the pagerank method for automatic detection of ... · the pagerank method for automatic detection...

The PageRank method for automatic detection of microseismic events Huiyu Zhu*, Jie Zhang, University of Science and Technology of China (USTC) Summary In microseismic monitoring, the fundamental task is to detect events automatically. The majority of microseismic events may suffer the limits from low signal-to-noise ratio for detection. Using a single master event to correlate the entire dataset may not work because events do not necessarily all exhibit sufficient similarity to the same event. During hydraulic fracturing, however, it is likely that event A may be similar to event B, and event B may be similar to event C, but event A may not be similar to event C on the same standard. The situation of this event connectivity is similar to web pages, in which page content similarity is detected by PageRank. PageRank is one of the initial web page searching algorithms implemented by Google to estimate the links between documents. Applying that technology to microseismic problems, we rank windows of recorded data for similarity measurement, thus detect which windows likely contain potential events. We generate synthetic microseismic events with different source mechanisms, and demonstrate that the approach can handle noise and variations in waveform data reasonably well. Introduction Low-permeability oil reservoir and gas shales are difficult to produce. Hydraulic fracturing technology is often applied to connect the pathway and force hydrocarbons flow out. The process of hydrofracturing may induce microseismic events, which may be monitored by a surface or downhole seismic array. During data processing, we build a velocity model and locate the microseismic events either by traveltimes or waveforms. These event locations may suggest where fracturing takes place. Among these efforts, however, the very first step is to detect hundreds to thousands of microseismic events from a large and noisy dataset. Most microseismic events are small and signal-to-noise ratio is low, thus, automatic detection is difficult. One may use master events to correlate data traces and detect weak events. Previous studies have also shown that the correlation detection can be effective as long as the separation between the master event and the target event is less than the dominant wavelength, and the master event and target events are similar (Gibbons and Ringdal, 2006). In real problems, sometimes using a single master event to correlate the entire dataset may not work. We often face with a problem that event A may be similar to event B, and event B may be similar to event C, but event A may not be similar to event C on the same standard. This is due to

source focal mechanisms associated with fracturing. The problem is similar to mining important pages among massive web pages, and it is solved by applying PageRank method to solve a connectivity matrix problem (Page et al., 1999). Motivated by Aguiar and Beroza (2014) applying PageRank to detect weak tremors during a large earthquake, we explore the method for detecting weak microseismic events. The PageRank method can be applied to rank windows of recorded data according to mutual links. A page will have a high rank if the sum of the ranks of its backlinks is high. Figure 1 shows a possible relationship among four events.

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Figure 1: Event relationship: window B is linked (similar) to window A, window A is linked to window D, window D is linked to window C, but window B is indirectly linked to window C (since B -> A -> D -> C). This relationship could be due to source focal mechanism associated with consistent fracturing pattern and variations of the pattern. The PageRank method The PageRank is the probability of surfing a certain web page under random surfing model. In the initial condition, the probability of each page is the same value. Like Markov Chain, PageRank is computed from the previous stage and it calculates the value iteratively.

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PageRank for microseismic event detection

Let n be the number of pages. To describe their relationship on links, we generate a connective matrix G. If there is a hyperlink from page i to page j, then gij=1, otherwise gij=0. Then G matrix can be very huge, but very sparse. Let cj be the column sum of G:

j iji

c g (1)

Then, let p be the probability that the random walk follows a link. A typical value for p is 0.85 and 1-p is the probability that some arbitrary page is chosen. So we can use δto represent a particular page that is randomly chosen, see the Equation 2. (1 )p n (2)

We generate A matrix, whose size is n by n. The elements in A are

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The matrix A is the transition probability matrix of the Markov Chain. The elements in A are all strictly between zero and one, and the column sums are all equal to one. We can apply Perron-Frobenius theorem, an important result in matrix theory, to such matrix. It concludes that a nonzero solution of the Equation 4 exists. x Ax (4) And it is unique to within a scaling factor. If this scaling factor is chosen so that

1ii

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Then, x is the state vector of the Markov Chain and is the PageRank value. We could solve the same matrix problem by replacing page with microseismic events in the above method. Application and examples We apply PageRank method in microseismic event detection. In synthetic test, we design a six-layer model (Table 1).

Thickness(km) Vs

(km/s) Vp/Vs Density(g/cm3)

0.5 3.1 1.72 600

0.15 3.3 1.73 620

0.2 3.4 1.73 610

0.15 3.3 1.73 600

0.3 3.2 1.73 630

∞ 3.7 1.73 650

Table 1: Model layer parameters.

We apply elastic wave modeling of a point earthquake source in a multi-layered half space using the Thompson-Haskell propagator matrix technique (Zhu and Rivera, 2002) to calculate synthetic waveforms with different source focal mechanisms. We assume receivers on the surface. We calculate eight events in total with magnitudes varying from -3 to 0. Table 2 shows the event information.

Depth (km)

magnitude Strike Dip Rake

0.96 -1.8 45 30 30 1.05 -2.3 45 45 30

1.12 -2 45 60 30 1.08 -1.7 45 90 30 0.99 -2.4 45 110 30

1.14 -2 45 120 30 1.14 -1.8 45 168 100

1.08 -2.2 45 198 170

Table 2: There are eight synthetic events. The strike of all the events is assumed exactly same but with dip and rake varying. We divide the data into the same length of windows. Each window is lagged by one sample point. Then we correlate each window with all other windows and calculate the correlation coefficient (CC) values of paired windows. During the calculation, we find the population of the correlation coefficient (CC) values following a normal distribution approximately as shown in Figure 2. We can establish a threshold of detection according to the population.

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Figure 2: The blue bars are the distribution of Correlation Coefficient (CC) values for window pairs. The red line is the theoretical normal distribution plot. The distribution of CC values allows norm distribution.

164SEG Denver 2014 Annual MeetingDOI http://dx.doi.org/10.1190/segam2014-1231.1© 2014 SEG

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We establish our detection threshold on the basis of Gaussian distribution with zero mean (where the mean is -0.0003, very close to zero, so we regard it as zero). We focus on the large positive values to declare a positive detection. For a normal distribution, we can use σ or 3σ as a measure to establish a threshold of detection. The positive threshold of σ corresponds to a two-sided significance level of 65%, while 3σ corresponds to a two-sided significance level of 99.7%. But there is a tradeoff between threshold and positive detection. As if we choose a higher threshold, it will provide more confident matches, but sacrifice some positive correlation results for the low-SNR data. If we give a lower threshold, it will give more positive correlation results, but there should be less confidence on the matches. Figure 3 shows a comparison between two different levels of threshold.

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Figure 3: A: synthetic data without noise. B: synthetic data with noise, and its SNR is -2.597. C and D are corresponding to the PageRank values for σ and 3σ as a threshold. Figure 3 gives us ideas on choosing the threshold value. In our test, we prefer to use σ to be the threshold, which should provide more potential matches.

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Figure 4: The result for low signal-to-noise data. The signal-to-noise ratio is -2.597. The power of noise is bigger than signal. The red circles correspond to events. Figure 4 shows the PageRank for synthetic data in Z direction. When we have calculated the PageRank for these window pairs, we got to know which windows have high probabilities of being linked, that is, the microseismic events we wanted to detect. In Figure 4 we find the fourth circle and the fifth one are not divided clearly. Because of the influence by noise, in this direction, we cannot recognize the events from noise. Thus, when the level of noise improves, the PageRank method works but not so robust. In the real problem, this situation often occurs: from one direction or on a single trace, the signal-to-noise ratio is too low to detect. To solve the problem, we can combine the other two directions (X direction, Y direction), or utilize multiple traces for calculation. The theory is the same. Figure 5 presents a case of multiple traces and the detection results.


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Figure 5: PageRank values of multiple traces. Events are marked by red lines. Conclusions: We applied the PageRank method for automatic event detection. It helps ranking microseismic events from noisy data. In our test, we divide the data into small windows and correlate these windows and calculate the Correlation Coefficient (CC) values. These windows are ranked following their links, and a matrix problem is solved. We use the statistical theory to generate a threshold to distinguish noise and signal. We make a comparison on different thresholds. We tested a single trace and multi-trace data, and found that multi-trace data offers more information for detection. The approach presents a great potential for event detection. Acknowledgments We thank our research group for helpful advice during this project.


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http://dx.doi.org/10.1190/segam2014-1231.1 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2014 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES

Aguiar, A. C., and G. C. Beroza, 2014, pagerank for earthquakes: Seismological Research Letters, 85, no. 2, 344–350, http://dx.doi.org/10.1785/0220130162.

Gibbons, S. J., and F. Ringdal, 2006, The detection of low magnitude seismic events using array-based waveform correlation: Geophysical Journal International, 165, no. 1, 149–166, http://dx.doi.org/10.1111/j.1365-246X.2006.02865.x.

Kummerow, J., 2010, Using the value of the crosscorrelation coefficient to locate microseismic events: Geophysics, 75, no. 4, MA47–MA52, http://dx.doi.org/10.1190/1.3463713.

Munro, K., 2004, Automatic event detection and picking of P-wave arrivals : CREWES Research Report, 16, 12–1.

Maxwell, S., 2010, Microseismic: Growth born from success: The Leading Edge, 29, 338–343, http://dx.doi.org/10.1190/1.3353732.

Page, L., S. Brin, R. Motwani, and T. Winograd, 1999, The pagerank citation ranking: Bringing order to the web: Technical Report Report, Stanford InfoLab.

Song, F., H. S. Kuleli, M. N. Toksöz, E. Ay, and H. Zhang, 2010, An improved method for hydrofracture-induced microseismic event detection and phase picking: Geophysics, 75, no. 6, A47–A52, http://dx.doi.org/10.1190/1.3484716.

Warpinski, N., 2009, Microseismic monitoring: Inside and out: Journal of Petroleum Technology, 61, no. 11, 80–85, http://dx.doi.org/10.2118/118537-JPT.

Zhu, L., and L. A. Rivera, 2002, A note on the dynamic and static displacements from a point source in multilayered media : Geophysical Journal International, 148, no. 3, 619–627, http://dx.doi.org/10.1046/j.1365-246X.2002.01610.x.


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the pagerank method for automatic detection of ... · the pagerank method for automatic detection...

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