Corresponding author: S. K. Ebmeier, Centre for the Observation and Modelling of Earthquakes and Tectonics, School of Earth Sciences, University of Bristol, Bristol BS8 1RJ, UK. (firstname.lastname@example.org)
 A systematic survey of 3 years of L band interferometric synthetic aperture radar (InSAR) measurements of the Central American Volcanic Arc shows a striking lack of magmatic deformation. We make measurements at 20 of the 26 historically active volcanoes and demonstrate that none were deforming magmatically (2007–2010), although we do measure shallow subsidence associated with flow deposits and edifice loading at three volcanoes. The minimum detection rates for our survey, as estimated from the variance in time series of radar path delay, are relatively high due to strong variability of tropospheric water vapor. We compare the average detection threshold (2.4 cm/yr) to published InSAR measurements and show that the majority (~78%) of deformation events would have been measurable with the same level of noise as Central America. We calculate that if magmatic volcano deformation were spread evenly across historically active volcanoes worldwide, the probability of none of Central America's 26 volcanoes deforming would be < 1%. The lack of magmatic deformation in Central America may be indicative of differences in magma storage relative to other well-studied continental arcs. The high proportion of basalts that ascend directly from depth relative to andesites stored in the shallow crust may limit the potential for high magnitude deformation. Magma stored in vertically elongated reservoirs and high parental melt volatile contents that result in bubble-rich, compressible magmas at shallow depths may also reduce surface deformation. We consider the measurement and analysis of a lack of deformation at active volcanoes to be essential for realizing the potential of regional scale InSAR surveys.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 The development of satellite based Interferometric Synthetic Aperture Radar (InSAR) has allowed volcano deformation to be measured at a continental scale [e.g., Pritchard and Simons, 2004a; Fournier et al., 2010; Philibosian and Simons, 2011; Biggs et al., 2011; Chaussard and Amelung, 2012] (see Table 2 and Supplementary Tables 1–2). InSAR uses the difference in phase between two time-separated radar images to measure small displacements of the Earth's surface at a precision of up to a few millimeters (comprehensive reviews of InSAR techniques are given by Massonnet and Feigl  and Bürgmann et al., ).
 Deformation has now been detected with InSAR at over 100 volcanoes worldwide, with marked differences between the number of observations of deformation at different volcanic arcs [Fournier et al., 2010], which are not obviously related to the number of historically active volcanoes. This disparity may be the consequence of both differences in the applicability of InSAR measurement under different environmental conditions and differences in magmatic processes. The extraction of information about deformation from differential phase requires the identification of phase shifts from other sources, including variations in tropospheric water vapor, differences in satellite viewing geometry and scattering properties of the Earth's surface.
 Environmental conditions that affect InSAR measurement vary systematically between different parts of the world. In Central America, several contributors to interferometric phase are of especially high magnitude [Ebmeier et al., 2013]. For example, tropospheric water vapor has both higher magnitude and greater variability in the tropics than in equatorial zones [e.g., Heleno et al., 2010]. Dense, rapidly growing vegetation also limits the use of InSAR measurements.
 In this paper, we describe the results of an InSAR survey of the Central American Volcanic Arc (CAVA), using images from the Advanced Land Observing Satellite (ALOS) satellite, which has provided a significant set of radar data capable of penetrating tropical vegetation (2007–2010). In order to understand the significance of our measurements, we produce time series of radar path delay for 20 historically active volcanoes and calculate a minimum radar detectable rate for deformation at each (section 2.1). We then discuss the implications of the lack of measurable deformation at volcanoes that erupted during our survey (sections 4.1 and 4.2). Comparison of minimum detection rates with the magnitudes of deformation measured by InSAR at other well-studied volcanic arcs (Kamchatka, Aleutians/Alaska, Cascades, Mexico, Andes, Italy, Greece, and Sumatra/Java) suggests that the apparent lack of deformation in Central America is not primarily the result of measurement artefacts (section 5). In section 5.1, we discuss some of the factors that may limit the geodetic expression of shallow magma movement in Central America.
2 Systematic Survey of Central America
 We used the first significant set of radar data capable of penetrating tropical vegetation (L band, ALOS Phased Array type L band Synthetic Aperture Radar, PALSAR) to search for volcano deformation in Central America between 2007 and 2010. Earlier InSAR surveys of Central America did not detect any volcano deformation but were limited in scope by the poor coherence of C band data [Zebker et al., 2000] and the limited quantity of L band data analyzed in broader survey mode [Fournier et al., 2010].
 We were able to construct an average of ~15 ascending interferograms for each historically active volcano and supplemented this with descending data where possible. The Repeat Orbit Processing software (ROI_PAC) [Rosen et al., 2004] was used to construct interferograms, which were unwrapped using a branch-cut algorithm [Goldstein et al., 1988]. Topographic correction was carried out using NASA's Shuttle Radar Topography Mission 90 m digital elevation model, interpolated, and resampled to a spacing of 30 m.
 Interferograms showing all Central American volcanoes were examined visually for anomalous phase patterns, while phase around historically active volcanoes was scrutinized in more detail (Figure 3) (our systematic approach is set out as a flowchart in Ebmeier et al. ). Results were considered inconclusive where fewer than three interferograms were coherent over the volcano's edifice, so that phase changes due to deformation and atmospheric water vapor could not be distinguished. At volcanoes where we had sufficient numbers of coherent interferograms, we examined the relationship between phase and perpendicular baseline separation to test for artefacts introduced by errors in the digital elevation model used in processing. We then used pairwise logic [e.g., Massonnet and Feigl, 1995], stacking [e.g., Pritchard and Simons, 2004a], and time series [e.g., Lundgren et al., 2001; Berardino et al., 2002] to examine the temporal and spatial properties of phase and to distinguish between atmospheric delays and deformation.
 Time series of radar path delay were constructed using a least squares approach [e.g., Lundgren et al., 2001], where the minimum constraint was applied to velocity rather than displacement [e.g., Berardino et al., 2002]. It was explicitly assumed that no deformation was taking place on the first acquisition date so that displacements were calculated relative to this date. Figure 1 shows line of sight radar delay for the coherent area surrounding the volcano summits. This is calculated relative to the average delay for an annulus centered on the volcano with radii chosen to encompass as large a continuously coherent area as possible without including topographic features associated with the volcano being studied (average inner radius 5–6 km). Referencing to the average of an area rather than an individual pixel minimizes the impact of atmospheric variation at a reference point, so that time series reflect just the differences between path delay over the volcano itself relative to the rest of the interferogram. Where phase coherence is discontinuous surrounding a volcano, we may lack a far-field unaffected by volcano deformation. This means that deep sources of deformation that produce displacements of long spatial wavelength can be harder to detect with InSAR, especially where deformation rates are low. Uncertainties in the time series were found using a Monte Carlo approach, where randomly generated atmospheric noise of mean amplitude 1 cm was added before inversion, neglecting the effects of spatial correlation. Error bars in Figure 1 therefore primarily reflect how well each acquisition date is linked to the rest of the network. Gaps in the time series where it was not possible to link independent groups of interferograms are shown in Figure 1 as gray bars.
2.1 Systematic Approach to Deformation Reporting
 Most InSAR papers publish details of deformation signals but do not comment on volcanoes where no deformation was observed. To make a meaningful comparison between volcanic arcs, it is vital to distinguish between volcanoes with good quality data but that were not deforming and those at which data quality were too poor for any measurement to be made. We therefore conduct a systematic survey of all volcanoes in the region, defining the limits of detectability at each.
 The duration of a deformation event measurable with InSAR is limited by the spacing of radar acquisition dates, while its magnitude is limited by the contributions of other sources of phase change and the total length of the period of observation. In Central America, the greatest contributions to differential phase come from variations in stratified water vapor [Ebmeier et al., 2013].
 The temporal resolution of our data (46 days at best) is low enough that we do not expect to observe “recoverable” deformation, where the ground deforms and then returns to its original position [e.g., Watson et al., 2000; Dzurisin, 2003]. The ALOS data have large gaps (up to almost 18 months for Track 173, Figure 1) and are generally irregularly spaced through time. We therefore limit ourselves to the consideration of deformation causing “permanent” change to the Earth's surface.
 Deformation can be identified in a single interferogram if it either (a) significantly exceeds the magnitude of atmospheric noise (δ) or (b) is spatially distinctive from atmospheric phase features. Where deformation results in permanent change to the ground, signal-to-noise ratio can be improved by “stacking” interferograms together [e.g., Biggs et al., 2007]. A stack of N-independent interferograms is expected to have more noise than any individual image (δstack = ). Examples of stacks of interferograms from Nicaragua are presented in Supplementary Figure 1, and several individual interferograms from this data set are shown in Ebmeier et al. .
 We use the root mean square variation of our time series (e.g., Figure 1) as an approximation of the typical magnitude of atmospheric noise in an interferogram or sum of consecutive interferograms (where the atmospheric contributions of dates appearing in consecutive interferograms cancel out). This value reflects the variance in radar path delay over the volcano summit relative to the rest of each interferogram and thus captures the atmospheric variability better than an average of maximum variances for full interferograms. The minimum detection rate for each volcano is then t, where N is the number of independent chains of interferograms, and t is the total time spanned by all of the interferograms used.
 Of the 26 historically active volcanoes in Central America [Venzke et al., 2002], we were able to make measurements at 20 (77%) (Table 1). Interferograms covering the remaining six, Ilopango, Concepción, Rincón de la Vieja, Miravalles, Irazú, and Turrialba, are not sufficiently coherent.
Table 1. Survey Results for Active Volcanoes in Central America
Number of interferograms refers to the number processed and used during any stage of analysis, the numbers used in time series generation were sometimes lower due to variable coherence and difficulties in unwrapping.
VEI 1 (13.1.08, 12.1.09 and from 11.2009), phreatic explosions, fumerolic activity, landslides
inconclusive: poor coherence
increase in degassing and seismic activity preceded a VEI 2 eruption (5.1.10-24.7.10)
inconclusive: poor coherence
 We observed two volcanoes in the CAVA deforming as a result of loading processes: steady, downslope movement of young lavas at Arenal, Costa Rica between 2005 and 2009 [Ebmeier et al., 2010] and the subsidence of young lavas at Santiaguito lava dome in 2009–2010 [Ebmeier et al., 2012]. We also detected a region of slow subsidence at Masaya, Nicaragua, confined to a ring fault system identified through ground-based geophysical surveys [G. Caravantes et al., Structures controlling volcanic activity within Masaya Caldera, submitted to Bulletin of Volcanology, 2013]. Although deformation due to loading may mask low magnitude displacements of similar spatial pattern, we expect magmatic deformation to have a longer spatial wavelength and smoother shape than loading signals. We see no evidence of magmatic deformation between 2007 and 2010 in the coherent regions surrounding Masaya, Santiaguito, and Arenal (although our ability to detect long wavelength deformation is limited by interferometric coherence in some cases) [e.g., Ebmeier et al., 2013].
 A selection of apparent deformation time series for the summit areas of historically active volcanoes is presented in Figure 1. At volcanoes where data were coherent, we examined the temporal development of the apparent deformation signal to distinguish between characteristics typical of water vapor and those potentially caused by deformation. Some volcanoes (e.g., Santa Ana, Figure 1g) show “jumps” in apparent displacement associated with particular satellite images. Although conceivable that this is a rapid, reversible displacement, as the feature is associated with just one image, it is much more likely to be caused by unusual levels of water vapor at the time the radar image was acquired. Such high magnitude water vapor artefacts have commonly been observed at large volcanic edifices (Table 1) [Ebmeier et al., 2013]. A lack of systematic temporal structure in apparent displacement (e.g., Figures 1k and 1l) is also indicative of varying levels of water vapor [e.g., Ebmeier et al., 2013].
 The similarities between the temporal development of apparent displacement at Atitlán, Fuego, and Acatenango (Figures 1 c, 1d, and 1e) and, to a lesser extent, Izalco and Santa Ana (Figures 1f and 1g) are indicative of stratified water vapor and also illustrate the high hydrological loading on the easternmost volcanoes in Guatemala and El Salvador. A correlation between phase delay (water vapor concentration) and topographic height commonly leads to volcanoes of similar edifice height showing similar radar path delays. It also leads to a correlation between apparent displacement time series variation and edifice height (discussed further in Ebmeier et al. , interferometric phase-topography relationships are discussed by Remy et al. ; Elliott et al. ). Where water vapor is persistently stratified, interferometric phase may be highly coupled for volcanoes constructed from the same set of SAR images. Although we have not attempted to do so here, in such circumstances, it may be possible to use the commonalities in phase variation at different spatial locations to remove atmospheric contributions from a time series.
 Our estimations of detection thresholds presented in Table 1 and Supplementary Table 3 vary between 0.6 cm/yr (at Momotombo, Nicaragua) and 6.2 cm/yr (at Santa Ana, El Salvador), with an average value of 2.4 cm/yr. High thresholds for detection are associated with low numbers of interferograms (shorter total time covered by data) and with high magnitudes of stratified water vapor artefacts over the larger volcanic edifices (e.g., at Atitlan, Acatenango, Fuego, and Santa Ana).
 Of the 20 historically active volcanoes in Central America where InSAR measurement was possible, we demonstrate that 10 (~50%) did not deform permanently above a rate of 2 cm/yr and 16 did not deform above a rate of 5 cm/yr (~80%) between 2007 and 2010. No evidence of deformation associated with magma movement was found.
4 Comparison to Eruptive Record
 In total, 14 of the 26 historically active volcanoes in Central America exhibited some level of activity between 2007 and 2010, including periods of lava effusion (e.g., Pacaya), strombolian activity (e.g., Fuego, Arenal), high flux degassing (e.g., Masaya), and fumerolic activity (e.g., Santa Ana, San Miguel). Five volcanoes had minor explosive eruptions during the period of our observations (Figure 1, marked as San Cristóbal, Telica, Masaya, Concepción, and Poás). A summary of activity from 2007 to 2010 is outlined in Table 1.
 Instances of eruptions where deformation is not observed are underreported in the InSAR literature, but a summary of explosive events where no deformation was measured is presented in Supplementary Table 4 and includes eruptions of similar and higher explosive index than those that occurred during our survey.
 There were few reports of deformation at any of Central America's volcanoes during our period of observation (2007–2010), with the notable exception of tiltmeter and leveling measurements of a potential inflation (2007) and subsequent deflation (early 2008) at Turrialba, Costa Rica, associated with the development of new fumerolic vents [e.g., Martini et al., 2010; Smithsonian Institution, 2008]. As our InSAR data were almost entirely incoherent in the area surrounding Turrialba, comparison with these data did not allow us to refine our estimations of detection threshold. Broadband seismometers have been used to measure cycles of recoverable, near-vent deformation at Fuego (tilt begins ~ 25 min before explosion) [Lyons et al., 2012] and Santiaguito (eruptive cycle of ~ 1 h) [Sanderson et al., 2010] at both temporal resolution higher and magnitudes lower than those recoverable from our InSAR data.
 Previous ground based measurements of deformation in Central America seem predominantly to have captured low-magnitude, spatially limited signals. For example, one dry tilt instrument 1 km South of Poás' crater has shown a general trend of subsidence since measurements began in 1989 (~ 6 µrad/yr) [Smithsonian Institution, 1993a, 1993b] but electronic distance meter measurements made across the volcano summit have not detected significant changes [e.g., Smithsonian Institution, 1993a, 1993b, 2000]. Similarly, leveling measurements across Irazú's crater area captured a period of expansion in 1991–1992 (horizontal expansion rate of 1.3 cm/yr) [Smithsonian Institution, 1993c]. Repeat elevation measurements at gravity stations in Masaya caldera between October 1994 and September 2001 recorded variations in height of average standard deviation 3.6 cm/yr [Williams-Jones et al., 2003], but these measurements show no systematic trends consistent with large-scale inflation or deflation, and it is unclear whether they would allow the identification of either short-lived or localized deformation (such as that we observe within Masaya's ring fault). In contrast, Eggers  measured deflation of up to 20 cm at Pacaya in 1979–1980, magnitudes that would have been well above our InSAR detection limits had a similar episode occurred between 2007 and 2010.
4.1 Explosive Eruptions
 The mechanism by which an explosive eruption is driven determines the character of deformation, if in fact any deformation occurs. For example, rapid cycles of inflation and deflation can be driven by conduit pressurization building up beneath a crystallized plug before explosion (e.g., Montserrat, deformation period 6–18 h) [Voight et al., 1999]. Even more rapid deformation cycles are associated with the growth of bubbles and ascent of mafic magma in an open conduit (e.g., Stromboli, deformation period ~ 250 s) [Genco and Ripepe, 2010]. In Central America, explosions at Fuego [Lyons et al., 2012] and Santiaguito [Sanderson et al., 2010] are associated with conduit pressurization processes. This deformation is beyond the temporal resolution of the ALOS data used in this study (satellite repeat time 46 days).
 Minor explosions associated with the clearing of a blockage in a dominantly open system are also unlikely to result in high-magnitude deformation. Explosions at Masaya have previously been attributed both to such “vent-clearing” processes and to interactions with the hydrothermal system (e.g., 23 April 2001, VEI 1) [Duffell et al., 2003], and the event during our measurement period (18 June 2008, VEI 1) [Smithsonian Institution, 2009] is expected to have been similar in character. Phreatic eruptions at Poás in 2008 and 2009 may have been associated with similar processes. Recent deployment of continuous GPS at Telica allowed measurement during a series of ash explosions in May 2011 and showed little deformation [Witter et al., 2011]. The nonjuvenile composition of the ash from these explosions combined with the lack of deformation suggests that this eruption was amagmatic. If the similarly explosive eruptions at Telica and San Cristóbal during 2007 and 2008 were similar in character to this eruption, then it seems likely that there was no significant coeruptive deformation associated with these events. Although there is an intriguing uplift of ~ 4 cm at San Cristóbal in August 2009, this feature is associated with just one acquisition date. As we were unable to construct any interferograms spanning the time between 16 September 2009 and 4 August 2010, we are unable to examine the temporal structure of this signal and perform tests that would allow us to confidently identify it as deformation rather than water vapor artefact.
 The majority of coeruptive deformation events measured with InSAR to date have captured the accumulation, emptying, and/or recharge of a reservoir, most commonly at depths above 5 km and almost all above 10 km depth (Table 2 and Supplemental Tables 1 and 2). Many examples of deformation accompanying dyke intrusion (Table 2) and a few instances of conduit processes or summit caldera subsidence (e.g., at Lascar and Colima) [Pavez et al., 2006; Pinel et al., 2011] have also been captured by InSAR measurement.
Table 2. Summary of Published InSAR Measurements of Coeruptive and Posteruptive Deformationa
Max. Rate (cm/yr)
We include note of best-fit analytical source model, source depth and volume change. Events marked ‘a’ were pre-eruptive, those marked ‘b’ were posteruptive. Events marked ‘c’ were limited to summit area only.
 A comparison of the explosive eruptions covered by our survey (Table 1) and some examples of those from the global literature that have produced measurable coeruptive deformation (Table 2) are presented in Figure 2a. We limit comparison to coeruptive deformation where it was considered reasonable to approximate the deformation source mechanism as a point. Contours of equal surface displacement for a point source in a uniform elastic half space [Mogi, 1958] are marked in Figure 2 in red. The range of deformation detection limits found for Central American explosions (at San Cristóbal, Telica, Masaya, and Poás) is indicated by an orange bar. The potential range of positions for the 2007–2008 Central American explosions is shown as a gray box in Figure 2a and is based on the assumption that any associated volume change was less than 10−4 km3, the maximum volume change expected for a VEI 2 eruption. Even if explosions at San Cristóbal, Poás, and Telica (2007–2009) were associated with the deflation and subsequent recharge of shallow reservoirs, differing from the 2011 Telica eruption described above, the volume changes (<10−4 km3) would have been among the lowest measured with InSAR (e.g., Llaima and Slamet) [Bathke et al., 2011; Philibosian and Simons, 2011].
 Although eruptions between 2007 and 2010 did not result in permanent deformation above the level of atmospheric noise, historical eruptions in Central America have been significantly larger. Figure 2b shows 20th century eruptions of explosivity index VEI 3 and greater. Of these larger eruptions, we expect the 1902 eruption of Santa Marìa to have produced high magnitude surface deformation (>10 cm), and Arenal's 1968 eruption (of a similar volume to eruptions where InSAR measurements have been successful at Okmok and Chaitén) [Lu and Dzurisin, 2010; Fournier et al., 2010] to have resulted in deformation of the order of a few centimeters, high enough to potentially be detectable with this study's measurement limits.
4.2 Persistent Activity
 Persistently active volcanoes show evidence of significant surface activity (e.g., degassing, fumerole fields, high surface temperatures) over extended periods of time, without a large associated extrusive flux [Francis et al., 1993]. Central American volcanoes where mass flux estimated from SO2 degassing flux and melt inclusion sulphur content exceed effusion rate by 2 or 3 orders of magnitude include Masaya, Pacaya, and Telica. Such processes are thought to be maintained through the convective overturning of magma within a network of conduits, where buoyant magma loses volatiles and heat to the atmosphere (or overlying hydrothermal system) and sinks to accumulate in the shallow to mid-depth crust [e.g., as described by Locke et al., 2003]. The rise and fall of magma level in a rigid conduit takes place on a time scale of weeks to months (days for Strombolian activity) and is not accompanied by deformation for mafic systems where magma is of a low enough viscosity not to couple to conduit walls. Observations of such processes have been made from microgravity measurements at Telica, Poás, and Masaya and have captured changes in conduit magma level [Rymer et al., 1995; Williams-Jones et al., 2003; Locke et al., 2003] apparently unaccompanied by large-scale deformation. The accumulation of degassed magma is therefore the only component of typical “open” system behavior expected to produce deformation.
Francis et al.  suggest that the accumulation of degassed magma may result in endogenous growth due to localized emplacement into and beneath a volcano's edifice, a process that, if shallow enough, should be detectable as deformation. It has also been suggested that magma may return to cumulate complexes at greater depths [e.g., Locke et al., 2003] or be recycled in an active reservoir [Harris et al., 1999]. In Central America, gravity measurements have not uncovered shallow magma accumulation at Masaya or Poás, although small increases in gravity at Telica between 1994 and 2000 indicate an accumulation of material at depths below several hundred meters [Locke et al., 2003].
 Measurements of surface deformation will be more sensitive to localized accumulation than to dispersed intrusion. We use our InSAR measurements to make an order of magnitude estimation of the depth below which localized magma accumulation could be taking place without causing measurable deformation. We estimate mass flux of degassing magma at three persistently active volcanoes from average degassing flux (QSO2) and estimations of decrease in melt sulphur content assuming complete degassing (ΔCS), as described by Kazahaya et al. . This is converted to a magma volume flux (ΔV) using an assumed magma density (ρm) of 2800 kg m−3 as follows:
where QSO2 is average degassing flux of SO2 [Mather et al., 2006], MS and M are the molecular masses of S and SO2, and Qeff is the effused volume flux (as presented in Table 3). We estimate ΔCS, the decrease in magma sulphur content assuming complete degassing expressed in ppm, from melt inclusion analyses [Walker et al., 2003; Sadofsky et al., 2008]. We choose the highest measured value for magma sulphur content (closest to parental melt concentration) in each case and assume complete degassing. The mass and volume fluxes presented in Table 3 may therefore be underestimates. Our estimation of magma mass flux at Masaya (4 × 1011 kg/yr) is of the same order of magnitude as Stoiber et al.'s  estimate of mass flux for 1980–1982, 1.9 × 1011 kg/yr, which assumes that 75% of the magma's sulphur content is lost during degassing.
Table 3. Selected Persistently Active Volcanoes in Central America, Where Activity Is Characterized by Open System Activitya
Since 1524, Stoiber et al. . Extrusive flux over the past two decades has been much lower than this.
Stoiber et al.  found 320 ppm S in melt inclusions in scoria from 1981. This is very low for a basalt [e.g., Wallace, 2005], and is therefore probably not representative of parental melt composition. Volume flux at Masaya may therefore be a factor of ~ 3 lower than our estimates (see Figure 3).
 We use our estimated volume fluxes in conjunction with our threshold detection rates, (Vr) for Masaya, Pacaya, and Telica (1.3, 3, and 1.8 cm/yr, respectively) to make order of magnitude estimates of minimum accumulation depth using an elastic half-space point source model (Figure 3c). Minimum depth would then be:
where Vr is threshold detection rate, and ν is Poisson's ratio.
 There are high uncertainties associated with our calculation of magma volume flux, primarily as a result of (1) the use of SO2 flux (QSO2) measurements that predate our period of InSAR measurements, (2) the use of melt inclusion measurements of sulphur content (ΔCS) that may not reflect true parental melt sulphur content, and (3) uncertainties in the effusive flux. We use the standard deviation in measurements contributing to Mather et al.'s  1997–2003 mean of measured SO2 flux [e.g., Andres and Kasgnoc, 1998; Duffell et al., 2003; Zimmer et al., 2004] to approximate temporal variability in SO2 flux. We show the effect of one standard deviation difference on our estimations of minimum depth in Figure 3. We also include estimations of depths for Masaya both made from published sulphur content and using a value of 1000 ppm in Figure 3 to illustrate the potential uncertainties introduced by choice of magma sulphur content.
 However, our order of magnitude estimations suggest that there is no localized magma accumulation above depths of ~ 4 km at Telica and none above depths of ~ 10 and ~ 40 km at Masaya and Pacaya, respectively. This makes the unrealistic assumption of elastic behavior down to the base of the crust, so true minimum detection depths are expected to be shallower than this.
 Our results, in common with gravity data [Locke et al., 2003], suggest that there is no shallow, localized accumulation of magma at persistently active volcanoes in Central America. Degassed magma is therefore likely to be (a) returning to great depth and/or (b) dispersed through the mid to lower crust in a large number of individually small intrusions so that volume changes are too small to result in surface deformation. The greater the area over which degassed magma is distributed, the lower the rates of any resultant surface deformation.
5 Comparison to Other Volcanic Arcs
 We compare our results to published measurements of deformation at other volcanic arcs (Figure 4a), separating observations into magmatic and non-magmatic processes (such as loading effects and the deformation of flow deposits). Any statistical comparison that relies on examining the temporal distribution of InSAR deformation measurements is problematic, because observation periods are not commonly reported in the literature, especially where no deformation was measured. We therefore test the statistical significance of the lack of deformation observed in Central America with respect to the distribution of deformation at historically active volcanoes at other volcanic arcs. Our null hypothesis is that all historically active volcanoes are equally likely to deform in a manner measurable with InSAR. We use Fisher's exact test of independence [Fisher, 1922] to examine the probability that each arc in Table 4 is part of the global set of InSAR measurements. For our purposes, an exact test is favorable over criteria that rely on the sample distribution approximately matching a theoretical distribution (e.g., Pearson's χ2 test) due to the small sample size (P values set out in Table 5).
Table 4. Arc Scale Comparison of InSAR-Measured Deformationa
No. of InSAR Measurements
No of volcanoes
No. of Historically Active
% > Threshold
Bold numbers in parentheses indicate the number of measurements that would have been possible with Central American limits applied. References that describe large-scale surveys are included in the table, information regarding individual volcanoes is summarized in Table 2 and Supplementary Tables 1 and 2.
Pritchard and Simons [2004b]; Lundgren and Lu .
Table 5. Probabilities of Observing the Number of Deformation Events Found at 14 Volcanic Arcs (as in Figure 4) According to a Fisher's Exact Test With the Null Hypothesis that Deformation Is Evenly Distributed Around the Worlda
Each arc was compared to the rest of the global literature separately. Values for which the deviation from the null hypothesis is significant (i.e. distribution of deforming volcanoes is not spatially random) are underlined.
 We do not reject our null hypothesis for non-magmatic deformation (Figure 4b), as this is distributed relatively evenly between active volcanoes. The probabilities of the observed distributions of magmatic deformation arising randomly, however, are considerably lower, and we find statistically significant (at the 95% level) deviations in the numbers of measurements of deformation in Central America, the Central Andes, and Aleutian Islands (Figure 4c). In both the Central Andes and Aleutians, the number of observations of deformation exceed the number expected per historically active volcano, while in Central America, they are significantly lower than expected. If deformation measurements were distributed evenly across the world's historically active volcanoes, the probability of none of Central America's 26 historically active volcanoes deforming in a manner measurable using InSAR would be < 0.01.
 An obvious concern given the different time periods of observations is that the length of time over which InSAR measurement has been possible might control the number of observations of volcano deformation at each arc. We do not think that this is the case, because arcs with exactly the same temporal coverage of InSAR measurements show a range in number of deformation measurements. Specifically, the recent availability of L band data (since 2007) has allowed the first InSAR surveys of volcano deformation to be made for Java, Lesser Sunda, Sumatra, the Northern Andes, and Central America (Figure 4, marked with a star), with the number of measurements of magmatic volcano deformation being 4, 1, 3, 2, and 0, respectively [Philibosian and Simons, 2011; Fournier et al., 2010; Biggs et al., 2009b; Chaussard and Amelung, 2012]. For these arcs, where suitable data have only been available since 2007, only Central America shows any statistically significant undersampling for magmatic deformation. As published InSAR surveys do not generally report a lack of deformation, or catalogue where measurement was possible, for the purposes of our comparison, we treat all historically active volcanoes where deformation was not reported as not deforming. We assume that the occurrence of deformation is independent of the factors that control whether or not InSAR measurement is possible. If we recalculate our statistical test with data for just the 20 volcanoes in Central America, where we were able to make InSAR measurements, the probability of not measuring magmatic deformation in Central America is about 0.02 (significant at the 95% level).
 This result indicates a systematic difference in the occurrence of deformation measurable with InSAR on the CAVA, relative to other well-studied arcs. We investigate whether this difference is likely to be due to particular difficulties in making InSAR measurements by comparing published deformation measurements to the average minimum measurable rate for Central America (2.4 cm/yr) (Table 4 and Supplementary Table 3. This allows us to make estimates of the approximate percentage of deformation measurements that would have been possible with similarly high levels of atmospheric noise to Central America (Figure 4d). Although the large majority of published measurements would have been possible (~80%), a slightly lower percentage of magmatic deformation events (73%) exceed our average minimum detection rate than nonmagmatic events (86%). If we repeat the Fisher tests of independence including just those deformation events that would have been observable in Central America, the probability of no historically active volcanoes deforming in Central America is even lower than that shown in Figure 4b, with a P value much lower than 0.01.
 Our analysis suggests a statistically significant difference in the number of measurements of magmatic deformation made in Central America relative to other parts of the world. As ~80% of published measurements exceed the average minimum detectable rate for Central America, this may imply some difference in the average character of magma storage.
5.1 Limiting Factors for Surface Deformation
 The factors that control the geodetic expression of magma movement at an individual volcano are numerous and complex. Magma flux, composition, storage depth, storage geometry, and the existence of an open conduit are all important. Although there may be general commonalities in these factors for volcanoes in the same regional setting (e.g., Table 6), local conditions may be equally significant (e.g., reservoir geometry may be affected by local stress fields). Factors affecting the occurrence of deformation may also vary along the length of a volcanic arc. In Central America, the existence of systematic along-strike variation in geochemistry and tectonic parameters are well-established [Patino et al., 2000; Carr et al., 2003; Bolge et al., 2009]. We therefore limit ourselves to suggesting factors that may have the potential to contribute to low geodetic expression of magma movement that are applicable across all or most of the CAVA.
Table 6. Summary of Physical Characteristics of Tectonic Parameters for Selected Well-Studied Segments of Volcanic Arcsa
In Central America, extension has both arc-parallel (*) and arc-normal (§) components
10 ± 5
5 ± 3
3 ± 0.9 × 10−3
−5 ± 5
0 ± 1
0.2 ± 0.07 × 10−3
−1 ± 1
0 ± 1
0.26 ± 0.05 × 10−3
2 ± 1
0 ± 1
0.95 ± 0.04 × 10−3
0.4 ± 0.04
0.14 ± 0.01
0.14 ± 0.04 × 10−3
8* and 4§ ± 2
11 ± 2
3.1 ± 0.8 × 10−3
−1 ± 1
10 ± 8
1.3 ± 0.4 × 10−3
0 ± 2
23 ± 2
6.6 ± 2 × 10−3
 The CAVA has a high proportion of basalts to andesites [Carr, 1984] relative to other continental arcs, suggesting that more magma potentially rises directly from the base of the crust without a period of crustal storage. The large density contrast at the base of the Central American crust (thickness = ~25–45 km) is thought to trap basalts at depths well below those for which volume changes are commonly detected geodetically. Volume changes would have to be both localized and exceed volumes on the order of 107–109 m3 to produce deformation of the order of 1 cm magnitude. Basalts are thought to ascend rapidly from depth during eruption (e.g., at Fuego, Guatemala or Cerro Negro, Nicaragua), with the only exception being around Masaya in Nicaragua where thinner crust allows the ascent of denser, more mafic material that becomes trapped by less dense layers in the shallow crust [Walker, 1993]. As basalts are at least as common as andesites in Central America, a large proportion of volcanic activity may not involve any stage of storage in the shallow crust.
 The compressibility of bubble-rich magma can accommodate some or even all of the volume change associated with a magmatic intrusion, so that large intrusions can result in low magnitude surface deformation [e.g., Johnson et al., 2000; Mastin et al., 2009]. This effect is most significant for pressure changes involving evolved, gas-rich magma at shallow depths [e.g., Mastin et al., 2008]. Conditions that affect the compressibility of a shallow magma include its temperature, time of residence in the crust (and therefore crystal content), parental melt content, and the degree of degassing, i.e., remaining exsolved gas content. In the absence of a detailed knowledge of all of these conditions, the problem of magma compressibility in Central America is underconstrained. However, if exsolved gas content at shallow depths correlates with parental melt volatile content, perhaps where little to no degassing has taken place, then the distinctively high water contents inferred for Central American parental melts [Wallace, 2005; Sadofsky et al., 2008] may result in particularly high magma compressibility.
 Vertically elongated magma reservoirs, thought to be common beneath stratovolcanoes, produce lower magnitude surface deformation than spherical reservoirs for the same depth and pressure change. For example, comparison of a vertically elongated ellipsoid (Yang et al. , major axis = 4 km, minor axis = 1 km) to a sphere of the same volume and with the same centre depth and pressure change (8 km and 0.5 MPa, respectively) suggests that maximum line-of-sight surface deformation for the ellipsoid is only ~40% that of the sphere. We expect vertically elongated structures, including dykes, persistently open conduits and ellipsoids, to be favored in transtensional or extensional regimes, although the specific geometry of magma storage at any volcano will depend on a combination of both regional and local stress fields. Regional stress in the CAVA is dominated by dextral shear associated with the movement of the fore-arc sliver to the northwest [Correa-Mora et al., 2009; La Femina et al., 2009; Alvarado et al., 2011] and by east-west extension accommodated by north-south trending normal faults (Table 6, comparison to other arc settings). Many magmatic centers in Central America are located in extensional zones (e.g., Burkart and Self ). Evidence also suggests that magma reservoirs beneath a number of Central American volcanoes may be vertically elongated (e.g., evidence from polybaric fractionation at San Miguel, El Salvador and narrow reservoir radius at Telica, Nicaragua) [Carr, 1981b; Roche and van Wyk, 2001].
 Despite many significant and comprehensive studies of the geochemistry [e.g., Carr et al., 2003; Bolge et al., 2009] and tectonics [e.g., La Femina et al., 2009; Alvarado et al., 2011] of the CAVA, a more complete knowledge of magma storage conditions, including stalling depths, magma reservoir geometries, residence time in the crust, and the exsolved gas content of magma reservoirs is needed to explore the relevance and relative importance of these factors in limiting surface deformation. In combination with deformation measurement, such data have the potential to promote the development of a more systematic understanding of the relationship between magmatic intrusion and crustal deformation.
 We examine L band InSAR data (2007–2010) for the Central American arc and are able to make measurements at 20 out of 26 historically active volcanoes. We use stacking and time series analysis to distinguish between potential deformation and water vapor artefacts in interferograms and estimate threshold deformation detection rates using time series for the historically active volcanoes (section 2). We find no evidence of magmatic deformation in Central America between 2007 and 2010.
 The lack of deformation accompanying explosions at Telica, San Cristóbal, and Poás is unsurprising for such minor eruptions, presumably associated with very small, if any, reservoir volume change or involving little fresh magma (section 4.1). Recent high degassing fluxes and the lack of deformation at Pacaya and Masaya volcanoes suggest that there are no points of localized accumulation of degassed magma at shallow depths (<10 km) in the elastic crust beneath them. This suggests that magma (a) returns to depths below our limits of geodetic detection and/or (b) is dispersed through the crust in multiple smaller intrusions (section 4.2).
 Our quantification of detection thresholds for InSAR at Central American volcanoes confirmed a lack of magmatic deformation, found to be statistically significant in relation to the distribution of published magmatic deformation measurements with respect to historically active volcanoes. In spite of high levels of stratified atmospheric water vapor and resulting high threshold for detection (average rate 2.4 cm/yr), we expect the majority of volcano deformation rates measured with InSAR in other parts of the world to have been possible under Central American environmental conditions (section 5). Future analysis of InSAR measurements of volcano deformation will depend on the publication of observations of a lack of deformation, as well as a systematic treatment of the uncertainties associated with InSAR.
 We suggest several factors that have the potential to limit magnitudes of surface deformation associated with volcanic activity in Central America (section 5.1). These include deep magma storage and rapid ascent, the potential impact of high parental meltwater content on shallow magma compressibility and the influence of vertically elongated magma reservoir geometries. Such factors may act in isolation or combination to result in reduced magnitudes of surface deformation in Central America relative to other volcanic arcs.
 All ALOS-PALSAR data were acquired through the WInSAR programme at the University of Miami and are copyright of the Japanese Space Agency (JAXA) and the Japanese Ministry of Economy, Trade and Industry (METI). Data were made available by the U.S. Government Research Consortium (USGRC) and the Alaska Satellite Facility (ASF). This work was supported by the National Environmental Research Council through the National Centre for Earth Observation (NCEO), of which the Centre for the Observation and Modeling of Earthquakes, Volcanoes and Tectonics (COMET) is a part. SKE was supported by an NCEO studentship, and JB was funded by the ESA Changing Earth Science Network and a Rosenstiel Postdoctoral Fellowship at the University of Miami. SKE is now supported by the NERC Increasing Resilience to Natural Hazards project: Strengthening Resilience in Volcanic Areas (STREVA). Many thanks to Batuhan Osmanoglu and to Scott Baker for lots of early technical help. This manuscript was improved following insightful reviews by Yosuke Aoki and an anonymous reviewer.