We present statistical evidence for a temporal link between variations in the El Niño–Southern Oscillation (ENSO) and the occurrence of earthquakes on the East Pacific Rise (EPR). We adopt a zero-inflated Poisson regression model to represent the relationship between the number of earthquakes in the Easter microplate on the EPR and ENSO (expressed using the southern oscillation index (SOI) for east Pacific sea-level pressure anomalies) from February 1973 to February 2009. We also examine the relationship between the numbers of earthquakes and sea levels, as retrieved by Topex/Poseidon from October 1992 to July 2002. We observe a significant (95% confidence level) positive influence of SOI on seismicity: positive SOI values trigger more earthquakes over the following 2 to 6 months than negative SOI values. There is a significant negative influence of absolute sea levels on seismicity (at 6 months lag). We propose that increased seismicity is associated with ENSO-driven sea-surface gradients (rising from east to west) in the equatorial Pacific, leading to a reduction in ocean-bottom pressure over the EPR by a few kilopascal. This relationship is opposite to reservoir-triggered seismicity and suggests that EPR fault activity may be triggered by plate flexure associated with the reduced pressure.
It is becoming increasingly apparent that small changes in environmental conditions provide a means whereby physical phenomena involving the atmosphere and hydrosphere can elicit a response from the Earth’s crust. McNutt & Beavan (1987) and McNutt (1999) propose, for example, that eruptions of the Pavlof (Alaska) volcano, from the early 1970s to the late 1990s, were modulated by ocean loading involving yearly, non-tidal, variations in local sea level as small as 20 cm. On a broader scale, Mason et al. (2004) present evidence in support of a seasonal signal in global volcanic activity, which they attribute to surface deformation accompanying the movement of surface water mass during the annual hydrological cycle. In relation to active faults, Rubinstein et al. (2008) have been able to correlate episodes of slow slip and the accompanying seismic tremor at subduction zones in Cascadia (Pacific northwest) and Japan with the rise and fall of ocean tides. Liu et al. (2009) show that such slow-slip earthquakes occurring beneath eastern Taiwan can also be triggered by reduced atmospheric pressure associated with passing typhoons. For the active Slumgullion landslide in southwest Colorado, Schulz et al. (2009) demonstrate a correlation between daily slip and diurnal tidal variations in atmospheric pressure.
Improving our understanding of such relationships between the atmosphere and hydrosphere, on the one hand, and the geosphere, on the other, is important for a number of reasons: (i) where a system, such as a fault, volcano or unstable rock mass, is critically poised, a small change in external environmental conditions may trigger a potentially hazardous response in the form of earthquake, eruption or landslide, respectively, (ii) major, short-period climatic signals, such as the El Niño–Southern Oscillation (ENSO) and the North Atlantic Oscillation, which involve significant variations in sea level and atmospheric pressure (e.g. Cane 1983; Rasmusson & Wallace 1983; Woolf et al. 2003), may also elicit a discernable and geologically significant reaction from the crust, and (iii) the driving mechanisms, such as ocean loading and atmospheric pressure change, have the potential to promote an enhanced geospheric response in a future warmer world characterized by accelerated sea levels and more intense storms associated with lower central pressures and higher surges. Here, we address point (ii) above by means of a statistical analysis of a putative relationship (Walker 1988, 1995, 1999) between the ENSO and episodic seismicity along the East Pacific Rise (EPR).
2. The El Niño–Southern Oscillation and the seismicity of the East Pacific Rise
The ENSO is the largest climate signal on Earth after the seasons and has widespread ramifications for global weather patterns. In the atmosphere, the prime manifestation of the ENSO is a see-saw in sea-level pressure (the southern oscillation) between the southeast Pacific sub-tropical high and a region of low pressure that stretches across the Indian Ocean from Africa to northern Australia. This difference is normally expressed in the form of the southern oscillation index (SOI), determined from the normalized sea-level pressure difference between Tahiti and Darwin. In the ocean, the ENSO is characterized by episodic warming (El Niño) or cooling (La Niña) of surface waters in the central and eastern Pacific, with an oscillation period that typically ranges from 2 to 7 years (Guilyardi et al. 2009). The meteorological influence of ENSO is global, with its El Niño phase, in particular, resulting in potentially hazardous weather conditions in regions both adjacent to, and remote from, its source. These include drought in Australia, southern Africa and south and southeast Asia, increased heavy precipitation in northwestern South America, and more winter storms and floods across the US Gulf Coast (Cane 1983). A detailed explanation of the ENSO and its drivers can be found in Cane (2005), but for the purposes of the present study, the key effect of the ENSO is upon the level of the ocean at low latitudes in the Pacific. Broadly speaking, normal conditions in the equatorial Pacific involve the easterly trade winds pushing warm surface water westwards, resulting in upwelling of deeper, colder water in the eastern Pacific. During a La Niña event (when the SOI is high), this cooling in the east is enhanced. In contrast, El Niño events (when the SOI is exceptionally low) are associated with a faltering, or even reversal, of the trade winds, leading to warm surface waters ‘sloshing’ back eastwards (Tsonis et al. 2005). Thus, a high SOI (La Niña) is associated with low sea levels in the eastern Pacific and a low SOI (El Niño) is associated with high sea levels in the eastern Pacific.
A link between the El Niño phase of the ENSO and crustal seismicity was first proposed by Walker (1988), who recognized a coincidence of extreme lows in the SOI and elevated seismic activity in the vicinity of the EPR. The relationship was subsequently (Walker 1995, 1999) elaborated and updated by the same author, focusing on the segment of the EPR between 20° S and 40° S. Walker (1999) proposes that all El Niño events since 1964 (up to and including 1998) have been preceded by anomalous seismicity along parts of the EPR, where ‘anomalous’ is defined as months having eight or more reported earthquakes (compared with an apparent long-term average of less than two), or months with seismic energy values of 9×1012 J or more. According to Walker (1999), the lead time between onset of anomalous seismicity and extreme lows in the SOI ranges from 5 to 15 months. This, the author presents as supporting a link between the elevated levels of seismicity and a trigger for El Niño emergence. Walker (1995) notes that the EPR between 20° S and 40° S contains one of the most rapidly spreading ridge segments on the planet, characterized by high levels of hydrothermal activity and submarine volcanic activity. This behaviour, the author suggests, could underpin the apparent temporal link between El Niño conditions, reflected in extreme lows in the SOI, and elevated levels of seismicity along this part of the EPR. While admitting the absence of direct evidence, Walker (1995, 1999) goes on to consider that the latter may be indicative of massive episodes of submarine eruptive activity. As a corollary, he speculates that the heating effect of such volcanism could result in thermal expansion of deep water sufficient to produce the approximately 200 Nm−2 reduction in atmospheric pressure at sea level required to promote the development of El Niño conditions. Walker (1999) presents other possibilities whereby submarine volcanism could warm surface waters sufficiently to reduce atmospheric pressure in the region and produce SOI lows that flag El Niño conditions. These include ‘massive plumes’ of hot water that penetrate the thermocline and ‘massive episodic heating’ of the ridge system triggering large earthquakes, increased numbers of earthquakes, sea-floor volcanism, hydrothermal venting and sea-floor spreading.
In a reply to Walker (1999), Hunt (2000) suggests that, rather than the observed seismicity reflecting a causative volcanic trigger for El Niño, it may be a consequence of changing environmental conditions precursory to El Niño emergence; specifically, systematic variations in sea level with the potential to induce small, additional crustal stresses. Hunt (2000) notes that every El Niño since 1960 (possibly excepting that of 1982–1983), was preceded by the development of anomalously large upward sea-surface slopes from east to west, driven by the trade winds. This resulted, in turn, in the development of anomalously low sea levels in the eastern Pacific prior to the onset of El Niño conditions (Wyrtki 1975). If higher sea levels associated with El Niño conditions prove to be capable of inducing increased seismicity in the EPR, then lowered sea levels, speculates Hunt (2000), might be capable of eliciting a similar response. Notwithstanding these suggestions, Hunt goes on to note that sea-level variations of tens of centimetres associated with the wholesale transfer of water mass during ENSO cycles would result in stress variations on the crust of less than 1×104 Nm−2, which he regards as being insufficient to affect earthquake frequencies. Hunt (2000) also emphasizes the fact that the role of atmospheric winds in triggering El Niño conditions is well established, making it difficult to accept the Walker model for triggering owing to volcanic heating of the deep ocean. Hunt concludes that the apparent correlation between El Niño emergence and EPR seismicity is coincidental.
It is noteworthy that the speculations of both Walker (1988, 1995, 1999) and Hunt (2000) have been undertaken in the absence of robust statistical analysis of the putative correlation between ‘anomalous’ seismicity and changing environmental conditions associated with the ENSO cycle and, in particular, with El Niño onset. In order to address this omission, we present here the results of a statistical study designed to shed light on the relationship between earthquake activity across the area of the EPR (20–40° S and 100–120° S) considered by Walker (1988) and (i) the ENSO, as measured by the SOI, and (ii) variations in sea-surface elevation. The period covered is from 1 February 1973 to 28 February 2009. Data sources are as follows: earthquake data are from the National Earthquake Information Center (NEIC; http://neic.usgs.gov/neis/epic/); SOI data (version Equatorial Eastern Pacific SLP, Standardized Anomalies) are from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC; http://www.cpc.noaa.gov/data/indices), not the more standard SOI obtained as the standardized difference in sea-level pressure between Tahiti and Darwin, as we want to focus on the eastern Pacific; and sea-surface elevation data are from the joint NASA/CNES satellite altimeter, Topex/Poseidon (http://ibis.grdl.noaa.gov/SAT/hist/tp.products/topex.html), these are sea-level deviations averaged in cells with dimensions of 4×1° (longitude × latitude), heights are relative to the 3 year mean (1993–1995), deviations are then averaged over the 20–40° S and 100–120° W, and the resulting monthly time series spans the period October 1992 to July 2002.
A number of authors have addressed the impact of the ENSO on sea-level variations (Wyrtki 1975; Cane 1983; Rasmusson & Wallace 1983; Woolf et al. 2003). Over the region 0–40° S and 100–120° W and the period October 1992 to July 2002, we corroborate the previously established correlation between the ENSO and sea level (figure 1). We computed estimates and confidence intervals of these correlations, with a lag ranging from 0 to 12 months, after which the sea level is compared with the aforementioned SOI (table 1).
3. Origins and distribution of seismic activity on the East Pacific Rise
Seismic activity on the EPR in the area of interest for this study, from the equator to 30° S latitude, originates from three types of structure associated with this plate boundary, perhaps the type example of a fast-spreading mid-oceanic ridge system (figure 2). Recent reviews of the structure of the EPR in our area of interest, emphasizing its subdivision and the development of microplates along the EPR, are provided by Searle et al. (1993) and Hey (2004).
(a) Three different sources of seismic activity on the East Pacific Rise
It is important to distinguish these three different seismic source types because they may respond in different ways to environmental forcing by the ENSO. Furthermore, the levels of activity differ markedly between the three, particularly in respect of the numbers of earthquakes large enough to be recorded as teleseismic events on global seismic networks, and thus appear in our primary data source, the NEIC earthquake catalogue for the time period from 1 February 1973 to 28 February 2009 (figures 2 and 3).
— Transform faults: zones of strike-slip faulting linking offset spreading centres. These structures are especially common in the northern part of the area of interest and are the sources of numerous large earthquakes. However, an analysis of the time–space distribution of these earthquakes along these and similar transform faults on the parts of the EPR to the north of the equator by McGuire (2008) indicates that seismic cycles of around 5 years are present: once a large (Mw∼6) earthquake occurs on any one part of a transform fault, it is about 5 years before another such earthquake occurs in the same location. McGuire (2008) attributes this short seismic cycle time to the moderate size of the individual earthquakes and the high rates of deformation and seismic loading that result from the rapid spreading of the EPR. For our purposes, however, the similarity between the proposed seismic cycle times and the interval between ENSO events makes statistical analysis of the occurrence of transform fault earthquakes problematic because of the potential for aliasing of the time distribution signal between the two sources of time variation. Future analysis of the variation in time interval between large earthquake pairs in transform faults as a function of the ENSO may help to elucidate the interaction between the seismic cycles and the ENSO, but at present, the numbers of such earthquake pairs (16 in the McGuire (2008) dataset) are too small to permit such an analysis.
— Spreading centres: the main plate boundary structures. Owing to the high rates of magma supply to the EPR, plate boundary spreading in the area of interest appears to be almost entirely accommodated by dike intrusion. There are very few large earthquakes in the NEIC dataset located on or near these spreading centres, and therefore interactions between the spreading centres and the ENSO will not be revealed by analysis of that dataset. However, distributions of microseismicity recorded by temporary deployments of ocean-bottom seismometers (OBSs) as part of research into the behaviour of the EPR spreading centres (Hey 2004; Stroup et al. 2009) indicate significant modulation of the microseismicity on diurnal and semi-diurnal tidal time scales. This is attributed to variations in fluid flow into the highly permeable crust at the spreading centre, along the dike swarms and out of the crust again at the celebrated ‘black smoker’ high-temperature hot springs located at intervals along the EPR spreading centres. We speculate that longer term OBS deployments on the EPR may reveal ENSO-related time variations in the level of microseismicity on these spreading segments and perhaps also links between the ENSO and larger, less frequent events that occur on the spreading centres, such as dike intrusions and sea-bed eruptions, but at present, data are insufficient to investigate this point. For the present purpose, perhaps the most significant result to be derived from the studies of spreading centre microseismicity is the remarkably high permeability of the spreading centre crust (approx. 10–13 to 10–12 m2) derived by Stroup et al. (2009), which implies that pressure variations associated with the ENSO may be transmitted into the pore fluids within the uppermost ocean crust on short time scales. We consider this point further below.
— Microplates along the EPR. A number of small microplates, some tens of kilometres across, are located along the EPR. These are thought to have been produced by unsteady propagation or jumping of spreading-centre segments across transform faults that result in isolation of small pieces of young oceanic crust between overlapping spreading centres connected by two, rather than one, broadly strike-slip fault segment. In plate-tectonic terms, this geometry is unstable and as a result, the microplates experience rapid rotation and high levels of internal deformation (Searle et al. 1993; Cogne et al. 1995; Hey 2004). They are, therefore, characterized by high levels of seismic activity, typically occurring in swarms lasting periods of the order of days, suggesting some component of magma intrusion as part of the deformation, rather than in mainshock–aftershock sequences. One such microplate, the Easter microplate (Searle et al. 1993), lies within our area of interest and, despite its small size produces about 40 per cent of all the earthquakes in the NEIC catalogue for the 0–30° S segment of the EPR. As seen in figure 4, over the Easter microplate, the relative position of the largest earthquake in groups of at least three earthquakes is roughly uniform; it cannot correspond to mainshock–aftershock sequences in which the largest earthquakes occur at the beginning of the sequences.
Once the transform faults are eliminated from the analysis for reasons discussed above, earthquakes within and around the microplates dominate the EPR earthquakes in the NEIC catalogue. Much of our statistical analysis (§4) therefore concentrates upon the Easter microplate area (20–28° S, 110–120° W). Conversely, the lack of large earthquakes on the spreading segments means that large-scale eruptive activity on them will only be indirectly related, through stress transfer, to levels of seismic activity at the main earthquake sites, the transform faults and the microplates. This presents some difficulties for the Walker (1999) model since the seismic response to stress transfer after the postulated ‘massive’ eruptions will not be immediate, thereby weakening the postulated time sequence of earthquakes followed by thermal effects in the ocean. Under these circumstances, we consider two alternative hypotheses for how ENSO and seismic activity on the EPR might be linked, both focusing upon how ENSO-driven changes in the sea level over the EPR might affect this very active plate boundary.
H1 Modulation of pore fluid pressure within the crust by sea-level variations. Pore fluid-pressure variations in fault zones can influence seismicity by changing the frictional resistance to fault slip. If permeability of the crust down to the seismogenic zone is sufficiently high, short-term variations in ocean-bed water pressure may propagate down into the crust and change fluid pressure on the fault zones where the earthquakes occur.
H2 Flexure of the crust and unclamping of fault zones by sea-level variations. Since the EPR is a plate boundary where the lithosphere on either side is much stronger than the boundary itself, the two plates on either side may flex in response to sea-level changes and so produce significant changes in the stresses transmitted across the plate boundary, especially to the microplates located within the EPR such as the Easter microplate.
(b) Pore fluids and permeability in mid-ocean ridge systems compared with continental crust: implications for possible mechanisms of linkage between the El Niño–Southern Oscillation and East Pacific Rise earthquakes
A link between fluid-pressure variations and seismic activity has long been recognized in the case of earthquakes in the continental crust triggered by filling of surface reservoirs (see Talwani 1997 for a review). Perhaps the most notorious example is the sequence of damaging earthquakes triggered by the filling of the Koyna reservoir in the Deccan region of India (Simpson et al. 1988). Notably, although the reservoir was first filled in 1962–1963, the seismic activity was initially limited, but became more intense and damaging from late 1967, with the largest events of magnitude 5.5 and 6.2 (comparable to the largest EPR earthquakes) causing a large amount of damage and a number of deaths. These delayed earthquakes at Koyna and other comparable examples are commonly relatively distant and deep (approx. 10 km). In other cases, the onset and peak of seismic activity is more immediate and directly linked to the reservoir filling, with the earthquake foci at shallow depths and close to the reservoir; in these cases, the earthquakes are generally small. Simpson et al. (1988) attributed the two contrasted types of seismic activity, on the one hand, to poroelastic deformation in effectively sealed but compressible fluid reservoirs, where loading by the water in the reservoir compresses the pores and raises pore fluid pressure immediately; and on the other, to the delayed effect of fluid diffusion into reservoirs at greater depths and distances that raises pore pressure over time scales of the order of years. Furthermore, they showed that the values of large-scale diffusivity implied by the time scale of delayed seismicity, even in the relatively rigid plate interiors, were relatively high, of the order of 100 m2 s−1. As noted by Simpson et al. (1988), these values are much higher than those obtained by laboratory measurements on intact rock samples, implying that the large-scale diffusivity is dominated by fluid flow through fracture systems.
The high levels of seismicity and the dense fault systems in the EPR microplates, such as the Easter microplate, imply high rates of ongoing brittle deformation and therefore the presence of abundant newly formed fractures. The well-known occurrences of hot brine springs (‘black smokers’) on the EPR also imply high crustal permeabilities. Although high thermal gradients and the chemically reactive nature of oceanic crust mean that such fractures will tend to seal over time, they are, nevertheless, likely to lead to high crustal permeability in the microplate and the vicinity of the plate boundary as a whole, and therefore to significant diffusion of fluid-pressure variations from the sea bed to depths within the crust. As noted by Jupp & Schultz (2004) and demonstrated for the EPR by Stroup et al. (2009), the depths to which such sea-bed pressure variations will be felt depends on the time scale of the variations (expressed in terms of a ‘skin thickness’ within which diffusion is effective). At constant diffusivity, (mainly influenced in fractured rocks by permeability variations; Lister 1974) the skin thickness will increase as the square root of the time scale of diffusion. Therefore, if diurnal tidal variations are only effective within the topmost approximately 3 km of crust (Stroup et al. 2009), the months time scales of ENSO-related sea-level variations would be expected to produce diffusion-controlled pore pressure variations in the topmost approximately 30 km of crust, comparable to, or significantly greater than, the depth range of the observed earthquakes in oceanic crust according to its age. In the young, hot oceanic crust of the EPR microplates, it is therefore likely that the depth range of pore fluid-pressure variations will be limited by a marked downward decrease in fracture abundance through the seismogenic zone into hot crust and mantle that deforms by ductile mechanisms and is therefore impermeable on the large scale. We conclude that the whole of the seismogenic zone of the EPR microplates could therefore be susceptible to the effects of ENSO-modulated pore pressure variations: it is reasonable to expect that even the largest microplate earthquakes could be susceptible to the ENSO. Whether or not this is actually the case will depend critically on the permeability structure of the seismogenic layer of the crust, so in principle, the nature of the statistical relationship between the ENSO and seismic activity will provide insights into the permeability structure of the Easter microplate.
While reservoir-related seismicity is usually associated with initial reservoir filling, in some cases, the seismicity has continued for decades and is associated with fluctuations in reservoir levels (Talwani 1997). In these cases, pore fluid-pressure fluctuations are thought to be associated with inflow and outflow of pore water as the reservoir level changes: thus deformation and the resulting seismicity are linked to the pressure changes.
The comparison with reservoir-induced seismicity therefore suggests two variants of hypothesis (H1) for permeability-controlled linkages between the ENSO and the seismicity of the Easter microplate. We refer to these as (H1A) and (H1B).
Hypothesis (H1A). Falling sea level reduces sea-bed pressure, hence overall load in the rocks beneath; but finite and relatively low permeability means that pore pressure at depth decreases more slowly, so the pore pressure is a higher fraction of total load; this may then lead to increased fault movement. This is opposite to the normal reservoir-related seismicity relationship, but may be appropriate to the EPR because of the crustal permeability structure noted above.
Hypothesis (H1B). Elevated sea level increases sea-bed pressure, and then absolute pore pressure as inflow into the sub-sea-bed rocks occurs. Again, the elevated pore fluid pressure may lead to increased fault movement. This hypothesis is similar to the normal relationship between reservoir levels and reservoir-induced seismicity. The effectiveness of this mechanism may be increased in the hot rocks near the EPR because the inflowing fluids are cooler and denser than the ambient fluids, so fluid-pressure gradients with depth are increased.
Either hypothesis can be framed in two ways, in terms of absolute sea level or rate of sea-level change: hypothesis (H1A) implies that increased seismicity will be associated with falling sea level or low absolute sea level, whereas hypothesis (H1B) implies that increased seismicity will be associated with rising sea level or high absolute sea level. However, we investigated the relationship between monthly sea-level changes (i.e. differences of 2 consecutive months) and seismicity, and unlike the correlations we report in §5, we found no significant influence of sea-level changes on seismicity (probabilities of a non-significant effect being in the range 28–54%). Hence, we focus on the effects of absolute sea level and not rate of sea-level change.
(c) Sea levels, plate flexure and East Pacific Rise seismicity
The alternative hypothesis (H2) for the relationship between the ENSO, sea levels and the EPR seismicity is similar to the models for modulation of fault activity at plate boundaries. As noted above, Rubinstein et al. (2008) have been able to correlate episodes of slow slip and accompanying seismic tremor at subduction zones in Cascadia (Pacific northwest) and Japan with the rise and fall of ocean tides; whereas Liu et al. (2009) show that such slow-slip earthquakes occurring beneath eastern Taiwan can also be triggered by reduced atmospheric pressure associated with typhoons. In these cases, the concept is that reduction in pressure normal to low-angle faults unclamps them and enables fault slip through a reduction in frictional resistance to slip. In the case of the faults on the EPR, because these are high-angle normal and strike-slip faults, the relationship may be more complex. Reduction in ocean-bed pressure over the plates to either side of the EPR will tend to allow them to flex upwards, especially in the relatively shallow water to either side of the EPR itself. This will tend to induce additional extension across the plate boundary, in particular freeing up the microplates to rotate, and so triggering seismicity within them. Conversely, increased sea level will cause the main plates to flex down and towards one another, so locking the microplates. This hypothesis (H2) therefore predicts that increased seismicity will be associated with a high SOI and La Niña conditions and, most notably, with the anomalously reduced sea levels that are precursory to El Niño emergence, similar to the prediction of the hypothesis (H1A) for the pore pressure–seismicity link, but opposite to the prediction of hypothesis (H1B).
4. Statistical modelling of sea level and the El Niño–Southern Oscillation influence on earthquakes
(a) Zero-inflated Poisson regression model
Poisson regression models are used to model the relationship between counts and other variables, and are a particular case of generalized linear models (GLMs) (McCullagh & Nelder 1989). In GLMs, the response variable is not related directly to the explanatory variables, a function—called link function—of the parameter of the distribution from which the response variable is drawn is assumed to be a linear combination of the explanatory variables. In Poisson regression models, the link function is the logarithm. We model the logarithm of the parameter of the Poisson distribution, which is also the mean and variance, as a linear combination of the explanatory variables.
The histogram of number of earthquakes per month from February 1973 to February 2009 can be seen in figure 5. Many months have no earthquake in the monthly number of earthquakes. After further examination of the NEIC record, earthquakes occurrence times (figure 6) are clustered over periods of up to a few months, suggesting two regimes: one non-susceptible and one susceptible, when some conditions are satisfied for seismicity to take place. The largest earthquakes generally do not occur at the beginning of each cluster, but are distributed through the clusters (figure 4). Therefore, these clusters of earthquakes are not mainshock–aftershock sequences, but represent groups of events that may be related to magmatic activity in the Easter microplate, or form sequences of fault ruptures propagating around the microplate boundaries.
When two regimes are present, a zero-inflated Poisson (ZIP) regression model can represent better the relationship between counts and explanatory variables than a standard Poisson regression model (Lambert 1992). Indeed, in a ZIP model, a probability of being in the non-susceptible mode is estimated, and only in the susceptible mode is the standard Poisson regression model fitted. We use the R package ‘ZIGP’ to fit the ZIP model (Czado et al. 2007). We considered various time scales, over which we explained the number of earthquakes occurring over that period, according to sea level or SOI variations: 2, 3 and 6 months. Indeed, the high permeability of the crust, as discussed in §3, is likely to enable the seismicity to be triggered by sea level or the ENSO over short-time frames of a few months maximum. A period of 1 month only, however, was deemed to be too short since earthquakes occurring at the beginning of the month following a high value of the ENSO or sea level ought to be counted.
Let us denote Yi the number of quakes over the months i to i+(m−1), where m is the length in months of the considered period (m=2,3,6). In the ZIP model, the distribution of Yi is assumed to be where the mean μ satisfies 4.1 and X is the explanatory variable (here the ENSO or sea-level index at month i). There is a so-called ‘logit’ relationship between the probability of being in the non-susceptible mode pi and the potential linear combination of variables leading to the non-susceptibility state of the system, as in GLMs whose response variable is binary (McCullagh & Nelder 1989). However, here we do not have access to information that could give some insight about the susceptibility of the crust to changes in sea level or the ENSO, so we assume a constant probability of susceptibility 4.2
(b) El Niño Southern–Oscillation results
Using east Pacific sea-level pressure anomalies, we retrieve the monthly SOI values from February 1973 to February 2009. We show below the results of fitting the ZIP model to explain the variation in the number of earthquakes in the region 20–28° S, 110–120° W by variation of the ENSO.
In all cases, we find significantly positive coefficients β1 in the regression (4.1), see table 2. For 2, 3 and 6 month periods, the probability of such a coefficient being statistically insignificant is less than 0.012; indeed, the z-value (or ratio between the estimated and its estimated standard deviation) is large. Therefore, for the 2, 3 and 6 month periods, we find that higher values of the SOI are indeed significantly triggering a larger number of earthquakes, with 95% confidence (our scientific hypothesis (H1A) in §3.)
The 6 month analysis does not suffer from a zero-inflated phenomenon as the number of earthquakes is not often 0 when we consider 6 month periods. As a result, the probability of being in a non-susceptible state p is only estimated to be 0.03. This probability was estimated to be 0.30 and 0.18, respectively, for the 2 and 3 month periods.
The average impact of ENSO on the number of earthquakes can be computed as a result of the analysis. A 1 unit increase in the SOI triggers either 0.095, 0.087 or 0.138 more earthquakes in the log scale over, respectively, 2, 3 and 6 months (with uncertainties, as measured by the standard errors of, respectively, 0.038, 0.03 and 0.02). For instance, in the case of the 2 month period, and in the susceptible state, comparing the case where the SOI is 2 versus 0, with the estimated intercept of 0.975 (neglecting the standard error of 0.041), we obtain a mean (as well as the variance) number of earthquakes over 2 months of 3.206 versus 2.651. Adding the effect of the increase in variance, these two distributions of earthquakes can yield dramatically different numbers of earthquakes. For 6 months, the numbers are, respectively, 7.38 and 5.60, also showing a large difference. Similar calculations for an SOI of −2 rather than 0 also show that a lower SOI would reduce the number of earthquakes: 2.192 versus 2.651 on average for the following 3 months in the susceptible state.
(c) Sea-level results
Since the physical mechanism explaining the variation of earthquake numbers is likely to be the absolute sea level, we focus on the estimation of the effect of absolute sea level, as measured by the Topex/Poseidon satellite instrument, on the number of earthquakes. The sea-level data are averaged deviations over the region 20–28° S, 110–120° W, from October 1992 to July 2002. The results are not as significant as in the ENSO regressions, but show that lower sea levels trigger more earthquakes, and higher sea levels produce less earthquakes, since the coefficients β1 for sea-level influence on earthquakes, in the log scale according to equation (4.1), are always negative: −0.048, −0.045 and −0.063, respectively, for the 2, 3 and 6 month following period (table 3).
One should expect more significant results for sea levels than for the ENSO, since sea level is more closely related to the amount of pressure exerted on the sea bed than SOI variations. However, the existing short period of sea-level data only permits us to conclude, at the 95% confidence level, that lower sea levels are linked to more earthquakes (higher sea levels are linked to less earthquakes) over the following 6 months (for a 3 month period, we only have a 90% confidence level). Calculations similar to those in the last section can quantify these differences.
(d) Evaluation of alternative hypotheses
Our results have implications for the three alternative hypotheses discussed above. We argue against hypothesis (H1B) since its prediction of increased seismicity associated with raised sea levels and low SOI values (El Niño conditions) is contrary to the results of our analysis. We cannot distinguish between hypotheses (H1A) and (H2) because their predictions are broadly similar, but both are generally consistent with the results of the analysis. We consider how further work might allow us to distinguish between them below.
Having a better understanding of the physical mechanisms leading to a susceptible regime of seismicity would enable us to pin down some potentially observable variables that may be a proxy for these physical mechanisms. As a result, we could fit the ZIP model much better by explaining the variability in the susceptibility through such a variable and hence provide a finer assessment of the impact that sea level has on submarine earthquakes. The presence of gaps in the seismicity over time scales of 1 or 2 months, but not on time scales of the order of 6 months, which is indicated by the marked decrease in the probability term pi in the zero-inflated distribution model, see §4a, indicates frequent switching between earthquake-susceptible and non-earthquake-susceptible states on time scales of a few months. Some possible mechanisms for the switching between susceptible and non-susceptible states include the following:
— One potential mechanism is that seismicity in the Easter microplate is driven on short time scales by dike emplacement in the adjacent spreading segments to the north and south, with seismicity more likely soon after dike-emplacement episodes have loaded the adjacent crust. However, the switching from susceptible to non-susceptible states on time scales of months is probably too short for this mechanism to be viable, as increments of deformation on these time scales will only be a fraction of the annual spreading rates of approximately 14 cm yr−1 (figure 2) and therefore small compared to the width of typical dikes (of order 1–3 m).
— Another potential mechanism for the switching is short-term variation in the permeability of the crust of the Easter microplate, such that at times, the permeability is high and ENSO-linked pore pressure changes can propagate down into the seismogenic region of the crust on time scales of the order of months, producing the statistical relationship that we observe, while at other times the permeability is lower. Rapid permeability changes seem plausible because of the high-temperature gradient and highly reactive nature of the oceanic crust, which will lead to high rates of mineral deposition in, and clogging of, fracture permeability, coupled with the rapid creation of fracture permeability by the intense brittle deformation associated with the rotation of the microplate.
— Finally, the seismicity may be self-modulating, in the sense that a fault may be brought into the susceptible regime through stress loading by recent earthquakes on adjacent faults, particularly if there is an increase in compression and consequent poroelastic fluid-pressure increases and/or flow of pore fluid out of the faulted region. A particularly interesting point is that such stress loading may amplify the effect upon seismicity of the small initial effect of the ENSO-induced fluid-pressure changes, with an increased level of seismicity itself producing more seismicity in a positive feedback. Testing this model, however, requires a more detailed examination of the spatial distribution of successive earthquakes within the fault zones in and around the Easter microplate, which is beyond the scope of the present study.
A formal study of the amount of data collection necessary to detect a significant effect, under various assumptions, is beyond the scope of the paper. Nevertheless, it is of interest to know how long a satellite series such as Topex/Poseidon needs to be kept in space to observe with high confidence such a relationship. This type of study has already been undertaken for other regression models (Guillas et al. 2004).
The negative relationship between sea level and numbers of earthquakes that we have identified has implications for the permeability structure of the crust of the Easter microplate. Since the rejected hypothesis (H1B) requires a high-permeability crust, whereas hypothesis (H1A) implies a lower permeability in the seismogenic zone where the large earthquakes are generated, and hypothesis (H2) is independent of permeability, our results point to lower large-scale permeability in the relevant regions of the Easter microplate. Further study of the permeability structure of the microplate may allow a distinction to be made between these two hypotheses. However, another alternative approach would be to determine whether there is, in fact, significant flexure of the plates as required by hypothesis (F), for example, by direct measurement of variations in ocean-floor pressure at suitable points on, and distant from, the EPR using the Deep-ocean Assessment and Reporting of Tsunamis buoy technologies developed for the Pacific Tsunami Warning System (Bernard et al. 2006), which could then be compared with measurements of sea-surface elevations.
Quantification of such plate flexure would enable a better understanding of the stress changes within the lithosphere at the plate boundary produced by ocean-bottom pressure changes. El Niño emergence is preceded by negative sea-elevation anomalies in the eastern Pacific and accompanied by positive anomalies, the combined change in elevation approaching 0.5 m in the strongest events, corresponding to an ocean-bottom load pressure changes of approximately 5 kPa. Sea-level reduction precursory to El Niño emergence ranges up to approximately 20 cm, resulting in a load pressure change of 1–2 kPA. Notwithstanding the scepticism of Hunt (2000), stress changes on these orders are increasingly becoming recognized as being sufficient to trigger a seismic response. Heki (2003), for example, demonstrates that snow load seasonally influences the seismicity of Japan through increasing compression on active faults and reducing the Coulomb failure stress by a few kilopascal. For neighbouring Taiwan, Liu et al. (2009) show that slow earthquakes in eastern Taiwan are triggered by stress changes of approximately 2 kPA on faults at depth, associated with atmospheric pressure falls caused by passing tropical cyclones. In the ocean basins, Wilcock (2001) provides convincing evidence for micro-earthquakes on the Endeavour segment of the Juan de Fuca Ridge (northeast Pacific) being triggered by the loading effect of ocean tides that result in vertical stress variations of 30–40 kPA. We emphasize, further, that plate flexure in response to these loads in the case of the Easter microplate at the EPR could produce larger stress concentrations at particular levels in the crust at the plate boundaries of the microplate itself. Furthermore, given particular permeability variations in the crust, the effects of the stress variations could be amplified by the inbalances in pore fluid pressures invoked in our hypothesis (H1A).
As speculated by Hunt (2000), we conclude that increased seismicity in the region of the EPR is associated with the development of a strong sea-surface gradient rising from east to west (Wyrtki 1975), leading to lower sea level across the EPR and a reduction in ocean-bottom pressure of a few kilopascal. The development of the gradient is driven by strong southeast trade winds and strengthening of the South Equatorial Current, leading to a build-up of water in the western equatorial Pacific. The length of sea-level data only permits us to conclude, at the 95% confidence level, that lower sea levels are linked to more earthquakes over the following 6 months. Using a longer time period, we are able to establish that higher values of the SOI trigger more earthquakes over the following 2, 3 and 6 months (and lower values of SOI less earthquakes). As proposed by Walker (1999), we suggest that monitoring of seismicity in the EPR may have a utility as an independent (non-meteorological) means of predicting future El Niño events. In a broader context, robust statistical correlation between the ENSO and seismicity in the EPR provides a further example of how variations in the atmosphere and hydrosphere can drive very small changes in environmental conditions, which can, in turn, elicit responses from the Earth’s crust. While there are no hazard implications in this case, in a future warmer world similar small (a few kilopascal to a few 10 s kilopascal) pressure changes associated with ocean loading owing to rising sea levels, or atmospheric unloading as a consequence of more intense cyclones, may have the potential to trigger significant earthquakes at major, submarine fault systems that are in a critical state.
The authors gratefully acknowledge Seymour Laxon for his help in accessing the Topex/Poseidon data.
One contribution of 15 to a Theme Issue ‘Climate forcing of geological and geomorphological hazards’.
- © 2010 The Royal Society