Delayed Dynamic Triggering of Disposal-Induced Earthquakes Observed by a Dense Array in Northern Oklahoma

Abstract

Recent increases in earthquake occurrence rates in Oklahoma have been linked to the injection of large volumes of saltwater, a byproduct of oil and gas extraction. Here we present a detailed study of remote earthquake triggering in an area of active injection-induced seismicity in northern Oklahoma using data from the LArge-n Seismic Survey in Oklahoma (LASSO) temporary array and nearby permanent broadband seismic stations. We estimate changes in earthquake rates and calculate the Coulomb failure stress changes on potential receiver faults due to passing teleseismic surface waves. A statistically significant increase in seismicity is observed ∼8 hr after the 16 April 2016 M_w 7.8 Ecuador earthquake. The Coulomb stress changes associated with the Ecuador earthquake are on the order of ∼1 kPa. Physical mechanisms consistent with the observed dynamic stress threshold include failure driven by activation of aseismic slip or hydrological response of the fault system.

Key Points

• Remote dynamic triggering is observed in a region of induced seismicity in northern Oklahoma
• Dynamic stress perturbations of a fraction of a kPa are observed to trigger earthquakes after a delay
• Delayed dynamic triggering mechanisms include aseismic slip or pore pressure redistribution

Plain Language Summary

The state of Oklahoma in the United States has experienced a large increase in the number of earthquakes over the last decade. Most of these earthquakes are thought to occur as a consequence of the long-term effect of saltwater disposal, resulting from energy production, at depths of 1–2 km into geologic formations. In this study, we examine how easily faults can be driven to fail, resulting in small earthquakes, in a region of northern Oklahoma. Using data collected during a month-long deployment of 1,833 seismic sensors in northern Oklahoma, we look at the timing and number of earthquakes that occur following the passage of the seismic waves from distant earthquakes that exert small, oscillating forces on the faults. We find that the number of earthquakes increases starting about 8 hr after the seismic waves from the 16 April 2016 M_w 7.8 Ecuador earthquake travel across the array. This study shows that a small increase in the forces experienced by faults in northern Oklahoma can sometimes cause earthquakes.

1 Introduction

Transient stresses generated by the passage of seismic waves from earthquakes have been observed to promote fault slip at regional and teleseismic distances; a phenomenon often referred to as remote dynamic triggering. Because static stresses fall off rapidly with distance (∼r⁻³) compared with dynamic stresses (∼r^−3/2), dynamic stresses are assumed to be the primary triggering mechanism at distances exceeding many multiples of the triggering earthquake's fault length (e.g., Freed, 2005; Hill & Prejean, 2015). The magnitudes of dynamic stresses shown to result in triggering are on the order of tens of kPa (e.g., Gomberg et al., 2001; Hill & Prejean, 2015; Hill et al., 1993). While remote dynamic triggering has been widely observed (Velasco et al., 2008), the exact causal mechanism(s) are still unknown. Several models have been proposed, including Coulomb failure criteria (Freed, 2005; Kilb et al., 2002; West et al., 2005), permeability enhancement and pore pressure changes (Brodsky et al., 2003; Elkhoury et al., 2006; Manga et al., 2012), subcritical crack growth (Atkinson, 1984; Brodsky & Prejean, 2005), rate-state frictional failure (Dieterich, 1994; Gomberg et al., 2001; Perfettini et al., 2003; Yoshida, 2018), the nonlinear elastic response of rocks (Johnson & Jia, 2005), and aseismic slip activation (Shelly et al., 2011). Identifying the physical mechanisms that initiate remote dynamic triggering at low stress amplitudes is key to identifying the conditions that result in fault failure (Brodsky & van der Elst, 2014).

Injecting fluids into the shallow layers of the crust, whether for hydraulic fracturing or saltwater disposal, has been shown to lead to increases in seismicity in locations where historical earthquake rates are low, such as the central and eastern United States (Ellsworth, 2013) and the Western Canada Sedimentary Basin (Atkinson et al., 2016). Recent studies show that dynamic stress triggering thresholds are on the same order of magnitude as solid Earth tides (e.g., B. Wang et al., 2015), supporting claims of Townend and Zoback (2000) of a critically stressed crust. In seeming contradiction to such claims, only a small percentage of injection wells are associated with induced earthquakes (Atkinson et al., 2016). Remote dynamic triggering may provide a way to probe the susceptibility of the crust to failure from other sources of stress perturbations, such as local saltwater disposal (van der Elst et al., 2013; B. Wang et al., 2015, 2018). In areas of induced seismicity, such as the central United States and the Western Canada Sedimentary Basin, dynamic triggering has been observed with stress perturbations of less than 10 kPa (van der Elst et al., 2013) and a fraction of a kPa (B. Wang et al., 2015, 2018), respectively. The onset of triggering can occur synchronously with teleseismic phase arrivals (Bansal et al., 2018; Gonzalez-Huizar et al., 2012; Hill et al., 1993, 2013; Pankow et al., 2004; B. Wang et al., 2015; W. Wang et al., 2015; West et al., 2005), or triggering may occur after a delay of several hours (Cattania et al., 2017; Johnson & Bürgmann, 2016; Parsons et al., 2014; Peng et al., 2015; van der Elst et al., 2013; B. Wang et al., 2015).

Here, we use data recorded by an array of 1,833 vertical-component nodal sensors deployed in northern Oklahoma, United States, from 14 April to 11 May 2016, termed the LArge-n Seismic Survey in Oklahoma (LASSO) array (Dougherty et al., 2016). We use a catalog of local earthquakes detected by the LASSO array to identify whether teleseismic surface waves trigger a statistically significant increase in seismicity within the study region. For each of the teleseismic events examined, we estimate the dynamic stress perturbations to determine if a stress threshold exists that can be associated with statistically significant changes in seismicity, and investigate possible causative mechanisms.

2 Local Seismic Catalog Development

To evaluate changes in earthquake rates within the array, we develop a local earthquake catalog using data recorded by the LASSO array. The available catalog from the Oklahoma Geological Survey (OGS) does not provide sufficient coverage of small magnitude events (Darold et al., 2015). We identify seismic events using a short-term average/long-term average detection technique applied to bandpass filtered (5–35 Hz) continuous data. Short- and long-term window lengths of 0.5 and 30 s, respectively, are used. We require that detections occur on at least 110 of the 1,833 nodal sensors to declare an event. We detect a total of 3,117 earthquakes during the deployment period, and events are located assuming a 1-D velocity model from Rubinstein et al. (2018). Event magnitudes are not estimated. False detections are removed by visual inspection of seismograms from the 60 closest stations to each event. Events located within 5 km of the array footprint (Figure 1) with depths shallower than 12 km (Figure S1) are included in the resulting catalog of 1,375 earthquakes, which is used for subsequent statistical analysis. The average number of events detected per hour is 51, with a somewhat lower number of events detected during daytime hours (48) than during nighttime hours (66; Figure S2).

Figure 1

Seismicity detected by the LASSO array (cyan circles). Only events located within 5 km of the footprint of the array are shown. Pink circles represent locations of earthquakes from the OGS catalog across a broader region. Overlapping pink and cyan circles represent events detected by both the OGS and LASSO with the location from the STA/LTA catalog. All earthquakes reported by the OGS in this area were detected by the LASSO array. Orange triangles are select broadband stations that operated during the array deployment period. Gray diamonds represent the stations of the array. Left bottom inset shows the regional location of the study area (red square). Right bottom inset shows focal mechanisms of M_w≥ 6 teleseismic events with potential to dynamically trigger events in Oklahoma. Gray beach balls represent events that were not followed by an increase in the local seismicity rate. Blue, yellow, red, and purple beach balls represent events that occurred in Ecuador, the North East Pacific Rise, Vanuatu, and Ecuador (Event H, Table S1), respectively. LASSO = LArge-n Seismic Survey in Oklahoma; STA/LTA = short-term average/long-term average; OGS = Oklahoma Geological Survey.

3 Teleseismic Earthquake Selection and Dynamic Stress Calculation

To look for evidence of remote dynamic triggering, we first search for the set of teleseismic events which occur during the ∼30-day LASSO array deployment period and determine their theoretical and observed dynamic stresses at the LASSO array. Our global search criteria selects all events with M_w ≥ 6.0 and depth ≤100 km. For each teleseismic event, we estimate the stress imposed by the surface waves by calculating the theoretical peak dynamic stress at the array and from measurements of the passing teleseimic waves on two local broadband stations. We note that the potential for stress contamination from nearby or regional earthquakes is negligible since no earthquakes with M_w ≥ 4.0 occur during the deployment period within 1,000 km of the array.

We calculate the theoretical Peak Ground Velocity (PGV) and resulting peak dynamic stress (σ_pd) using an empirical ground motion regression (Lay & Wallace, 1995; van der Elst & Brodsky, 2010; Velasco et al., 2004):

(1)

(2)

(3)

where M_s is the surface wave magnitude, A₂₀ is the amplitude (in microns) of surface waves with a 20-s period, Δ is the teleseismic source-receiver (epicentral) distance in degrees, T is the surface wave period (20 s), G is the shear modulus, and c is the shear-wave velocity. We consider M_s = M_w as a first approximation and assume typical crustal values for G and c (32 GPa and 3.5 km/s, respectively).

Measured PGV values of surface waves for each teleseismic event come from the two nearby broadband stations (OK.CROK and GS.OK032; Figure 1). We apply a 0.1-Hz lowpass filter to the data and measure PGV values on vertical, radial, and transverse components (Figure 2). PGV values do not change significantly even if we increase the lowpass corner of the filter to 0.5 Hz. We then calculate the σ_pd from the peak filtered amplitude measurement using equation 3 (Figure 2).

Figure 2

PGV or peak dynamic stress (σ_pd) at the LASSO array for the observed teleseismic events. Solid curves show the estimated PGV or σ_pd as functions of epicentral distance for three magnitudes that span the magnitude range of the observed teleseismic events, using the empirical ground motion regression (equations 1-2, and 3). Dashed horizontal lines represent previously identified triggering thresholds. Gray stars indicate events that were not followed by an increase in the local seismicity within the LASSO array. Blue, yellow, red, and purple stars represent the same events as in Figure 1. (a) PGV and σ_pd at the LASSO array from the empirical ground motion regression equations for the distances and magnitudes of the observed teleseismic events. (b) Measurements of the maximum PGV on the closest broadband stations to the LASSO array (Figure 1) on the vertical component. Waveforms were lowpass filtered at 0.1 Hz to measure the maximum shaking. (c) and (d) are the same as (b) but on the radial and transverse component, respectively. PGV = Peak Ground Velocity; LASSO = LArge-n Seismic Survey in Oklahoma.

Equation 3 provides the peak dynamic stress values without considering the relative orientation between incident Love and Rayleigh wave particle motions, receiver fault orientation(s), or depth (e.g., Gomberg et al., 2001; Hill et al., 1993; Husker & Brodsky, 2004; Prejean et al., 2004; B. Wang et al., 2015). However, if fault orientations are known (e.g., based on focal mechanisms), one can estimate the stress resolved onto specific faults imposed by incident Love and Rayleigh waves (e.g., Gonzalez-Huizar & Velasco, 2011; Miyazawa & Brodsky, 2008; West et al., 2005; Figure 3a). We use the same approach as in Gonzalez-Huizar and Velasco (2011). In this formulation, the displacement in the radial (U_x) and vertical (U_z) direction for a Rayleigh wave is defined by

(4)

(5)

where A is the amplitude, ω is the angular frequency, κ_x is the horizontal wave number, and z is depth (Stein & Wysession, 2009). Coefficients have values of B = −0.85, C = 0.58, D = −0.39, and E = 1.47 (Stein & Wysession, 2009).

Figure 3

(a) Schematic diagram showing surface waves propagating in the radial (x), transverse (y), and vertical (z) directions across a receiver fault with an arbitrary orientation (modified from Stein & Wysession, 2009, and Gonzalez-Huizar & Velasco, 2011). (b) and (c) are the displacements measured on the transverse component (Love waves) and vertical component (Rayleigh waves), respectively, for the M_w7.8 Ecuador earthquake. Displacement was measured using a narrow filter around 30 s. (d) and (e) represent the changes in the CFF caused by Love waves and Rayleigh waves, respectively, on a receiver fault with left lateral strike-slip motion. (f) and (g) represent the changes in CFF on a receiver fault with normal motion. (h) and (i) represent the changes in the stress for a strike-slip fault and a normal fault, respectively, for different filter passbands. Blue, yellow, red, and purple symbols represent the same events as in Figure 1. CFF = Coulomb Failure Function.

Similarly, the displacement in the transverse direction (U_y) for a Love wave can be described as

(6)

(7)

where c₁ is the apparent velocity of the Love waves and β₁ is the shear velocity for the layer (Stein & Wysession, 2009). We rotate the data on the two nearby broadband stations into radial, transverse, and vertical components. We measure displacement amplitudes on each of the transformed components in narrow passbands around 10, 20, 30, and 40 s and use the peak amplitudes in equations 4-5, and 6 to transform the peak displacements into a stress tensor ( ) with

(8)

where λ and G are the Lamé parameters and U_i, U_j, and U_k represent the displacement on each component (Shearer, 2009). We assume that the receiver fault is embedded in a homogeneous Poisson solid (λ = G = 32 GPa). Since the effect of σ^D on the fault depends on the fault orientation (Gonzalez-Huizar & Velasco, 2011; West et al., 2005), we rotate σ^D into fault plane coordinates (Figure 3) using the Euler angle matrices (see Arfken et al., 2011, and the appendix of Wu et al., 2011). Finally, the change in the Coulomb Failure Function (ΔCFF) can be defined for each type of faulting mechanism as

(9)

(10)

(11)

(12)

where μ represents the frictional coefficient, δσ_n the change in fault normal stress, and δσ_d and δσ_s the change in fault shear stress in the dip and strike direction, respectively (Gonzalez-Huizar & Velasco, 2011). We adopt a frictional coefficient value (μ) of 0.6.

We use the above approach to calculate the stress perturbations generated by passing surface waves resolved onto receiver fault orientations. The number of available focal mechanisms for events in this area is low, so we use the focal mechanism solutions for the two largest events that occurred within the footprint and just prior to the deployment (Figure 4). The first event is described by a M_w 4.6 left lateral strike-slip mechanism with strike of 305° and dip of 80°, which occurred on 30 November 2015, and the second by a M_w 3.9 normal faulting mechanism with strike of 85° and dip of 60°, which occurred on 20 November 2015 (Alt & Zoback, 2016; Herrmann, 2016). Figure 4 shows the locations of these two events as well as other focal mechanisms obtained by Herrmann (2016) that exhibit similar faulting styles to the two largest events. Alt and Zoback (2016) distinguish the preferred slip plane orientation for the events in Herrmann (2016). We do not have precise fault geometries for all 1,375 earthquakes in the catalog, nor their precise depths. So, while not comprehensive, the two above focal mechanisms allow us to provide an order of magnitude estimate of the ΔCFF stresses required to initiate triggering in or near the LASSO array.

Figure 4

Focal mechanisms and maximum stress orientations in the LASSO array region from Herrmann (2016) and Alt and Zoback (2016), respectively. Red beach balls represent the dominant faulting mechanisms and numbers are the magnitudes for the events selected as target faults. LASSO = LArge-n Seismic Survey in Oklahoma.

4 Statistical Tests of Earthquake Rate Changes

We perform four statistical tests (β, Z, P, and γ) to analyze the change in the seismicity rate after each teleseismic event. Although the β-statistic is one of the most commonly used methods to quantify the occurrence of dynamic triggering (Hill & Prejean, 2015), it is normalized by only one event distribution (e.g., the number of events before the stressing event). Here we include other statistical tests that have more rigorous normalizations (defined below) or are more sensitive to the number of events (for cases where the number of events is low; Marsan & Nalbant, 2005; Marsan & Wyss, 2011). For example, the Z-statistic is a more symmetric version of the β-statistic (Aiken et al., 2018; Marsan & Wyss, 2011). We examine two reference times (t = 0): the theoretical arrival time of the P wave or the surface wave. Both reference times are calculated using TauP (Crotwell et al., 1999), with the PREM (Dziewonski & Anderson, 1981) velocity model for the P wave and an assumed velocity of 2 km/s for the surface wave. We assume 2 km/s for the surface wave speed to provide an approximate upper bound to the time for the bulk of the teleseismic energy to traverse across the LASSO array. We evaluate whether there is a statistically significant change in earthquake rate after each teleseismic event reference time using a set of window lengths spanning 1 to 48 hr. The time window selection is based on the trade-off between ensuring there are a sufficient number of events for the statistical analysis in the shortest window lengths and avoiding correlating activity not necessarily related to dynamic triggering in the longest time window (Husker & Brodsky, 2004). Previous studies (van der Elst & Brodsky, 2010; van der Elst et al., 2013; B. Wang et al., 2015) use time windows longer than the 2-day-long window used here. We use a maximum window length of 48 hr because the array was only deployed for 1 month and because teleseismic events occur closely spaced in time near the beginning of the deployment. In general, all of the tests described below are equivalent when the number of earthquakes is large, but the P and γ tests are more appropriate when populations of events or crustal volumes are small and/or the time windows considered are short (Marsan & Nalbant, 2005). Each of the above statistical tests also assumes that the earthquake catalog follows a Poisson distribution. We test the null hypothesis that the LASSO catalog is Poisson distributed and find that we cannot reject the null hypothesis at the 95% confidence level. It is possible that events following a stressing event deviate from a Poisson distribution for some period of time, but to establish triggering, we need only to capture changes in the average rates before and after the stressing event.

The β-statistic (Matthews & Reasenberg, 1988) is a measure of the difference between the number of events that occur versus the expected number of events normalized by the standard deviation:

(13)

where , N_b, and N_a are the number of earthquakes before and after the stressing event (i.e., the teleseismic P wave arrival and surface wave), respectively, and t_b and t_a are the time window lengths before and after, respectively. Here we consider time windows of equal length, that is, t_a = t_b. In cases where no events occurred in the “before” time window, t_b, we set N_b = 0.25 to stabilize the β value. A β ≥ 2.0 indicates a change in seismicity with a 95% significance.

The Z-statistic (Habermann, 1987) defines the difference between the mean rate of seismicity in the period before and after the stressing event as

(14)

A Z value of Z = 1.96 indicates a 95% significance. Thus, to indicate a change in the seismicity rate, we use a threshold of Z ≥ 2.0.

The probability of triggering (P) as formulated by Marsan (2003) measures how significant the seismicity rate change is:

(15)

where λ_b and λ_a are the mean seismicity rates before and after a stressing event and f_b and f_a are the probability density functions. The probability P assumes that n earthquakes can be observed when the mean rate is λ₀ during a certain time window Δt, that is, , if they represent a Poisson process. Equation 15 can be rearranged as (Marsan & Wyss, 2011)

(16)

where Γ is the incomplete Gamma function. By definition, values for the probability of triggering belong on the interval [0,1], where P < 0.5 indicates a decline in seismic activity and P > 0.5 indicates an increase. The confidence level of 95% corresponds to a value of P > 0.975 (in the case of activation).

The γ-statistic (Marsan & Nalbant, 2005) is a different way to visualize the probability of triggering and is defined by

(17)

A value of γ ≥ 1.6 represents a 95% confidence level of rejecting the null hypothesis of seismic quiescence (Marsan & Wyss, 2011).

The above tests (β, Z, P, and γ) compare the seismicity directly before (N_b) and after (N_a) the stressing event. We will refer to them as basic statistical tests. In cases where triggering is implied by the above statistical tests we undertake an additional, more rigorous test, which we subsequently refer to as a “mean-comparison test.” The mean-comparison test method evaluates the significance of seismicity rate changes that follow the teleseismic arrivals against the fluctuations in earthquake rates over the duration of the deployment. In other words, since our catalog is limited to ∼30 days, we compare changes against an effective “background rate” which is assumed to be represented by fluctuations over the catalog length. The mean-comparison test also allows us to account for fluctuations in the seismicity rate which include possible day-night variations due to noise. Thus, the mean-comparison test compares the seismicity (N_a) for a defined time period (t_a) after the P wave arrival (and surface wave) versus the number of events (N_i) in all other possible time windows (n) with the same duration as t_a, divided by the number of possible time windows. Each statistical test can then be redefined by their mean-comparison counterpart as

(18)

(19)

(20)

(21)

where i∉ represents all time windows other than the windows directly before and after the P wave arrival and before and after the surface wave arrival. We repeat this test for intervals of 1 to 48 hr, in 1-hr increments, to verify that any significant triggering is independent of the choice of time window.

5 Results

We find 14 candidate teleseismic events that meet the global search criteria (Figures 1 and S3 and Table S1). The results of the basic statistical tests (equations 13-15, and 17) for all 14 teleseismic events are given in Figure 5 and the supporting information (Figures S3–S7). Threshold values of β ≥ 2.0, Z ≥ 2.0, P ≥ 0.975, and γ ≥ 1.6 are used to define statistically significant increases in seismicity following a mainshock. The threshold value for each test is selected to be at the 95% confidence interval. Of the 14 events, three are associated with significant (delayed) increases in seismicity using the basic tests (Figures 5 and S4). These three events occurred in Ecuador, the North East Pacific Rise (NEPR), and Vanuatu. At first glance, a fourth event appears to be associated with triggering (Figure 5), however we discuss below why event H is not considered to be associated with any seismicity increases.

Figure 5

Basic statistical tests for the Ecuador (blue), NEPR (yellow), Event H (purple), and Vanuatu (red) earthquakes for a time window of 48 hr. Horizontal dashed lines represent significance thresholds. Reference time (t = 0) is the P wave arrival. NEPR = North East Pacific Rise.

The largest event is a M_w 7.8 earthquake in Ecuador (Figure 1) that occurred at a depth of 20.6 km on 16 April 2016. Out of the three components, the surface waves from this event produce the largest expected and observed PGV on the transverse component (Love wave; Figure 2). This PGV value exceeds the expected and observed (transverse) PGV of all other candidate events by almost an order of magnitude. The event with the second-highest expected and measured PGV values is a M_w 6.6 NEPR earthquake that occurred at a depth of 10 km on 29 April 2016 (Figures 1 and 2). For this event, we observe the largest PGV values on the vertical and radial components. The third event, where the basic statistical tests suggest dynamic triggering, is a M_w 6.4 Vanuatu earthquake that occurred at a depth of 16 km on 14 April 2016 (Figures 1 and 2). The peak ground motions generated by this event are below previously reported triggering thresholds (Brodsky & Prejean, 2005; Cochran et al., 2004; van der Elst & Brodsky, 2010; B. Wang et al., 2015).

We do not observe any significant increase in the seismicity for any of the remaining candidate teleseismic events (Figures S5–S7). To try and further exclude the possibility that events below the detection threshold were triggered following the remaining teleseismic events, we additionally follow the method of Velasco et al. (2008) and stack the histograms of all of the remaining events to look for a suggestion of delayed triggering. The stacked histograms also do not show any indication of seismicity increases following the remaining teleseismic events. The ground motion on the vertical and radial components for all remaining events have PGV≤ 1 ×10²μm/s or σ_pd < 1 kPa, with some events surpassing the dynamic triggering threshold reported by van der Elst and Brodsky (2010) and B. Wang et al. (2015; Figure 2). Although the statistical analysis of Event H (Figures 5 and S4) suggests associated triggering, the mean comparison test for this event shows no significant increase in seismicity (Figures 6 and S9). Furthermore, its PGV value is lower than 10 μm/s (Figure 2) and estimated ΔCFF is < 20 Pa (Figure 3), which is well below the lowest reported triggering threshold (Figure 2; van der Elst & Brodsky, 2010). We therefore categorize Event H as having a coincidental increase in seismicity, that is, not related to dynamic triggering.

Figure 6

(a) Daily count of earthquakes detected by the LArge-n Seismic Survey in Oklahoma array and origin times of each teleseismic event during the same time period (gray vertical lines). The four teleseismic events that were followed by an increase in the local seismicity are indicated by red (Vanuatu), blue (Ecuador), purple (Event H), and yellow (NEPR) lines. (b) Local earthquake count 24 hr before and after the P wave arrival of the M_w 7.8 remote earthquake that occurred in Ecuador. The magnitude and timing of the only local event detected by the OGS during this time period is also shown (green dot). Times shown are UTC. Origin time of the teleseism is shown by the blue line. (c) β, Z, γ, and P mean-comparison statistical tests (defined in section 4) performed for time windows of 1 hr up to 48 hr for each of the four teleseismic events. Reference time (t = 0) is the P wave arrival. Black dashed lines represent the significance thresholds. STA/LTA = short-term average/long-term average; OGS = Oklahoma Geological Survey; NEPR = North East Pacific Rise.

We estimate the ΔCFF for the Ecuador, NEPR, and Vanuatu events by projecting the dynamic stresses resulting from the surface waves onto the two dominant fault planes discussed in section 3 and shown in Figure 3. Most of the seismicity occurs above 12 km depth (Figure S1), and we report the maximum ΔCFF in the top 12 km. Note that the maximum stress resulting from Rayleigh waves is concentrated in the upper 2–3 km, but the maximum stress from Love waves is concentrated in the first 15 km (see depth dependence in equation 6; Figures 3d–3g).

Love and Rayleigh waves with a period of 30 s generate the largest ΔCFF for the Ecuador earthquake (Figure 3). The Love waves for this event generate a larger magnitude ΔCFF on left lateral, strike-slip faults (Figure 3h) compared to normal faults (Figure 3i), while the Rayleigh waves have a larger effect on the normal fault orientation (Figures 3h and 3i). The σ_pd for the Ecuador event is in the range of 1–10 kPa (Figure 2). When this stress is projected onto the optimally oriented fault geometries within the array footprint, the ΔCFF drops to < 1 kPa (Figure 3). The NEPR event generates comparable ΔCFF values to the Ecuador event for Rayleigh waves with a period of 20 s for both receiver fault orientations (Figures 3h and 3i). The Vanuatu event generates ΔCFF < 5 Pa in all cases.

Figures 6 and S8 show histograms of the number of events that occur within 5 km of the array footprint versus time, with details around the time of the three events of interest. Since the basic statistical tests suggest significant triggering occurred following the Ecuador, NEPR, and Vanatu events, we also check whether the mean-comparison test implies significant triggering. The results of the mean-comparison statistical tests, calculated as a function of window length, are shown in Figure 6 and described below.

Following the Ecuador earthquake, the β, Z, γ, and P basic statistical tests indicate a significant increase in seismic activity, starting 8 hr after the arrival of the P wave (Figure 5) or the surface wave (Figure S4). The β, Z, and γ mean-comparison tests also suggest an increase in the seismicity rate for window lengths as short as 7 hr (Figures 6c and S9), reaching maximum values for the 12-hr-long windows of β = 6.7, Z = 3.4, and γ = 3.9. We note that the P test does not quite exceed the significance threshold (0.974). The time window lengths for which the threshold is exceeded according to the mean-comparison tests range between 7 and 48 hr (Figures 6c and S9). The β statistic also suggests a seismicity increase for the 1-hr time window following the P wave arrival (Figure 5); however, when the surface wave arrival is used as the reference time the increase in seismicity is not significant (Figures S4 and S9). From the histograms of number of events, we note that the highest seismicity rates occur ∼7–10 hr after the P or surface wave arrival, but there is no evidence for immediate dynamic triggering.

The basic statistical tests also suggest elevated seismicity following the P or surface waves of the Vanuatu event (Figures 5 and S4). The β mean-comparison test suggests an increase in seismicity for window lengths ranging between 6 and 19 hr (Figures 6c and S9). The Z and γ mean-comparison tests also suggest an increase in seismicity, but the time window lengths over which the significance thresholds are exceeded are only 4 and 8 hr, respectively (Figures 6c and S9). The mean-comparison P test does not suggest a significant increase in the seismicity rate for any window length. So, while there is suggestion of increased seismicity rates following the Vanuatu event, the length of the time windows in which the mean-comparison tests surpass the thresholds varies. Given the low PGV values (Figures 2 and 3) and results of the mean-comparison tests, we suggest the evidence for dynamic triggering following the Vanuatu event is weak. For the NEPR event, none of the mean-comparison statistical tests confirm a significant change in the seismicity rate (Figures 6c and S9). Therefore, it is unlikely that the NEPR event caused dynamic triggering. In summary, we conclude that only the Ecuador event is followed by a significant increase in seismicity based on all statistical tests.

We also examine whether the increase in seismicity following the Ecuador mainshock may have been caused by an aftershock sequence following a local, moderate magnitude event before or near the time of the teleseismic surface wave arrival. We use the OGS catalog to search for events which occurred within 20 km of the LASSO array around the time of the Ecuador earthquake. The largest local earthquake during this time period is a M_L = 2.8 event that occurred ∼15 km southeast of the array (Figures S10 and 6b). This local earthquake generates PGV values of <25 μm/s at station OK032, which is significantly lower than PGVs generated by the Ecuador teleseismic surface waves at the same location. This local earthquake occurs after the highest peak in the seismicity rate following the Ecuador teleseismic earthquake (Figure 6b). We also examine the spatial distribution of seismicity in the 12 hr following the P wave arrival of the Ecuador event, finding a diffuse set of event locations (Figure S10) distributed across the array. The widespread distribution of locations suggests that the observed peak seismicity is independent of a localized aftershock or swarm sequence(s).

6 Discussion

Recent studies have observed dynamic triggering in regions where seismicity has been linked to anthropogenic activities, including hydraulic fracturing (Han et al., 2017; B. Wang et al., 2015, 2018), wastewater disposal (van der Elst & Brodsky, 2010), reservoir impoundment (Bansal et al., 2018), and coal mining (W. Wang et al., 2015). Using a catalog of local earthquakes detected by the LASSO array, we find evidence for triggering following seismic phase arrivals of one teleseismic event: the 16 April 2016 M_w 7.8 Ecuador earthquake.

In the following discussion, we compare the dynamic stress estimates for the Ecuador earthquake with the results of previous studies and differentiate between studies that estimate PGV and σ_pd (Bansal et al., 2018; Brodsky & Prejean, 2005; Gomberg et al., 2001; Hill et al., 1993; Husker & Brodsky, 2004; Peng et al., 2010; B. Wang et al., 2015, 2018) versus studies that project the stresses onto one or more preferred fault orientations to determine ΔCFF (Aiken et al., 2018; Cattania et al., 2017; Gonzalez-Huizar & Velasco, 2011; Han et al., 2017; Hill, 2008, 2012; Miyazawa & Brodsky, 2008; Tape et al., 2013; van der Elst et al., 2013).

For tectonically active regions, remote dynamic triggering is observed when σ_pd is on the order of tens of kPa (e.g., Gomberg et al., 2001; Hill & Prejean, 2015; Hill et al., 1993). Dynamic stress thresholds as low as 4 kPa have been reported in brittle-ductile transition zones (Aiken et al., 2013; Chao et al., 2012; Peng et al., 2010), some anthropogenically induced seismic areas (B. Wang et al., 2015, 2018), and geothermal fields (Aiken & Peng, 2014). Similarly, we observe triggering following the Ecuador earthquake with peak dynamic stresses (σ_pd) of only a few kPa. Such low dynamic stress values may suggest that the faults are critically stressed in areas of wastewater disposal, where increased fluid pressures along faults may reduce the failure stress (Sumy et al., 2017).

We also examine the cumulative energy density as a possible indicator of dynamic triggering. The Ecuador earthquake generates less than 20 J s/m² for the cumulative energy density (Figure 7). This value is lower by more than an order of magnitude in comparison with other areas where remote dynamic triggering has been observed, like Long Valley Caldera (Brodsky & Prejean, 2005) and Canada (B. Wang et al., 2015). However, both studies found that cumulative energy density was not a good indicator of when dynamic triggering is expected to occur.

Figure 7

(a) Normalized vertical seismograms recorded at station CROK, lowpass filtered with corner at 0.1 Hz, for each of the three teleseismic earthquakes that were followed by an increase in seismicity. (b) Cumulative energy density ( ) for each of the teleseismic events. We assume a density (ρ) of 3,000 kg/m³ and phase velocity (c) of 3 km/s. For both plots, zero time represents the P wave arrival of the teleseismic event. NEPR = North East Pacific Rise.

Remote dynamic triggering was previously reported ∼100 km south of the LASSO array in Prague, Oklahoma, where the stress perturbation (ΔCFF) was estimated to be ≥ 5 kPa (van der Elst et al., 2013). The order of magnitude difference between the stress amplitudes reported by van der Elst et al. (2013) and those estimated here (ΔCFF∼0.7 kPa) could result from several factors. First, the dense station coverage afforded by the LASSO array allows us to detect smaller magnitude events that would not have been detectable with the four sparsely distributed stations used by van der Elst et al. (2013). Second, pore fluid pressures may be higher and/or there may be more critically stressed faults near the LASSO array. Third, previous studies have suggested a greater propensity for triggering in extensional tectonic regimes compared to compressional regimes (Harrington & Brodsky, 2006; Prejean & Hill, 2009). The stress orientation in Oklahoma is relatively stable (Alt & Zoback, 2016), but stress magnitudes are less compressive in northern Oklahoma where the LASSO array is located compared to central Oklahoma, where the triggering near Prague was observed.

In addition to observing that small stress perturbations can trigger local earthquakes, we observe a delay in the increase of seismicity, with higher seismicity starting ∼7 hr after the teleseismic P and surface wave arrivals. Furthermore, we find that only windows longer than 8 hr show a statistically significant increase in seismicity. While some studies show triggering can occur within the surface wave train, that is, with zero delay time (Gonzalez-Huizar et al., 2012; Hill et al., 1993; Husker & Brodsky, 2004; Pankow et al., 2004; Rubinstein et al., 2007; B. Wang et al., 2015; Warren-Smith et al., 2018; West et al., 2005), others have shown delays of a few seconds (Brodsky et al., 2000; Hill et al., 1993) and up to several hours (Cattania et al., 2017; Johnson & Bürgmann, 2016; Parsons et al., 2014; Peng et al., 2015).

The ∼7-hr delay in the response to the Ecuador event suggests that a simple Coulomb failure criteria is insufficient to explain our observations. To explain a delayed response, Shelly et al. (2011) proposed that teleseismic surface waves can trigger aseismic creep events, which may subsequently trigger seismic slip on fault patches embedded within the aseismically slipping region. While aseismic slip has not (yet) been observed near the LASSO array, nor elsewhere in Oklahoma, field-scale experiments show that fluid injection into a fault system can generate both aseismic and seismic slip (Guglielmi et al., 2015). Creep events have been found to be triggered by passing teleseismic surface waves in strike-slip faulting environments. For example, Tape et al. (2013) observed evidence of aseismic slip in Alaska triggered by Love waves from the M_w 8.6 2012 Sumatra earthquake that culminated in a M_w 3.9 earthquake. We cannot reject that the delayed triggering response observed following the Ecuador earthquake is due to triggered aseismic creep.

Another potential mechanism that may explain the delayed response is rate-state frictional failure (Brodsky & van der Elst, 2014; Dieterich, 1994; Gomberg et al., 2001; Perfettini et al., 2003; Yoshida, 2018). In this mechanism, dynamic stresses change the friction, which leads to fault slip (Brodsky & van der Elst, 2014). However, a delayed response from the rate-state frictional physics is difficult to reconcile with our delay time observation, since the nucleation time (delay) is thought to be on the order of hundreds of seconds (Beeler & Lockner, 2003), while the delay in response that we observe is on the order of 8 hr.

An alternate mechanism to explain delayed remote dynamic triggering is the hydrological response of faults to dynamic strains (Brodsky et al., 2003; Elkhoury et al., 2006; Manga et al., 2012). Dynamic strains/stresses can unclog fractures blocked with colloids or precipitates (Brodsky et al., 2003), thereby enhancing permeability within the fractures and encouraging fluid flow that, in turn, alters the pore pressure distribution along faults (Elkhoury et al., 2006). The expected amplitude, timing, and duration of any such pore pressure changes has not been established, but in situ measurements show increases in permeability following teleseismic events (Elkhoury et al., 2006; Xue et al., 2013). Additionally, recent numerical models (Zheng, 2018) show that the stress perturbations from surface waves can be amplified or deamplified by two or three orders of magnitude within the fracture system of the fault, potentially increasing the likelihood of unclogging fractures and changing the fault permeability structure. Such a model may explain why stress perturbations of ∼1 kPa could conceivably cause triggering.

Additionally, pore pressure redistribution is likely to have a variable effect on individual fault patches, due to the complexity of fault permeability architecture (Caine et al., 1996). We observe widespread seismicity following the Ecuador earthquake (Figure S10) that may reflect the diverse response of fault structures under the LASSO array. We estimate that pore pressure redistribution can extend for distances of ∼1 km in the time frame of triggering observed here, using the pore fluid diffusion equation (Shapiro et al., 1997), where r is distance, D is diffusivity (1–4 m²/s; Keranen et al., 2013), and t is time (assuming the observed delay time of 8 hr). Kroll et al. (2017) show pressure increases and decreases in deep Arbuckle wells in Oklahoma in response to strain from local earthquakes. And Barbour (2015) reports that strainmeter and pore pressure measurements can differ by a factor of 3 at distances of ∼15 km, suggesting the response to a stress perturbation may be highly variable.

7 Conclusions

We use the seismicity detected by the LASSO array in northern Oklahoma to investigate the occurrence of dynamic triggering. Without the local earthquake catalog generated using the LASSO array data, it would not have been possible to identify or demonstrate the statistical significance of dynamic triggering. The OGS detected only 20 earthquakes within the spatial footprint and duration of the LASSO array deployment, whereas the LASSO deployment identified 1,375 events which are used in this study. Our statistical tests and the overall low PGV values of the teleseismic waves suggest that no other teleseismic event generated dynamic triggering. We find that small stresses ( kPa or ΔCFF∼ fraction of a kPa) generated by passing surface waves of a M_w 7.8 earthquake in Ecuador (16 April 2016) resulted in a statistically significant increase in seismicity levels in northern Oklahoma, a region of active wastewater injection. Future analysis of other earthquake-earthquake interactions in this area may help to establish if there is a minimum stress amplitude and/or frequency threshold required before triggering occurs, and/or if the triggering is due to a physical processes that requires a shaking threshold is exceeded before initiating. The observed ∼7-hr delay in the onset of a seismicity increase suggests that local earthquake triggering may have been caused by aseismic slip and/or localized pore-pressure redistribution that began with the passage of these surface waves.

Acknowledgments

Seismic waveform data used in this study were obtained from the Incorporated Research Institutions for Seismology Data Management Center (http://ds.iris.edu/mda). LASSO data are available at Dougherty et al. (2016). Regional and global earthquake information was obtained from the Oklahoma Geological Survey Earthquake Catalog (http://www.ou.edu/ogs/research/earthquakes/catalogs) and the Advanced National Seismic System Comprehensive Earthquake Catalog (https://earthquake.usgs.gov/earthquakes/search/), respectively. Figures were made with GMT (Wessel et al., 2013) and part of the data analysis was performed using ObsPy (Krischer et al., 2015). We thank J. Ashburn, N. Campbell, X. Chen, F. Clerc, P. Cox, C. Criley, K. Galvin, N. Ghouse, J. Goussi, J. Guzman, D. Hollis, S. Li, B. McKevitt, J. Morris, J. Pfau, A. Thiel, N. van der Elst, E. Vuittonet, M. Weingarten, and I. Woelfel for their work installing and/or retrieving the LASSO array. We thank Associate Editor Y. Kaneko, Editor Y. Ben-Zion, E. Roeloffs, J. Gomberg, and two anonymous reviewers for their comments. We also thank the Grant County Board of Commissioners for allowing us to deploy the LASSO array on public land. This work was partially supported by a Ruhr University Bochum new faculty start-up fund.