussian distribution and effective signal obeys non-Gaussian distribution. Accounting for the above assumptions and characteristic of negentropy, an automatic arrivaltime picking method based on AN is presented for microseismic data in this paper. We will describe how to use AN analysis method to pick first arrivals in time domain. The concrete steps are shown as: firstly, extract independent random sequence with zero average and unit variance through the normalized microseismic signal. Secondly, divide microseismic data into several frames, calculate the value of AN of each frame to acquire statistical data, draw the corresponding AN spectral curve. Finally, a suitable threshold function is designed to find the boundary between noise and signal, so as to determine the first arrival time. First of all, according to Eq. (2), we know that the input microseismic sequence needs to be normalized before calculating the approximate negentropy, that is, how to obtain a random sequence x with zero mean and unit variance. For the sequence y = {yi, i = 1, 2, …n} with n
Fig. 4. First arrival times picking by three methods for synthetic records. a) Single-channel record (SNR = −12 dB) and picking results of AIC method, STA/LTA method and AN method. b) AIC spectral curve and final picking at the minimum. c) STA/LTA ratio spectral curve and final picking at the maximum. d) AN spectral curve and final picking at the first sample exceeding the threshold.
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Fig. 5. First arrival times picking by three methods for multi-channel synthetic records with different SNRs. a)–c) Noisy record with 50 channels (SNR = −3 dB) and final picking of AIC method, STA/LTA method and AN method. d)–f) Noisy record with 50 channels (SNR = −12 dB) and final picking of AIC method, STA/LTA method and AN method.
data points as the input microseismic sequence, random sequence x can be normalized as follows (Nazarpour et al., 2005): y¼
n 1X y; n i¼1 i
σ2 ¼
x¼
ð6Þ
n 1 X ðy −yÞ2 ; n−1 i¼1 i
Then, we divide the normalized sequence x into frames to ensure the stability of microseismic data since it is not stationary all the time. Here, frame length and frame shift are two important parameters, which directly affect the picking effect. The larger frame length is, the smoother
ð7Þ
y−y ; σ
ð8Þ
where y and σ2 represent the mean and variance of microseismic sequence y, respectively. y is a sequence with the same size of y and each element is y. x is the normalized sequence with n data points, zero mean and unit variance. Table 1 Picking results of AIC, STA/LTA and AN in condition of different SNRs. SNR
−9
−10
−11
163 163 162 166 164 171 153 234 470
187
450
22
STA/LTA picks (ms) 159 156 157 158 156 159 156 159 159
383
484
352
159
159
159
Actual value (ms) AIC picks (ms)
AN picks (ms)
−1
−2
−3
−4
−5
−6
−7
−8
−12
160
159 159 159 159 159 159 159 159 159
Fig. 6. Absolute average error after AIC, STA/LTA and AN methods.
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the AN spectrum curve is. But it cannot be so long to ensure the accuracy of picking. Fig. 1 a) is a real microseismic data with sampling points of 400. The sampling interval is 0.001 s and dominant frequency of effective signal is 300 Hz. In order to ensure the consistency of experimental data, frame length and frame shift are 38 points and 3 points, respectively. After normalization, the value of approximate negentropy of microseismic data in each frame is calculated according to the AN function in Eq. (5). We plot the AN spectrum curve corresponding to each frame as shown in Fig. 1 b). Through the AN spectrum curve, it is obvious that the AN values of noise segment and effective signal segment are different, which illustrates the feasibility of AN method effectively. In order to achieve accuracy of arrival-time picking from AN spectrum curve, we need to set an appropriate threshold. How to choose a simple and reliable threshold method is also the key point in this paper. By analyzing the characteristics of AN spectral curve, we propose a simple threshold calculation function. A weighting value is designed based on the difference between the maximum and the minimum of AN spectral curve. The sensitivity and accuracy of threshold are adjusted by the weighting factor. The formula is defined as follows:
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factor of AN spectral curve in Fig. 1 b) is 0.3, the corresponding threshold in the example is shown with a dotted line. We can detect the first frame through the intersection of AN spectrum curve and threshold line, then pick up the specific data points correspond to the real arrivals according to the conversion formula Eq. (10).
At ¼ ð F−1Þ F s þ
Fl ; 2
ð10Þ
where At represents the arrival-time picking, F is the frame including first-arrival time. Fs and Fl represent frame length and frame shift, respectively. b F2l c is the integer portion of the value of b F2l c. The frame including arrival time in Fig. 1 b) is transformed using Eq. (10) to get the specific position of microseismic arrival time as shown in vertical line in Fig. 1 a). Finally, the first arrival picking framework diagrams by the proposed AN method is given as follows in Fig. 2. 3. Experiments
thr ¼ α ð maxðNJ Þ− minðNJ ÞÞ 0 b α b 1;
ð9Þ
where thr is threshold, α is the weighting factor, which adjusts the sensitivity of threshold. In practice, α is relatively small to avoid false picking. Through many experiments and observation of the results, we set α as 0.3 to ensure the accuracy of arrival-time picking. The weighting
In order to prove the feasibility and effectiveness of AN method for the first arrival time picking, we have selected multiple sets of experiments on synthetic records and real three-component microseismic data. We compare the proposed method with AIC and STA/LTA methods for arrivals picking in condition of different SNRs.
Fig. 7. Field record. a) X-component, b) Y-component, c) Z-component.
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3.1. Synthetic records First, we generate a series of synthetic records. Dominant frequency of effective signal is 300 Hz, sample frequency is 1000 Hz, sampling points are 1024, and first arrival keeps constant at 160 ms for each channel. We add Gaussian white noise of different amplitudes to this pure record to obtain noisy records with different SNRs from −1 dB to −12 dB. Fig. 3 a) is a single-channel with SNR of −3 dB, the first 400 sampling points are shown. In order to illustrate the better performance of the proposed method, we respectively compare it with AIC and STA/LTA methods. The comparison results of AIC method, STA/LTA method and AN method are shown in Fig. 3 b), c) and d), respectively. Fig. 3 b) shows the picking result of AIC method. In the least squares sense, the minimum value represents the worst fitting degree of noise and signal, this point corresponds to the arrival time and it is shown in Fig. 3 b). Fig. 3 c) shows the picking result of STA/LTA method. The maximum value in this STA/LTA curve represents maximum difference of the ratio of short-time window and long-time window, this point corresponds to the arrival time and the detection result is shown in Fig. 3 c). Fig. 3 d) shows AN spectrum curve and line of threshold according to Eqs. (5) and (9). The intersection of AN curve and threshold function is the frame including the first arrival time. We can obtain the specific position of first arrival time shown in Fig. 3 d) according to the corresponding relationship between the frame and data points in Eq. (10). Finally, all the picking results of three methods are marked with different lines in Fig. 3 a). From observation of these results, we know that the detected first arrival time are 162 ms (AIC method), 157 ms (STA/LTA method) and 159 ms (AN method), respectively. Comparing with the given first arrival time 162 ms, the errors of these three methods are
less than 0.5%. So these three methods all can detect the first arrival time accurately in the condition that the SNR is −3 dB. Then we compare these methods on a single-channel with SNR of −12 dB and sampling points of 1024 are shown in Fig. 4 a). The detection results of these three methods are given in Fig. 4 b) to d). In the same way as in Fig. 3, it can be seen that the picking result of AIC method is 22 ms, the result of STA/LTA method is 352 ms and the result of AN method is 159 ms. Compared with the actual arrival time 160 ms, the picking errors of AIC and STA/LTA method are 13.8% and 19.2%, respectively. In contrast, the error of the proposed AN method is 0.1%, which is much lower than the other two methods obviously. In order to avoid the accidental results, we make a model of a synthetic record containing 50 channels with SNRs from −1 dB to −12 dB, picking the arrivals using AIC, STA/LTA and the proposed AN methods. Fig. 5 shows the picking results by these three methods in conditions of both high and low SNRs. Fig. 5 a), b) and c) are the picking results of noisy synthetic records with SNR of −3 dB using the above three methods. Fig. 5 d), e) and f) are the picking results of noisy synthetic records with SNR of −12 dB using the above three methods. From these experimental results, we can see that when the SNR is −3 dB, the picking results of these three methods are similar to the actual arrival time. They all can give accurate results. However, when the SNR is reduced to −12 dB, the performances of the other two methods get worse obviously. However, the result of the proposed AN method is still accurate with small error. Table 1 shows the statistics of the detection results of noisy records, whose SNRs varies from −1 dB to −12 dB using AIC, STA/LTA and AN methods.
Fig. 8. Arrivals picking results of X-component by three methods. a) AIC method, b) STA/LTA method, c) AN method.
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Fig. 9. Arrivals picking results of Y-component by three methods. a) AIC method, b) STA/LTA method, c) AN method.
Fig. 10. Arrivals picking results of Z-component by three methods. a) AIC method, b) STA/LTA method, c) AN method.
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From the statistical data in this table, we can see that average picking errors (SNR from −1 dB to −7 dB) of the three methods are 0.5%, 0.3% and 0.1%, respectively. The picking results of the three methods are more effective. However, the picking error of AIC method is as high as 7.4% when the SNR is lower than −8 dB; and 2.7% when the SNR is lower than −10 dB. When SNR is from −8 dB to −12 dB, we can see that the results of AIC method and STA/LTA method are unsatisfactory, which is shown in gray boxes. However, the proposed AN method still works well and its average picking error is less than 0.1% when the SNR is from −1 dB to −12 dB. So the new method is more accurate and reliable comparing with AIC and STA/LTA methods.
Fig. 6 shows the absolute average error lines of AIC, STA/LTA and AN methods by analyzing the picking results of 100 channels in condition of SNR from −1 dB to −12 dB. 3.2. Actual record Finally, we test our proposed AN method by applying a set of real three-component microseismic data and compare it with AIC and STA/ LTA methods. There are 15 channels in this microseismic record and 512 sample points in each channel as shown in Fig. 7. We can see from the real three-component microseismic data that different
Fig. 11. Single-channel picking results of AIC, STA/LTA and AN methods. a) X-component, b) Y-component, c) Z-component.
Y. Li et al. / Journal of Applied Geophysics 152 (2018) 100–109
components have different SNRs and amplitudes. The picking results by AIC, STA/LTA and AN methods are respectively shown in Figs. 8, 9 and 10. Fig. 8 shows the picking results after the three methods of Xcomponent in Fig. 7 a). The effective signals of X-component are weaker and SNRs are low. From the picking results of three methods, we can see that AIC method can hardly pick up the first arrivals, STA/LTA method has a large picking error in the first channel, the new proposed AN method can pick accurately for each channel. Fig. 9 shows the picking results after the three methods of Ycomponent in Fig. 7 b). The effective signals of Y-component are stronger than X-component and SNR is higher. From the picking results of three methods, we can see that AIC method can hardly pick up the first arrival time, STA/LTA method has a large picking error in the fifth channel; the new proposed AN method can pick accurately for each channel. Fig. 10 shows the picking results after the three methods of Zcomponent in Fig. 7 c). The effective signals of X-component are stronger and SNR is higher. From the picking results of three methods, we can see that AIC method has a large picking error in the first channel, STA/ LTA method and the new proposed AN method can pick accurately for each channel. Moreover, we extract one channel from the X, Y and Z components in Figs. 8, 9 and 10, respectively. Giving the single-channel picking results of three components by AIC, STA/LTA and AN methods in Fig. 11. It can be seen from the single-channel waveforms in Fig. 11 that when the SNR is high, the picking results of the three methods are similar and their picking errors are small. However, when the SNR becomes lower, the picking errors of AIC method and STA/LTA method get larger, but the proposed AN method still has good accuracy and reliability for picking the first arrivals in all the three components. 4. Conclusions A novel method for first arrival time picking of three-component microseismic records based upon approximate negentropy (AN) theory is proposed in this paper. The fundamental concepts and principles of negentropy have been described. We use its characteristic that can detect differences of non-Gaussian characteristic between signal and noise and introduce a suitable expression of AN. In addition, the following conclusions can be drawn through the design of picking step and comparative analysis in experiments: AN method has better picking effect than conventional AIC and STA/LTA methods on synthetic microseismic records with SNR as low as −12 dB and dominant frequency of signal as high as 300 Hz. Overall, the proposed method is more efficient, accurate and stable for actual three-component microseismic data with low SNRs. However, as a novel proposed method, it still needs improvement in some aspects. We will try to detect multievents records, modify approximate negentropy expression and locate microseismic source, thus to expand microseismic exploration. Acknowledgements We express our gratitude to sponsors of Key Project of National Natural Science Foundation of China (No. 41730422) and National Natural Science Foundation of China (No. 41574096 and No. 41404081) for their support of the research described in this document.
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Contents lists available at ScienceDirect
Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo
Arrival-time picking method based on approximate negentropy for microseismic data Yue Li, Zhuo Ni, Yanan Tian ⁎ Department of Communication and Engineering, Jilin University, Changchun, China
a r t i c l e
i n f o
Article history: Received 17 January 2017 Received in revised form 28 December 2017 Accepted 16 March 2018 Available online 20 March 2018 Keywords: Arrival-time picking Approximate negentropy Microseismic data Low SNR
a b s t r a c t Accurate and dependable picking of the first arrival time for microseismic data is an important part in microseismic monitoring, which directly affects analysis results of post-processing. This paper presents a new method based on approximate negentropy (AN) theory for microseismic arrival time picking in condition of much lower signal-tonoise ratio (SNR). According to the differences in information characteristics between microseismic data and random noise, an appropriate approximation of negentropy function is selected to minimize the effect of SNR. At the same time, a weighted function of the differences between maximum and minimum value of AN spectrum curve is designed to obtain a proper threshold function. In this way, the region of signal and noise is distinguished to pick the first arrival time accurately. To demonstrate the effectiveness of AN method, we make many experiments on a series of synthetic data with different SNR from −1 dB to −12 dB and compare it with previously published Akaike information criterion (AIC) and short/long time average ratio (STA/LTA) methods. Experimental results indicate that these three methods can achieve well picking effect when SNR is from −1 dB to −8 dB. However, when SNR is as low as −8 dB to −12 dB, the proposed AN method yields more accurate and stable picking result than AIC and STA/LTA methods. Furthermore, the application results of real three-component microseismic data also show that the new method is superior to the other two methods in accuracy and stability. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Exploration of shale gas, coalbed methane or other unconventional oil and gas is the focus of oil and gas industry in the future, which is also the issue that the whole world concerns about. Hydraulic fracturing and microseismic monitoring methods have been widely used in oil and gas exploration. Source location is very important in microseismic data processing (Belayouni et al., 2015; Zhang et al., 2015; Li and Song, 2017). Denoising and picking of microseismic data are the two key steps for events identification and source location (Han and van der Baan, 2015; Velis et al., 2015). However, microseismic data is featured with huge amount of data, widely distributed frequencies and low signal-to-noise ratio (SNR). Accurate and quick arrival-time picking methods remain in urgent need. So far, numerous methods of arrival-time picking both in time and frequency domains have been presented for single-component and three-component records by scholars from various countries. Akaike information criterion (AIC) and short/long time average ratio (STA/LTA) are two representative approaches for microseismic first arrival picking. AIC is often used with auto-regressive method (AR-AIC) to divide the input signal into some locally stationary segments, each of which is ⁎ Corresponding author at: Nanhu Road 5372, Changchun 130012, China. E-mail address: [email protected] (Y. Tian).
https://doi.org/10.1016/j.jappgeo.2018.03.012 0926-9851/© 2017 Elsevier B.V. All rights reserved.
assumed to be represented as an auto-regressive model. Sleeman and van Eck (1999) used an optimal separation of two stationary time series, which can calculate AIC directly without considering the convergence of AR. Meanwhile, the minimum of AIC spectrum is considered to be the first arrival time. St-Onge (2011) indicated that this quick method could be implemented for picking large volumes of microseismic data. However, AIC method can always find a minimum in condition of high SNR. Yet it cannot recognize the microseismic signal buried in highamplitude noise accurately. Thus, AIC method is generally not used alone but combines with other picking methods. STA/LTA is a conventional method for microseismic events identification in time domain. The method divides characteristic function according to the different lengths of short and long time windows. It utilizes the characteristics of absolute amplitude, energy and envelope of microseismic signal. Then the ratio between average values of the new time series is calculated, the maximum of which is considered as the first arrival time. In addition, several other modified methods based on it have been proposed later. Wong et al. (2009) developed a modified energy ratio (MER) method. Akram (2011) used standard deviation in a moving time window to pick P-wave arrival time. Gou et al. (2011) used STA/ LTA method combined with an envelope method to detect the arrival time of local events. However, the disadvantage of STA/LTA method is that it is difficult to select an appropriate length of time window for picking accurately in low SNR. Other feasible picking methods involving
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Fig. 1. a) Actual microseismic data and final picking result (vertical line). b) AN spectral curve and final picking result (dot) at the first sample exceeding the threshold.
polarization proposed to pick the first arrival times by Moriya (2008, 2009). Küperkoch et al. (2010) presented an iterative method for picking onset of seismic events based on higher order statistics (HOS) method. Sheng et al. (2015) used CWT to analysis microseismic signal and applied HOS method to first arrival picking. Liao et al. (2010) used the fractal dimension and polarized method together for automatic P/ S-wave arrivals picking. Zhang et al. (2003) developed an automatic P waves picking method based on wavelet transform combined with AIC analysis. Capilla (2006) used Haar wavelet to identify seismic data. Wavelet transform combined STA/LTA method has been proposed by Rodriguez (2011) and Li et al. (2016). Al-Shuhail (2015) used the super virtual seismic interferometer method to pick up first arrivals in petroleum seismic data. An et al. (2015) developed the extended super-virtual interferometer. Tan et al. (2014) proposed method combined correlation and polarization. Qu et al. (2015) developed a method first-arrival picking that combined cross-correlation and AIC methods. Akram and Eaton (2016a) improved the method based on crosscorrelation. Kim et al. (2016) suggested a fast picking method by combing stacking and cross-correlation approaches. Tan and He (2016) developed a cross-correlation and least-squares-based algorithm to identify microseismic events. In addition, Zhu et al. (2016) proposed a method based on fuzzy C-means clustering for arrival-time picking on
microseismic data. These picking methods above offer the reliability of arrival time picking and have many places worth for our reference. However, the picking accuracy of these methods is limited by strong noise. In other words, weaker amplitudes of microseismic data make arrival-time picking difficult in low SNR (Akram and Eaton, 2016b). In view of the above problems, finding an arrival time picking method with fast calculating speed and high picking precision needs more discussion and studies by experts in this field. Based on the characteristics of microseismic data itself, this paper presents a new picking method based upon approximate negentropy (AN) theory. Compared with the existing picking methods, the new method can achieve accurate arrival picking when SNR is as low as −12 dB. Meanwhile, its calculation process is simple, fast and accurate. This paper is arranged as follows. First, AN theory is introduced briefly and its application process in microseismic signal is described concretely including the selection of approximate function and the design of threshold function. Then, we evaluate the performance of the proposed method using a synthetic seismic record, in which dominant frequency of effective signal is 300 Hz. The SNRs range is from −1 dB to −12 dB. Moreover, we compare its picking result with AIC method and STA/LTA method. Comparison results show that the proposed method performs better in the aspect of first arrival time picking than the other two methods.
Fig. 2. Framework diagrams of first arrival picking by the proposed AN method.
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Besides, experimental results on a real three-component microseismic record also show that the new method can even pick accurately in condition of lower SNR as −12 dB. 2. Basic theory 2.1. Approximate negentropy (AN) Let y = {yi, i = 1, 2, ⋯, n}T be a random vector of n data points. Negentropy of the digital waveform y is defined as follows: 0
J ðyÞ ¼ H ðy Þ−H ðyÞ;
ð1Þ
where y′ is a Gaussian random vector with the same covariance matrix as y, H(y) is entropy of sequence y and H(y′) is entropy of sequence y′. Negentropy is regarded as the amount of structure of the distribution of y. For random variables with the same variance, the distribution concentrated on a certain value has largest negentropy. Namely, the more “random” the distribution of y is, the smaller its negentropy is. Because Gaussian distribution can be considered as the least structured of all distributions. Negentropy does not vary with the amplitudes of signals and can be interpreted as a classical non-Gaussian measuring method. Negentropy value is equal to zero for Gaussian distribution. For nonGaussian distribution, negentropy value is positive. In view of microseismic characteristics of low SNR, weak signal and strong noise, the property of negentropy has good applicability for arrival-time picking.
In practical applications, calculation of negentropy relies on the prior probability of random variables, but exact probability of microseismic data is unknown, which makes the calculation of negentropy extremely complicated and difficult to achieve. Therefore, this paper constructs a proper function of approximate negentropy to apply to arrival-time picking on microseismic data. There are many approximate negentropy methods, the approximate method based on maximum entropy criterion (minimum negative entropy) is widely used and relatively sensitive to signals. The expression is described as follows: J ðxÞ ¼
n X
2
ki fE½Gi ðxÞ−E½Gi ðx0 Þg ;
ð2Þ
i¼1
where operator E represents the calculation of mathematical expectation and each non-quadratic function Gi(.) must be orthogonal in a certain sense. i means the number of comparison equation Gi(.), the higher the value of i is, the more accurate the approximation of negentropy is. Random vector x is a sequence of zero mean and unit variance with n data points, which is generated from sequence y after normalization. The vector x′ has a Gaussian distribution with zero mean and unit variance. Each ki is a positive constant and n is an integer greater than or equal to 1. Generally, n = 2 and k1 = k2 = 1. The selection of a suitable contrast function Gi(.) is an important task, which affects confidence level of picking. In practice, the choice of contrast equation Gi(.) should satisfy at least two conditions: 1) the calculation of the equation should be simple and fast. 2) The equation
Fig. 3. First arrival times picking by three methods for synthetic records. a) Single-channel record (SNR = −3 dB) and picking results by AIC method, STA/LTA method and AN method. b) AIC spectral curve and final picking at the minimum. c) STA/LTA ratio spectral curve and final picking at the maximum. d) AN spectral curve and final picking at the first sample exceeding the threshold.
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can detect the super-Gaussian or the sub-Gaussian component. In order to satisfy the above selection criteria to obtain a more robust estimate, we choose two appropriate non-quadratic contrast equations of Gi(.) for sequence ζ = {ζi, i = 1, 2, …, n}, which are defined as: !
G1 ðζÞ ¼ − exp
G2 ðζÞ ¼
−ζ2 ; 2
1 4 ζ : 4
ð3Þ
ð4Þ
One of the main features of these two different contrast functions is that G1(ζ) and G2(ζ) are piecewise linear approximations. G1(ζ) has good robustness and can be used to detect the super-Gaussian properties of independent components and G2(ζ) is suitable for estimating the subGaussian properties of random variables. It is known that x′ is the stanqffiffi dard normal distribution sequence. So E½G1 ðx0 Þ ¼ 12 and E½G2 ðx0 Þ ¼ 34 are calculated by using mean value formula. Therefore, the new approximate function of negentropy we proposed can be described as: ANðxÞ ¼
( rffiffiffi)2 −x2 1 1 3 2 − þ E x4 − : E − exp 2 4 4 2
ð5Þ
Here, random vector x obtained from normalization of microseismic data is a sequence of zero mean and unit variance. AN(x) represents the approximate negentropy of random sequence x. It can be seen that the
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proposed AN method is not only be easily defined, rapidly calculating, but also has good statistical properties. 2.2. Arrival-time picking based on AN When a Gaussian random sequence passes through a linear filter, the output result is still subject to Gaussian distribution. According to the central limit theorem, microseismic random noise can be seen as an infinite number of independent identically distributed noise sources that work together in ideal conditions. So in ideal conditions, microseismic random noise can be regarded as Gaussian distribution and effective signal obeys non-Gaussian distribution. Accounting for the above assumptions and characteristic of negentropy, an automatic arrivaltime picking method based on AN is presented for microseismic data in this paper. We will describe how to use AN analysis method to pick first arrivals in time domain. The concrete steps are shown as: firstly, extract independent random sequence with zero average and unit variance through the normalized microseismic signal. Secondly, divide microseismic data into several frames, calculate the value of AN of each frame to acquire statistical data, draw the corresponding AN spectral curve. Finally, a suitable threshold function is designed to find the boundary between noise and signal, so as to determine the first arrival time. First of all, according to Eq. (2), we know that the input microseismic sequence needs to be normalized before calculating the approximate negentropy, that is, how to obtain a random sequence x with zero mean and unit variance. For the sequence y = {yi, i = 1, 2, …n} with n
Fig. 4. First arrival times picking by three methods for synthetic records. a) Single-channel record (SNR = −12 dB) and picking results of AIC method, STA/LTA method and AN method. b) AIC spectral curve and final picking at the minimum. c) STA/LTA ratio spectral curve and final picking at the maximum. d) AN spectral curve and final picking at the first sample exceeding the threshold.
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Fig. 5. First arrival times picking by three methods for multi-channel synthetic records with different SNRs. a)–c) Noisy record with 50 channels (SNR = −3 dB) and final picking of AIC method, STA/LTA method and AN method. d)–f) Noisy record with 50 channels (SNR = −12 dB) and final picking of AIC method, STA/LTA method and AN method.
data points as the input microseismic sequence, random sequence x can be normalized as follows (Nazarpour et al., 2005): y¼
n 1X y; n i¼1 i
σ2 ¼
x¼
ð6Þ
n 1 X ðy −yÞ2 ; n−1 i¼1 i
Then, we divide the normalized sequence x into frames to ensure the stability of microseismic data since it is not stationary all the time. Here, frame length and frame shift are two important parameters, which directly affect the picking effect. The larger frame length is, the smoother
ð7Þ
y−y ; σ
ð8Þ
where y and σ2 represent the mean and variance of microseismic sequence y, respectively. y is a sequence with the same size of y and each element is y. x is the normalized sequence with n data points, zero mean and unit variance. Table 1 Picking results of AIC, STA/LTA and AN in condition of different SNRs. SNR
−9
−10
−11
163 163 162 166 164 171 153 234 470
187
450
22
STA/LTA picks (ms) 159 156 157 158 156 159 156 159 159
383
484
352
159
159
159
Actual value (ms) AIC picks (ms)
AN picks (ms)
−1
−2
−3
−4
−5
−6
−7
−8
−12
160
159 159 159 159 159 159 159 159 159
Fig. 6. Absolute average error after AIC, STA/LTA and AN methods.
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the AN spectrum curve is. But it cannot be so long to ensure the accuracy of picking. Fig. 1 a) is a real microseismic data with sampling points of 400. The sampling interval is 0.001 s and dominant frequency of effective signal is 300 Hz. In order to ensure the consistency of experimental data, frame length and frame shift are 38 points and 3 points, respectively. After normalization, the value of approximate negentropy of microseismic data in each frame is calculated according to the AN function in Eq. (5). We plot the AN spectrum curve corresponding to each frame as shown in Fig. 1 b). Through the AN spectrum curve, it is obvious that the AN values of noise segment and effective signal segment are different, which illustrates the feasibility of AN method effectively. In order to achieve accuracy of arrival-time picking from AN spectrum curve, we need to set an appropriate threshold. How to choose a simple and reliable threshold method is also the key point in this paper. By analyzing the characteristics of AN spectral curve, we propose a simple threshold calculation function. A weighting value is designed based on the difference between the maximum and the minimum of AN spectral curve. The sensitivity and accuracy of threshold are adjusted by the weighting factor. The formula is defined as follows:
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factor of AN spectral curve in Fig. 1 b) is 0.3, the corresponding threshold in the example is shown with a dotted line. We can detect the first frame through the intersection of AN spectrum curve and threshold line, then pick up the specific data points correspond to the real arrivals according to the conversion formula Eq. (10).
At ¼ ð F−1Þ F s þ
Fl ; 2
ð10Þ
where At represents the arrival-time picking, F is the frame including first-arrival time. Fs and Fl represent frame length and frame shift, respectively. b F2l c is the integer portion of the value of b F2l c. The frame including arrival time in Fig. 1 b) is transformed using Eq. (10) to get the specific position of microseismic arrival time as shown in vertical line in Fig. 1 a). Finally, the first arrival picking framework diagrams by the proposed AN method is given as follows in Fig. 2. 3. Experiments
thr ¼ α ð maxðNJ Þ− minðNJ ÞÞ 0 b α b 1;
ð9Þ
where thr is threshold, α is the weighting factor, which adjusts the sensitivity of threshold. In practice, α is relatively small to avoid false picking. Through many experiments and observation of the results, we set α as 0.3 to ensure the accuracy of arrival-time picking. The weighting
In order to prove the feasibility and effectiveness of AN method for the first arrival time picking, we have selected multiple sets of experiments on synthetic records and real three-component microseismic data. We compare the proposed method with AIC and STA/LTA methods for arrivals picking in condition of different SNRs.
Fig. 7. Field record. a) X-component, b) Y-component, c) Z-component.
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3.1. Synthetic records First, we generate a series of synthetic records. Dominant frequency of effective signal is 300 Hz, sample frequency is 1000 Hz, sampling points are 1024, and first arrival keeps constant at 160 ms for each channel. We add Gaussian white noise of different amplitudes to this pure record to obtain noisy records with different SNRs from −1 dB to −12 dB. Fig. 3 a) is a single-channel with SNR of −3 dB, the first 400 sampling points are shown. In order to illustrate the better performance of the proposed method, we respectively compare it with AIC and STA/LTA methods. The comparison results of AIC method, STA/LTA method and AN method are shown in Fig. 3 b), c) and d), respectively. Fig. 3 b) shows the picking result of AIC method. In the least squares sense, the minimum value represents the worst fitting degree of noise and signal, this point corresponds to the arrival time and it is shown in Fig. 3 b). Fig. 3 c) shows the picking result of STA/LTA method. The maximum value in this STA/LTA curve represents maximum difference of the ratio of short-time window and long-time window, this point corresponds to the arrival time and the detection result is shown in Fig. 3 c). Fig. 3 d) shows AN spectrum curve and line of threshold according to Eqs. (5) and (9). The intersection of AN curve and threshold function is the frame including the first arrival time. We can obtain the specific position of first arrival time shown in Fig. 3 d) according to the corresponding relationship between the frame and data points in Eq. (10). Finally, all the picking results of three methods are marked with different lines in Fig. 3 a). From observation of these results, we know that the detected first arrival time are 162 ms (AIC method), 157 ms (STA/LTA method) and 159 ms (AN method), respectively. Comparing with the given first arrival time 162 ms, the errors of these three methods are
less than 0.5%. So these three methods all can detect the first arrival time accurately in the condition that the SNR is −3 dB. Then we compare these methods on a single-channel with SNR of −12 dB and sampling points of 1024 are shown in Fig. 4 a). The detection results of these three methods are given in Fig. 4 b) to d). In the same way as in Fig. 3, it can be seen that the picking result of AIC method is 22 ms, the result of STA/LTA method is 352 ms and the result of AN method is 159 ms. Compared with the actual arrival time 160 ms, the picking errors of AIC and STA/LTA method are 13.8% and 19.2%, respectively. In contrast, the error of the proposed AN method is 0.1%, which is much lower than the other two methods obviously. In order to avoid the accidental results, we make a model of a synthetic record containing 50 channels with SNRs from −1 dB to −12 dB, picking the arrivals using AIC, STA/LTA and the proposed AN methods. Fig. 5 shows the picking results by these three methods in conditions of both high and low SNRs. Fig. 5 a), b) and c) are the picking results of noisy synthetic records with SNR of −3 dB using the above three methods. Fig. 5 d), e) and f) are the picking results of noisy synthetic records with SNR of −12 dB using the above three methods. From these experimental results, we can see that when the SNR is −3 dB, the picking results of these three methods are similar to the actual arrival time. They all can give accurate results. However, when the SNR is reduced to −12 dB, the performances of the other two methods get worse obviously. However, the result of the proposed AN method is still accurate with small error. Table 1 shows the statistics of the detection results of noisy records, whose SNRs varies from −1 dB to −12 dB using AIC, STA/LTA and AN methods.
Fig. 8. Arrivals picking results of X-component by three methods. a) AIC method, b) STA/LTA method, c) AN method.
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Fig. 9. Arrivals picking results of Y-component by three methods. a) AIC method, b) STA/LTA method, c) AN method.
Fig. 10. Arrivals picking results of Z-component by three methods. a) AIC method, b) STA/LTA method, c) AN method.
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From the statistical data in this table, we can see that average picking errors (SNR from −1 dB to −7 dB) of the three methods are 0.5%, 0.3% and 0.1%, respectively. The picking results of the three methods are more effective. However, the picking error of AIC method is as high as 7.4% when the SNR is lower than −8 dB; and 2.7% when the SNR is lower than −10 dB. When SNR is from −8 dB to −12 dB, we can see that the results of AIC method and STA/LTA method are unsatisfactory, which is shown in gray boxes. However, the proposed AN method still works well and its average picking error is less than 0.1% when the SNR is from −1 dB to −12 dB. So the new method is more accurate and reliable comparing with AIC and STA/LTA methods.
Fig. 6 shows the absolute average error lines of AIC, STA/LTA and AN methods by analyzing the picking results of 100 channels in condition of SNR from −1 dB to −12 dB. 3.2. Actual record Finally, we test our proposed AN method by applying a set of real three-component microseismic data and compare it with AIC and STA/ LTA methods. There are 15 channels in this microseismic record and 512 sample points in each channel as shown in Fig. 7. We can see from the real three-component microseismic data that different
Fig. 11. Single-channel picking results of AIC, STA/LTA and AN methods. a) X-component, b) Y-component, c) Z-component.
Y. Li et al. / Journal of Applied Geophysics 152 (2018) 100–109
components have different SNRs and amplitudes. The picking results by AIC, STA/LTA and AN methods are respectively shown in Figs. 8, 9 and 10. Fig. 8 shows the picking results after the three methods of Xcomponent in Fig. 7 a). The effective signals of X-component are weaker and SNRs are low. From the picking results of three methods, we can see that AIC method can hardly pick up the first arrivals, STA/LTA method has a large picking error in the first channel, the new proposed AN method can pick accurately for each channel. Fig. 9 shows the picking results after the three methods of Ycomponent in Fig. 7 b). The effective signals of Y-component are stronger than X-component and SNR is higher. From the picking results of three methods, we can see that AIC method can hardly pick up the first arrival time, STA/LTA method has a large picking error in the fifth channel; the new proposed AN method can pick accurately for each channel. Fig. 10 shows the picking results after the three methods of Zcomponent in Fig. 7 c). The effective signals of X-component are stronger and SNR is higher. From the picking results of three methods, we can see that AIC method has a large picking error in the first channel, STA/ LTA method and the new proposed AN method can pick accurately for each channel. Moreover, we extract one channel from the X, Y and Z components in Figs. 8, 9 and 10, respectively. Giving the single-channel picking results of three components by AIC, STA/LTA and AN methods in Fig. 11. It can be seen from the single-channel waveforms in Fig. 11 that when the SNR is high, the picking results of the three methods are similar and their picking errors are small. However, when the SNR becomes lower, the picking errors of AIC method and STA/LTA method get larger, but the proposed AN method still has good accuracy and reliability for picking the first arrivals in all the three components. 4. Conclusions A novel method for first arrival time picking of three-component microseismic records based upon approximate negentropy (AN) theory is proposed in this paper. The fundamental concepts and principles of negentropy have been described. We use its characteristic that can detect differences of non-Gaussian characteristic between signal and noise and introduce a suitable expression of AN. In addition, the following conclusions can be drawn through the design of picking step and comparative analysis in experiments: AN method has better picking effect than conventional AIC and STA/LTA methods on synthetic microseismic records with SNR as low as −12 dB and dominant frequency of signal as high as 300 Hz. Overall, the proposed method is more efficient, accurate and stable for actual three-component microseismic data with low SNRs. However, as a novel proposed method, it still needs improvement in some aspects. We will try to detect multievents records, modify approximate negentropy expression and locate microseismic source, thus to expand microseismic exploration. Acknowledgements We express our gratitude to sponsors of Key Project of National Natural Science Foundation of China (No. 41730422) and National Natural Science Foundation of China (No. 41574096 and No. 41404081) for their support of the research described in this document.
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