Observations of static Coulomb stress triggering of the November 2011 M5.7 Oklahoma earthquake sequence



In November 2011, a M5.0 earthquake occurred less than a day before a M5.7 earthquake near Prague, Oklahoma, which may have promoted failure of the mainshock and thousands of aftershocks along the Wilzetta fault, including a M5.0 aftershock. The M5.0 foreshock occurred in close proximity to active fluid injection wells; fluid injection can cause a buildup of pore fluid pressure, decrease the fault strength, and may induce earthquakes. Keranen et al. [2013] links the M5.0 foreshock with fluid injection, but the relationship between the foreshock and successive events has not been investigated. Here we examine the role of coseismic Coulomb stress transfer on earthquakes that follow the M5.0 foreshock, including the M5.7 mainshock. We resolve the static Coulomb stress change onto the focal mechanism nodal plane that is most consistent with the rupture geometry of the three M ≥ 5.0 earthquakes, as well as specified receiver fault planes that reflect the regional stress orientation. We find that Coulomb stress is increased, e.g., fault failure is promoted, on the nodal planes of ~60% of the events that have focal mechanism solutions, and more specifically, that the M5.0 foreshock promoted failure on the rupture plane of the M5.7 mainshock. We test our results over a range of effective coefficient of friction values. Hence, we argue that the M5.0 foreshock, induced by fluid injection, potentially triggered a cascading failure of earthquakes along the complex Wilzetta fault system.

1 Introduction

As the population of the United States continues to grow, so does the demand for energy resources. Earthquakes in the continental interior of the United States have historically been rare, yet in 2011 alone, moderate-sized earthquakes occurred in Colorado, Texas, Oklahoma, Ohio, and Arkansas. These earthquakes occurred in close proximity to fluid injection wells, which suggest that ongoing oil and natural gas activities may be to blame [e.g., Horton, 2012; Keranen et al., 2013; Kim, 2013]. The November 2011 Oklahoma sequence includes the largest earthquake (M5.7) ever correlated with wastewater injection [Keranen et al., 2013]. These recent events suggest that some fluid injection wells, especially those close to densely populated areas, could pose a significant seismic risk.

In 1993, fluid injection began within oil fields structurally contained by the Wilzetta fault, a complex, ~200 km long, Pennsylvanian-aged fault system near Prague, Oklahoma [Way, 1983; Joseph, 1987]. On 5 November 2011, a M5.0 earthquake (Event A) ruptured the Wilzetta fault, in close proximity to several injection wells (red and white inverted triangles in Figure 1 [Keranen et al., 2013]). This earthquake was followed less than 24 h later by a M5.7 earthquake (Event B; Figure 1), located less than 2 km southwest of Event A. Following Event B, the partial catalog of Keranen et al. [2013] reports over a thousand aftershocks that propagate unilaterally away from the fluid injection wells, including a M5.0 aftershock on 8 November 2011 (Event C; Figure 1). All three M ≥ 5.0 earthquakes exhibit strike-slip fault geometries consistent with rupture on three independent focal planes (Global Centroid Moment Tensor (GCMT) catalog [www.globalcmt.org]), which suggests that three separate portions of the Wilzetta fault system were activated.

Figure 1.

(a) The three M ≥ 5.0 events (yellow stars), placed at their Oklahoma Geological Survey locations with focal mechanisms from the Global Centroid Moment Tensor catalog. The locations for 110 events with the best quality focal mechanism solutions determined in this study are shown by black dots. The Wilzetta fault system (dark gray lines) is compiled from regional [Joseph, 1987] and detailed local [Way, 1983] studies. Active injection wells close to Event A (red inverted triangles) may be responsible for triggering earthquakes along these faults. Fluid injection takes place within fault-bounded reservoirs (gray shaded regions), depleted from earlier oil and natural gas extraction. Additional nearby fluid injection wells (white inverted triangles) affect the pore pressure and hydrogeologic parameters in this region and complicate the Coulomb fault failure analysis. The University of Oklahoma deployed a total of eighteen stations in the epicentral region; the stations are LC (for Lincoln County, Oklahoma) and their number, but are identified here by number for the sake of clarity. (b) The map shows the 47 stations used in this study, color coded by operating agency as identified in the legend. The EarthScope Transportable Array stations are also labeled. The inset box identifies the region shown in Figure 1a. The inset box within the map of Oklahoma in the legend shows the region identified in this map. Topography data is NASA ASTER data with 10 m resolution in the United States.

The proximity of earthquakes to active fluid injection wells, the unilateral progression of aftershocks away from Event A, and the shallow earthquake depths (83% <5 km deep; ~20% located within sedimentary units where fluids are injected) led Keranen et al. [2013] to conclude that fluid injection was responsible for triggering the M5.0 foreshock. Furthermore, Llenos and Michael [2013] used the epidemic-type aftershock sequence model to analyze the catalog of M > 3 earthquakes in Oklahoma and observe an increase in the aftershock productivity of earthquakes after 2009; they suggest that an underlying triggering mechanism such as fluid injection may be to blame.

Earthquake activity may be promoted when stress is increased on a fault by as little as 0.1 bar [Stein, 1999]. Small increases in stress due to earlier earthquake activity [e.g., Harris, 1998; Stein, 1999; King and Cocco, 2001; Steacy et al., 2005], an increase in pore pressure from fluid injection or reservoir impoundment [e.g., Nur and Booker, 1972; Zoback and Harjes, 1997; Gahalaut and Hassoup, 2012], dynamic stress changes due to passing seismic waves [e.g., Gomberg et al., 2001, 2003], or even tidal stress [e.g., Cochran et al., 2004; Stroup et al., 2007, 2009; Crone et al., 2011] can trigger earthquakes. The last M5.0 earthquake in Oklahoma occurred in 1952, and the rare occurrence of three large (M ≥ 5) earthquakes and numerous aftershocks in Oklahoma suggests that even relatively stable intraplate regions of the brittle continental crust may be critically stressed and near frictional failure [e.g., Zoback and Harjes, 1997]. A buildup of pore pressure after ~18 years of fluid injection likely triggered the M5.0 foreshock [Keranen et al., 2013]; we investigate whether the resulting static stress change from the foreshock may have caused cascading failure [e.g., Dodge et al., 1995, 1996] that led to the mainshock and subsequent aftershock sequence.

In this study, we use the Coulomb 3.3 software [Toda et al., 2011b], which implements the elastic half space of Okada [1992], to model the static stress changes through time and to investigate whether the M5.0 foreshock (Event A) is responsible for the cascading failure of the Wilzetta fault system in Oklahoma. We detect and relocate 110 earthquakes previously identified in the Oklahoma Geological Survey (OGS) catalog and/or the earthquake catalog of Keranen et al. [2013] and determine their focal mechanism solutions with the HASH software [Hardebeck and Shearer, 2002, 2003]. We calculate the Coulomb stress change on the nodal planes of these events, as well as determine the regional stress direction from their principal axes. The regional stress direction derived from the focal mechanism solutions provides us with information to determine a specified fault plane (SFP) that is most favorably oriented for failure; thus, we also calculate the Coulomb stress changes for each aftershock on the SFP orientation. We compare the number of events consistent with Coulomb stress triggering for both the limited set of focal mechanism solutions and for the SFPs of the more complete earthquake catalog. These analyses provide insight into whether the M5.0 foreshock (Event A), triggered by injection [Keranen et al., 2013], results in a Coulomb stress change that encourages failure of the M5.7 mainshock (Event B) and the subsequent aftershock sequence along the Wilzetta fault system.

2 Coulomb Fault Failure

The brittle failure of faults is thought to be due to the combination of the normal (confining) and shear stress conditions, commonly quantified as the static Coulomb failure criterion [e.g., King et al., 1994]. Static Coulomb stress changes caused by earthquake rupture can help explain the distribution of aftershocks [e.g., Reasenberg and Simpson, 1992], as aftershocks will occur when the Coulomb stress exceeds the failure strength of the fault surface. The static Coulomb fault failure (∆CFF) is defined as

display math(1)

where ∆τ is the change in shear stress on the fault (positive in the direction of slip), ∆σ is the change in normal stress (positive for fault unclamping), ∆p is the change in pore pressure, and μ is the coefficient of friction, which ranges from 0.6 to 0.8 for most intact rocks [see Harris, 1998, and references therein].

In this region of Oklahoma, where fluid injection into 1–2 km deep wells near the foreshock epicenter, has been used to dispose of wastewater since 1993 [e.g., Keranen et al., 2013], the effect of pore pressure cannot be neglected. The pore pressure change immediately after a change in stress, where there is no fluid flow (undrained conditions), is

display math(2)

where β is the Skempton's coefficient and σkk is the sum of the diagonal elements of the stress tensor [Rice and Cleary, 1976]. The Skempton's coefficient describes the change in pore pressure that results from a change in an externally applied stress and often ranges in value from 0.5 to 1.0 [e.g., Green and Wang, 1986; Hart, 1994; Cocco and Rice, 2002].

For plausible fault zone rheology, where the fault zone materials are more ductile than the surrounding materials, σxx = σyy = σzz [Rice, 1992; Simpson and Reasenberg, 1994; Harris, 1998]; thus, math formula. Equations (1) and (2) combined with this assumption lead to

display math(3)

where μ′  = μ(1−β) is the effective coefficient of friction. The effective coefficient of friction generally ranges from 0.0 to 0.8, but is typically found to be around 0.4 (μ = 0.75, β = 0.47)  for strike-slip faults or faults of unknown orientation [Parsons et al., 1999]; this value is commonly used in calculations of Coulomb stress changes to minimize uncertainty [Stein et al., 1992; King et al., 1994; Toda et al., 2011a].

The location and geometry of the source rupture, as well as the slip distribution over the source plane, play an important role in calculating the Coulomb stress change. Based on earthquake magnitude, we model the source geometry with the empirical relations of Wells and Coppersmith [1994] for strike-slip faults, which are built into the Coulomb 3.3 software [Toda et al., 2011b]. For Events A–C, we use the GCMT reported magnitudes and focal mechanism solutions, and the OGS reported locations for the rupture centroid. We use the OGS locations here instead of the GCMT locations, because the locations are based on proximal station information and have smaller locations errors, more closely match the aftershock distributions, and are more consistent with the regions of highest shaking intensities according to “Did You Feel It?” (http://earthquake.usgs.gov/earthquakes/dyfi/events/us/b0006klz/us/index.html). Events A and C (both M5.0) have rupture dimensions of ~2.82 km in rupture length and ~2.91 km in rupture width, respectively, while Event B (M5.7) has rupture dimensions of ~8.31 km in rupture length and ~5.41 km in rupture width, consistent with the aftershock distribution shown by Keranen et al. [2013]. We model Events A and C with ~0.14 m and Event B with ~0.3 m of predominantly strike-slip motion and tapered into five 1 × 1 km nested rectangles of slip to avoid unphysical stress concentrations near the fault ends. The taper used here is the default in the Coulomb 3.3 software; we also test a range of realistic tapers and find that this did not change our results. Finite fault inversion methods [e.g., Liu and Archuleta, 2004, and references therein] could not be applied to these earthquakes due to their small magnitudes (M < 7) and inadequate station coverage before the events; thus, the events are modeled with uniform slip across the rupture surface.

The representations of the “source” faults (faults which have slip), as described above, are used to determine the Coulomb stress change on the “receiver” faults (faults onto which the stress change is resolved). While each earthquake reduces the net regional stress, each event can result in local stress increases that trigger other earthquakes. Aftershock productivity is encouraged when a fault, of specified orientation, experiences a stress increase, especially when the stress change is larger than an assumed threshold value of ~0.1 bar (or 0.01 MPa) [Stein, 1999]. This relatively low threshold, compared to background crustal stress levels, suggests that the faults are near failure before the earthquakes [e.g., Stein and Lisowski, 1983; Zoback and Townend, 2001]. Based on this assumed threshold, we examine whether aftershock activity is promoted in regions of stress increase (greater than 0.1 bar stress change), inhibited in regions of stress decrease (less than −0.1 bar stress change), and neither promoted or inhibited in regions where stress changes range between −0.1 and 0.1 bar [e.g., Reasenberg and Simpson, 1992]. However, a limitation of the Coulomb stress modeling approach is that it often underestimates the number of aftershocks within the regions of Coulomb stress increase directly adjacent to (within <5 km of) the fault plane, which is due to assumptions of planar fault geometry and a smooth slip distribution along the fault [e.g., Hardebeck et al., 1998; Smith and Dieterich, 2010].

The parameters in equation (3) need to be considered as a function of time, as the stress distribution from the M5.0 foreshock will be different than the stress distribution due to the combination of the M5.0 foreshock and M5.7 aftershock, and so forth. We therefore consider each M ≥ 5.0 earthquake (Events A–C) as a “mainshock” that has its own distribution of aftershocks and explore the Coulomb stress distribution and potential triggering of aftershocks through time. Note that due to the short-term (coseismic) time frame taken into consideration, we neglect the alteration of pore pressure caused by the fluid flow in the Coulomb stress modeling, consistent with Beeler et al. [2000] and Cocco and Rice [2002].

3 Earthquake Detection and Location Techniques

In the week that followed Event A (the M5.0 foreshock), we deployed 31 continuously recording, three-component seismometers within 100 km of the sequence from the Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL), Rapid Array Mobilization Program (RAMP), the University of Oklahoma (OU), and the United States Geological Survey (USGS) (Figure 1). The temporary instruments augment the existing seven EarthScope Transportable Array (TA) stations [Meltzer et al., 1999] and the nine USGS NetQuakes accelerometers mostly located near Oklahoma City that are configured to trigger on M > 3.0 events. Thus, a total of 47 stations recorded the sequence. The partial catalog of Keranen et al. [2013] reports over 800 aftershocks in the days and months following Event A.

In this study, we initially examine 217 earthquakes originally identified in the OGS catalog and/or the catalog of Keranen et al. [2013] that occur between Event A until the end of 2011. We remove the instrument response and apply station specific filters to convert acausal finite impulse response filtered data to causal. Acausal filters can affect the phase onset of the seismic waves and may hinder the proper picking of the phase and polarity information [Scherbaum and Bouin, 1997]. (Appendix A details specifics on the instrument and data logger type, as well as sample rate.) We manually pick visible P wave and S wave arrivals with the Seismic Analysis Code software to improve azimuthal coverage for the focal mechanism analysis compared to the analysis of Keranen et al. [2013]. For each pick, we assess the character of the phase onset (emergent or impulsive) and the quality of the pick (0–4, where 0 is best and 4 is worst). Since polarity information will be important for the focal mechanism analysis, we also assess the first motion for each P wave pick by assigning a positive or negative (up or down) polarity to each pick.

We require P wave and/or S wave picks on a minimum of seven stations for earthquake relocation. With the P wave and S wave pick timing, onset, and quality information, we locate individual earthquakes with the Hypoinverse algorithm [Klein, 2002] based on a one-dimensional P wave velocity model of Keranen et al. [2013] and a P wave-to-S wave velocity ratio of 1.73. On average, we use a combination of 46 P wave and S wave picks to constrain the hypocenters, with the S wave picks weighted at 50% compared to the P wave picks, as the S wave onset is more difficult to determine and can be obscured by the P wave coda. The initial hypocentral location is set to the latitude and longitude of the closest station (i.e., the station with the earliest arrival time) with a trial depth of 5 km. We then perform an initial absolute relocation analysis of the individual earthquakes with the Velest algorithm [Kissling, 1988; Kissling et al., 1994], which is a technique to improve the hypocentral location and reduce the root-mean-square (RMS) travel time residuals. We further refine the event locations in a relative sense with the hypoDD double-difference algorithm [Waldhauser and Ellsworth, 2000; Waldhauser, 2001]. The hypoDD algorithm iteratively solves for hypocentral variations, in a least squares sense, by minimizing the residuals of travel times between pairs of nearby events recorded on a common station, thus removing bias due to velocity model errors. (For a detailed description of these procedures, the reader is referred to the works of Sumy et al. [2013] and Kroll et al. [2013]). The hypocenters of the 110 events for which high-quality focal mechanism solutions are determined (discussed in the next section), including their relative relocation errors and travel time residuals, are listed in Appendix B. In general, the relative relocation errors and travel time residuals significantly decrease for events later in the sequence that occur after the installation of additional stations (i.e., recorded by more stations). For the 72 events also cataloged by Keranen et al. [2013], the epicentral locations differ by ~400 m on average, while the remaining 38 events only cataloged by the OGS differ by ~1.3 km on average.

4 Focal Mechanism Determination

We determine focal mechanism solutions from the P wave polarity (first-motion) picks and S/P amplitude ratios with the program HASH [Hardebeck and Shearer, 2002, 2003]. The HASH algorithm computes takeoff angles from source to receiver and performs a grid search over all possible focal mechanisms to identify the acceptable set of solutions for each earthquake. One benefit of using HASH over other focal mechanism algorithms, such as FPFIT [Reasenberg and Oppenheimer, 1985], is that it takes into account possible uncertainties in the polarity information and takeoff angles, which could be affected by errors in the hypocenter location and velocity model. The preferred focal mechanism solution and its uncertainties are defined as the average and spread of the set of acceptable focal mechanisms, respectively.

We use the manually picked P wave polarities from the earthquake detection and relocation analysis, as described above. The default in HASH is polarity information from at least eight stations (for at least two station measurements in each quadrant); however, we require a minimum of seven polarities to determine a focal mechanism solution. This allows us the potential to solve for focal mechanisms when only the EarthScope TA stations are available, as they provide favorable azimuthal station coverage especially during the early part of the sequence when very few temporary stations are deployed. We did not restrict mechanisms based on azimuthal station gap or takeoff angle at this stage. In addition, we modify the HASH algorithm to minimize the number of misfit high-quality polarity picks (0–1 quality; 100% and 75% weighting, respectively); HASH traditionally uses impulsive arrivals only, regardless of pick quality. We estimate pick error to be around 5%, which is the percentage of outlier picks thrown out by the hypoDD double-difference analysis.

To further refine these mechanisms, we calculate the S/P amplitude ratio. The S/P amplitude ratio is generally independent of path effects, site effects, or instrument response and is to first order, directly proportional to the seismic energy radiation pattern about the focal sphere [Hardebeck and Shearer, 2003]. The S/P amplitude ratio reaches a peak value near the nodal planes, where the P wave amplitude becomes small while the S wave amplitude is large. Furthermore, the S/P amplitude ratio becomes small near the P (most compressive) and T (least compressive) axes, where the P wave polarities are large and S wave radiation reaches a minimum. The S/P amplitude ratio used in conjunction with the P wave polarity information can thus provide better constraints on the focal mechanism solutions, since the amplitudes have a range of values and can more precisely constrain the location of the observation on the focal sphere [e.g., Hardebeck and Shearer, 2003].

To calculate P wave and S wave amplitudes, we filter the three-component waveforms above 1 Hz frequency to remove low-amplitude, long-period noise. We use the P wave and S wave arrival times to select windows for the S/P amplitude ratio measurement, because it is one of the most robust and simplest approaches [Hardebeck and Shearer, 2003; Yang et al., 2012]. For the P wave, the noise window is between −2.5 and −0.5 s before the P wave and the signal window starts 10% of the S-P time (in s) before the P pick and ends 50% of the S-P time (in s) after the P wave pick (Figure 2). For the S wave, the noise window is from 50% to 75% of the S-P time before the S wave pick and the signal window is from 10% of the S-P time before to 100% of the S-P time after the S wave pick (Figure 2). We choose to use a percentage of the S-P time for the window lengths, because the time between the P and S arrivals varies significantly across the network (~4 s on average); we wanted to ensure that we had appropriately short windows for nearby stations (with <1 s S-P times) while still recording the peak amplitudes at more distant stations that have longer-period energy. We use the peak-to-peak difference in each window and apply a vector summation across all three components to obtain the noise and signal amplitudes, respectively [Yang et al., 2012]. For HASH, the minimum S/P amplitude ratio for use in the focal mechanism calculation is set at 3.0, and the acceptable variation in the S/P amplitude ratio as a result of noise is set at 0.3 in log10 scale, which is consistent with other studies [i.e., Hardebeck and Shearer, 2003; Yang et al., 2012].

Figure 2.

Three-component velocity waveforms (in nm/s) for a M2.7 event on 16 November 2011, recorded by station LC02 (annotated in Figure 1a). Gray windows show periods where peak-to-peak noise is measured before the P wave and S wave arrivals and for the P wave and S wave signals, respectively. Dashed lines mark the temporal extent of each window; note that the noise window before the S wave arrival begins where the P wave arrival window ends (discussed in the text). For each window, the dots mark the maximum and minimum amplitudes. The two solid lines show the picks of the P wave (~11.65 s) and the S wave (~12.9 s), respectively.

We use a 5° angle step across strike, dip, and rake to search for all possible solutions and show an example of the set of all possible solutions (gray nodal planes) and the preferred solution (black nodal planes) for the P wave polarities alone and the combination of P wave polarities and S/P amplitude information, respectively, in Figure 3. The root-mean-square angular difference between the acceptable nodal planes and the preferred nodal plane is the nodal plane uncertainty [Hardebeck and Shearer, 2002; Yang et al., 2012]. The mean of the nodal plane uncertainties is the best single indicator for focal mechanism quality [Kilb and Hardebeck, 2006]. The quality of the focal mechanisms also depends on how well our observations cover the focal sphere or the azimuthal gap between stations. If the azimuthal gap is large, our knowledge of the focal sphere, and thus the correct focal mechanism, will be limited, regardless of the number of observations. Thus, we base the quality of our mechanisms (A: best; D: worst) on the mean nodal plane uncertainty and the azimuthal station gap, like Yang et al. [2012]. We focus on the 110 events with A and B quality focal mechanism solutions, which have mean nodal plane uncertainties of ≤25° and 25°–35°, respectively, and have azimuthal station gaps of ≤90°. The 95 A quality and 15 B quality focal mechanism solutions are shown in Figure 4 and listed in Appendix C.

Figure 3.

The focal mechanism solutions for a M2.7 event on 16 November 2011 (same as Figure 2) with (a) P wave polarity information only and (b) with both P wave polarity and S/P amplitude ratio information, respectively. Stations are projected onto a stereonet, where compressional (up) polarities are indicated with an “x” and the dilatational (down) polarities with an open circle. For stations with S/P amplitude ratio information, the symbols are scaled by their log10 S/P amplitude. Stations with polarity information only are shown by small gray symbols in Figure 3b. The distribution of acceptable focal mechanism solutions (gray curves) and the preferred solution (black curve) for (c) P-polarity information only, and (d) for both P polarity and S/P amplitude ratios. We report the preferred solution for this event (event #86) in Table C1.

Figure 4.

Focal mechanism solutions for the 110 earthquakes with A or B quality mechanisms computed with the HASH software, including the focal mechanism solution for the M5.7 mainshock (epicenter shown by a black star). These solutions use both first-motion polarities and S/P amplitude ratios. Focal mechanisms with at least one nodal plane consistent with the rupture planes of Evens A or B are shown in black, and those consistent with the rupture plane of Event C are shown in gray. Anomalous earthquakes (as defined in the text) are shown with magenta focal mechanism solutions. The earthquakes are split between two maps for the sake of clarity.

Within a strike variation of ≤25° (the maximum mean nodal plane uncertainty of A quality mechanisms), 69 events (~63% of the focal mechanisms) have at least one nodal plane consistent with the GCMT-determined rupture planes of Events A and B (black colored focal mechanisms in Figure 4), and 24 events (~22% of the focal mechanisms) have at least one nodal plane consistent with the GCMT-determined rupture along the fault plane of Event C (gray colored focal mechanisms in Figure 4). The remaining 17 earthquakes (14% of the mechanisms; M0.7–3.5) are considered anomalous, as these earthquakes have either dip-slip mechanisms (dip ≤65°) and/or a rupture plane inconsistent with the orientation of Events A–C (magenta colored focal mechanisms in Figure 4). In regions of complicated fault geometry like the Wilzetta fault system, dip-slip mechanisms tend to occur within regions where the faults link together and could be due to the change in stress orientation from one fault to the other [Engeln et al., 1986; Sumy et al., 2013].

5 Coulomb Stress Changes Derived on Assumed Rupture Planes

We calculate Coulomb stress changes on the nodal planes of the 110 high-quality focal mechanism solutions in their rake directions (Figure 5). The calculation of Coulomb stress changes on the nodal planes of aftershock focal mechanism solutions is a strict test of the Coulomb hypothesis, as it requires no assumptions about the regional stress state or aftershock fault geometry [Toda et al., 2011a]. Shear stress changes are similar on either nodal plane, but normal stress changes will vary [Hardebeck et al., 1998]; thus, we calculate the Coulomb stress change on the nodal plane that is most consistent with the orientation of rupture for the three largest events (Events A–C).

Figure 5.

The Coulomb fault failure shown for the focal mechanism solutions for (a) earthquakes after Event A, including our focal mechanism solution of the M5.7 mainshock (Event B), which is denoted by “HB” (or HASH Event B); (b) earthquakes after Events A and B, labeled with their event number (Tables B1 and C1), and (c and d) earthquakes after Events A–C. The earthquake epicenters are color coded by its ΔCFF, in bar.

We find that Event A exerts an ~1.3 bar Coulomb stress increase on the hypocenter of Event B, resolved onto the fault plane. This finding suggests that while fluid injection may have triggered the M5.0 foreshock (Event A) [Keranen et al., 2013], Event A likely triggered the M5.7 mainshock (Event B). Events A and B however exert an ~5.6 bar negative Coulomb stress change on the GCMT focal mechanism solution for Event C. In Table 1, we report the number of earthquakes that are promoted (Coulomb fault failure (ΔCFF) > 0.1 bar; red epicenters in Figure 5), inhibited (ΔCFF < −0.1 bar; blue epicenters in Figure 5), or neither (−0.1 bar ≤ ΔCFF ≤ 0.1 bar; white epicenters in Figure 5) as a function of time and focal mechanism (i.e., consistent with Events A–C or anomalous). Overall, we observe that ~60% of the earthquakes experience positive Coulomb stress change that would promote failure and ~40% of the aftershocks show negative Coulomb stress change that would inhibit failure for Coulomb stress change resolved onto the earthquake nodal plane. We also find that the percentage is robust, as it does not change even when we examine the maximum Coulomb stress change on either nodal plane.

Table 1. ΔCFF (in bars) Computed on Inferred Rupture Plane for A and B Quality Focal Mechanisms
EventNumber of AftershocksΔCFF < −0.1−0.1 ≤ ΔCFF ≤ 0.1ΔCFF > 0.1
Event A30 (0%)0 (0%)3 (100%)
Event B (Normal)83 (37.5%)0 (0%)5 (62.5%)
Event B (Anomalous)31 (33.3%)0 (0%)2 (66.6%)
Event B (Total)114 (36%)0 (0%)7 (64%)
Event C (Normal)8240 (49%)0 (0%)42 (51%)
Event C (Anomalous)141 (7%)0 (0%)13 (93%)
Event C (Total)9641 (43%)0 (0%)55 (57%)
TOTAL11045 (41%)0 (0%)65 (59%)

To further test our results, we examine a range of effective coefficient of friction values (μ′) between 0.0 and 0.8 (Table S1 in the supporting information), which includes the shear stress change alone (μ′ = 0.0). The shear stress change (Δτ) does not depend on which rupture plane is considered, nor does it depend on the coefficient of friction we choose. In addition, we perform 2000 random resamples of the focal mechanism solutions for each earthquake (Table S2 in the supporting information), where the event location is kept constant and the focal mechanism solutions are randomly subsampled from the existing set. We observe the same distribution of earthquakes, in that 60% of earthquakes lie within the regions of Coulomb stress increase and 40% lie within the regions of Coulomb stress decrease, regardless of the effective coefficient of friction and/or the particular focal mechanism from the set. Thus, we find that the percentage of events that are encouraged is robust, regardless of slight changes in fault orientation away from the rupture planes of the three M ≥ 5.0 events; in fact, Parsons [2002] observed this same percentage in a global study of Ms ≥ 7.0 earthquakes that occurred outside of the classical aftershock zone, which may suggest this ratio persists across many spatial scales of earthquake catalogs.

One might expect that a greater number of the events would have a positive Coulomb stress change resolved onto their nodal planes. The observed distribution most likely reflects a limitation of the Coulomb stress model, in that stresses near the causative fault plane are predicted to decrease when resolved on the prescribed fault geometry consistent with the mainshock [Hainzl et al., 2009]; thus, we observe that ~40% of the focal mechanism solutions are modeled with negative Coulomb stress changes. In effect, our Coulomb model predicts no aftershocks along the main fault plane due to the assumption of uniform stress drop across the rupture surface and a perfectly planar fault; please refer to the discussion section below. It is important to note that while many of the focal mechanism solutions exhibit similar geometry to the M ≥ 5 earthquake rupture planes, small changes in the receiver fault geometry could significantly affect the Coulomb stress calculation. Thus, we investigate the Coulomb stress change for the earthquake catalog reported by Keranen et al. [2013], with the assumption that each earthquake has a focal mechanism consistent with the regional stress orientation.

6 Coulomb Stress Changes Estimated on Specified Receiver Fault Planes

In this section, we examine the Coulomb stress change on specified receiver fault planes (SFPs), which for our study are those expected to fail based on the regional stress direction. This analysis differs from “optimally oriented” fault planes (OOPs), as it removes any dependence on the regional stress amplitude, which can result in a local, often small, rotation in the fault plane orientation in the near-field region of a large-magnitude earthquake [e.g., King et al., 1994; Harris, 1998]. Many of our focal mechanism solutions (~85% of the catalog; Table 1) are consistent with the rupture of the M ≥ 5 events, which contradicts the assumption of local rotation of the fault plane near the source rupture. We therefore examine the Coulomb stress change on earthquakes from the catalog of Keranen et al. [2013] following Events A and B on the SFP consistent with the regional stress direction, without regard for the regional stress amplitude.

To define the regional stress direction, we use the 110 focal mechanism solutions from the aftershock sequence (Figure 4 and Appendix C) to find the azimuth and plunge of the principal stress directions with the methods described by Michael [1984] and Hardebeck and Michael [2006]. As a first pass, we plot the P and T axes (or the most and least compressive stress directions, respectively) of each focal mechanism solution in Figure 6a. The use of P and T axes from the focal mechanisms however more closely represents the moment tensor and not the stress tensor. Thus, we perform a regional-scale stress inversion for the 110 focal mechanism solutions, with the nodal plane that is most consistent with the rupture orientation and aftershock distribution of Events A–C [e.g., Michael, 1987]. We find that on average, the azimuth and plunge for σ1 (most compressive stress direction) is ~80° and ~5°, for σ2 (intermediate stress direction) is approximately −21° and ~65°, and lastly, for σ3 (least compressive stress direction) is ~172° and ~24°, respectively (Figure 6b). The best stress inversion results along with the 95% confidence interval after 2000 bootstrap resamples are shown in Figure 6b. We assume for the stress uncertainty analysis that 90% of the nodal planes of the focal mechanism solutions are correctly identified as the rupture plane [i.e., Hardebeck and Shearer, 2002, 2003]. Based on the regional stress orientation, the SFP has a nodal plane with a strike of 214°, which is most consistent with the inferred rupture orientation of Events A and B (Figure 6c).

Figure 6.

(a) Stereographic projection of the P axis and T axis orientations of the 110 focal mechanisms, color coded by time as defined in the legend. (b) The stress inversion solution for the most compressive (σ1, black star), intermediate (σ2, yellow star), and least compressive (σ3, white star) principal stress axes. The 95% confidence intervals after 2000 bootstrap resamples are color coded by axis and defined in the legend. The relative stress ratio (ϕ) is 0.24, with a 95% confidence interval between 0.07 and 0.48. (c) The best fit regional focal mechanism solution based on the stress inversion. The focal mechanism is most consistent with the focal mechanism solutions of Events A and B.

To further test whether Event A triggered subsequent seismicity, we calculate the Coulomb stress change as a function of time on a 0.5 km × 0.5 km horizontal grid at 1 km depth intervals between 0 and 10 km, which covers the entire depth range of the aftershocks we relocate here, as well as those in the catalog of Keranen et al. [2013]. We associate each aftershock in the catalog of Keranen et al. [2013] to the closest grid node to estimate the Coulomb stress change at the event's hypocentral location (Figures 7a and 7b). We find that ~55% of the earthquakes that occurred between the M5.0 foreshock (Event A) and the M5.7 mainshock (Event B) occurred within the regions where the estimated Coulomb stress change resolved onto the SFPs is positive and would promote failure (Figure 7a and Table 2). Thus, we observe that Event A triggered the majority of earthquakes up through Event B. However, for the 182 earthquakes that occurred between the M5.7 mainshock (Event B) and the M5.0 aftershock (Event C), only 23% lie within the regions of Coulomb stress increase (Figure 7b).

Figure 7.

The Coulomb stress change (ΔCFF) is mapped on specified fault planes on the aftershocks that follow (a) the M5.0 foreshock (Event A) and (b) the M5.7 mainshock (Event B). In addition, we also examine the ΔCFF on the GCMT solutions for (c) the aftershocks of Event A on the GCMT solution of Event B and (d) the aftershocks of Event B on the GCMT solution of the M5.0 aftershock (Event C), respectively. Thick black lines represent the surface projection of the rupture planes of each M ≥ 5.0 earthquake. The aftershocks are color coded by the Coulomb stress change calculated on its closest grid point (~0.5 × 0.5 × 1.0 km) in space, as a function of depth and averaged over the entire seismogenic depth from 0 to 10 km.

Table 2. Coulomb Stress Change for Aftershocks (μ′ = 0.4)
EventsNumber of AftershocksΔCFF < −0.1−0.1 ≤ ΔCFF ≤ 0.1ΔCFF > 0.1
On Specified Receiver Fault Planes
Following Event A19967 (34%)23 (12%)109 (55%)
Following Event B182133 (73%)7 (4%)42 (23%)
On Global Centroid Moment Tensor Solutions
Following Event A on Event B19941 (21%)6 (3%)152 (76%)
Following Events A–B on Event C182117 (64%)1 (1%)64 (35%)

To further test our results, we examine the Coulomb stress change on the SFP as a function of the effective coefficient of friction (μ′) and find that ~55–63% and ~23–31% of the earthquakes fall within the regions of Coulomb stress increase following Event A and Event B, respectively (Table S3 in the supporting information). Thus, for SFP, the effective coefficient of friction only results in a slight (<10%) change in the number of events that fall into regions of Coulomb stress increase or decrease. Furthermore, we calculate the Coulomb stress change on earthquakes between Events A and B as if they had the same rupture plane orientation of the GCMT solution of Event B and on earthquakes between Events B and C as if they had the same rupture plane orientation of the GCMT solution of Event C, respectively (Figures 7c–7d). We find similar results to the SFP analysis described above; in that, ~76% of aftershocks occur within the regions of Coulomb stress increase following Event A and that only ~35% of aftershocks occur within regions of Coulomb stress increase following Event B (Table 2).

Again, we test our results as a function of the effective coefficient of friction (μ′) and find that ~58–66% of the earthquakes that occur between Events B and C locate within the regions of Coulomb stress increase when μ′ is 0.0–0.2. When the effective coefficient of friction is larger (0.4–1.0), the percentage is dramatically reduced to ~20–35% (Table S3 in the supporting information). Thus, when we use the GCMT rupture plane orientations, we find that the results are more sensitive to the effective coefficient of friction value chosen, with ~40% more events experiencing Coulomb stress increase when μ′ is 0 compared to when μ′ is 1.0. In this region, we might expect a low effective coefficient of friction if fluid from injection is migrating along the fault, which would cause an increase in pore pressure. An increase in pore pressure would reduce the normal stress along the fault and drive the fault toward failure. In addition, an effective coefficient of friction of zero represents the contribution of the shear stress alone, which would be the same along either nodal plane, and thus removes any nodal plane ambiguity. The shear stress change may provide the most stringent test of the Coulomb stress change following the M5.7 mainshock (Event B), as many of the focal mechanism solutions of earthquakes between Events A and B (Figure 5b) are either consistent with Event B or C or exhibit a slight rotation (within 25°) away from these rupture planes. Thus, at low effective coefficients of friction, we find that earthquakes that occur between Events B and C are consistent with triggering by the static Coulomb stress change that results from the contribution of the foreshock and mainshock (Events A and B combined) when considered on the GCMT focal mechanism orientation of Event C; however, this result is not confirmed by the SFP geometry for earthquakes following Event B (Table S3 in the supporting information).

As a final test of our Coulomb stress change modeling, we assign each of the aftershock hypocenters (Figure S1 in the supporting information), with the 110 focal mechanism solutions estimated in this study. For example, there are a total of 21,890 unique focal mechanism-hypocenter combinations for 199 earthquakes that occur between Events A and B, respectively. We find that 62% of the earthquakes that occur between Events A and B locate within regions of Coulomb stress increase, while only ~31% and 37% fall within regions of Coulomb stress increase following Events B and C, respectively (Figure S1 and Table S4 in the supporting information). Overall, the result of these tests suggests that the M5.0 foreshock (Event A) triggered the majority of its own aftershocks up through the M5.7 mainshock (Event B); however, again, the modeling suggests that the combination of Events A and B may not have triggered subsequent events, which we will discuss in greater detail below.

7 Discussion

In this study, we find that the Coulomb stress change at the location of the M5.7 mainshock (Event B) is consistent with triggering by the M5.0 foreshock (Event A). This result is upheld through various tests of the method, including Coulomb stress change analysis on the focal mechanism solutions of 110 earthquakes, on the specified fault plane orientation derived from the regional stress inversion of these focal mechanism solutions, as well as on the GCMT focal mechanism solutions of the major M ≥ 5.0 earthquakes. However, we also find that Events A and B impart a negative Coulomb stress change on the M5.0 aftershock (Event C). Even when the Coulomb stress change that results from Event A alone is considered on the rupture plane of Event C, the net effect is an ~2.9 bar Coulomb stress decrease.

These findings beg the question as to why the rupture fault plane of Event C is activated in the first place, since its rupture orientation is so different from that of Events A and B. Many of the focal mechanism solutions in the sequence are consistent with the right-lateral strike-slip orientation of Events A and B; however, several events are also consistent with that of Event C (Figure 4). Furthermore, some of the events have nodal planes that are rotated away from either Events A and B or from Event C resulting in an ambiguity in which nodal plane is the correct rupture plane orientation. This observation, as well as the presence of some dip-slip focal mechanisms, suggests that there are complex rupture geometries present due to the interconnected fault system [e.g., Way, 1983; Joseph, 1987]. Interestingly, aftershocks that follow Event B (Figures 7b and 7d and Figure S1 in the supporting information) also appear along the fault plane that fails in Event C; this observation suggests that this fault plane is activated prior to Event C, although the fault plane is not oriented for failure based on the regional stress direction (Figure 6c). Many of the earthquakes along the rupture plane of Event C show an apparent Coulomb stress decrease (Figures 7b and 7d). The modeling results suggest that the static Coulomb stress change from Events A and B do not trigger Event C. This may suggest that other processes like dynamic stress triggering [e.g., Felzer and Brodsky, 2005] and/or an increase in pore pressure due to fluid flow [e.g., Cocco and Rice, 2002] are to blame for this event. However, this result more likely reflects the limitations of near-field Coulomb stress modeling with respect to the proximity of earthquakes to one another as well as to the ruptured fault surface.

In general, a large-magnitude earthquake decreases the stress along a fault, yet we observe the greatest number of aftershocks close to the ruptured surface. This observation seems to defy the concept of static stress triggering; however, small-scale heterogeneities along the ruptured surface result in patches of stress increase along the fault, which play a role in the promotion of aftershock activity [e.g., Hainzl et al., 2010]. Stress changes caused by a major earthquake are difficult to estimate close to the fault, as there exists small-scale slip variability along the rupture interface [e.g., Helmstetter and Shaw, 2006; Marsan, 2006], nonplanar fault geometry [Smith and Dieterich, 2010] and heterogeneous pre-rupture stresses. Since differential stress ultimately drives earthquake activity, spatial clustering of aftershocks may in fact result from the distribution of high- and low-stress regions [e.g., Parsons, 2008; Parsons et al., 2012]; thus, we might expect aftershocks to also occur within regions of apparent Coulomb stress decrease [e.g., Steacy et al., 2004; Hainzl and Marsan, 2008]. Even with the most sophisticated slip models, the lack of information about the stress and slip distribution along the fault plane led Hardebeck et al. [1998] to conclude that Coulomb fault failure would be unable to predict the occurrence of near-fault aftershocks (<5 km away from the causative fault).

Here we assume uniform stress drop across the entire rupture surface, as a lack of local stations (for Event A) or lack of nearby on-scale recording (for Events B and C), and relatively small magnitudes of the earthquakes preclude detailed knowledge of the slip along the fault planes of Events A–C. A finite fault inversion of slip for Events B and C is the subject of ongoing research [Shengji Wei, personal communication, 2013] and is out of the scope of this manuscript. In addition, we model the ruptures as simple planar faults, as the small-scale geometry of the fault planes is unknown; Smith and Dieterich [2010] show that very small-scale deviations from a perfectly planar fault result in large stress heterogeneities near the fault. Most of the earthquakes locate very close to the fault planes of Events A, B, and C (within <5 km), so a significant portion of the events are modeled to have negative Coulomb stress changes. This includes the M5.0 aftershock (Event C), whose rupture plane abuts up against that of Event B (Figure S1c in the supporting information).

In addition, we only model the effect of the largest three events in the earthquake sequence and do not investigate the multiple complex stress interactions between the aftershocks themselves. The next largest magnitude earthquake in our catalog, besides the three M ≥ 5.0 earthquakes, is a M4.0 earthquake (event #4 in Tables B1 and C1). Stress maps are considered stable as long as the largest aftershocks are considered down to a level of Mmax–1.5 [Hainzl et al., 2010]. Thus, for our stress maps to be stable, we consider only the three earthquakes of M4.2 and larger (M5.0 foreshock, M5.7 mainshock, and M5.0 aftershock). In addition, small errors in the aftershock location could also contribute to our observation that some earthquakes occur when Coulomb stress changes suggest failure would be inhibited (Figures 5 and 7).

When a realistic slip distribution and background stress field is considered, a highly variable suite of failure planes is expected, such that a variety of aftershock mechanisms occur within a kilometer or less of one another [e.g., Kilb et al., 1997]. Although many of the focal mechanism solutions in our study are consistent with the rupture planes of Events A–C, anomalous focal mechanism solutions (Figure 5) may provide additional evidence of complex fault interactions and fault geometry. The variability in the focal mechanism solutions of aftershocks, and therefore incomplete knowledge of the receiver fault geometry, may present an additional limitation of our study.

In Oklahoma, the poroelastic response from fluid injection is also important to consider as an external trigger of earthquakes in this region. The instantaneous coseismic stress changes that we model here represent a “snapshot” of the Coulomb stress field immediately following each M ≥ 5 earthquake, and coseismic stress changes occur on a time scale that is too short to allow for the loss or gain of pore fluid by diffusive transport (fluid flow) [Rice and Cleary, 1976; Cocco and Rice, 2002]. Poroelastic strain transfer has shown to initiate earthquakes along OOPs [Nur and Booker, 1972; Zoback and Harjes, 1997; Shapiro et al., 2006; Guglielmi et al., 2008; Durand et al., 2010; Daniel et al., 2011]; however, these small transient strains (<1 MPa) may die off too quickly and therefore be insufficient to trigger subsequent earthquake activity [Hainzl and Ogata, 2005].

8 Summary and Conclusions

In summary, we detect and locate 110 earthquakes that have sufficient P wave polarity and S/P amplitude ratio information that is suitable for high-quality focal mechanism solutions. The focal mechanism solutions are predominantly consistent with the inferred strike-slip rupture plane orientation of Events A–C (~85% of the catalog; Table C1); however, the remaining 15% of the events that exhibit variations in strike and anomalous dip-slip focal mechanism solutions may reflect the complex fault geometry in the epicentral region. We calculate the Coulomb stress changes on the inferred rupture plane of the focal mechanism solutions and find that ~60% of the aftershocks including the M5.7 mainshock (Event B) occur within the regions of stress increase (>0.1 bar). Since most of the aftershocks occur close to the ruptured portions of the fault plane (on average, <2.5 km away from the closest rupture plane), the overall low percentage may reflect our limited knowledge of the stress and slip variability along the fault plane, nonplanar fault geometry, and stress heterogeneities due to the mechanical properties of the faulted medium.

Our findings suggest that the volume of fluid injection may not limit the mainshock magnitude and/or cumulative moment release, as McGarr [2014] previously suggested. Static Coulomb stress changes due to Event A are consistent with triggering of Event B, which suggests that fluid induced events such as the M5.0 foreshock in Oklahoma, can trigger larger events if a nearby fault is critically stressed. This key, but not unexpected, observation has implications for estimating seismic hazard from injection.

Appendix A: Instrument Type and Data Logger Information

Table A1 contains general information regarding the seismic array deployed in the epicentral region of Events A–C. The main operating agencies are the University of Oklahoma Rapid Aftershock Mobilization Program (OU RAMP), the United States Geological Survey Pasadena, California, and Golden, Colorado offices, and the Array Network Facility, which manages the EarthScope Transportable Array. Information regarding the station names, instrument and data logger types, and sample rates (in Hz) are shown. The OU RAMP “LC” (Lincoln County, Oklahoma) stations are labeled by number only in Figure 1a, while the EarthScope TA stations are labeled in Figure 1b. Note that the sampling rate of stations LC01–LC03 was increased from 100 Hz to 250 Hz after the mainshock occurred.

Table A1. Instrument Type and Data Logger Information
Operating AgencyStation NamesInstrument TypeData Logger TypeSample Rate (in Hz)Notes
OU RAMPLC01–LC03Nanometrics Trillium CompactTaurus Standard 47 k100 
OU RAMPLC01–LC03Nanometrics Trillium CompactTaurus Standard 47 k250Sample rate changed after Event B
OU RAMPLC04–LC08Nanometrics Trillium CompactTaurus Standard 47 k250 
OU RAMPLC09–LC10EpisensorReftek 130250 
OU RAMPLC11–LC18Guralp CMG40TReftek 130250 
USGS NetQuakesOK001[2,4,5,8,9-12]GeoSig Force Balance Accelerometer AC-63GMS-18-NetQuakes200 
USGS GoldenOK020–OK022Nanometrics Trillium CompactReftek 13040 
USGS PasadenaOKR01–OKR10Nanometrics Trillium CompactReftek 130200 
EarthScope TATUL1, V35A, W35A, U35A, X36AStreckeisen STS-2Quanterra 33040 
EarthScope TAV36AGuralp CMG3TQuanterra 33040 
EarthScope TAW36AStreckeisen STS-2.5Quanterra 33040 

Appendix B: Hypocentral Catalog

Table B1 is a compilation of the relative relocations of 110 earthquakes with A or B quality focal mechanism solutions. An identification number is for the 110 earthquakes relocated in this study, while a letter denotes the OGS locations of the three main events detailed in this study. Note that event #3 is the relative relocation of the M5.7 mainshock (Event B). The hypocenter date, time, and location are given, as well as the earthquake magnitude. For our relocations, the 2σ horizontal and vertical errors and the root-mean-square travel time residual from the hypoDD double-difference analysis are provided. Error information for Events A–C is provided by the OGS.

Table B1. Hypocenter Information and Constraints for 110 Earthquakes With A and B Quality Focal Mechanism Solutions
Hypocenter Information Hypocenter Constraints
   Location Error (m) 
IDDate (DD/MM/YYYY)Time HH:MM:SS.SSLatitude (°N)Longitude (°E)Depth (km)MHorizontalVerticalRMS Travel Time Residual (s)

Appendix C: Focal Mechanism Catalog

Table C1 is a compilation of the 110 A and B quality focal mechanism solutions. The number in the first column is the event number for each earthquake, while the letter denotes the GCMT solution of Events A–C. The magnitude of the event (M) is also given and is the same as Table B1. The focal mechanism parameters of the best fit double-couple solutions are presented in Table C1, including the plunge (δ) and azimuth (ε) of the compressional (P), null (B), and tensional (T) axes, as well as the strike (φ), dip (θ), and rake (λ) of the two nodal planes. In addition, the number of P wave and S wave picks and S/P amplitude ratio observations (NOBS), the focal plane uncertainty (FPU), azimuthal station gap (GAP), and the quality of the HASH focal mechanism solution [Hardebeck and Shearer, 2002, 2003] are also provided.

Table C1. Principal Axes, Double-Couple Component Focal Mechanisms, and Constraints
  Principal AxesFocal Mechanism Solution 
  P axisB axisT axisNodal Plane 1Nodal Plane 2Focal Mechanism Constraints
IDMδεδεδεφθλφθλNOBSFPU (deg)GAP (deg)Quality
A5.01616472315872207731752998517GCMT solution
B5.70189879132795488−17832488−2GCMT solution
C5.015314731607469174635984164GCMT solution


The U.S. Geological Survey, Oklahoma Geological Survey, Oklahoma State University, and the University of Oklahoma provided personnel to assist with field installations. The University of Oklahoma and U.S. Geological Survey funded field acquisition costs. The PASSCAL instrument center and U.S. Geological Survey provided RAMP instruments and logistical support. We gratefully acknowledge the discussions with H. Meighan and the reviews provided by J. Hardebeck, T. Parsons, D. Kilb, and an anonymous reviewer. Funding provided by NSF EAR-PF-1049609 (D.F. Sumy), and the IRIS Summer Internship Program (M. Wei) supported this research.