Swarms of repeating stick-slip icequakes triggered by snow loading at Mount Rainier volcano

Authors


Abstract

We have detected over 150,000 small (M < 1) low-frequency (~1–5 Hz) repeating earthquakes over the past decade at Mount Rainier volcano, most of which were previously undetected. They are located high (>3000 m) on the glacier-covered edifice and occur primarily in weeklong to monthlong swarms composed of simultaneous distinct families of events. Each family contains up to thousands of earthquakes repeating at regular intervals as often as every few minutes. Mixed polarity first motions, a linear relationship between recurrence interval and event size, and strong correlation between swarm activity and snowfall suggest the source is stick-slip basal sliding of glaciers. The sudden added weight of snow during winter storms triggers a temporary change from smooth aseismic sliding to seismic stick-slip sliding in locations where basal conditions are favorable to frictional instability. Coda wave interferometry shows that source locations migrate over time at glacial speeds, starting out fast and slowing down over time, indicating a sudden increase in sliding velocity triggers the transition to stick-slip sliding. We propose a hypothesis that this increase is caused by the redistribution of basal fluids rather than direct loading because of a 1–2 day lag between snow loading and earthquake activity. This behavior is specific to winter months because it requires the inefficient drainage of a distributed subglacial drainage system. Identification of the source of these frequent signals offers a view of basal glacier processes, discriminates against alarming volcanic noises, documents short-term effects of weather on the cryosphere, and has implications for repeating earthquakes, in general.

1 Introduction

Mount Rainier, a 4392 m glacier-clad active stratovolcano in Washington State (Figure 1), is one of the most dynamic landscapes in the world and thus also one of the seismically noisiest. Clear identification of seismic events and assessment of source mechanisms is a fundamental aspect of both volcano monitoring and understanding landscape dynamics. Researchers must be able to distinguish seismicity generated by volcanic activity from ice movement, wind, rock fall, debris flows, and human activity: not always a straightforward task. Benign events related to glacier activity, like surface crevassing, serac collapse, and basal sliding, can mimic subtle signals that are often associated with volcanic fluid or gas movement [Weaver and Malone, 1976; West et al., 2010; Thelen et al., 2013]. Nowhere is this more obvious, perhaps, than at Mount Rainier. Mount Rainier is the most glacier-clad mountain, by volume, in the conterminous United States [Hoblitt et al., 1998] and is also an active volcano with the largest at-risk population in the country [Ewert et al., 2005]. The convergence of these factors makes timely and accurate identification of seismic events at Mount Rainier both difficult and an issue of great public concern.

Figure 1.

Seismic stations and glaciers at Mount Rainier. White dots indicate three-component stations. LON, PANH, and OBSR are broadband stations, others are short period. Black triangle indicates weather station PVC. Box shows extent of lower right inset map of summit area showing locations of select event families from this study; maximum horizontal location errors are shown in gray. For some locations the formal errors are smaller than the dot and are not visible. Upper right inset map shows regional location of Mount Rainier. The locations of the Paradise and Sunrise visitor center areas are indicated.

This challenge was illustrated in May and June 2010 when analysts at the Pacific Northwest Seismic Network (PNSN) and U.S. Geological Survey Cascade Volcano Observatory (CVO), responsible for monitoring the volcano, observed a swarm of low-frequency (<5 Hz) repeating earthquakes. Too small to trigger automated event detection algorithms, the earthquakes were instead detected visually on seismic records due to their regular recurrence intervals and nearly identical waveforms. This activity was of concern because repeating low-frequency seismicity often accompanies—and has been a precursor to—volcanic activity at volcanoes worldwide [Chouet et al., 1994]. However, low-frequency and repeating earthquakes have also been attributed to glacial activity [e.g., Jonsdottir et al., 2009; Carmichael et al., 2012]. After fully characterizing the swarm, Thelen et al. [2013] concluded that the swarm was probably glacial in origin, most likely basal stick-slip sliding. The main line of evidence was the correlation between two bursts of repeating earthquake activity that coincided with the timing of two passing storms. Thelen et al. [2013] attributed the appearance of the swarm to a glacial speedup triggered either by the rapid input of water in the spring [e.g., Harper et al., 2007] or snow loading.

Though Thelen et al. [2013] answered some questions regarding these events, their study also opened up new ones. Spring melt and snowfall happen every year, and Mount Rainier is always covered in glaciers. Why, then, did we not see these repeating earthquakes more frequently? The only other times this type of activity had been documented at Mount Rainier were three much shorter-lived swarms of repetitive earthquakes in the early 1990s, again only detected by visual inspection of seismic data. Are the glaciers at Rainier changing, or does this type of seismic activity occur all the time and we just did not know to actively look for it?

Second, assuming the source mechanism is, in fact, glacial, what exactly are the glaciers doing and what is triggering this change in behavior? Understanding the glacial processes responsible can contribute to our knowledge of glacier dynamics, but we first need to understand the fundamental source of this anomalous seismicity. Mount Rainier is a good setting for this because it has been seismically monitored continuously for decades, with continuous digital data stretching back about 12 years. Weather records stretch back even further. This long time series of observations allows us to look at secular trends as well as seasonal changes, whereas many seismicity studies of glaciers are done using temporary arrays and/or during the summer field season.

Third, assuming Thelen et al. [2013] was correct in hypothesizing that the source is basal stick-slip sliding of glaciers, what causes the sliding behavior to transition from aseismic smooth sliding to seismic stick-slip sliding? This has ramifications not only for understanding the basal processes of glaciers [e.g., Zoet et al., 2013b] but also as an analog for understanding why and when the same transition takes place on slipping tectonic faults. Repeating earthquakes have been observed over a wide range of scales and environments, from the aforementioned glacial and volcanic environments, to crustal faults [Nadeau et al., 1995; Dreger et al., 2007] and during episodic tremor and slip [e.g., Shelley et al., 2007]. Seismic behavior in these settings can also be modulated by minor stress changes such as tidal stresses [Sweet et al., 2012; Rubinstein et al., 2008; Nakata et al., 2008] or dynamic triggering from teleseismic waves [e.g., Peng et al., 2009]. Understanding how small variations in stress from snow loading and/or basal fluid pressures can cause a glacier to change from aseismic to repetitive, stick-slip sliding can lend insight to similar processes in other environments.

These three questions motivated the current study. In the first section, we detail the study area and describe the characteristics of the low-frequency repeating earthquakes that are the focus of this investigation. Next, we describe the catalog of repeating earthquake activity over the past decade at Mount Rainier that we compiled by searching through the entirety of the archived continuous seismic data. We then use this catalog to investigate how these earthquakes behave over time, how they correlate with and react to weather forcing, where they are located, and how their source locations migrate over time. Finally, we discuss what these observations can tell us about the source processes responsible for generating these earthquakes and discuss the wider implications in terms of understanding glacier dynamics, the physics of stick-slip behavior, and repeating earthquakes, in general.

2 Background

2.1 Mount Rainier

Mount Rainier is located about 90 km southeast of Seattle within Mount Rainier National Park. The volcanic part of the mountain is almost completely covered in glaciers: it has the highest concentration of glacial ice in the coterminous United States [Driedger and Kennard, 1986] (Figure 1). As of 2008, Mount Rainier glaciers cover 87 km2, but most are thinning and retreating, having lost a total of 13–15% of the ice volume from 1970 to 2008 [Sisson et al., 2011]. The glaciers are thin in the steep upper sections, ranging from about 30 to 80 m, and become thicker, reaching up to 200 m at lower elevations [Driedger and Kennard, 1986]. The glaciers are characterized as temperate alpine glaciers, meaning they are at their melting point from surface to bed throughout the year. Their movement is dominated by basal sliding [Hodge, 1974]. The glaciers are fed by an average of 16.3 m of snow that fall each year [National Park Service, 2013].

In part because of the large amount of water stored as ice and snow on its flanks, Mount Rainier is also the most hazardous volcano in the U.S., designated as a “decade volcano” by the National Academy of Sciences [Swanson et al., 1994]. Recent estimates put 2.5 million people and $40 billion in assets at risk from lahars originating at the volcano [Cakir and Walsh, 2012]. Lahars are debris flows that often occur because of the rapid melting of ice and snow during eruptive activity. The largest lahars in the past 10,000 years have reached as far as Puget Sound, and many densely populated areas overlie old lahar deposits [Hoblitt et al., 1998]. Mount Rainier has not erupted since the middle to late 1800s [Mullineaux et al., 1969], but the last major eruptive period was about 1000 years ago [Sisson and Vallance, 2009].

Because there is so much at stake, Mount Rainier is monitored in near real time for signs of volcanic activity, primarily through seismic and geodetic monitoring. The seismic monitoring network (Figure 1) consists of 10 stations within 20 km of the summit. Three short-period high-gain stations, named RCM, RCS, and STAR, are located high on the mountain, at around 3000 m elevation. All three are vertical component sensors except STAR, which has three components. The rest of the stations are a mix of broadband, three-component stations (OBSR, PANH, and LON) and vertical component short-period stations (RER, FMW, LO2, and RVC (not shown)). The data from these stations are telemetered, and seismic activity is monitored jointly by the PNSN and CVO. Additionally, weather is monitored hourly in near real time at several weather stations. We use data from all seismic stations and the PVC weather station (Figure 1) near the Paradise Visitor Center, operated by the Northwest Weather and Avalanche Center (www.nwac.us).

2.2 Earthquake Characteristics

The low-frequency repeating earthquakes that are the focus of this study have several general characteristics. They are small, with magnitudes ranging from less than −1 to 0, they are located at high elevations (>3000 m), and their waveforms and locations indicate they are within a few hundred meters of—if not at—the surface [Thelen et al., 2013]. They often occur at regularly spaced intervals, with some scatter around a mean (Figure 2a), and have highly similar waveforms between events in the same family (Figure 2b). In this study, “family” refers to a set of earthquakes that share a similar waveform, and “swarm” refers to an uptick in earthquake activity that is not a main shock/aftershock sequence. Though recurrence intervals are regularly spaced and waveforms are highly similar in the short term, there can be both gradual evolutions and sudden jumps in both factors over the duration of a family [Thelen et al., 2013]. We characterize these events as “low frequency” because their frequency content is much lower than a similarly sized tectonic earthquake occurring deeper in the volcano. The first arrivals are emergent rather than having a clear and sharp first motion (Figure 2c). We estimate the mean frequency content of each event using the dominant frequency [Snieder, 2006]. A typical low-frequency repeating earthquake at Mount Rainier has a dominant frequency of ~5 Hz (Figure 2d).

Figure 2.

Characteristics of the low-frequency repeating earthquakes at Mount Rainier. (a) The earthquakes repeat at semiregular intervals with nearly identical waveforms. (b) These five events are the repeating waveforms highlighted in Figure 2a plotted on a consistent amplitude scale. (c) The (top) frequency of these events is lower than (bottom) regular, local, volcano-tectonic earthquakes. (d) A histogram of the dominant frequency of all repeating event families detected since 2003 shows that most have a dominant frequency below 8 Hz (blue), the cutoff used in this study (vertical line).

The low first arrival amplitudes and low-frequency content are most likely a result of path effects rather than due to the source [Thelen et al., 2013]. The waves are strongly altered and attenuated as they travel through the shallow, heterogeneous subsurface. This is typical of any shallow earthquake in stratigraphically complex volcanic terrain because the wave paths from source to station are primarily through the heterogeneous, low-velocity shallow layers. Higher-frequency waves are attenuated much more rapidly than lower frequency waves [Stein and Wysession, 2003] giving the waveforms a low-frequency character. Also, as shallow body waves graze the surface, surface waves develop that attenuate less rapidly and can also have lower frequency content [Neuberg and Pointer, 2000]. This is supported by active and passive source studies on Cascade Volcanoes that were found when icequakes and artificial explosions were recorded by seismic stations located nearby on the ice; the waveforms were impulsive and had broadband waveforms, but the same event recorded on rock farther away yielded the low-frequency emergent waveforms typical of these repeating earthquakes [Weaver and Malone, 1976, 1979; Allstadt et al., 2012].

3 Detection and Characterization

3.1 Comprehensive Repeating Earthquake Search

3.1.1 Methods

In order to determine whether there have been other repeating earthquake sequences in the past that went undetected, we conduct a comprehensive search for repeating earthquakes through the archived, continuous, digital seismic data. Archived data go back to 2001 for some seismic stations, but we start the search in 2003 because there are large gaps in the data until that point. We search for repeating earthquakes at each seismic station individually and combine detections later. Individual repeating earthquakes are typically small and only appear on the three edifice stations (RCS, RCM, and STAR). However, archived data from STAR are only available starting in 2010, so in order to present a consistent picture of patterns in activity over time, we only present detection results from RCS and RCM, which have remained relatively unchanged since before 2003.

We filter the data between 1 and 10 Hz and use a short-term average/long-term average (STA/LTA) pick detector (short window of 0.8 s, long window of 7 s, STA/LTA ratio of 4) to find potential events. We extract 25 s of data around each pick time, starting 5 s before. There are often several thousand event pick times per day on each station because Mount Rainier is such a seismically noisy place. In order to save on computing time, we cut out detections that are unlikely to contain a repeating earthquake event by excluding events with a signal width [Meier and Lee, 2009] greater than 15 s, which eliminates rumbly events from wind noise and rockfalls.

Then, using codes modified from Carmichael [2013], which perform unsupervised clustering so the user does not need to define template events to detect repeating earthquakes, we cross correlate every event with every other event in each day and group them into families. To be grouped together, all events must have a normalized cross correlation of >0.7 with all other events in the family. Any ungrouped events within each day are discarded. To save on computing time, we define that in order to be detected, a repeating earthquake must repeat at least once within the same day—a condition easily met for the repeating earthquakes we are searching for. Next, we compute a median stack for each family of events detected in each day to suppress noise and condense the family into a single representative waveform. Then we compare the stacks from each day to every other day within that month and group them again into larger families. All event families are visually examined and any false families (e.g., calibration pulses, data spikes, and repeating waveforms from nearby Mount St. Helens) are deleted. The remaining families are then restacked and compared with all the families detected in the adjacent 3 months on either side and regrouped again. At this step we use a higher correlation coefficient cutoff of 0.8 because we are comparing stacks so noise is suppressed.

To make the catalog as complete as possible, a stacked waveform from each family is scanned through the data as a template, pulling out any missed detections within 1 month on either side of the first and last event detection of that family. We use a lower cross-correlation threshold of 0.6 in order to pull out even events with a low signal-to-noise ratio. Any event that is grouped into more than one family is deleted except for the instance with the highest correlation with a family. Finally, once this catalog is completed for both RCS and RCM, we compare the two catalogs. Families for which at least 10% of the total events overlap between the two stations are considered to be the same family.

3.1.2 Results

The results of this search are shown in Figure 3, events detected by at least one station are shown in red; those detected on both RCS and RCM are shown in blue. We only show events with a dominant frequency of less than 8 Hz on this figure. We define 8 Hz as a cutoff for a low-frequency repeating earthquake because there is a clear clustering of the dominant frequency of repeating earthquakes families below 8 Hz (Figure 2d). Families with a higher dominant frequency typically do not appear on more than one station, do not repeat at regular intervals, and do not show seasonality [Allstadt et al., 2012], suggesting they are related to a different source, probably crevassing local to one station [e.g., Neave and Savage, 1970]. We do not address these types of events in this study.

Figure 3.

Repeating, low-frequency earthquakes detected per hour at stations RCS and RCM. Blue indicates detections that occurred on both stations; gray shading indicates when at least one station had an abnormal signal RMS (i.e., was not functioning properly). Box delineates period of only background repeating earthquake activity, which coincides with the summer months. Black bars in 2010–2013 indicate the span of select families; the thicker line delineates the span of 90% of the events in that given family.

Figure 3 reveals that low-frequency repeating earthquakes have been happening all along; we just did not know to look for them. Individual events often show up only at the three highest stations, so the seismic network does not detect them automatically, and visual detection is difficult because noise levels at these high mountain stations are high and variable. For this reason, only the most obvious sequences were noticed in the past.

Second, Figure 3 shows that though there is always a background level of low-frequency earthquake activity that hovers around ~5 events per hour, the big swarms of activity like the ones that originally attracted attention to this phenomenon [e.g., Thelen et al., 2013] only occur from late fall to mid-spring: essentially the accumulation season. Most swarms reach at least 20 events per hour but sometimes exceed 50 events per hour. The low event counts in summer are not a result of seasonal changes in background noise levels; there is no seasonality to the noise levels for RCS, and for RCM noise levels are actually higher in winter because this station is highly susceptible to wind noise during storms.

A third conclusion one can make from Figure 3 is that there is a secular increase in low-frequency repeating earthquake activity starting in the autumn of 2009. This cannot be attributed to changes in the seismic stations. The changes that have occurred at RCM include a change in the type of sensor from a Kinemetrics Ranger SS-1 to a Mark Products L4 on 6 August 2006 and a replacement of the L4 on 13 August 2010. The gain was halved on 1 April 2008 and then increased by half on 13 August 2008 and has stayed stable since. RCS has been a Mark L4 sensor since 2003, the only change was that it was replaced with a new one on 7 July 2005 and moved to a safer location a few meters away on 26 July 2006. The only gain change since 2003 was when the gain was halved on 1 April 2008. None of these changes correspond to obvious changes in the number of repeating earthquakes detected.

RCS records more repeating earthquakes than RCM, probably because it has less down time and is immediately adjacent to two major glaciers, so its catalog is more complete. It also contains more higher-frequency events, likely from nearby crevassing. We detect 299,558 repeating earthquakes grouped in 840 families at RCS. Of these families, 559 families containing 150,271 events are classified as low frequency. At RCM, we detect 61,772 repeating earthquakes in 372 families, 369 of these are low frequency, containing 61,398 events. Eighty-seven families are detected on both RCS and RCM. The rest of the families that are not shared are either too low energy to appear above the noise on the other station or one of the stations is either not working or too noisy.

To clarify the complex behavior of the swarms of earthquakes, we next focus on a time period containing a few consecutive swarms and plot a timeline of repeating earthquake activity starting in December 2011 (Figure 6). The swarms are typically composed of more than one dominant family that all start around the same time, typically coinciding with an increase in the snow depth recorded at PVC. Each family tends to start out with large variability in the correlation between individual events and the stack of all events in the family, but after a few hours or days, the waveforms become more consistent (i.e., highly correlated). Then, the correlation and event rate gradually drift and the family ends. When another storm passes through and drops more snow, old families tend to shut off and new families appear and follow a similar pattern, though there are exceptions to these trends; for example, family 681 does not shut off when a second storm passes through (Figure 6).

3.2 Correlation With Weather

A comparison of weather to repeating earthquake activity over 4 years (Figure 7a) shows that the start of each swarm of earthquake activity coincides with a period of intense precipitation in almost every case. In fact, the only obvious exception visible in Figure 7a is the repeating earthquake swarm in February 2010 where there is only minor precipitation beforehand. This correlation is particularly apparent in the stormy winter of 2011–2012; each clear step up in the snow level coincides with a clear peak in earthquake activity.

To quantify this relationship, we performed a normalized cross correlation between precipitation (water equivalent), most of which is snow, recorded at PVC and repeating low-frequency earthquake activity. To understand the significance of a correlation between these two distinct processes, we adopted methods similar to those used by Martini et al. [2009] by randomizing the precipitation data so they have the same statistics but randomly assigned timing and performing the cross correlation between these random data and the vector of repeating earthquakes per hour 10,000 times to estimate the maximum correlation value that could be obtained by random chance. These maxima are shown as dashed horizontal lines in Figure 7.

The resulting correlation oscillates with a period of about 1 year (Figure 7b) because both processes are seasonal, though there is a lag in the oscillation of about a month. This is probably because the repeating earthquake activity does not start to appear until a few weeks into the accumulation season, as is apparent in Figure 7a. The peak correlation is obtained when the repeating earthquake activity lags 1–2 days behind the precipitation, indicating a slight delay between when precipitation falls and when the repeating earthquake activity appears. This peak with a correlation coefficient of 0.34, which exceeds the maximum correlation value that could be obtained randomly (0.2), has a broad base, particularly on its right side, indicating that there is variability in the lag time skewed toward longer times by up to a few days.

3.3 Locations

Knowing the location of these events is crucial to understanding their source. Yet locating individual events using traditional methods is nearly impossible because the signals only clearly appear on, at most, the three edifice stations, and even on these stations precise timing of the first P wave arrivals is impossible because the signal does not emerge from the noise until sometime after the first P wave arrival. However, since these earthquakes repeat up to several thousand times, we are able to line the seismograms up in time and stack the signals to suppress noise and augment the signal (Figure 4). We obtain the time lags to apply to data from all seismic stations using the cross correlation from the station with the clearest waveforms, typically RCS. If there are sufficient repeats of an event, a clear signal with very low noise emerges on the three highest stations and a less clear but still usable signal emerges on the more distant stations where before there was no observable signal whatsoever. We use the median stack rather than the mean stack to minimize the influence of outliers like spikes in the data.

Figure 4.

(left) Record section demonstrating that a single occurrence of one of these earthquakes (in this case, from family 796) only appears above the noise level at the three summit stations, but when data from hundreds of events are lined up in time and stacked, the noise is suppressed and the signal emerges at stations as far as 20 km from the summit. (middle) This processing allows events to be located and the first motions to be determined on the closest stations. First motions are indicated with gray arrows. (right) The spectrum of these stacks shows that there is very little energy above 6 Hz, there are no clear shared spectral peaks between stations, and higher frequencies are more attenuated further from the volcano.

The clarification of the signal is such that clear P and S wave arrival times are sufficient in number and clarity to use traditional location methods for families that have hundreds to thousands of repeats. We are usually able to determine the direction of the first motion on the three closest stations. Almost all families have mixed first motions on the vertical components, though for some families, some of the first motions are too small and uncertain to say for sure (Figure 5). Unfortunately, because there are at most only three good first motions for any family, estimating focal mechanisms is not possible.

Figure 5.

First arrivals of stacks of the waveforms of four event families. In some cases, the amplitude of the first arrival is so low that it is comparable to the preevent noise levels (which are almost zero), and the first motion is uncertain. However, even taking these into account, most events show mixed first motions.

We only attempt to locate families that had enough repeats to clarify the signal sufficiently upon stacking to determine at least eight good arrival times. We focus on families that had more than 700 repeats that occurred since 2010 because that is the earliest date archived data are available for three of the seismic stations (STAR, OBSR, and PANH). The characteristics of the eight families with a sufficient number of clear first arrival times are summarized in Table 1, and black bars in Figure 2 show when each of these families occurred. The number of days and amount of precipitation that occurred prior to the onset of each event are also reported in Table 1. We estimate the precipitation at the location of each family by taking the ratio between the long-term average annual precipitation at the earthquake location and the location of PVC as predicted by the Parameter-elevation Regressions on Independent Slopes Model (PRISM) climate model [PRISM Climate Group, 2004] and multiplying the precipitation actually recorded at PVC by that ratio.

Table 1. Characteristics of Select Event Families
Family NumberNumber of EventsMedian Recurrence Interval (min)Dominant Frequency (Hz)Antecedent Precip (cm)Snow Height Increase at Paradise (m)Days of Antecedent Precip
523175011.33.62.6No data2.6
52822052.95.13.2No data0.7
55291810.64.4No data0.92.8
681283919.03.81.40.21.5
68282416.63.68.00.33.2
69211465.94.07.90.94.9
78594913.43.75.80.45.7
79610514.43.611.314.8

Once we pick the phase arrivals, to locate earthquakes we use the program SPONG, an adaptation of FASTHYPO [Herrmann, 1979], which has been benchmarked against HYPOINVERSE [Klein, 1985], and was used for many years for routine earthquake locations at the PNSN. The program estimates traveltimes using a 1-D velocity model and embeds stations within the first layer to account for differences in station elevation—very important for a 4392 m volcano—and also includes station corrections to account for variability in the real velocity structure. We start with the PNSN 1-D velocity model for Mount Rainier (R4, derived from the C model) that was developed for all of the Cascade Mountains using recorded earthquakes and known explosions [Malone and Pavlis, 1983; Leaver, 1984] and adapted for Mount Rainier based on tomography work by Moran et al. [1999]. We modify the PNSN model by thickening the first layer and moving the zero datum to the summit of the volcano to allow events to be located at high elevations. We embed the seismic stations at the correct elevations within the top layer of the model and adjusted the station corrections slightly for the very localized events high on the mountain. This velocity model, R8, is shown in Table 2.

Table 2. R8 Velocity Model Used to Locate Select Event Families
Depth Range, From Summit (km)P Wave Velocity (km/s)
0–4.44.4
4.4–7.45.6
7.4–12.46
12.4–20.46.4
20.4–38.46.7
38.4–47.47.1
47.4+7.8
Station NameStation Correction
RCS−0.18
RCM−0.06
STAR0.08
PANH−0.10
OBSR0.15
FMW−0.22
RER−0.16

The results of locating the eight select families in this manner are reported in Table 3 and shown in map view in Figure 1. The root-mean-square differences between observed and calculated traveltimes are very low (0.02 to 0.16 s), and formal spatial errors are low as well (0 to 0.34 km horizontal, 0.5 to 0.7 km vertical). Of course, uncertainties are actually higher because we are using a 1-D velocity model to locate earthquakes in a highly heterogeneous medium, but this is ameliorated somewhat by the station corrections. The depths of all locations are very shallow, within a few hundred meters or less of the surface elevation at the event locations. In some cases, the location program fixed the depth very close to zero (i.e., the summit) to stabilize the solution when it could not converge on a depth to allow the other three parameters to adjust. In those cases the reported vertical depths are less reliable.

Table 3. Locations and Source Movement of Select Event Families
Family NumberLatitudeLongitudeRMS (s)Number of Phases Used in LocationMax Horizontal Error (km)Vertical Error (m)Elevation of Location (m)Elevation of Surface at Location (m)Slope (Within 100 m Radius)
  1. a

    NA: not available.

  2. b

    Event depth fixed by location program.

52346°51.75′−121°45.98′0.0390NAa4382b417513°
52846°51.83′−121°46.37′0.0880.347003952420629°
55246°51.82′−121°46.04′0.10110.236004072417436°
68146°51.29′−121°44.72′0.0880.01NAa4362b384230°
68246°51.06′−121°45.04′0.1690.03NAa4382b407930°
69246°51.07′−121°44.72′0.0280NAa4388b379440°
78546°51.75′−121°45.66′0.08110.185004042402546°
79646°50.92′−121°44.87′0.14100.02NAa4382b384439°

There are two clusters of locations. Four families from the north cluster (523, 528, 552, and 785) are located at a steep glacier that terminates at a cliff—past this point ice continues downslope by breaking off and falling. The location of these four families close to each other is consistent with the similarity of the first few seconds of their waveforms, but the codas are different, indicating that they are not identically located. The waveforms of the eastern cluster (681, 682, 692, and 796) are not nearly as similar to each other, suggesting they are more distributed in their locations. All locations are in very steep areas with surface slopes of more than 30° in most cases—the steepest being 46° (Table 3).

3.4 Recurrence Time Versus Event Size

Figure 6 suggests that the behavior of event families, such as their interevent correlation and recurrence intervals, change over time. In order to look more closely at these changes, we plot the time since the last earthquake (recurrence interval) against a proxy for energy called pseudoenergy, which is the integral of the squared uncorrected velocity seismogram. We also add a third variable to the plot, the date of each event, to see how the previous two variables change over time. We compute pseudoenergy using only the highest amplitude part of the signal (a 4 to 7 s window) to minimize noise bias since signal-to-noise ratios are low. We plot the data in two different ways to better visualize what is occurring. Figure 8 shows these results for three of the event families with the highest energy (and thus the least scatter due to noise), and the most interesting behavior as recorded at RCS.

Figure 6.

Timeline showing the evolution of repeating earthquake families (December 2011 to February 2012) with at least 100 repeats during two snowstorms. Each individual earthquake is a circle plotted on a line corresponding to its event family. The family name is labeled at left. The number of earthquake occurrences contained in each family is labeled at right. The color of each circle corresponds to the cross correlation between that individual event and the stack of all the events in that family. The snow depth measured at PVC is shown in gray.

There are some very clear systematic patterns that emerge, but no clear dominant pattern, suggesting that several factors are at play. For short periods of time, psuedoenergy scales linearly with recurrence interval: the shorter the time since the last earthquake, the smaller the next event. However, the slope of this line changes systematically over time in all three cases as shown by the drifting in slope angle of fits to the slope of this line for discrete time periods (shown in the background of Figure 8 (left)). All three families start with a lot of scatter, then, after a day or two, form a distinct linear trend that either gradually drifts or suddenly jumps after a few days to steeper slopes and higher energies. This then gradually drifts back down to more shallowly sloped positive linear trends but tending toward higher recurrence intervals until the family disappears. Family 681 drops to very small events at the end before it dies out. If we look at the same data in a different way, at the evolution of recurrence interval over time and plot precipitation on the same figure (Figure 8, right), we see that the sudden jumps in the slope of the lines actually correspond to the addition of more snow in most cases, and the reaction to additional snow is more immediate, unlike the delayed reaction to snowfall exhibited at the initiation of each family. However, there are also times when additional snow falls (e.g., on 6/4 during family 528), and there is no obvious change in the behavior of any of the variables, so the story is not simple. Generally, there is a trend toward either having more frequent smaller events or less frequent bigger events, and the recurrence interval generally increases over time.

3.5 Source Migration Over Time—Coda Wave Interferometry

3.5.1 Methods

The gradual evolution of the waveforms of each family over time evidenced by gradual decorrelations (Figure 6) suggests incremental changes in the source mechanism, seismic velocities, or the source location. The latter is the most likely of the three given the other evidence for a glacier-related source because a source either within the ice or related to material embedded at its base would be expected to move with the glacier. Determining whether the source is moving, and if so, how fast, can help further illuminate the source process. We use coda wave interferometry to determine the source separation between earthquakes that are located near each other [Snieder and Vrijlandt, 2005]. This enables tracking the movement of the source of each event family over time and can even be done using a single station.

Coda wave interferometry exploits changes in the coda of the waveform (the end of the signal), which is composed of scattered waves, to determine source offsets. When the source position of an earthquake moves from the original “unperturbed” location to a new “perturbed” location, some of the wave paths lengthen and some shorten, and thus, the contribution from some wave trajectories comes early and some later. The change in arrival times summed over all wave trajectories is approximately zero, but the variance of the changes in arrival times increases the further the source location moves [Snieder and Vrijlandt, 2005]. This can be harnessed to estimate the size of the movement of the centroid of repeating earthquakes over time but not the direction. Travel time variance can be obtained by finding the maximum time-shifted normalized cross-correlation coefficient between sliding windows of the coda of the two waveforms being compared, where each window gives a separate estimate scattered around a mean value [Robinson et al., 2011].

The relation between the traveltime variance inline image and movement of the source δ depends on the type of source mechanism [Snieder and Vrijlandt, 2005]. The waveforms of the repeating earthquakes recorded at Mount Rainier are too low in amplitude and altered by path effects to determine the source mechanism from the seismograms. However, assuming the hypothesis of Thelen et al. [2013] is correct, that these are basal stick-slip earthquakes and that source displacement is along the ice-rock contact, the source displacement δ for a double couple source can be calculated by the following:

display math(1)

Where α and β are the P and S wave velocities of the volume around the source, respectively [Snieder and Vrijlandt, 2005]. A different source mechanism or different seismic velocities will just change the magnitude of the source movement, but not the pattern of its movement over time.

We focus our efforts on the select families chosen earlier (Table 2 and Figure 1). The seismic signals of individual events are too noisy in the coda to apply this technique so we instead stack sets of 50 to 75 consecutive events to suppress the noise in the signal. We require the events to all occur within half a day of each other to avoid stacking events together that have significantly different waveforms. These strict requirements for stacking mean that we cannot observe source movements at the start and end of event families in some cases because too few earthquakes occur close enough together in time. We then compute cross correlations between every stack and every other stack for each 0.24 s window in the coda. We apply the corrected normalized cross correlation [Douma and Snieder, 2006], which uses the characteristics of the noise prior to the start of the event to reduce the bias in the cross correlation due to noise contamination. We find this to be very important because offsets between stacks are so small (i.e., true correlations were so high) that neglecting to correct for noise resulted in an overestimate of the source offset because noise biases the correlations to lower values.

In order to compute source offsets uniformly, we define the coda as starting 2 s after the first arrival and lasting for 6 s past that point. We choose a short window length in order to avoid cycle skipping [Robinson et al., 2011], and we allow the windows to overlap by 75% between adjacent windows to recapture information lost at the edges of each window due to the 25% taper. Each time window results in an independent estimate of inline image, and thus, independent estimates of the source separation δ once equation (1) is applied. We take the mean offset μδ as the best estimate of the offset between the pair of stacks being compared and use the standard deviation σδ to estimate uncertainties.

In order to apply equation (1) to obtain source displacement δ from inline image, we need to know the average seismic velocities of the volume around the source location. The velocity structure of the edifice of Mount Rainier is highly heterogeneous and unknown, so we instead make a best estimate of the mean seismic velocities at the source and then apply reasonable upper and lower bounds. Active source tests at Mount St. Helens, a neighboring stratovolcano, yielded an estimate of β = 200–650 m/s (W. Thelen, personal communication, 2013) and α = 800–1500 m/s for the shallow layers of the edifice [Weaver and Malone, 1976]. Mount Rainier is composed more of andesite lava flows [Fiske et al., 1988], while Mount St. Helens is composed more of lower velocity ash and block flows, so we use the larger end of the values observed at Mount St. Helens as a lower bound for the shallow subsurface of Mount Rainier: α = 1300 m/s and β = 650 m/s. As the upper bound, we use the seismic velocity of glaciers at Mount St. Helens (prior to the 1980 eruption) measured by Weaver and Malone [1976] to be α = 3150 m/s and assume α/β = 2 because the shallow surface is most likely fractured and filled with fluids. High α/β ratios have been measured in the shallow subsurface in similar environments like Mount St. Helens (W. Thelen, personal communication, 2013) and the Coso Geothermal field [Lees and Wu, 2000]. A ratio of 2 results in an upper limit on β of 1600 m/s. The true values are most likely somewhere between these bounds. Our best estimates are α = 2000 m/s and β = 1000 m/s.

Since coda wave interferometry does not allow us to resolve the direction of motion, only the absolute offset, we assume that the source is continuously moving farther away from the initial location, a fair assumption for a glacier sliding down a mountain. We estimate the source separation between each stack and every other stack and then perform a least squares inversion in order to determine the overall source movement over time that best fits the relative offsets observed between all pairs using a modification of methods developed by Hotovec-Ellis et al. [2014].

We weight each pair by half of the standard deviation of the offset estimate. We regularized the solution using both first and second order Tikhonov regularization, (corresponding to a flat and smooth model, respectively), giving twice as much weight to the first order regularization. Since we assume offsets are always positive, the inversion is biased. In order to ensure the results are particularly robust and not just showing source movement because of this bias, we require that the variance reduction of the solution be more than two standard deviations higher than the mean variance reduction of the inversion of the same data randomly reordered 30 times. This can be considered equivalent to 95% confidence that the variance reduction of the inversion of the real data is significantly different than the variance reduction of the randomized data.

We do this inversion separately for each component of each edifice station (RCS, RCM, and three components for STAR) in order to achieve up to five independent estimates of the source movement over time for each event family, though for most families only a few of the components yield results that pass the test for robustness described above.

3.5.2 Results

The results are shown graphically in Figure 9. Variance reductions range from 79 to 93% but are above 85% in most cases. The results show that at least seven of the eight select families are moving. The eighth, family 682, has no robust solutions. Average speeds over the duration of each family range from 0.8 to 4.3 m/d for our best estimate of seismic velocities at the source (0.5–2.8 and 1.3–6.8 m/d for upper and lower bounds, respectively). These are feasible velocities for alpine glaciers [Kamb, 1964], though perhaps higher than typical small alpine glaciers. In most cases, separate components and stations, which provide independent estimates of source movement over time, yield similar or even nearly identical results, including showing the same bends in the trajectory. For example, results obtained separately for both RCS and RCM for family 681 show a sudden slowing in the velocity on 6 January 2012 and for family 796 the results for RCS and RCM both show the same flattening starting on 22 December 2012 and then increase in movement rate again halfway through 23 December 2012. Family 552 has the most solid result, with all five components yielding the same movement rate of ~3.5 m/d. In a few cases, the shape of the movement over time is slightly different between stations (e.g., families 523, 692, and 785) suggesting these solutions are not as reliable. Family 681 lasts far longer than any of the other families and also is the slowest on average; the upper bound estimate of velocity is lower than the lower bound estimate for almost all other families.

4 Discussion

4.1 What Is the Source Mechanism?

Using the observations above, we can narrow down the potential source mechanisms of these events. First of all, the occurrence of swarms of these repeating earthquakes in glacier-covered areas every year for at least the past decade without any subsequent volcanic activity, together with the high correlation of activity with precipitation (Figure 7), strongly supports a glacial rather than volcanic source for the majority, if not all, of the low-frequency repeating earthquakes that we detected.

Figure 7.

(a) Daily temperatures recorded near seismic station RCM and snow height and precipitation (water equivalent) recorded at PVC, compared with repeating earthquake activity. Dotted lines are plotted showing peaks in repeating earthquake rate and tend to correspond to peaks in precipitation in most cases. (b) Normalized cross correlation between hourly repeating earthquake activity and precipitation. (c) A blowup of several days around zero lag showing the clear peak that occurs around 1–2 days lag. Horizontal dashed lines indicate the maximum correlation obtained when the precipitation data were randomized and correlated against earthquake occurrence 10,000 times.

Having settled on a glacial source as the most likely option, there are many different glacial seismic sources that have been documented. A few are easy to rule out. Surface crevassing is the most common type of alpine glacier seismic source [Neave and Savage, 1970; Deichmann et al., 2000; Walter et al., 2009], and this source can repeat and occur in swarms of activity if extensive crevassing is occurring in the same area. Deeper crevassing associated with surface water making its way to the bed has also been observed in a few cases and can repeat [Carmichael et al., 2012; Moore et al., 2013]. However, crevassing is unlikely to explain the observed low-frequency earthquakes because seismic events generated by crevassing typically can only be detected at seismic stations directly on the ice or on rock very close by [Thelen et al., 2013; Weaver and Malone, 1979]. Besides the fact that crevassing events release very little seismic energy, steep glaciers are poorly coupled physically to their bed [Kamb, 1970] and thus do not transmit seismic waves efficiently from ice into rock [Weaver and Malone, 1979]. The most convincing argument against crevassing is the fact that pure tensile cracking is a volumetric source, and all first motions should be the same [Walter et al., 2013], but we observe a mix of up and down first motions for most families (Figure 5), indicating that the source has some shear component, as would be the case for stick-slip sliding.

Falling ice, like calving and serac collapses, also can generate low-frequency earthquakes [Qamar, 1988; ONeel et al., 2007; Roux et al., 2008; Tsai et al., 2008; Thelen et al., 2013], and this source can repeat if ice falls in the same location over and over again [e.g., Jonsdottir et al., 2009], but it is highly unlikely that this is the source of the events in this study because ice is unlikely to fall exactly the same way thousands of times and at very regular intervals.

Another often invoked source interpretation for glacier seismicity is hydraulic transients resonating in fluid-filled cracks and fluid-driven cracking [St. Lawrence and Qamar, 1979; Metaxian et al., 2003; West et al., 2010], the same source mechanism often proposed for low-frequency earthquakes related to volcanic activity [e.g., Chouet et al., 1994]. This type of source could repeat if a water-filled crack opened in discrete incremental events, or if hydraulic transients were repeatedly excited by flowing water, for example. But sources of this type typically have a harmonic waveform dominated by a few discrete frequencies that would appear as shared spectral peaks on multiple seismic stations. This is not observed for any of the select families (compare spectra in Figure 4, for example), though the resonant character of the signal could be lost due to the alteration of the signal in the shallow heterogeneous subsurface [Thelen et al., 2013]. Stronger evidence against this source mechanism is the fact that the events from this study have mixed polarity first motions. Opening cracks and unsteady fluid flow should have all the same first motions. Though in exceptional cases this type of source could result in mixed polarity first motions if the fluid-driven crack is a shear failure rather than tensile, for some complex combination of multiple source mechanisms, or if a compensated linear vector dipole (CLVD) mechanism were invoked. CLVD has been used as a mechanism for earthquakes generated by magma injection [e.g., Kanamori et al., 1993] but to our knowledge, never for icequakes. Furthermore, there is no clear physical explanation for why events with mechanisms involving flowing water would occur more often in winter when less water is flowing through the system, or why such events should correlate with snowfall, so we consider this source also unlikely as the main source, though it is possible that some of the hundreds of thousands of events detected in the past decade could be of this origin.

Walter et al. [2013] proposed that basal icequakes can be caused by opening and closing bed-parallel cracks in response to basal water pressure changes that can have mixed polarity first motions if the cracking has some shear component. Though we cannot rule this out, we do not favor it as the source mechanism here because it is hard to conceive this type of event being repeatable thousands of times at regular intervals as often as every few minutes. Furthermore, as discussed earlier, events that are completely in the ice at steep mountain glaciers are not well recorded on rock stations because the ice is poorly coupled to its bed on average [Weaver and Malone, 1979], so these events would have to be large in order to be recorded at the observed distances.

This leaves basal stick-slip sliding as the source mechanism that best fits the observations. This mechanism has been invoked for glaciers over a range of types and sizes through seismic observations [e.g., Ekstrom et al., 2003; Zoet et al., 2012; Weaver and Malone, 1976, 1979; Caplan-Auerbach and Huggel, 2007], geodetic methods [Wiens et al., 2008; Winberry et al., 2013], and direct observation [e.g., Vivian and Bocquet, 1973].

The mixed polarity first motions that we observe (Figure 5) are consistent with shear failure, such as basal stick-slip sliding. A stick-slip source can be nondestructive and repeatable, as required to fit the observations as well. Stick-slip basal sliding occurs at the interface between the glacier and underlying rock and/or till and thus is better coupled to the ground, which can explain why these events can be observed over 10 km away after signal processing while this is not the case for seismic events from surface crevassing. Furthermore, stick-slip events could move with the glacier if the asperity failing elastically were a patch of dirty ice (embedded rocks) rather than a stationary asperity like a bedrock bump.

Finally, these earthquakes exhibit behavior that suggests healing is taking place. Healing means the sliding stops, and the static friction on the fault recovers and increases to higher levels over time after it dropped during unstable slip. This is a fundamental requirement for stick-slip behavior [Scholz, 1998] and resulting behavior would be that the longer the time since the last earthquake, the larger the next earthquake, as we observe (Figure 8). In fault mechanics, this behavior is referred to as slip predictable [Shimazaki and Nakata, 1980; Scholz, 1998] and can be considered a sign that healing is taking place between events [Zoet et al., 2012]. Energy (and thus pseudoenergy) is linearly proportional to magnitude and therefore also linearly proportional to average slip if the fault area remains stable. Therefore, for a pure slip-predictable model with a constant loading rate, a positive linear trend should emerge between pseudoenergy and recurrence interval, as we observe (Figure 8), at least for short time periods when external loading was relatively constant.

Figure 8.

Variations of recurrence interval (time since the last quake) and pseudoenergy over time for three families (523, 528, and 681) plotted in two different ways. (left) The relation between recurrence interval and pseudoenergy. Gray lines show a least squares fit to data points from discrete time intervals showing that the slope of the positive trending line relating recurrence interval and pseudoenergy changes over time. The R2 is above 0.5 for solid lines, above 0 for dashed, and dotted is a visual fit. The black arrow illustrates the migration taken in the relation over time. (right) Recurrence interval evolution over time. Cumulative precipitation recorded at PVC is plotted in the background. On all plots, the color of the dots responds to the date of each event indicated on the color bar. Families 523 and 528 were both in the year 2010; 681 started at the end of 2011.

4.2 Why Is This Behavior Transient and Triggered by Precipitation?

Assuming our interpretation thus far is correct, the question remains: how can such a small additional load as that due to a new layer of snow trigger this activity and why is it temporary? Glaciers are complex systems, and a number of possible scenarios could be invoked, but we present our favored hypothesis that best fits the observations and the current state of knowledge about glacier sliding.

Stick-slip sliding is the result of frictional instability. Theory dictates that for a sliding plane to be capable of stick-slip sliding, two conditions must be met: the material of the sliding plane must be “velocity weakening” (i.e., friction decreases as sliding velocity increases), and the fault plane must “heal” over time in order to recover strength after sliding (i.e., static friction on the plane increases the longer the two sides are held together) [Scholz, 1998]. We know, based on Figure 8, that for our events the latter is true. However, whether or not stick-slip sliding occurs in a medium that meets these characteristics depends on the external loading. A stable sliding regime, like the aseismic sliding of ice over rock that is typically modulated by plastic flow and pressure melting and refreezing [Kamb, 1964], can transition into an unstable (stick-slip) sliding regime in two ways: (1) if the effective normal stress is increased or (2) if there is a sudden jump in the sliding velocity [Scholz, 1998]. It is likely that the added load of snow causes one or both of these changes to occur, and the change is high enough to transition the sliding regime from conditionally stable (smooth, aseismic sliding) to unstable sliding (stick slip) temporarily. We argue that the initiation of these repeating event families is best explained by a sudden increase in sliding velocity rather than just an increase in normal stress. This is because the coda wave interferometry results (Figure 9) indicate that the sources start out moving fast. In most cases, even the lower bound on the velocity estimates exceeds the highest average daily glacier surface velocities measured at several glaciers at Mount Rainier using ground-based radar interferometry of 2 m/d [Allstadt et al., 2013] and the fastest longer-term average surface ice velocities observed by Hodge [1974] at Nisqually glacier of 0.8 m/d near the equilibrium line. Almost all of the families then gradually slow down after a few days until they disappear (Figure 8), suggesting that the glaciers responsible were perturbed to a higher velocity initially and then gradually recover.

Figure 9.

Source movements over time for select event families derived from coda wave interferometry. Black lines indicate the best estimates, and gray lines indicate the upper and lower bounds on the possible offsets based on the range of possible seismic velocities. The mean source speed for the best estimate of seismic velocities around the source area are shown for each family along with the mean speeds for the upper and lower bounds in parentheses. Solutions for which the start time of the useable data was later than the results from other station components are migrated to the mean offset at their starting point.

This change in sliding velocities over time is also reflected in the plots of the relation between recurrence interval and pseudoenergy (Figure 8). The slope of the relation between recurrence interval and pseudoenergy is directly proportional to the moment rate, and assuming the fault area is stable, it is therefore also directly proportional to slip rate (i.e., sliding velocity) [Stein and Wysession, 2003]. Thus, as the glacier slows down, the angle of this line would drift to shallower slopes. This pattern, does, in fact, appear at the tail end of all three families shown in Figure 8. However, this simple interpretation is complicated by the fact that when more snow falls, the slope of the linear trend steepens in all three cases. In the absence of other evidence, we would guess this means that the slip rate increases (i.e., the glacier speeds up in response), but the coda wave interferometry results show that the glaciers actually slow down when more snow falls in all three cases (though not every time snow falls). This suggests that the added normal load of the snow increases the friction on the sliding plane enough to make the events bigger (higher stress drop) but less frequent. However, it seems to only be enough to affect event behavior once a family has already been initiated, suggesting that once an area begins sliding in a stick-slip manner, it becomes highly sensitive to minor external stress perturbations.

Zoet et al. [2013a] found in lab tests of ice sliding against rock that if initial lubrication of the sliding plane is low (i.e., the glacier is cold and/or the base is well drained and highly fractured) and a sudden increase in sliding velocity occurs, the increased velocity results in increased frictional melting (i.e., increased lubrication). This is equivalent to the velocity-weakening property required for stick-slip sliding. The temporary increase in lubrication at this spot causes a drop in dynamic friction on the fault, causing slip to accelerate. To compensate for this acceleration, sliding continues a bit past the point where dynamic friction equals the strength of the fault. This instability that causes this “overshoot” is responsible for stick slip [Scholz, 1998], causing the sliding plane to stick and allowing it to heal and rebuild strength and then start the cycle again. Zoet et al. [2013a] propose that the healing mechanism for glacial stick slip is refreezing. This healed fault will be reloaded as the surrounding areas continue to slide around this sticky patch, and the cycle will repeat over and over again until another change sends it back into the stable sliding regime. Zoet et al. [2013a] found that dirty ice is more favorable to stick-slip sliding because frictional melting is higher. The basal ice at Mount Rainier is most likely extremely dirty at its bed because the rocks that compose much of the mountain are weak and easily crumbled. In fact, beyond just being “dirty,” there is likely also much larger debris, even large boulders, embedded in the ice at Mount Rainier as well. Zoet et al. [2013a] also found that for stick-slip sliding to occur, the additional lubrication added due to frictional melting had to have a way to drain away from the sticky patch rather than building up, so the rock must be porous or fractured. We believe something similar is responsible at Mount Rainier: a glacier speeds up suddenly, causing a transition to stick-slip sliding in an area of the bed favorable to frictional instability like a patch of debris-filled basal ice passing over an area of porous or fractured substrate.

However, this leaves the question of how the tiny load of added snow causes a speedup, why there is a delay of a day or two, and why the behavior is temporary. Assuming the glaciers are 30 to 60 m thick [Driedger and Kennard, 1986], the added snow weight prior to the appearance of the select families (1.4–11.3 cm water equivalent, Table 1) is just 0.03–0.4% of the glacier load. It could be that the glaciers involved are already close to a critical point where a tiny increased load could push it over a threshold. Alternatively, the delay in triggering time suggests a time-dependent mechanism such as changes in basal hydrology.

The winter subglacial drainage systems of alpine glaciers are characterized by a distributed system of isolated cavities that can be filled with stagnant melt water from geothermal and frictional heating [Fountain and Walder, 1998]. Because these cavities are hydrologically isolated, and thus poorly drained in the winter, high fluid pressures can build up [Mathews, 1964]. Many glaciers are also underlain by a spatially variable and discontinuous layer of rock debris that can also hold and transport water, though water transport is limited by the hydraulic conductivity of the material and is often less efficient than other means [Fountain and Walder, 1998].

When a load of snow falls on the glacier during a storm, there are a few immediate effects. The driving (shear) stress σs and the effective normal stress σNeff (normal stress minus basal fluid pressure σNeff = σN  −  pw) are both increased at a ratio depending on the slope angle. The increased effective normal stress also results in increased frictional forces that resist the increased driving stresses by an amount proportional to the friction coefficient. However, the immediate increase in any of these stresses would be just 0.05–0.2% (assuming slopes of 30°–45°) for the amount of snow that occurs prior to any of the select families so the glacier would have to be extremely sensitive, i.e., the initial effective basal normal stress would need to be very low due to high basal fluid pressures.

However, in addition to simply direct loading, the lag and sensitivity to small changes in load suggests that a time-dependent process, perhaps related to changes in subglacial hydrology, may be responsible. When an additional normal load from the snow is added to the glaciers, it squeezes the pressurized basal cavities which have the immediate effect of slightly increasing the fluid pressures, pw, in each cavity temporarily because they are poorly drained, poorly connected, and cannot easily adjust in the winter. This would perturb the distribution of subglacial water, eventually pushing some water into adjacent areas, but would take time to occur because the movement of water in response to the pressure increase is limited by the hydraulic properties of the system. This gradual redistribution of fluids could have the effect of lubricating a larger area of bed (i.e., reducing the areally-averaged effective stresses) or possibly just by lubricating localized areas that were supporting more of the stress. This could then increase sliding velocities but with a time delay that provides a potential explanation for the 1–2 day lag. Then, as explained earlier, a sudden increase in sliding velocities can trigger stick-slip sliding [Scholz, 1998] at patches of the bed where conditions are favorable to stick-slip sliding (i.e., colder, dirtier, and better drained [Zoet et al., 2013a]).

The change in event location over time (Figure 9) suggests a migrating dirty patch moving over, for example, a patch of fractured bedrock or other porous substrate. This patch is most likely a different area than those responsible for the increased velocities because it must be poorly lubricated initially. Thelen et al. [2013] estimated that the size of the seismogenic patch for these low-frequency earthquakes could range from 0.4 to 104 m2, a very small fraction of the area of any glaciers involved, meaning just part of the glacier bed is seismogenic; the rest is sliding aseismically. The family disappearance can occur either when the dirty ice patch moves beyond this area or excess fluid pressures have had sufficient time to drain away and sliding velocities drop back down to previous levels. In most cases, event families die off in about a week or two, which provides a time limitation for these processes.

Basal conditions of glaciers are highly variable [Fountain and Walder, 1998] and there are likely to be places that meet conditions favorable to stick-slip sliding at the base of any glacier [Zoet et al., 2013a]. If more than one place under a single accelerating portion of a glacier meets the requirements, or if more than one glacier responds in this way, there can be multiple simultaneous event families, as observed (Figure 6). The idea that certain parts of certain glaciers are more prone to the observed behavior is supported by the fact that event families with highly similar waveforms reappear in different years (Figure 10). Since we showed earlier that the asperities for the event families shown are mobile, these reoccurring families are most likely the result of stick-slip sliding occurring again in a very similar location to where it occurred before rather than the same exact asperity being reactivated. This supports the idea that the shape and characteristics of the material composing the bed of the glacier is an important factor in determining whether it generates these events or not.

Figure 10.

Event families (red text) that share similar waveforms as the select families (brown text). Waveforms shown are the stack of all events recorded at RCS.

Steep glaciers may be particularly prone to transient stick-slip sliding because they are less stable to begin with, making them more prone to increases in sliding velocity from minor changes in the system. They also are less likely to have thick layers of deformable basal till beneath them that may favor aseismic sliding like lower parts of the glaciers might. These factors may explain why the locations of at least the select event families are at glaciers that end at a cliff and thus do not have a typical terminus to lend additional support as opposed to other areas.

There is the question of why this behavior does not also occur in the late spring and summer when rapid and high volume inputs of water cause sliding velocity increases [e.g., Harper et al., 2007; Fudge et al., 2009]. The absence of swarms of repeating low-frequency earthquakes in the summer is probably due to the significant difference in the configuration of the subglacial drainage system between summer and winter. The summer configuration is efficient and well connected [Fountain and Walder, 1998] and thus can rapidly adjust to changes in the system making prolonged swarms unlikely. The absence of repeating earthquake swarms during the spring melts when the basal configuration may still be distributed and there can be rapid influxes of rain and melt water could be because there may just be too much water coming too fast. When there is a lot of basal fluid in the system, widespread bed separation occurs, removing areas of higher drag [Mair et al., 2001]. Stick-slip sliding may be triggered for a short time with the initial influx of water but could quickly be shut off as more and more water enters the system, providing more and more lubrication that cannot be drained away fast enough to allow stick-slip sliding to continue. This is consistent with the observations: there are low-frequency repeating earthquakes occurring year round, just not in the big long-lasting swarms that occur during the accumulation season (Figure 3). Furthermore, the much larger but far less frequent icequakes observed at Mount Rainier and other Cascade volcanoes by Weaver and Malone [1979] and Moran et al. [2009] were classified as basal stick-slip events. Those events occur predominantly in the summer, indicating that stick-slip sliding probably occurs at some locations of some glaciers year round, just not in the prolonged swarms of small repeating earthquakes that seem to rely on winter-like subglacial drainage conditions.

Precipitation does not tend to trigger swarms of repeating earthquakes early in the accumulation season (Figure 7). It takes a few weeks of winter conditions for them to start to appear, which may be the amount of time required for the subglacial conduits to collapse viscously and for the drainage system to transition from summer to winter conditions.

The apparent increase in low-frequency repeating earthquake activity over the past 10 years (Figure 3) may simply be a function of storminess. For example, the most repeating earthquake activity was detected in the winter of 2011–2012, which also was characterized by fewer storms but each dropping larger amounts of snow (Figure 7). This would be more likely to trigger sudden velocity increases by the mechanisms we propose than many small storms depositing snow incrementally.

4.3 Broader Implications

Beyond proposing a solution to the puzzle of a peculiar seismic source on one mountain, the findings of this study and our proposed mechanisms have wider implications both in glaciology and beyond. This case adds to the body of knowledge on alpine glacier behavior. We show that some parts of some glaciers can be extremely sensitive to minor changes in external loading. Our observations suggest that if conditions are right, surges in basal sliding velocity can be triggered by surface loading that is a fraction of a percent of the total overburden load, at least in the winter months when the subglacial drainage system is composed of poorly connected cavities. Furthermore, though stick-slip behavior has been confirmed geodetically for large shallowly sloping ice streams in Antarctica [e.g., Wiens et al., 2008]; this is the strongest evidence of seismicity resulting from stick-slip glacial sliding at steep, temperate, alpine glaciers that we know of. The long-term year-round record of repeating earthquake activity provides a window into seasonal differences in the behavior of alpine glaciers, particularly the behavior of the high reaches of alpine glaciers in wintertime—an essentially inaccessible environment that is difficult to study with other methods. The behavior documented here adds to the spectrum of known glacier behavior. This may also have ramifications for subglacial morphology, as Zoet et al. [2012] suggests stick-slip sliding may have a connection to erosional processes.

The repeating earthquakes at Mount Rainier can also provide insight into repeating earthquakes and earthquake behavior in other environments, provided we understand the limitations of the analogy (e.g., ice melts at a much lower temperature than rocks). It is rare to have such an extensive catalog of earthquakes that occur so frequently: nearly 300,000 repeating earthquakes with more occurring every day. This allows us to identify certain seismicity patterns that we do not typically have enough data to observe for regular earthquakes. For example, we showed that these events show slip-predictable behavior on short timescales, but even minor changes in external loading, such as a tiny increase in the normal load or a gradually decreasing slip rate throw off this relation, but in systematic ways (Figure 8). Shelley [2010] and Shelly and Johnson [2011] observed similarly abrupt changes in the recurrence intervals of small stick-slip earthquakes and nonvolcanic tremor on the San Andreas Fault near Parkfield due to minor stress changes from nearby earthquakes. Ocean and Earth tides and even dynamic loading from seismic waves of distant earthquakes also change the normal and shear stresses in the Earth by amounts that are a tiny fraction of the total driving stresses but have all caused observable changes in the behavior of tectonic events [e.g., Rubinstein et al., 2008; Nakata et al., 2008; Peng et al., 2009]. Apparently, even minor changes in the stress field can alter fault behavior on a range of scales, even for glaciers. The mechanism we invoked as a trigger for the swarms of glacier quakes at Mount Rainier, fluid redistribution and increased aseismic slip around a sticky patch, has been invoked as a trigger for swarms in tectonic environments [e.g., Vidale and Shearer, 2006; Vidale et al., 2006]. Additionally, many of the approaches we used to study repeating earthquakes at Mount Rainier can be applied to these other environments, including repeating events at volcanoes that are not related to ice movement, to further expand our understanding of repeating seismicity and stick-slip behavior.

5 Conclusions

In this study, we compiled a comprehensive catalog of repeating earthquake activity that occurred over the past decade at Mount Rainier. We found nearly 300,000 repeating earthquakes. About half had dominant frequencies below 8 Hz (low frequency), and many repeat at regular intervals, the type of event that motivated this study. We found that this type of seismicity has occurred every year for at least the past decade, but previously went almost completely undetected. Though low-frequency repeating earthquakes occur year round at a background level of about five per hour, big swarms of activity occur only in late autumn to early spring.

We used this catalog to fully characterize this type of earthquake, to understand the source, and to confirm that the source is glacial and not related to volcanic activity. We found that the swarms often are composed of several distinct families occurring at different areas of the mountain simultaneously. Swarms correlate strongly with precipitation, peaking sharply at a 1–2 day lag. Within each family, we showed that recurrence intervals, interevent correlations, and event energy all vary over time, often gradually, but sometimes suddenly, and these sudden changes often correlate with minor changes in loading (≪1%) from snowfall. We used coda wave interferometry to track the migration of these event sources over time and found that the sources move at glacial speeds, but somewhat faster initially, then slowing down over time. We also found evidence that fault healing occurs between events based on linear relations between recurrence interval and event energy. By stacking hundreds of nearly identical events, we were able to pick out the first P wave motions at several stations and found that most events show mixed polarities, suggesting a shear source.

These observations are consistent with our hypothesis that most, if not all, of the low-frequency repeating earthquakes we documented are manifestations of stick-slip basal sliding of glaciers and that the transition from smooth aseismic sliding to stick-slip sliding is triggered by changes in subglacial hydrology in response to snow loading. We hypothesize that the added weight squeezes the poorly connected and pressurized subglacial cavities and drives some water into adjacent areas, lubricating more of the bed and resulting in a temporary velocity increase. This mechanism could explain the observed time lag between snowfall and earthquake swarm appearance. A basal configuration composed of isolated and distributed cavities is typical of winter, which could partially explain why these events occur primarily in the winter months. We located some families of events with high enough accuracy to identify under which glaciers they likely occurred and found that all of the locatable families were located in thin steep areas, particularly glaciers that terminate at a cliff edge, suggesting this type of glacier is most sensitive to minor perturbations in external loading. The abundance of repeating stick-slip icequakes at Mount Rainier when they are not so often observed at other temperate glaciers may be a function of the material at the bed of the glacier. The volcanic rocks that compose Mount Rainier are highly heterogeneous and also very weak and crumbly near the surface that likely results in very dirty basal ice that lab tests have found to favor stick-slip sliding [Zoet et al., 2013a].

The behavior of repeating earthquakes at Mount Rainier that we document here provides a particularly complete data set that provides insight into glacier behavior, and even tectonic fault behavior. The benefit of this data set documenting the stick-slip sliding of glaciers is that it is a good case for seismology to benefit from the rich body of knowledge from glaciology and vice versa to improve understanding in both cases. In some ways, the glaciers at Mount Rainier provide a giant natural fault laboratory that we have been inadvertently recording for over a decade for testing ideas in both disciplines. We have only just begun to analyze the database of repeating earthquakes that we compiled and there is undoubtedly more to be learned.

Acknowledgments

Many thanks to Mount Rainier National Park Staff and Climbing Rangers; and J. Vidale and S. Moran for their advising; J. Carmichael for sharing his multiplet detection codes; R. Hahn and A. Rasmussen for meteorological advice; B. Hallet, E. Waddington, and T.J. Fudge for glaciology feedback; and everyone who helped with field work (even though the mountain sabotaged most of our efforts) particularly P. Neff, K. Poinar, M. Stevens, J. Connolly, D. Gibbons, E. Sofen, R. Carns, S. Matthiesen, A. Pickering, C. Moore, and D. Shean. Additionally, reviews from Fabian Walter and two anonymous reviewers significantly improved the manuscript. This work was supported in part by the U.S. Geological Survey under contract G10AC00087 to the Pacific Northwest Seismic Network (PNSN), the University of Washington Earth and Space Sciences Department awards, and the Colorado Scientific Society. The PNSN, the IRIS Data Management Center, and Cascade Volcano Observatory provided logistical support and seismic data. The seismic data used can be downloaded for free from IRIS.