automatic determination of first-motion polarity and its...

ArticleVol. 21, No. 5, p. 695702, October 2017http://dx.doi.org/10.1007/s12303-017-0022-8pISSN 1226-4806 eISSN 1598-7477 Geosciences JournalGJAutomatic determination of first-motion polarity and its application to focal mechanism analysis of microseismic events

Juhwan Kim1, Jeong-Ung Woo1, Junkee Rhie1*, and Tae-Seob Kang2

1School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Republic of Korea2Department of Earth and Environmental Sciences, Pukyong National University, Busan 48513, Republic of Korea

ABSTRACT: A method for automatically determining first-motion polarities is developed, with a view to its application to thefocal mechanism analysis of massive microseismic events caused by hydraulic fracturing. The method is based on two assumptions:the existence of a point source, which has negligible effects of fault finiteness and rupture directivity; and a laterally homogeneousstructure, which has azimuthally isotropic propagation characteristics. Under these assumptions, the event waveforms recorded ateach station share a common source time function shape, with varying amplitudes, that is dependent on the radiation pattern fromthe source. With respect to the reference waveform with the highest signal-to-noise ratio (SNR) among all the waveforms at eachstation for an event, the relative polarities of waveforms at other stations are estimated using cross correlation analysis. The absolutepolarities of each waveform are then defined using the reference waveform, whose SNR can be further enhanced using the stackedwaveforms after corrections of relative polarities and time lags between the reference and target waveforms have been made. Then,a grid-search algorithm can be incorporated to invert focal mechanisms using the automatically measured polarities for a givenevent. Since the procedure requires only the evaluation of a cross-correlation coefficient, it can be incorporated into an automatedalgorithm. The method is applied to determine the focal mechanism solutions of microseismic events occurring in a shale gas playwhere commercial production is ongoing. Two types of focal mechanism solutions are found to be dominant: vertical dip-slip, andstrike-slip. The strike-slip events occur due to re-activation of natural fractures connecting cracks opened by hydraulic fracturing.For the vertical dip-slip events, it was observed that their strikes are consistent with the direction of maximum horizontal stress,which supports the theory that slips occur on the horizontal bedding planes due to the opening of vertical cracks generated byhydraulic fracturing.

Key words: automatic determination, P-wave polarity, focal mechanism, hydraulic fracturing, microseismic event

Manuscript received September 19, 2016; Manuscript accepted April 28, 2017

1. INTRODUCTION

Hydraulic fracturing involves the high-pressure injection offluids into rocks to increase pore pressures and consequentlygenerate fractures through tensional opening of the planesperpendicular to the direction of minimum principal stress(Hubbert and Willis, 1957). Subsequently, the introduction ofproppants injected with fluids prevents opened cracks fromclosing, and enhances permeability over an extended period

of time. These basic processes make the commercial production ofnatural gas through hydraulic fracturing possible. Since thepermeability and final productivity of a gas is controlled byboth newly generated fractures and pre-existing natural fractures, itis important to identify such fractures and understand thecharacteristics of entire fracture networks (Fisher et al., 2002;Gale et al., 2007). Some microseismic events are thought to beinduced by hydraulic fracturing directly, while others are relatedto the re-activation of natural fractures during the hydraulicfracturing process. As it is possible to distinguish both of theseevents on the basis of their hypocenters and focal mechanismsolutions, an analysis of microseismic events can provide valuableinformation that can be used in gas productivity estimation(Kratz et al., 2012; Neuhaus et al., 2012; Snelling et al., 2013b).

Focal mechanism determination is based on the observation

*Corresponding author:Junkee RhieSchool of Earth and Environmental Sciences, Seoul National Univer-sity, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of KoreaTel: +82-2-880-6731, Fax: +82-2-871-3269, E-mail: [email protected]

The Association of Korean Geoscience Societies and Springer 2017

696 Juhwan Kim, Jeong-Ung Woo, Junkee Rhie, and Tae-Seob Kang

http://dx.doi.org/10.1007/s12303-017-0022-8 http://www.springer.com/journal/12303

that seismic radiation patterns vary for different source mechanisms(Lay and Wallace, 1995). Many microseismic events occur over avery short period of time, and have magnitudes that are extremelysmall; often less than zero (Davies et al., 2013). As a result, P-wavepolarities are widely used to characterize small earthquakes(Lay and Wallace, 1995). In this study, we develop an automatedprocedure to measure the polarities of first P arrivals and todetermine focal mechanisms from the measurements. We thenvalidate the method by applying it to an analysis of microseismicevents occurring during hydraulic fracturing for shale gasproduction. Additionally, we discuss the physical mechanismsdriving these microseismic events on the basis of a comprehensiveinvestigation of focal mechanism solutions, the local stress field,and the distribution of known natural faults and fractures.

2. DATA AND METHODS

In this study, we used waveform data from microseismicevents that occurred in a commercially operated shale gas play inthe Horn River Basin. The Horn River Basin contains threemain shale gas resource formations, where multi-stage horizontalhydraulic wells are operated (Pyecroft et al., 2015). Waveformdata are recorded during multiple hydraulic fracturing stagesby a shallow buried array consisting of 98 three-componentgeophones, with apertures of around 8 km (Fig. 1b). We usedpredetermined hypocenters based on the arrival times, whichwere measured from the 5–50 Hz band-pass filtered waveformbased on the short-term average/long-term average (STA/LTA)method (Woo et al., 2017). The 1D velocity (Fig. 1d) structure

Fig. 1. (a) Map of the study area in northern America and the locations of several basins. The blue dot indicates the study region. (b) Geom-etry of geophone array overlaid with a surface projection of well trajectories. Station locations are marked by orange triangles and the welltrajectories are shown as gray lines. (c) Distribution of azimuths and take-off angles of P-waves (green dots) traveling from an artificial sourceto each geophone. Here the location of the artificial source is presumed to be the origin of (a) and its focal depth is 2.6 km. (d) The 1-D velocitymodel of P-wave velocity (blue) and S-wave velocity (red) for calculating take-off angles with respect to the stations in (b). The arrow indicatesthe depth of the Evie and the Muskwa formations at which the hydraulic fracking was conducted.

Automated focal mechanism analysis of microseismic events 697

http://www.springer.com/journal/12303 http://dx.doi.org/10.1007/s12303-017-0022-8

constructed from the well-logging data was used todetermine the hypocenters of the arrival times.

The method proposed in this study is based on the twofollowing assumptions. First, that the effects of fault finitenessand the directivity of rupture propagation can be ignored becausethe size of the event is sufficiently small. Second, given thatthe propagation effects from the source to the stations can beconsidered uniform, the waveforms recorded at each stationshould share a common source time function shape, whoseamplitudes are exclusively controlled by the radiation patternfrom the source. The source depths are usually around 2500 m,and the P-waves are measured at surface stations. Althoughthe propagation characteristics are not identical due to differencesin take-off angles, and the fact that the velocity structures arenot entirely homogeneous, the differences are not consideredsignificant because the propagation distances are short and thevelocity structures can be approximated as layered structures(Fig. 1d). In addition, the effects of fault finiteness and rupturedirectivity can be discounted because the sizes of the fracturesassociated with microseismic events are smaller than thewavelengths being considered here.

Under these assumptions, in order to measure the relativepolarities between two different waveforms, we calculate theircross-correlation coefficient (CC), which is a metric used todetermine the similarity between two time series. Here, if theabsolute value of maximum CC is larger than the absolute valueof minimum CC, it indicates that two waveforms are similarand have the same polarities. If the opposite is true, and the

absolute value of minimum CC is larger than the absolutevalue of maximum CC, it indicates that the similarity of the twowaveforms will increase when the polarity of either waveformis changed. Such a relationship can be explained by the twowaveforms having different polarities.

Owing to the fact that this characterization only requiresthe calculation of a single CC, we can effectively automate theprocess described above. The detailed calculation is as follows.First, we identify the ±0.05 s time window with respect to theP-wave arrival time, and upsample the waveform to 2000 Hzfrom 500 Hz using a cubic spline (Rutledge and Phillips, 2003).Then we select the waveform with the highest SNR among allof the waveforms for each event. Taking this as a referencewaveform, we then calculate CCs for all pairs of reference andrecorded waveforms. The maximum and minimum CCs aremeasured and their absolute values are compared to determinethe relative polarities of each waveform with respect to thereference waveform (Fig. 2). To prevent cyclic skipping, weintentionally reduce the amplitudes after the period of thefirst peak in the reference waveform, using a cosine taper (Fig. 3).Here, we define the period of the first peak through auto-correlationof the reference waveform. Next, to determine the absolutepolarities from the relative polarities, we stack all waveformsafter correcting the relative polarities. In this correction, if twowaveforms have the same or opposite polarities, they are summedor subtracted, respectively. During stacking, the waveformsare also aligned using the time lags measured when calculatingCC. The stacked waveforms will therefore have the same polarity

Fig. 2. Schematic example showing the automatic procedure for identifying relative polarities. The 0.1-s time windows centered on the P-wavearrival time on each waveform are cut and normalized to their maximum amplitude (a, b). After selecting the reference waveform with thegreatest signal-to-noise ratio, the cross-correlation coefficient (CC, denoted as between (a) and (b)) between the reference waveform andtarget waveform is calculated, and its maximum (blue circle) and minimum (red circle) are measured (c). The polarity of the target waveformis different from that of the reference waveform when the absolute value of maximum CC is smaller than that of the minimum, as describedin the upper panels. In the opposite case, the polarities of both waveforms are the same (lower panels).



as the reference waveform but with much higher SNR, whichgreatly facilitates the automatic measurement of the absolutepolarity of the reference waveform. To determine the absolutepolarity of the stacked waveform, we measure the polarity ofthe first sample point at which its absolute amplitude exceeds20% of the largest absolute amplitude.

The computer program FOCMEC (Snoke, 2003) is used todetermine focal mechanism solutions using the automaticallymeasured polarities. This program finds two nodal planes thatcan explain the observed polarities well, using a grid search ofstrike, dip, and rake (see the examples in Fig. 4). The qualityof the solutions can be controlled by defining the amount ofpolarity data that can be used for finding solutions. In this study,since we want to find only reliable solutions, we allow only oneor zero data points to differ from the predicted polarities. Inaddition, if more than 100 possible solutions are suggested foran event, even when strict conditions are applied, we exclude thatevent from further analysis because the uncertainty of thesolution is too high.

Using the successful focal mechanism solutions, we classifythe events according to a scheme proposed by Frohlich (1992). Itinvolves a ternary graph to classify diverse focal mechanisms(Fig. 5). The three mechanisms represent the thrust, strike-slip,and normal-slip components if sin2 P > 0.59, sin2 B > 0.75,

and sin2 T > 0.75, respectively. At the three vertices, each dipangle of the P, B, and T axes (P, B, and T) equals 90°.

For those events whose focal mechanism solutions cannot

Fig. 3. Illustration of the tapering procedure. (a) Waveforms before andafter tapering. (b) Auto-correlogram calculated to find the period ofthe first peak. (c) Cosine tapering function.

Fig. 4. Examples of the focal mechanism solutions for four eventsdetermined using the FOCMEC software. Solid and open circles denotethe compressional and dilatational P-wave polarities, respectively. Withone error of polarity allowed at most, all possible solutions are representedas gray lines. The two upper examples show poorly determined casesof dip-slip events, whereas the two bottom examples indicate well deter-mined cases of strike-slip events.

Fig. 5. The ternary diagram presenting the density of the focal mech-anism solutions determined using the FOCMEC software. The illus-trated focal mechanism solution amid the P vertex and T vertex isthe example of a dip–slip event (DE), which is the predominant focalmechanism type in the alternative and hybrid methods.



be determined by FOCMEC, we attempt to classify the eventtype using an alternative method that determines only thetype of the event from polarity data, rather than their specificfocal mechanism solutions. Since it is well reported that strike-slipand vertical dip-slip are the dominant faulting types formicroseismic events occurring during hydraulic fracturing(Snelling, 2013a), we attempt to assign all events as strike-slipevents (SE), vertical dip-slip events (DE), or other events (OE)such as oblique slips not included in the other two types. Todo this, we fix the dip of one nodal plane at 90° and search forthe best strike to match the observed polarities (Fig. 6). Then,for strike-slip and vertical dip-slip, the dip of the other nodalplane is fixed at 90° and 0°, respectively, and the portion of polaritydata conforming to these planes for the best fitting strike canbe used to define SE and DE. If both SE and DE can explainthe data equally, we classify the event as an OE. The summaryof the procedure for automated focal mechanism analysis isgiven in Figure 7.Fig. 6. Same as Figure 4, but determined using the alternative method

described in the text.

Fig. 7. The summary of the automatic procedure for focal mechanism analysis.



3. RESULTS AND DISCUSSION

Using the automated process described above, we use FOCMECto determine the focal mechanism solutions of 1875 eventsfrom a total of 8362 recorded events; around 73% of these canbe classified as strike-slip events (Fig. 8c). The number ofestimated focal mechanism solutions is much lower than thenumber of recorded events. This bias can be easily explainedby considering the spatial distributions of the stations. Sinceall the sensors in the array are located within a narrow regionabove the hypocenters, the P-wave sampling area on the focalsphere is also very limited (Fig. 1c). Therefore, the informationcontained in the P-wave polarity data is not sufficient toconstrain the dip of a nodal plane with a low dip angle. Thus,in the case of a vertical dip-slip event with a horizontal nodalplane, there are many possible solutions that can explain the

observed polarities. As per our methodology, if more than100 solutions were possible, we excluded those events fromfurther analysis because the uncertainty of the solution wastoo high (upper two cases in Fig. 4). The approach resulted inthe accurate identification of a relatively small number of verticaldip-slip events by FOCMEC. Therefore, it is likely that therelative proportions of faulting types determined by FOCMECdo not reflect the actual occurrence of strike-slip and verticaldip-slip events. In fact, it is well known that vertical dip-slipevents mainly occur as a result of hydraulic fracturing, andhave been previously reported from our study area (Snellinget al., 2013a).

The result from our alternative method, which was devisedto overcome the problem of indeterminate focal mechanismsolutions for cases that had a poor range of take-off angle,reveals that the numbers of DE, SE, and OE are 3028, 2834, and

Fig. 8. (a–c) Locations of vertical dip-slip (a, b) and strike-slip (c) events. Focal mechanism solutions indicated in (a–c) are representativesolutions of each type. The strike of the focal mechanism solution in (a, b) and the arrow shown in (a) are matched with the direction ofthe horizontal stress maximum (Hmax), N60°E. The dashed circle in (c) indicates the unidentified structure, which is inferred as a fault orfracture. (d) Illustration of the possible processes generating vertical dip-slip events in profile view. Red and blue beach balls correspond tothe events shown in (a) and (b), respectively. Note that the focal mechanisms in (d) are illustrated as the projection into a depth profile whilethe focal mechanisms in (a) and (b) are represented with the conventional lower hemisphere projection. The green line indicates the pre-exist-ing fault geometries described in Snelling et al. (2013a).



1102, respectively. Here we counted only those events whosesolutions fit more than 80% of the polarity data. The problemsfaced by FOCMEC in classifying vertical dip-slip events do notapply to the strike-slip movements, because both nodal planesshould have high dipping angles and the good azimuthal coverageof our case study makes them easy to identify. Therefore, wedecided to combine the focal mechanism solutions of strike-slip and vertical dip-slip events determined by FOCMEC withthe results of the alternative method, after excluding the 492events assigned conflict faulting types by the two methods. Thisgives final numbers of vertical dip-slip and strike-slip eventsof 2536 and 1383, respectively, and so the frequency of strike-

slip events is only 54.53% of that of the vertical dip-slip events.The results of the various classifications of focal mechanismsare summarized in Table 1.

The strikes of most of the classified events are consistentwith the direction of the local maximum horizontal stress,NE-SW, and the dominant strike-slip sense is right-lateral (Figs.8a and b). Variations in the distribution of the two faultingtypes show that all of them are scattered across the entire region.However, some of the strike-slip events appear to occur alignedwith specific geometry, a pattern not seen in the case of thedip-slip events (dashed circle line in Fig. 8c). The most popularhypothesis for the generation of microseismic events positsthat vertical dip-slip events are directly associated with tensionalopening caused by hydraulic fracturing, while strike-slip eventsare generated by the re-activation of natural fractures (Rutledgeet al., 2013). Focused on this hypothesis, the geometry of Figure8c (dashed circle line) looks like some unidentified faults orfractures.

Considering the focal mechanism solution of a vertical dip-slip event, slip could occur vertically on a vertical plane whosestrike is parallel to the direction of maximum horizontal stress,or along a horizontal plane in the direction of minimumprincipal stress. Since tensional opening occurs on a vertical

Table 1. Summary for classification of focal mechanism by variousprocedures

Strike Event(SE)

Dip-slip Event(DE)

Other Event(OE)

FOCMEC(a) 1469 – –Alternative Method 2834 3028 1102

Hybrid Method 1383 2536 –(a)The classification for the focal mechanisms obtained from the FOC-MEC method were based on Frohlich (1992), which classifies focal mecha-nisms into the three types; strike-slip, normal, and thrust. Hence, thisprocedure cannot be used to classify the dip-slip events and other events.

Fig. 9. Histogram showing the frequency of events with differing strikes. The events with dextral and sinistral shear senses are depicted inblue and red, respectively. Here a nodal plane with a similar strike of Hmax is considered to represent a shear sense. An illustration explainingthe possible mechanisms is shown in the inset, which is modified from the Rutledge et al. (2004). The red star and red focal mechanism inthe inset correspond to the red bars in the bar graph. The blue star and blue focal mechanism in the inset correspond to the blue bars inthe bar graph. When the ground is affected by shear force parallel to the strike of Hmax, earthquakes that occurred on oblique faults becomestrike-slip events, whereas tensional force is generated at the fractures parallel to the shear force. Note that the highest frequencies of the twocolors have different strikes, and are symmetric to N60°E, which is the direction of Hmax.



plane, we consider that the latter is more likely to occur in suchcases. Indeed, slip on a horizontal bedding plane has beenreported as a result of shear stress acting at the tip of fracturesopened by tensional stresses (Rutledge et al., 2013; Fig. 8d).

For the strike-slip events, we observed that their strikeangles are systematically smaller or larger than the azimuth ofmaximum horizontal stress depending on their shear senses(Fig. 9). This observation can be explained by the hypothesisthat strike-slip events occur on natural fractures, connectingnew fractures that have developed as a result of a tensionalopening (Rutledge et al., 2004).

4. CONCLUSION

We developed an automatic method for detecting the firstmotion polarities of P-waves, and applied the method to thedetermination of focal mechanism solutions of microseismicevents induced by hydraulic fracturing. Most of the focal mechanismsolutions could be classified as strike-slip or vertical dip-slipmovement. Among them, some strike-slip events are alignedin specific geometries in a region where dip-slip events are rarelyobserved. This observation, along with the results of the analysisof focal mechanism solutions supports the widely acceptedhypothesis that vertical dip-slip events occur as a direct resultof hydraulic fracturing, whereas strike-slip events occur dueto the re-activation of natural fractures. These results verifythat our method of automatic detection of P-wave polaritiesworks effectively. Since the proposed method can be appliedto any microseismic waveform data recorded at proximal distances,we expect it to be useful in a wide variety of applications.

ACKNOWLEDGMENTS

This work was supported by the Korea Institute of EnergyTechnology Evaluation and Planning (KETEP) and the Ministryof Trade, Industry & Energy (MOTIE) of the Republic of Korea(No. 20132510100060).

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