Tara Shreve
email: tshreve@carnegiescience.edu

R Grandin

M Boichu

Reservoir depressurization driven by passive gas emissions at Ambrym volcano

Keywords: Subsidence, Degassing processes, Magma replenishment

Persistent volcanic degassing explains steady subsidence at Ambrym from 2015-

2017

• Subsidence ends in 2017, as magma influx balances depressurization from degassing

• We estimate a magma influx of ∼0.16 km 3 over 14 months before the 2018 eruption

Abstract

Despite being a widespread and common process, the impact of passive volcanic degassing on the pressurization state of a magma reservoir is not well understood. If mass loss due to gas emissions results in reservoir depressurization and surface subsidence, the pressure difference between a shallow reservoir and deep magma source may result in magma recharge and eventually trigger an eruption. It is therefore important to determine how a simplified reservoir-conduit system responds to such degassing processes. Here we use an extreme example of persistent volcanic degassing-Ambrym-as a case study to relate sulphur dioxide mass flux with reservoir depressurization and edifice-scale subsidence, both measured from satellite-based remote sensing observations. A geodetic inversion of surface displacements measured with Interferometric Synthetic Aperture Radar modeled using the Boundary Element Method provides bounds on the reservoir pressure change during an episode of subsidence at Ambrym from 2015 to 2017. These results are input into a lumped parameter theoretical model developed by [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF], and the free parameters (e.g., reservoir size and conduit radius) are systematically explored. We find that the 2015-2017 subsidence episode is consistent with pressure decreasing at a rate of -5.2 to -2.0 MPa year -1 in a reservoir at ∼2 km b.s.l., as a result of passive degassing. The subsidence episode is observed to end abruptly in October 2017, and no significant deformation is detected in the 14 months leading up to a rift zone intrusion and submarine eruption in December 2018, despite substantial degassing. We explain this lack of pre-eruptive deformation by an influx of ∼0.16 km 3 of magma into a shallow (< 2 km b.s.l.) reservoir that counterbalances the depressurization caused by degassing. This recharge volume is comparable with the volume of magma subsequently extracted from Ambrym's reservoir in December 2018. We conclude that at some open-vent passively degassing volcanoes, deflation caused by degassing may reduce or even cancel any inflation signal caused by magma influx. Nonetheless, detection of pre-eruptive recharge can be achieved by monitoring changes in the long-term deformation rate.

Introduction

Persistent passive degassing is observed at volcanoes worldwide [START_REF] Carn | A decade of global volcanic SO 2 emissions measured from space[END_REF].

From 2005-2015, of the 1500 terrestrial volcanoes with possible activity in the Holocene [START_REF] Siebert | Earth's Volcanoes and Their Eruptions: An Overview[END_REF], at least 6% (91) were passively degassing above the detection threshold of satellite measurements (∼30 tons day -1 ) [START_REF] Carn | A decade of global volcanic SO 2 emissions measured from space[END_REF]. Degassing-related hazards depend on gas composition, dispersion, and emission duration. In cases of persistent passive (non-eruptive) degassing, areas of >1000 km 2 (e.g., Masaya volcano, Nicaragua) can be affected by acid rain or noxious volcanic smog, as well as fluoride contamination of water [START_REF] Williams-Jones | Hazards of Volcanic Gases[END_REF][START_REF] Cronin | Environmental impacts on health from continuous volcanic activity at Yasur (Tanna) and Ambrym, Vanuatu[END_REF][START_REF] Allibone | Dental fluorosis linked to degassing of Ambrym volcano, Vanuatu: A novel exposure pathway[END_REF].

Cases of sustained high gas flux are mainly observed at volcanoes characterized by open-system degassing. In such systems, exsolved gas within a magma conduit or reservoir segregates from the melt and is released into the atmosphere during non-eruptive periods [START_REF] Cashman | Volatile controls on magma ascent and eruption[END_REF]. Theoretical models show that gas emission can result in a pressure change of a magmatic reservoir, and that pressure changes can also influence gas exsolution [START_REF] Tait | Pressure, gas content and eruption periodicity of a shallow, crystallising magma chamber[END_REF][START_REF] Boichu | A model for episodic degassing of an andesitic magma intrusion[END_REF][START_REF] Boichu | Degassing at La Soufrière de Guadeloupe volcano (Lesser Antilles) since the last eruptive crisis in 1975-77: Result of a shallow magma intrusion[END_REF][START_REF] Anderson | Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes[END_REF][START_REF] Kazahaya | Budget of shallow magma plumbing system at Asama Volcano, Japan, revealed by ground deformation and volcanic gas studies[END_REF]. As we show in this study, contrary to the inter-eruptive uplift typ-ical of the 'classic volcano deformation cycle' [START_REF] Biggs | Global volcano monitoring: What does it mean when volcanoes deform?[END_REF], eruptions may be counterintuitively preceded by periods of reservoir depressurization [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF][START_REF] Girona | Degassing during quiescence as a trigger of magma ascent and volcanic eruptions[END_REF].

From 2005-2015, Ambrym (Vanuatu), Kīlauea (Hawai'i), and Nyiragongo (Democratic Republic of Congo) volcanoes were among the ten strongest passively degassing volcanoes on Earth, influenced by the presence of lava lake activity [START_REF] Carn | A decade of global volcanic SO 2 emissions measured from space[END_REF].

At these open-vent volcanoes, surface deformation can be measured by satellite using interferometric synthetic aperture radar (InSAR). While deformation can be used to constrain reservoir overpressure through geodetic modeling, estimates must account for uncertainties on the host rock elastic moduli and reservoir geometry. Combining InSAR deformation measurements with remote sensing gas measurements may provide an opening for long-term studies linking changes in reservoir pressure (and potentially uplift or subsidence) and volcanic degassing. Our study demonstrates this possibility using a multiparametric approach to investigate the effect of volcanic degassing on reservoir pressurization at Ambrym volcano in Vanuatu from 2015-2018. Ambrym is a basaltic volcanic island which hosts a 12-km wide caldera and two main volcanic cones (Marum and Benbow), within which are semi-permanent lava lakes that have been active since at least the 1980's [START_REF] Robin | Top-Down Precursory Volcanic Seismicity: Implications for 'Stealth' Magma Ascent and Long-Term Eruption Forecasting[END_REF][START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF]. In particular, we investigate a period of inter-eruptive ground subsidence, coinciding with high gas flux, at Ambrym. The subsidence episode preceded a major intrusion crisis that led to the extinction of the lava lakes for more than 2.5 years (at the time of writing, February 2022) [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF], after they had been active for at least 3 decades.

To explore physical mechanisms explaining ground subsidence at Ambrym, we first estimate reservoir depressurization rates using geodetic modeling. Then, we use a lumped parameter theoretical model that couples gas emissions with reservoir depressurization, developed in [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF], to explain the estimated depressurization rates and their variation over time. This is the first time the theoretical model of [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF] is applied using observations at an active volcano. The effect of magma replenishment will also be considered to explain an abrupt change in depressurization rate that occurred around October 2017, 14 months before a large dike intrusion and submarine eruption that occurred in December 2018 [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF][START_REF] Hamling | Large-Scale Drainage of a Complex Magmatic System: Observations From the 2018 Eruption of Ambrym Volcano, Vanuatu[END_REF][START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF]. We posit that pre-eruptive reservoir pressurization, associated with magma recharge, may have been balanced by reservoir depressurization due to passive degassing, resulting in a net pressure change of zero prior to the 2018 rift zone eruption, explaining the lack of pre-eruptive uplift.

Data and Methods

2015-2017 Subsidence Episode and 2018 Eruption

InSAR measures ground displacements after a VEI 2 eruption in February 2015, when an intra-caldera vent opened and fed a lava flow (Figure 1a) [START_REF] Hamling | Goldilocks conditions required for earthquakes to trigger basaltic eruptions : Evidence from the 2015 Ambrym eruption[END_REF][START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF]. A time series is processed with the software MintPy [START_REF] Yunjun | Small baseline InSAR time series analysis: Unwrapping error correction and noise reduction[END_REF] using images acquired by the European Space Agency's satellite constellation Sentinel-1 (S1) (Figure 1a,b and Section 2.3). The first available Sentinel-1 image was acquired on 30 October 2015. The S1 time series and an interferogram from the Japanese Space Agency's satellite ALOS-2 spanning 21 March 2015 to 28 October 2017 both estimate a maximum subsidence velocity of ∼10 cm year -1 . An additional ALOS-2 interferogram indicates the subsidence began between March and June 2015 (Figure S1), after the February 2015 eruption (Section 2.3). The subsidence continued until October 2017, after which it ended abruptly (Figure 1b).

Starting 14 December 2018, 14 months after the end of the subsidence episode, an intra-caldera eruption began at Ambrym, followed by a rift zone intrusion and submarine eruption [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF][START_REF] Hamling | Large-Scale Drainage of a Complex Magmatic System: Observations From the 2018 Eruption of Ambrym Volcano, Vanuatu[END_REF][START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF]. Ambrym's caldera subsided by up to 3 meters, and the lava lakes were completely drained [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF][START_REF] Hamling | Large-Scale Drainage of a Complex Magmatic System: Observations From the 2018 Eruption of Ambrym Volcano, Vanuatu[END_REF]. Although >0.4 km 3 of magma was intruded into the rift zone [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF][START_REF] Hamling | Large-Scale Drainage of a Complex Magmatic System: Observations From the 2018 Eruption of Ambrym Volcano, Vanuatu[END_REF], causing drastic changes to the activity at Ambrym (e.g., lava lake drainage), less than 5 cm of precursory deformation occurred in the year before the event (Figure 1b). Despite a lack of pre-eruptive uplift, two primary observations indicate an increase in magma and gas supply to the system, which may have been precursors to the 2018 eruption. First, a new thermal anomaly ∼1 km to the south of the main lava lake hosted in Marum crater is detected using Sentinel-2 images sometime between 23 June 2016 and 10 March 2018 (Video S1). This indicates either a new vent for gas emissions or the presence of magma close to the surface, although discriminating between the two is ambiguous without additional observations. While the new vent may be a redirection of gas or magma that was already present at depth, its surface manifestation indicates a deviation from background activity. Second, the lava lake level rose rapidly in the weeks before the 2018 eruption, as documented by [START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF], which can indicate an increase in magma influx to the system, according to [START_REF] Patrick | A review of controls on lava lake level: insights from Halema'uma'u Crater, Kīlauea Volcano[END_REF]; [START_REF] Burgi | Recent Activity of Nyiragongo (Democratic Republic of Congo): New Insights From Field Observations and Numerical Modeling[END_REF]Global Volcanism Program (2017c).

2015-2018 SO 2 Gas Emissions

To estimate temporal variation of the sulphur dioxide (SO 2 ) budget emitted by Ambrym, we calculate the daily SO 2 mass by integrating OMI/Aura SO 2 Total Column over a 150 km-radius circular area centered on Ambrym. We use the Level 2 Version 003 lower tropospheric (TRL) products (corresponding to a center of mass altitude at 3 km [START_REF] Li | OMI/Aura Sulphur Dioxide (SO 2 ) Total Column 1-orbit L2 Swath 13×24 km V003[END_REF]), keeping pixels with a cloud fraction lower than 30% and a column amount greater than 0.3 DU, and removing acquisitions affected by OMI row anomalies. We also remove acquisitions affected by emissions from nearby Ambae volcano in 2017-2018, by discarding dates coinciding with a thermal anomaly at Ambae by MODIS (from MOD-VOLC [START_REF] Wright | MOD-VOLC: Near-real-time thermal monitoring of global volcanism[END_REF])), and by applying an additional automated procedure relying on the ratio between the gas mass around Ambrym and Ambae (see details in Text S1).

We observe that the daily SO 2 mass burden released passively by Ambrym remains nearly constant between the February 2015 and December 2018 eruptions (Figure 1b).

As shown in Figure S2, this observation is consistent with the steadiness of the annual mean SO 2 flux over the 2015-2018 time interval according to the NASA database (https:// so2.gsfc.nasa.gov/kml/OMI_Catalogue_Emissions_2005-2019.xls, updated following [START_REF] Carn | A decade of global volcanic SO 2 emissions measured from space[END_REF]). The consistency between SO 2 mass and flux also holds from 2005 through to 2019, even if SO 2 flux varied substantially before 2015 (Figure S2). This ex-cellent consistency indicates that our estimates of SO 2 mass burden at Ambrym, once averaged over several months, are a good proxy of, and nearly proportional to, the SO 2 flux. Since January 2019, SO 2 emissions have reduced to below the detection threshold of satellites, in stark contrast with Ambrym's persistent degassing over the past decade.

We conclude that the SO 2 flux at Ambrym remained essentially constant in the 2015-2018 time interval. Because the major volcanic gas species is H 2 O, we assume that the mean SO 2 gas flux in the 2015-2018 time interval (7 kt day -1 ) can reasonably approximate the mean water vapor gas flux using the mass ratio of H2O SO2 ≈ 15 from the average molar ratios obtained during two field campaign measurements of Ambrym's bulk gas emissions in October 2007 (Table 1 in [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF]). Since there are no estimates of this ratio during the time period of interest, we assume it is constant and discuss the possible effects of a 50% increase or decrease in H 2 O flux on our results in Section 4.1.1. We proceed under the assumption that Q = QH2O ≈ 110 kt day -1 .

Geodetic Inversion

To estimate magma reservoir depressurization, we invert surface displacements measurements spanning March 2015 to October 2017 measured by ALOS-2 and S1. Interferograms were processed using the Interferometric SAR scientific computing environment (ISCE) [START_REF] Rosen | The InSAR scientific computing environment[END_REF]. We multilook ascending S1 interferograms (Track 81) 36 times in range and 12 times in azimuth, filter with a power spectrum filtering strength of 0.3 and unwrap with SNAPHU [START_REF] Chen | Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization[END_REF]. The ascending ALOS-2 interferograms (Track 101) are multilooked 8 times in range and 16 times in azimuth, fil-tered with a power spectrum filtering strength of 0.2, and unwrapped with a coherencebased NSBAS module ("MPD") described in [START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF]. A 12 m TanDEM-X Global DEM is used to remove the topographic phase contribution [START_REF] Wessel | TanDEM-X Ground Segment -DEM Products Specification Document[END_REF].

We calculate an S1 InSAR small baseline time series using MintPy with 63 acquisitions to generate and invert 169 interferograms in radar geometry, with temporal baselines ranging from 12 days to 1 year (interferogram network shown in Figure S3) [START_REF] Yunjun | Small baseline InSAR time series analysis: Unwrapping error correction and noise reduction[END_REF]. It is common practice to fit and remove a phase ramp, which may be due to orbital or timing inaccuracies. However, we skip this step because the lack of a nondeforming reference area results in an unstable ramp estimate, which biases the displacement measurements. A comparison of different inversion strategies indicates no meaningful difference between an inversion with uniform weighting and an inversion weighted by the inverse of the phase variance, most likely due to the redundancy of the dense interferometric network (Yunjun et al., 2019) (Figures S3, S4, and Text S3). The two inversion strategies result in different temporal coherence estimates, which determine pixel masking (Figure S4), and we proceed with the time series weighted by the inverse of the phase variance. Finally, we correct the time series for atmospheric effects using the ERA-5 atmospheric model implemented in MintPy with the PyAPS software [START_REF] Yunjun | Small baseline InSAR time series analysis: Unwrapping error correction and noise reduction[END_REF]. The ERA-5 correction is an improvement to the empirical correction based on the relationship between phase delay and elevation (also available in MintPy), which causes spurious jumps in the time series (Figure S5).

Figure 1b shows the displacement time series (acquisitions every 12 days) for various locations at Ambrym from 30 October 2015 to 13 December 2018. Subsidence is mea-sured, elongated SE-NW within the caldera. The average velocity of the point of maxium subsidence is ∼10 cm year -1 , calculated from 30 October 2015 to 31 October 2017, after which subsidence ends. We note that the subsidence stops two months after a seismicity increase on 25 August 2017 (accompanied by a change in eruptive activity), according to a Vanuatu Meteorology and Geo-Hazards Department report (Global Volcanism Program, 2017a) (green vertical line, Figure 1b). Seismicity declined and eruptive activity stabilized by the end of November 2017 (Global Volcanism Program, 2017b). Using the Defvolc 3D Mixed Boundary Element Method (BEM) code [START_REF] Cayol | 3D mixed boundary elements for elastostatic deformation field analysis[END_REF][START_REF] Fukushima | Finding realistic dike models from Interferometric Synthetic Aperture Radar data: The February 2000 eruption at Piton de la Fournaise[END_REF] and Neighborhood Algorithm [START_REF] Sambridge | Geophysical inversion with a neighbourhood algorithm -I. Searching a parameter space[END_REF](Sambridge, , 1999a) (See [START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF] for a summary of the BEM and Text S2 for a description of the inversion scheme and uncertainty estimation), we perform a joint inversion of the Sentinel-1 velocity map and ALOS-2 ascending interferogram (scaled to obtain displacement in cm year -1 ). See Text S3 for a detailed description of data preparation for the geodetic modeling, which includes downsampling, estimating the data covariance matrix, and creating the topography mesh.

Model Coupling Gas Emissions and Reservoir Depressurization

Numerous theoretical models exist to explain pressure change due to degassing processes (i.e., volatile exsolution and escape from a magmatic system) [START_REF] Tait | Pressure, gas content and eruption periodicity of a shallow, crystallising magma chamber[END_REF][START_REF] Boichu | A model for episodic degassing of an andesitic magma intrusion[END_REF][START_REF] Boichu | Degassing at La Soufrière de Guadeloupe volcano (Lesser Antilles) since the last eruptive crisis in 1975-77: Result of a shallow magma intrusion[END_REF][START_REF] Anderson | Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes[END_REF]. In particular, a theoretical model developed by [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF] addresses the relationship between passive degassing and inter-eruptive reservoir depressurization on timescales of years. [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF] assume the reservoir is connected to the surface by an open conduit, and that the pres- Table 2: A description of the symbols used in Cases 1-3, as well as the ranges chosen for the parameters in this study. Symbols with no range presented are calculated from the defined parameters.

1.9 km b.s.l.

b.

Sentinel-1 velocity map sure in the reservoir equilibrates the weight of the magma in the conduit. Consequently, mass changes within the system (either in the conduit or reservoir) due to degassing result in reservoir depressurization, causing ground subsidence. This model takes into account whether volatiles are degassed from the conduit or reservoir, as well as the viscoelastic behavior of the host rock, magma replenishment, and magma density changes. We proceed with this theoretical model to couple passive degassing and reservoir depressurization at Ambrym volcano.

This model simplifies the relationship between mass loss by degassing and reservoir depressurization by assuming the following:

1. A magma reservoir is connected to an open, magma-filled cylindrical conduit with a fixed length L. The reservoir's magma pressure is magmastatic (Figure 3a).

2. Gas mass in the conduit is much smaller than the (incompressible) melt (liquid and solid phase) mass in the conduit (i.e., m m,c (t) m g,c (t)).

3. The melt in the conduit is a mixture of an undegassed parent melt and a denser, degassed melt.

4. Gas separation may occur in the conduit or reservoir. Without magma recharge, degassing can continue until the total degassed volatile mass equals that of the initial mass of bulk dissolved volatiles in the undegassed magma.

5. We assume a mean degassing rate Q that is constant over months to years. In Section 2.2, we demonstrate that the mean SO 2 flux is constant, while temporal variations in the H2O SO2 ratio are unknown and henceforth assumed constant.

6. Crystal content is neglected, temperature (T ) of the system is constant, gas solubility depends only on pressure, and the gas mass within the reservoir is calculated at a mean depth.

7. Melt volume decreases during degassing of H 2 O. No other volatiles are considered.

8. The host rock of the system is a half-space with a Maxwell viscoelastic rheology (with a bulk modulus k and an effective viscosity µ).

Using these assumptions, this model can be used to gain a first-order understanding of the relationship between a system's degassing flux and depressurization. We investigate whether this model can explain the reservoir depressurization estimated from geodetic models at Ambrym. We then discuss the role of magma replenishment and its effect on the reservoir pressurization rate.

Based on the first assumption above, the pressure change at the base of the conduit at time t can be written as

∆P (t) = P (t) -P (t 0 ) = g(m m,c (t) + m g,c (t)) πR c (t) 2 -P (t 0 ), (1)
where P (t) and P (t 0 ) are the pressure within the reservoir at time t and t 0 , m m,c (t)

is the melt mass within the conduit of constant length L (Figure 3a), m g,c (t) is the gas mass within the conduit, R c (t) is the conduit radius, and g is gravity. Equation 1 describes a pressurized reservoir which is sustaining the weight of the magma-filled cylindrical conduit, which acts on a surface area of πR c (t) 2 [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF].

Taking the time derivative of this equation, we can obtain the rate of pressure change:

d∆P (t) dt = g ρm,c (t)V m,c (t) πR c (t) 2 1 ρm,c (t)V m,c (t) ρg,c (t) dV g,c (t) dt + V g,c (t) dρ g,c (t) dt +ρ m,c (t) dV m,c (t) dt + V m,c (t) dρ m,c (t) dt - 2 R c (t) dR c (t)
dt .

(2)

We have substituted m m,c (t) = ρm,c (t)V m,c (t) and m g,c (t) = ρg,c (t)V g,c (t), where ρm,c (t), V m,c (t), ρg,c (t), V g,c (t) are the mean melt and gas density and volume in the conduit, respectively.

We further simplify Equation 2 by assuming an elastic host rock, a constant gas and melt density in the conduit ( dρ g,c (t) dt = 0 and dρ m,c (t) dt = 0), a conduit radius that does not change significantly over time ( dR c (t) dt = 0), and that the mean gas density in the conduit is significantly smaller than the mean melt density (ρ g,c (t) ρm,c (t)).

We then obtain:

d∆P (t) dt = g ρm,c (t) πR c (t) 2 dV m,c (t) dt . (3)
After considering the relationship between the volume of magma in the reservoir and the partial density of water in a silicate melt, ρ w , we can rewrite the above equation as:

d∆P (t) dt πR c (t) 2 g ρm,c (t) + V r (t) k r = - Q ρ w , (4)
which yields, by integration, assuming Q is constant, Equation 45 from [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF]:

∆P (t) = - g ρm,c (t 0 )k r Qt πR c (t 0 ) 2 ρ w k + gρ w ρm,c (t 0 )V r (t 0 ) . (5)
The full derivation can be found in Text S4.

Equation 5 can be used to compare the depressurization measured with geodetic modeling (average ∆P ∝ surface deformation) at Ambrym to the theoretical depressurization of the magmatic system by passive degassing (using Q as input, using OMI to measure SO 2 mass, then converting to H 2 O mass). The remaining parameters necessary to calculate ∆P (t) are fixed based on previous studies (Table 2-without magma replenishment, Cases 1-3-and Table S1-with magma replenishment, Case 4).

Results

Geodetic Source Estimation

We invert for the location, depth, axes lengths, and pressure change per year of a sub-horizontal ellipsoid beneath Ambrym's caldera (dip fixed to 0 • ). See Table 1 for the inverted parameters and final geometries. The final estimated source geometry is an ellipsoid elongated N • 147 at a depth of ∼2.8 km beneath the craters (1.9 km b.s.l., Fig-

ure 2). The northwest tip of the source is located beneath Benbow, and the source extends beneath the caldera for more than 9 km to the SE, oblique to the N • 110 rift zone.

The mean pressure change per year of the ellipsoid is -3.56 MPa year -1 , ranging between -5.2 to -2.0 MPa year -1 when including an error of one standard deviation from the mean (Table 1), given a Young's modulus of 5 GPa and Poisson's ratio of 0.25. The best-fit model has a pressure change of -2.15 MPa year -1 (Table 1). The Young's modulus is estimated from laboratory measurements, according to [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF], yet this parameter is still unconstrained at the scale of the volcanic edifice. These errors are propagated into both the geodetic and theoretical modeling. The Young's modulus may realistically range from 0.5 to 10 GPa. This will affect the estimated pressure change, due to the relationship ∆V r ∝ Vr∆P G [START_REF] Anderson | Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes[END_REF], where V r is the volume of the reservoir, ∆V r and ∆P are its volume and pressure change, respectively, and G is the host rock shear modulus. It follows that the pressure change of the best-fit model may range from -4.2 to -0.2 MPa year -1 . A pressure change of -4.2 MPa is within the range of uncertainties from the theoretical model discussed in Section 3.2, while -0.2 MPa could only be obtained with unreasonably large (V r > 300 km 3 ) reservoir volumes (Section 3.2 and Figure S8). Such uncertainties emphasize the sensitivity of this model to the volcanic conduit and reservoir geometries, which are often unknown. Future studies using seismic wave velocities to calculate the dynamic shear modulus, then converted to the static shear modulus (e.g., [START_REF] Grandin | Sequence of rifting in Afar, Manda-Hararo rift, Ethiopia, 2005-2009: Time-space evolution and interactions between dikes from Interferometric Synthetic Aperture Radar and static stress change modeling[END_REF], or using experimental studies of rock samples from the edifice (e.g., [START_REF] Heap | Towards more realistic values of elastic moduli for volcano modelling[END_REF], could further constrain the host rock properties.

Because the subsidence rate is approximately constant, we assume that the depressurization rate bounds of -5.2 to -2.0 MPa year -1 and the source geometry also remain constant. By combining the depressurization rate with the mean degassing SO 2 flux estimated in Section 2.2, we investigate whether a model coupling mass loss by passive degassing and reservoir depressurization reasonably explains these estimates. We acknowl-edge that other physical mechanisms may drive subsidence on time scales of months to years, including viscoelastic response of the reservoir tapped during the 2015 eruption (depending on the viscoelastic shell radius and whether the reservoir is refilled) [START_REF] Segall | Magma chambers: What we can, and cannot, learn from volcano geodesy[END_REF], as well as cooling and crystallization of magma (Caricchi et al., 2014;[START_REF] Townsend | Linking surface deformation to thermal and mechanical magma chamber processes[END_REF]. In addition, deformation rates can change abruptly due to energy released from seismic swarms, although typically this occurs during uplift episodes. We conclude that these mechanisms are unlikely because of the relatively short time period of subsidence (2.5 years), the high deformation rate (∼1 cm month -1 ), and the abrupt end to the subsidence.

Reservoir Depressurization Rate With No Magma Replenishment

We explore various cases to investigate the effect of the fixed model parameters on reservoir depressurization rate. This includes fixing whether the host-rock is either elastic or viscoelastic, or if gas exsolution occurs in the conduit or reservoir. Finally, we discuss the effect of magma replenishment on the reservoir depressurization rate.

Elastic Rheology (Case 1)

We calculate the theoretical reservoir depressurization rate at Ambrym in an elastic halfspace, for a range of reservoir volumes V r (t 0 ) and conduit radii R c (t 0 ), given a water vapor flux of Q ≈ 110 kt day -1 . The higher the gas flux Q, the higher the depressurization rate. We also explore a range of reasonable values for the free parameters. For example, the reservoir bulk modulus k r may realistically vary from 5×10 8 to 1×10 10

MPa. As k r increases, the host rock becomes more rigid. On the contrary, if the reser-voir is compliant, reservoir deformation helps sustain the reservoir's internal pressure.

Finally, we fix the initial bulk volatile content, α (used to calculate ρ w ; see Text S4), to 1.3 wt% [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF]. For a given Q, the lower the value of α, the higher the depressurization rate. This is because for a lower α, a greater volume of magma will need to lose gas to sustain the same Q. However, for a lower α, the melt density change after degassing would be smaller, which could partly compensate, or even counterbalance, the higher depressurization rate. The density of the parent melt is assumed to be ρ nd = 2430 kg m -3 and the density of the degassed melt is ρ c = 2670 kg m -3 (values implemented in [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF]). The influence of ρ nd and ρ c on depressurization rate is shown in Figure S6. Following [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF], we assume steady-state convection in a conduit that consists of 50% parent melt (undegassed) and 50% degassed melt, and the constant mean melt density is ρm,c (t) = ρm,c (t 0 ) = 2550 kg m -3 .

Figure 3b shows the theoretical depressurization rates for Case 1 when k r = 5× 10 8 Pa, Q = 110 kt day -1 , α = 1.3 wt%. According to Shreve et al. ( 2021), Ambrym's reservoir has a minimum size of 1 km 3 . For completeness, we assume a range of reservoir volumes from 1-35 km 3 and conduit radii from 10-700 m. While [START_REF] Allard | Degassing dynamics of basaltic lava lake at a top-ranking volatile emitter: Ambrym volcano, Vanuatu arc[END_REF] inferred a 3 m radius for the upper section of Benbow's conduit to sustain the magma convection needed to explain the SO 2 flux, there have been no direct measurements of the conduit diameter. We therefore investigate a wide range of conduit radii to explore the effect of this parameter on the model outputs. Our models indicate that the depressurization rates at Ambrym inferred from geodesy (between -5.2 and -2 MPa) can be reached for large conduit radii (R c > 400 m) when reservoir volumes are small (V r ≈ 1 km 3 ).

For larger reservoirs (V r > 12 km 3 ), the conduit radius connecting the lava lakes to the reservoir may be as low as 10 m.

3.2.2 Viscoelastic Rheology, Gas Exsolves in Conduit (Case 2)

Case 1 assumes an elastic half-space, and we wish to investigate how viscoelasticity affects the response of the host rock to mass loss by degassing. We still assume that there is no exsolved gas in the reservoir and introduce a host rock with a Maxwell viscoelastic rheology. Gas is exsolved in and degassed from the conduit of length L, which has an initial gas volume fraction β c = 0.1. As in Case 1, we impose steady-state magma convection in the conduit.

Despite the addition of viscoelasticity, for the range of parameters of interest (V r = 1-35 km 3 and R c = 10-700 m), no meaningful difference is noted between Case 1 and Case 2 (Figure S7). For larger values of V r , the solutions begin to diverge when the host rock becomes less viscous (µ ≈ 10 17 Pa s, Figure S7c). Aside from the minimum viscosity necessary to maintain topography, we have no constraints on this parameter for the host rock at Ambrym. Therefore, we proceed with Case 3 by setting the effective viscosity of the crust to µ = 10 18 Pa s (Table S1) and allowing for gas exsolution in the reservoir.

Viscoelastic Rheology, Gas Exsolves in Reservoir (Case 3)

We assume that gases may exsolve within the reservoir according to Henry's Law

(n r (t) = α-S[P (t 0 )-∆P (t)] 1 2 when α > S[P (t 0 )+∆P (t)] 1
2 ) (e.g., [START_REF] Huppert | The role of volatiles in magma chamber dynamics[END_REF]. Assuming the conduit is completely degassed (ρ m,c = 2670 kg m -3 ), and given that α = 1.3 wt%, S = 4×10 -6 Pa -1/2 for water, and that ∆P (t) P (t 0 ) = ρ m,c gL ≈ 52 MPa, the depth of the reservoir when gas exsolution occurs is L < 1 gρm,c ( α S ) 2 ≈ 400 m.

If we assume a slightly larger α (e.g., 2.1 wt% as estimated by Moussallam et al.

( 2021)), gas exsolution may occur at deeper levels, ∼1 km. This is still too shallow to exsolve bubbles in a reservoir residing at 2-4 km depth, as estimated for the shallowest levels of Ambrym's magmatic system [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF][START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF]. Geodetic inversions estimate a reservoir depth of ∼2 km beneath Ambrym's lava lakes. We can therefore conclude, according to Henry's Law, that there is no exsolved H 2 O in the reservoir. In this case, Case 3 will have the same result as Cases 1 and 2, where gas exsolution occurs within the conduit.

Reservoir Depressurization Rate With Magma Replenishment (Case

4)

In Section 3.2, depressurization rates estimated at Ambrym from geodetic observations can be obtained using the theoretical model for reservoir volumes > 12 km 3 . Using an end member scenario that is consistent with the best-fit mean depressurization rate of -2.15 MPa year -1 , we investigate the change in depressurization rate that occurred in October 2017. Between October 2017 (t 0 ) and December 2018 (t 1 ), we assume no net depressurization of the magmatic system ( d∆P (t 1 -t 0 ) dt = 0) because the time series displacements are within the data uncertainty (∼1 cm),. One possible mechanism that could change the depressurization rate is a decrease in passive degassing. There is, however, no meaningful change in the gas flux measured by satellite during this time period (Figure 1b and Figure S2). Therefore, we hypothesize that the depressurization rate change is due to magma replenishment from a deeper reservoir into the shallow reservoir, counterbalancing the degassing-induced depressurization and resulting in no net pressurization of the shallow reservoir. Building on the previous findings of Cases 1-3, we attempt to constrain the magma replenishment rate.

We address two possible scenarios:

1. The deeper source is not overpressurized (∆P s (t) = 0). Shallow reservoir depressurization results in a pressure gradient between the shallow and deeper sources.

Passive magma replenishment begins as soon as the depressurization began, at the latest in June 2015.

2. Alternatively, the deeper source is overpressurized (i.e., active replenishment, ∆P s (t) > 0). The deep and shallow sources become (instantaneously) connected in October 2017, and the deep reservoir overpressure remains constant.

Both scenarios will consider a viscoelastic behavior of the host rock. Therefore, we can no longer use the simplified Equation 5 to calculate the reservoir pressure change.

Without the simplifications of Equation 2 outlined in Section 2.4, d∆P (t) dt is instead expressed as

d∆P (t) dt = C 1 (t) + C 2 (t)∆P (t) C 3 (t) , (6)
where the constants C 1 (t), C 2 (t), and C 3 (t) are functions of the parameters in Equation 2(See also Equation 34 in [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF], which includes the rate of magma re-plenishment). The full expansion of these constants and a table of parameters used in this study can be found in Table 2, Text S5, and Table S1.

Following [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF], the pressure change in the shallow reservoir can be expressed with an equation of the form

∆P (t) = -∆P ∞ (1 -e -Γt ), (7)
where ∆P ∞ = C1(t0) C2(t0) and Γ = -C2(t0) C3(t0) , assuming C 1 (t), C 2 (t) and C 3 (t) do not vary significantly with time from their initial values.

The volumetric rate of magma replenishment is

dV rep dt = λ(t)(∆P s (t) -∆P (t)), (8)
where ∆P (t) is the pressure change in the shallow reservoir, ∆P s (t) is the deep source overpressure, and λ(t) is, as defined by [START_REF] Girona | On depressurization of volcanic magma reservoirs by passive degassing[END_REF], the hydraulic strength (or strength of connectivity between the shallow and deep reservoirs), as derived from the Hagen-Poiseuille law for the volumetric flow rate, given laminar fluid flow in a conduit [START_REF] Anderson | Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes[END_REF][START_REF] Mével | Magma injection into a long-lived reservoir to explain geodetically measured uplift: Application to the 2007-2014 unrest episode at Laguna del Maule volcanic field[END_REF].

λ(t) = πR d (t) 4 8M µ nd , (9)
where R d (t) is the radius of the dike connecting the deeper magma source to the shallow reservoir, M is the length of the dike, and µ nd is the viscosity of the replenished, undegassed magma. The maximum Reynold's number Re

= ρmM Vrep πR 2 d µm , given ρ m < 2700 kg m -3 , V rep < 5 m 3 s -1 , M < 15 km, µ m > 10 4 Pa s and R d > 2 m, is ∼1600
. This is smaller than the Re crit ∼2000 that defines the bounds between laminar and turbulent flow (Turcotte & Schubert, 2014).

The first scenario addresses passive replenishment, or when the deeper source is not overpressured (∆P s (t) = 0). Regardless of the input parameters, the depressurization rate decays exponentially (Equation 7). This decrease is not consistent with the abrupt pressure rate change observed in October 2017 (Figure S9). Therefore, we proceed with the model of active replenishment, considering instead an overpressured deep source (∆P s (t) > 0).

As mentioned previously, we assume that a hydraulic connection is created between the deep and shallow reservoirs in October 2017 (t 0 ), and the connection remains steady until the eruption in December 2018 (t 1 ). This hydraulic connection may occur when the pressure difference between the shallow and deep reservoirs reaches a critical value, after which any crystallized magma (i.e., a stiff plug) in the connecting dike begins to flow upwards [START_REF] Girona | Degassing during quiescence as a trigger of magma ascent and volcanic eruptions[END_REF]. As hotter material from the deep reservoir flows into the dike, the dike unplugs and the two reservoirs become hydraulically connected. This unplugging also occurs within two months of the seismicity increase noted by the VMGD (Figure 1b) (Global Volcanism Program, 2017a). As volume is lost during gas emission, the resulting pressure decrease in the shallow reservoir is compensated by a renewed magma inflow from a deeper reservoir, and a pressure balance is obtained in the shallow reservoir (∆P (t 1 ) -∆P (t 0 ) = 0). The replenished volume is calculated for each consecutive time step t n+1 using Equation 8, given the pressure state of the shallow reservoir at time t n , a fixed λ(t 0 ), and a ∆P s (t > t 0 ) > 0.

As stated in Equation 8, the volume of replenished magma (Figure 4a), is a function of the deep reservoir overpressure ∆P s (t), the dike radius and length, and the magma viscosity. Because we have no constraints on these parameters, we instead explore the tradeoff between the lumped parameter λ(t 0 ) (hydraulic strength) and the deep source overpressure ∆P s (t 0 ) (Figure 4c, assuming a V r = 29 km 3 and R c = 10 m, resulting in a shallow reservoir pressure change of ∼2.15 MPa year -1 ). A pressure balance occurs for a wide range of ∆P s (t 0 ) and λ(t 0 ). However, the volume of replenished magma does not vary based on the depressurization rate measured, because the melt volume decrease in the conduit-reservoir system when ∆P (t n ) = ∆P (t n+1 ) (i.e., no net pressure change)

is also constant and defined by 4a). In the case of no net pressure change, Equation 6 can be simplified to

dV m (t) dt = dV d (t) dt + dV rep (t) dt = - Q ρ w + λ(t 0 )(∆P s (t 0 ) - ∆P (t)) (Figure
d∆P (t) dt = 0 =⇒ Q ρ w -λ(t 0 )(∆P s (t 0 ) -∆P (t)) - ∆P (t) µ (V r (t 0 ) + V m,c (t 0 )) = 0, (10)
where volume change is determined by the balance between volume loss due to degassing, volume increase due to magma influx, and the viscous response of the conduit and reservoir. As shown in Figure 4a, the total replenished volume necessary to create a pressure balance ∆P (t n+1 ) -∆P (t n ) = 0 within the shallow reservoir is ∼0.16 km 3 over 14 months, or a magma supply rate into the shallow reservoir of ∼4.3 m 3 s -1 .

Discussion

Volume of Ambrym's Reservoir

Using a simplified conceptual model of a volcanic plumbing system (a single conduit hydraulically connected to a shallow reservoir fed by a deep source), the subsidence rates at Ambrym estimated with geodetic models can be obtained with a smaller reservoir volume (V r ≈ 1 km 3 ) and a conduit radius of >400 m. We consider this unrealistic based on studies showing that conduit radii are <200 m (e.g., [START_REF] Stephens | Transient deformation associated with explosive eruption measured at Masaya volcano (Nicaragua) using Interferometric Synthetic Aperture Radar[END_REF].

As mentioned previously, the upper section of Benbow's conduit is estimated to have a radius of 3 m [START_REF] Allard | Degassing dynamics of basaltic lava lake at a top-ranking volatile emitter: Ambrym volcano, Vanuatu arc[END_REF]. This narrow conduit would be consistent, given our calculations, with a magma reservoir volume >12 km 3 .

Previous estimates of Ambrym's shallow magmatic reservoir have ranged from 0.5 [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF] to 9.5 km 3 [START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF], with no estimates in the range of >12 km 3 . This may imply one of the following:

1. The model is oversimplified, and does not represent Ambrym's plumbing system, or 2. previous reservoir volume estimates are underestimated.

We address each of these possibilities in turn.

Model Parameters Affecting Depressurization Rates

Given the high gas flux at Ambrym, the geodesy-derived depressurization rates require a large reservoir because it will need to be subjected to a smaller pressure change to result in the same volume change due to gas emissions (recall ∆V r ∝ Vr∆P G ). In this study, the geometry of the reservoir-conduit system is simplified. We assume a single conduit extending from the surface to 2 km b.s.l., from which gas can exsolve and escape, causing magma convection in the conduit. Volcanic conduits have been imaged to depths of up to a few hundred meters within the edifice using muon tomography [START_REF] Tanaka | Cosmicray muon imaging of magma in a conduit: Degassing process of Satsuma-Iwojima Volcano, Japan[END_REF]), but at deeper depths (>1 km) magma ascent is thought to occur by porous flow through the thermally weakened, yet crystal-rich host rock [START_REF] Mckenzie | The generation and compaction of partial melts[END_REF]. In addition, Ambrym has two active craters with multiple vents that were passively degassing during the time period of interest, and their connection at depth is not understood. Throughout this study, we assume a single conduit connects the reservoir to the surface, which may oversimplify reality.

Another factor that affects the pressure change within the reservoir, but is not considered in this model, is magma compressibility. Withdrawal of a compressible magma from the system mutes reservoir pressure changes, because magma volume increases as the magma ascends and decompresses. Therefore, the magma density in the reservoir should be considered to account for this volume change, similar to Case 3 (when gas exsolves in the reservoir). However, using the pressure-dependent model based on Henry's law, no water vapor exsolves at depths of ∼2 km. Past studies of Ambrym indicate that magma compressibility in the reservoir may be higher than for gas-poor basalts [START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF][START_REF] Hamling | Goldilocks conditions required for earthquakes to trigger basaltic eruptions : Evidence from the 2015 Ambrym eruption[END_REF]. These results imply that magma compressibility at Ambrym may be high enough to cause larger reservoir volume estimates, but the full implications of magma compressibility are outside this study's scope.

In addition, due to the unconstrained depth of the deeper reservoir, we assume that InSAR surface displacements are only influenced by pressurization of the shallow reservoir [START_REF] Du | Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake[END_REF][START_REF] Rivalta | Magma compressibility and the missing source for some dike intrusions[END_REF]. Petrological constraints from previous work (e.g., [START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF]) based on melt inclusion entrapment pressures from the 2018 eruptive products indicate that magma may be stored at depths of up to 9.5 km b.s.l. Clinopyroxene barometry estimates a magma plumbing system that reaches depths of 14 km b.s.l. [START_REF] Firth | Variable conditions of magma storage and differentiation with links to eruption style at Ambrym volcano, Vanuatu[END_REF][START_REF] Sheehan | Staged storage and magma convection at Ambrym volcano, Vanuatu[END_REF]. However, given that only one melt inclusion from the 2018 eruption was used to estimate the depth of 9.5 km b.s.l. [START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF], we cannot robustly constrain the deeper reservoir location.

Assuming a spherical point pressure source [START_REF] Mogi | Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them[END_REF], an elastic medium, and the estimated magma influx (∼0.16 km 3 ), the reservoir would need a depth >25 km for subsidence to be <5 cm in the satellite LOS. This reservoir may be shallower than 25 km if magma compressibility results in muted ground displacements, however, as mentioned previously, we do not further explore effects of magma compressibility.

Finally, as mentioned in Section 2.2, the H 2 O flux used to estimate the depressurization rate is based on the assumption of a constant H2O SO2 ratio, as well as a SO 2 CMA at 3 km. If these assumptions are incorrect, the H 2 O flux used as input for the theoretical model would be biased. Therefore, we run the model for H 2 O fluxes ±50% (55 or 165 kt; Figure S10). The estimated reservoir volume is >5 km 3 for a conduit radius R c ∼ 10 m, and the total replenished volume is V rep = 0.077 km 3 when Q = 55 kt and 0.232 km 3 when Q = 165 kt.

Underestimation of Reservoir Volume Estimates

Previous studies have put bounds on Ambrym's reservoir volume using either magma chamber residence times [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF], or with geodesy [START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF]. The former estimated a minimum reservoir volume of 0.5 km 3 at depths of ∼3.8 km below the summit according to the magma influx rate needed to explain the mean SO 2 plume flux (∼7800 tons day -1 ) [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF][START_REF] Bani | First estimate of volcanic SO 2 budget for Vanuatu Island arc[END_REF]. [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF] acknowledge that this reservoir is connected to the lava lakes by a shallower plumbing system, which we hypothesize is the depressurized reservoir imaged with geodesy in this study.

In addition, they conclude that in order to accommodate the recycling of degassed magma, the magma plumbing system must be larger than 0.5 km 3 .

By relating geodetic models to the SO 2 flux measured by OMI satellite-based UV spectrometers, [START_REF] Shreve | What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption[END_REF] estimates that the minimum reservoir size is 1 km 3 , with possible reservoir volumes as high as 9.5 km 3 . However, these may also be underestimates, because they depend on the assumed host rock shear modulus, which is not well constrained at Ambrym. This study cannot further constrain the upper bound on the size of the degassed reservoir at Ambrym. Nonetheless, the results presented here are consistent with the conclusions that previous studies have underestimated the reservoir volume, and that it may be as large as 12 km 3 .

Magma Replenishment Prior to the 2018 Eruption

Magma Supply Rate

According to our study, approximately 0.16 km 3 of magma would have been needed

to replenish the shallow reservoir to counteract the subsidence from degassing, equivalent to a magma supply rate into the shallow reservoir dV rep dt ≈ 4.3 m 3 s -1 . In a previous study, [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF] estimates that 25 m 3 s -1 of magma is necessary to sustain the SO 2 flux released at the surface. However, the estimate from [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF] corresponds to the volume of the magma batch that loses its gas and is recycled deeper in the system per unit time. On the other hand, our estimate corresponds to the volume lost in this recycling process, due to density changes during degassing, hence representing a fraction of the recycled volume of [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF]. The ratio between the two estimates is approximately equal to a "shrinkage ratio" β = ρc-ρ nd ρ nd = ∆ρ ρ nd ≈ 10%, defined as the density increase of the magma due to degassing (see Text S6 for a detailed derivation).

The magma supply rate estimated in this study (4.3 m 3 s -1 ) is on the same order of magnitude as the mantle-driven surge in magma supply rate at Kīlauea in 2006, during the eruption from the Pu'u ' Ō'ō-Kupaianaha vent system which began in 1983 [START_REF] Poland | A mantle-driven surge in magma supply to Kīlauea Volcano during 2003-2007[END_REF]. The supply rate was estimated to range between 6-7 m 3 s -1 , depending on the assumed magma compressibility [START_REF] Poland | A mantle-driven surge in magma supply to Kīlauea Volcano during 2003-2007[END_REF]. This estimate was made using a calculation similar to [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF], with SO 2 flux used as a proxy for lava effusion rates and consequently magma supply rate [START_REF] Poland | A mantle-driven surge in magma supply to Kīlauea Volcano during 2003-2007[END_REF] also includes volume change due to geodetic modeling of uplift that occurred in 2006). However, at Kīlauea, the degassed magma is assumed to have erupted from the Pu'u Ō'ō vent (as opposed to being recycled) and been replenished at the same rate with magma from depth.

Therefore, these calculations are more comparable to our estimate than the supply rate estimated by [START_REF] Allard | Prodigious emission rates and magma degassing budget of major, trace and radioactive volatile species from Ambrym basaltic volcano, Vanuatu Island arc[END_REF].

Stealth Magma Replenishment

Recent conceptual models describe volcanic unrest and eruption (in particular initial conduit formation) in three phases. The first is "staging", which can occur either at the end of a previous eruption, during intereruptive time periods, or immediately preceding an eruption (Roman & Cashman, 2018). In the case of replenishment at Ambrym, the latter seems the most likely. Earthquakes detected in mid-2017 were the first indication of magma replenishment to shallower levels (Global Volcanism Program, 2017a), possibly indicating the shear failure of host rocks due to a magma intrusion. Further analysis of seismic data is necessary to discriminate between the processes causing seismicity in August 2017.

Around the same time, the number of active vents increased, also indicating a magma influx into the system (Video S1). After an increase in lava lake level [START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF], the shallow reservoir destabilized, causing the initial intra-caldera eruption of 14 December 2018, and eventually tapped the deeper magmatic system the following day [START_REF] Shreve | From prodigious volcanic degassing to caldera subsidence and quiescence at Ambrym (Vanuatu): the influence of regional tectonics[END_REF]. The deeper portion of the magmatic system (>6.5 km b.s.l.) fed the rift zone intrusion and submarine eruption, according to melt inclusion entrapment pressures [START_REF] Moussallam | How to turn off a lava lake ? A petrological investigation of the 2018 intra-caldera and submarine eruptions of Ambrym volcano[END_REF].

The pressure balance due to the combined effects of degassing and magma replenishment results in a low stress change on the host rocks, effectively equivalent to a "rate or volume that is too low/small to produce detectable seismicity" [START_REF] Robin | Top-Down Precursory Volcanic Seismicity: Implications for 'Stealth' Magma Ascent and Long-Term Eruption Forecasting[END_REF]. This demonstrates the possibility of a replenishment volume and rate that is large compared to other geodetically-derived magma replenishment rates (e.g., 187 ×10 6 m 3 over 7.3 years at Laguna del Maule (Le [START_REF] Mével | Magma injection into a long-lived reservoir to explain geodetically measured uplift: Application to the 2007-2014 unrest episode at Laguna del Maule volcanic field[END_REF]) without notable seismicity in the months prior to the eruption (according to VMGD reports).

Conclusion

This study attempts to quantify the influence of persistent degassing on the pressurization state of a magma reservoir, ultimately allowing for more accurate forecasts of future activity. The theoretical model is a simplistic view of reality (e.g., only one shallow reservoir and conduit, assumes steady conduit convection, etc.), but the uncertainties and tradeoffs presented in this study may be further reduced at a volcanic system with more instrumentation, or a longer time series of passive degassing and ground displacement.

Despite the theoretical model's simplifications, we can conclude that:

1. continuous passive degassing is a plausible mechanism to drive ∼2.5 years of reservoir depressurization and subsidence at Ambrym volcano, and 2. "stealth" replenishment of magma may have occurred in the 14 months prior to the 2018 eruption, resulting in a net pressure balance in the shallow magmatic sys-tem, explaining the abrupt cessation of subsidence in October 2017 and the absence of pre-eruptive uplift prior to the December 2018 eruption.

These findings have implications for the monitoring of Ambrym volcano. InSAR geodesy demonstrates a lack of substational uplift (<5 cm, Figure 1b) in the 12 days prior to the 2018 eruption. However, InSAR detected changes in the long-term deformation trend, in particular the abrupt end of a subsidence episode after 2.5 years. We interpret the subsequent lack of subsidence as indirect evidence for magma influx from depth in the 14 months preceding the 2018 eruption, a conclusion that cannot be drawn from degassing and thermal anomalies alone. As quantitative in-situ measurements (such as GNSS or gravity measurements and lava lake level heights) are seldom available, multiparametric remote sensing observations (radar, gas and thermal satellite imagery) provide an alternative means of detecting magma replenishment over time scales of months to years before eruptions.

Figure 1 :

 1 Figure 1: Time series of InSAR LOS displacement, thermal anomalies, and

Figure 1 :

 1 Figure 1: (cont.) The three triangles plotted on 21 March 2015 overlap at 0 m. At each

Figure 2 :

 2 Figure 2: Inversion results. a. Geodetic observations (top row), synthetic displace-

Figure 3 :

 3 Figure 3: Degassing-induced depressurization theoretical model. a. A schematic

Figure 4 :

 4 Figure 4: Effect of magma replenishment. a. The replenishment volume over time for three cases: an overpressurized and underpressurized reservoir (pink and blue lines, respectively) at t 1 (December 2018) and a reservoir with a pressure balance (grey line). b. The lower and upper bounds and

Table 1 :

 1 The estimated best-fit ellipsoid model parameters, as well as the mean model and uncertainties (one standard deviation from the mean). Obtained from jointly inverting the Sentinel-1 time series and ALOS-2 interferogram with Defvolc. The best-fit ellipsoid is visualized in Figure2.

	Symbol	Description	Range used in this study	Reference
	d∆P dt	pressure change rate during quiescence	-5.2 to -2.0 MPa year -1	This study
	Q	total mean gas flux	110 kt d -1	Carn et al. (2017), Allard et al. (2015)
	t	time of passive degassing	∼4 years	This study
	Rc	volcanic conduit radius	≤ 300 m	Allard et al. (2016)
	Vr	volume of the reservoir	5 × 10 8 -3 × 10 10 m 3	Shreve et al. (2021)
	L	length of the magma column (up to the average reservoir depth)	∼2 km	This study
	α	mass fraction of dissolved volatiles in parent melt	1.3 wt%	Allard et al. (2015)
	kr	bulk modulus accounting for chamber compressibility (Text S4)	5 × 10 8 -1 × 10 10 Pa	Heap et al. (2019)
	g	gravity	9.8 m s -2
	ρm,c	mean density of melt inside the magma column	2550 kg m -3	Girona et al. (2014)
	ρg,c	mean density of gas inside the magma column	≤ 200 kg m -3	Girona et al. (2014)
	ρc	density of fully degassed melt in the column	2670 kg m -3	Girona et al. (2014)
	ρnd	density of the parent undegassed magma	2430 kg m -3	Girona et al. (2014)
	γc	volume fraction of degassed melt in the magma column	0.5	Girona et al. (2014)

Acknowledgments

We thank the Japan Aerospace Exploration Agency (JAXA 6th Research agreement no. 3245) and the European Space Agency (ESA) for providing access to the radar imagery used in this study. A portion of the ALOS-2 data was provided under a cooperative research contract between Geospatial Information Authority of Japan and JAXA.

The ownership of ALOS-2 data belongs to JAXA. We would like to thank Francisco Delgado, Hélène Le Mével, Yan Zhan, Társilo Girona, and Patrick Allard for thoughtful discussions and insights which helped bring this manuscript to fruition. The authors would

also like to thank two anonymous reviewers and the editor for their constructive comments. Several calculations used the S-CAPAD cluster of IPGP. Marie Boichu would like to acknowledge support from the VOLCPLUME ANR project (ANR-15-CE04-0003-01). This project has also received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 665850.

We also acknowledge support from the FAIR-EASE project, which received funding from the European Union's Horizon Europe Framework Programme (HORIZON) under grant agreement No. 101058785. This is IPGP contribution number 4263.


domain: info spi

text:
Hamzeh Ahangari

Ihsen Alouani

Ozcan Ozturk

Smail Niar

Atika Rivenq

Register File Reliability Enhancement Through Adjacent Narrow-width Exploitation

Keywords: Register file, reliability, soft error rate, SER, narrow-width, 7T/14T SRAM

essential necessity. Consequently, finding suitable technique for RF reliability enhancement is a new kind of challenge when compared to cache memories.

In this paper, we propose a relatively different approach to exploit vacant spaces in RF to keep redundant data. This novel idea combines both architectural and circuit techniques to achieve more robustness in RF. Provided that one of two SRAM cells is vacant, meaning it is filled with a dummy sign bit, those two SRAM cells are joined together in circuit level by means of two transistors to make one more robust SRAM cell. The signals to apply such joining is issued by reliability control unit.

II. RELATED WORK

In some studies, register duplication is proposed. For example, in [START_REF] Memik | Increasing register file immunity to transient errors. InDesign, Automation and Test in Europe[END_REF] by means of register renaming unit, unused registers are detected and exploited to preserve redundant copies of other registers.

In-Register Duplication (IRD) is proposed in [START_REF] Hu | In-register duplication: Exploiting narrowwidth value for improving register file reliability. InDependable Systems and Networks[END_REF], [START_REF] Hu | On the exploitation of narrow-width values for improving register file reliability. Very Large Scale Integration (VLSI) Systems[END_REF] in which, by an opportunistic idea, dummy sign bits of narrowwidth register values are replaced with replication of meaningful bits during RF write operation. In read operation, replicated and original bits are bitwise compared to find mismatch as error indication. Additionally, two parity bits are embedded for each half. By means of both error detection mechanisms, which together are similar to a 2D parity system, they added error detection/recovery for narrow width values stored in RF. Nevertheless, long operands are not protected by IRD. If applied to 32-bit RF, this disadvantage is more serious, because long operands are frequent.

All of the above-mentioned works are architectural level ideas based on information redundancy and explicit comparison operation. The main difference of our work is that we combine a circuit level hardening technique with narrow width duplication. In addition to reducing SER, by clever replication in two paired registers, unlike IRD works [START_REF] Hu | In-register duplication: Exploiting narrowwidth value for improving register file reliability. InDependable Systems and Networks[END_REF], [START_REF] Hu | On the exploitation of narrow-width values for improving register file reliability. Very Large Scale Integration (VLSI) Systems[END_REF], we protect long operands better than previous works. Provided that a long operand is next to a short one, priority is given to long operand and replication of its more significant bits are done on dummy sign bits of short operand.

Abstract-Due to the increasing vulnerability of CMOS circuits, new generations of microprocessors require an inevitable focus on reliability issues. As the Register File (RF) constitutes a critical element within the processor pipeline, it is mandatory to enhance the RF reliability to develop fault tolerant architectures. This paper proposes Adjacent Register Hardened RF (ARH), a new RF architecture that exploits the adjacent byte-level narrowwidth values for hardening registers at runtime. Registers are paired together by some special switches referred to as joiners. Dummy sign bits of each register are used to keep redundant data of its counterpart register. We use 7T/14T SRAM cell [START_REF] Fujiwara | Quality of a bit (QoB): A new concept in dependable SRAM. InQuality Electronic Design[END_REF] to combine redundant bits together to make a single bit cell which is, by far, more resilient against faults. Our simulations show that with 3% to 12% power overhead and 10% to 20% increase in area, in comparison to baseline RF, we can obtain up to 80% reduction in soft error rate (SER).

I. INTRODUCTION

In recent years, as sub-micron technology dimensions sharply decreased to a few nanometer range, new types of challenges are introduced. Reliability of electronic circuits is one such concern which calls for more investigation. Since microprocessors are becoming more vulnerable to various types of faults than past.

By growing chip density, Soft Error Rates (SER) per system grows. Similarly in newer technologies, particles with lower energy are able to induce fault causing an increase in SER. Moreover, protecting microprocessors memory and sequential elements is critical because of its direct impact on systems reliability and data correctness. Cache memory, register file (RF), flipflop (FF) and latch are usual sequential parts of a microprocessor architecture, each of which requires its own suitable solutions for reliability enhancement. Both cache and RF are based on SRAM memory structure. However, since their characteristics and applications differ, their prevalent reliability techniques also differ. In caches, ECC is an effective technique for protection against faults. However, unlike cache, due to timing and power overheads, ECC is not an appropriate solution for register file reliability. In RF, activity rate per address is higher than cache memories, making power consumption more important. Additionally, RF is in processor's critical path and priority of performance is an

III. OUR ARCHITECTURE

Our approach tries to improve reliability of RF by exploiting unused bits of integer numbers in adjacent registers for hardening cells. For any number in range of minimum to maximum possible values in 2's complement system, only one single sign bit is sufficient for correct representation of the number. The remaining sign bits are just multiple copies of the same sign bit and are vain redundant bits. Based on this, instead of preserving multiple redundant bits for sign, we suggest to exploit them to enhance the reliability of adjacent registers. Adjacent Register Hardening (ARH) is very efficient to protect highly critical data within an application using dummy bits of non-critical registers. Since the content of registers are unveiled at run time, the extent of reliability increase is application dependent. Figure 1 shows that, on average, numbers with effective length of one byte constitute more than half of the numbers stored in the RF, in the tested benchmarks.

The implementation consists of retrieving the data to be stored, the technical solution to enhance reliability and perform the different read/write access. As detailed in next section, instead of relying merely on high-level architectural solutions, in our implementation we get benefit from a fast circuit level technique combined with higher-level architectural control, to build a highly flexible reliability solution.

A. Circuit Level Reliability Enhancement

7T/14T [START_REF] Fujiwara | Quality of a bit (QoB): A new concept in dependable SRAM. InQuality Electronic Design[END_REF] proposed combining two SRAM cells in circuit level to achieve more reliability or performance dynamically (Figure 2 left). According to this idea, two memory cells are joined upon request to store single bit of data. Joining is done by activating two transistors that connect the internal nodes of two cells to each other. For biasing toward reliability and not performance, just one of the two wordline signals is used for read or write operation [START_REF] Fujiwara | Quality of a bit (QoB): A new concept in dependable SRAM. InQuality Electronic Design[END_REF]. If joiners are not activated (CTRL="L", if switches are nMOS), then the proposed structure works normally as two separated conventional 6T SRAM cells. JSRAM cell [START_REF] Ahangari | JSRAM: A Circuit-Level Technique for Trading-Off Robustness and Capacity in Cache Memories[END_REF] is an extension of 7T/14T cell to combine four cells in a ring fashion to achieve full immunity against single bit errors by providing an auto correction mechanism (Figure 2 right). It is also capable of tolerating multiple bit upsets (MBUs). Since the reliability enhancement in our current work is in a statistical way and is dependent on the values stored in registers, using 7T/14T cell is more justified.

In our proposed architecture, adjacent registers of RF are joined together by 7T/14T technique. Generally, each bit can be joined to any number of bits from any register, by embedding multiple switches in between. Nevertheless, to avoid excessive area overhead and complexity, we limit this idea by just allowing each bit to be joined into a unique bit of a specific register. Thus, registers are paired together, bit by bit, during RF design. The benefit of pairing non-adjacent registers would be less probability of being affected by MBU, but obviously with more routing overhead. Currently we opt to combine neighbor registers.

B. Architecture Level Organization

To enhance the RF error resiliency, we take advantage of the reconfigurable aspect of the 7T/14T cell. Instead of relying on ECCs or extra memory space for reliability enhancement, we opt for an opportunistic approach that exploits unused bits within the stored data. To optimize the reconfiguration circuitry, as well as the additional bit cells, we opted for a byte-level granularity. Accordingly, the idle bytes are used to harden registers against errors.

Considering byte level granularity, a judicious one-to-one mapping between bytes of two registers is required to exploit the empty bits efficiently. Dummy sign bits are on the lefthand side (MSB side), while real data bits are on the other side. Thus, first obvious paradigm of mapping is in a crossed way, byte-0 of one register to byte-3 of the paired register, byte-2 to byte-1 and so on. However we've taken into account a second point in byte mapping. Faults in more valuable bits of an integer, lead to more absolute numerical error. While the best mapping is application dependent, we extracted the distribution of operand length for our benchmarks as had been shown in Figure 1. Operands with lengths of one byte and four bytes are dominant ones. Then paired registers of length oneone, one-four and four-four are more frequent. This means byte mapping has to be biased toward protecting one-one and one-four combinations (four-four can not be protected). Hence, Fig. 3. Top: Three bytes of "ZYXW" number in reg-i are replicated in sign bits of reg-i+1. "V" number in reg-i+1 is not replicated. Bottom: easy routing by byte reordering. by limiting ourselves to at most four groups of byte-to-byte joiners, we take mapping of Figure 3 as most efficient one which leads to better RF error resiliency. For a 32-bit RF, four control signals are required for controlling this mapping.

One superiority of our work in comparison to In-Register Duplication (IRD) works is that, by pairing registers, ARH can protect long operands. For example, in Figure 3, reg-i occupies four bytes and three of these bytes are protected by reg-i+1 which occupies only one byte. However in IRD, long operands which represent larger integers are not protected.

Below, we describe the mechanism for basic write/read operations:

1) Write Access: Mechanism behind the write operation is critical to achieve efficiency. During write operation, only meaningful bytes are written, while dummy sign bits should not be written and respective bytes in register are left intact. Because those bytes may be keeping the redundant data of the other paired register. This can be satisfied by having byte selectable write enables. Besides this, when those meaningful bytes are being written, while their counterpart bytes in the other register are not in use, in this situation control signal of joiners have to be activated. According to electrical characteristics of 7T/14T cell, if joiner is activated and one of the paired cells is written, the other one is written automatically as well. By exploiting this property, by single write operation, redundant data is quickly written at the same time into the redundant byte of the other paired register.

Above-mentioned mechanism requires modification to ALU and RF decoder. The ALU should simply detect effective length of integer numbers. In addition to storing data within the targeted register address, 2-bit effective length value (EL) is also stored beside the register (Figure 4). Considering EL value, only write enable signals of necessary bytes are activated, allowing writing the data with size of effective length into register.

By means of available EL value of the paired register (paired register of the register which is being written), unused bytes of paired register are determined to store redundant data. Then proper control signals are generated by a simple two-level AND-OR circuit.

During the write access, the reliability controller unit sets the configuration to adapt the available idle bytes to protect the data which is being written. Although extra circuitry of reliability controller is on critical path, by combining it with decoder during logic synthesis, the delay overhead is minimized. For easier routing, bytes of one of registers can be reordered. The required multiplexer is in parallel with decoder and not inside critical path (Figure 4 left).

2) Read Access: The read access architecture is modified to cope with the reliability enhancement process. Once a register's idle bytes are exploited for hardening cells, they should be replaced with actual sign value during the read access to insure data integrity.

As shown in Figure 4 right, the reliability controller unit selects whether the forwarded data would be the "directly read byte" or the "sign byte", depending on the register effective width. If the byte-reordering has been already employed in write operation, actual order have to be recovered again. To avoid the timing overhead of sign bit detection, sign bit can also be stored explicitly like EL in write operation. Otherwise, sign bit has to be determined by finding MSB bit of most significant byte in read operation. All these are performed by a multiplexer as depicted in Figure 4 right. This multiplexer selects one of four inputs: directly read byte, reordered byte, all 0/1 for sign extension of positive/negative numbers.

IV. EXPERIMENTS

To confirm the circuit functionality and calculate area and power overheads, simulation with HSPICE was performed with 22nm predictive technology model library [START_REF]Predictive technology model[END_REF]. Transistor sizes for typical 22nm SRAM cell were chosen from [START_REF] Shin | Advanced MOSFET designs and implications for SRAM scaling[END_REF]. Ratio values are: cell ratio = W P D/W P G = 2.02 and pullup ratio = W P U/W P G = 1.18. Wordline pulse width is chosen as 1ns.

We selected typical values of original SER and improved rates using 7T/14T SRAM cell form [START_REF] Fujiwara | A dependable SRAM with 7T/14T memory cells[END_REF] and [START_REF] Yoshimoto | Bit error and soft error hardenable 7T/14T SRAM with 150-nm FD-SOI process[END_REF]. Although those experimental results are related to SRAM chips fabricated in different technologies (65nm and 150nm), we only considered the improvement ratios, not the exact values, as an approximation. Although SER per system increases sharply by technology size reduction, but SER per memory bit grows gently [START_REF] Baumann | Soft errors in advanced computer systems. Design and Test of Computers[END_REF]. Therefore, sensitivity of improvement to technology is not expected to be high.

In this section, the system-level experimentations are presented for a typical 32 x 32 bit register file, where power oriented experiments were conducted. In order to get accurate simulation results, a WATTCH power simulator [START_REF] Brooks | Wattch: a framework for architecturallevel power analysis and optimizations[END_REF] was modified by estimating the cycle-accurate power consumption using HSPICE results. Hence, cycle-level simulations based on a 5-stage pipeline out-of-order processor modeled by a SimpleScalar simulation environment [START_REF] Austin | SimpleScalar: An infrastructure for computer system modeling[END_REF] were performed. We extensively modified the simulator code to support the proposed reliability enhancement technique.

For this evaluation, benchmarks from two different sets of applications, namely the SPEC CPU2000 benchmark suite [START_REF]Spec cpu2000 benchmarks[END_REF] and MiBench [START_REF] Guthaus | MiBench: A free, commercially representative embedded benchmark suite[END_REF], were compiled for the Alpha instruction set architecture.

To evaluate the error resilience of ARH RF, we developed an exhaustive fault injection platform where the injected error locality is randomly defined. Considering again the benchmark distribution depicted in Figure 1, and referred SER of protected and unprotected bits, normalized error rates are shown in Figure 5.

The increase in static power because of joiner switches is negligible. Our power consumption simulations show that the overall power overhead does not exceed 12% in the worst case.

Operand detection circuit is very simple and it has no effect on latency. For each pair of bits, two switches are added in between them. Depending on type of switches and number of read and write ports of RF, area overhead is indicated to be around 10%-20% [START_REF] Fujiwara | A dependable SRAM with 7T/14T memory cells[END_REF].

V. CONCLUSION AND FUTURE WORK

In this work we proposed a novel narrow-width register duplication technique. By a new approach, we exploit dummy sign bits for hardening data bit cells at circuit level, benefiting from configurable 7T/14T SRAM cell structure. According to the proposed technique, adjacent registers are paired together. Nonsignificant bits of one register are exploited for reliability enhancement of the other register. This aspect not only affords protection to long-length values but also is very efficient in critical data protection. Results show that by benefiting from considerable SER improvement of 7T/14T and a judicious byte pairing, error rates of integers stored in RF are reduced significantly in comparison to baseline RF.

Fig. 1 .

 1 Fig. 1. Distribution of effective length of numbers in 32-bit RF in some benchmarks.

Fig. 2 .

 2 Fig. 2. Left: 7T/14T memory cell with nMOS joiners [6] right: JSRAM cell with nMOS joiners [1].

Fig. 4 .

 4 Fig. 4. Left: Write Access Circuit, Wordline and Joiner Signals Right: Read Access Multiplexer

Fig. 5 .

 5 Fig. 5. Normalized error rate of ARH RF vs conventional RF.


Jimmy Petit

François José Rouillard

François Cabestaing

Somatosensory Gating for an SSSEP-based BCI

come

What is Sensory Gating? [START_REF] Voisin | Is somatosensory excitability more affected by the perspective or modality content of motor imagery?[END_REF] Sensory gating, or gating, is the capacity of the brain to filter out stimuli perceived as irrelevant during a goal-oriented activity.

Idea of an SSSEP-based BCI exploiting Somatosensory Gating

III V VI

What are SSSEP?

A sustained vibrotactile stimulus of the skin produces resonance-like evoked potentials named Steady-State Somatosensory-Evoked Potentials or SSSEP. They appear as an increase of activity at the frequency of stimulation.

  Observed effect (subject #10) Screening results (subject #10) Somatosensory Gating for an SSSEP-based BCI Jimmy Petit 1 , José Rouillard 1 & François Cabestaing 1 1. Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France Centre de Recherche en Informatique, Signal et Automatique de Lille

•

  Performing Motor Imagery (MI) with one or two arms. • Sustained vibrotactile stimuli on both wrists produces two SSSEP. • The Gating resulting from the MI should decrease the amplitude of the respective SSSEP. • The amplitude of the two SSSEP are used as classification features. Mandatory step: Screening procedure 2,3 • Objective: Identify the stimulation frequency with the highest SSSEP. • How: Train of stimulations of 2 s, at different frequencies: from 14 to 32 Hz. • Amplitude estimation: fast Fourier Transform. Illustration of a command selection in this context Motor Imagery with the right arm: An experiment to test the Somatosensory Gating for an SSSEP-based BCI Setup: • Subject is sitting in front of a computer. • Frequency of Stimulation (FOS) identified during a screening session. • C-2 Tactors tapped to both wrists 4 . • EEG amplifier & Laptop: powered by batteries. Experimental Conditions: • Stay IDLE. • Performing Motor Imagery (MI) with one arm. Signal Processing: Preprocessing: • Non-causal highpass filter at 5 Hz. • Peak-to-peak signal amplitude for eye blinks detection. Trial removed, if significant. Subject #10: ≈ 15% of data rejection. Amplitude estimation: • Narrow non-causal bandpass filter. • Signal squared. • Smoothen by a moving average (window length = 30 x FOS periods).

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