Possible deep connection between volcanic systems evidenced by sequential assimilation of geodetic data

The existence of possible deep connections between nearby volcanoes has so far only been formulated on the basis of correlation in their eruptive activities or geochemical arguments. The use of geodetic data to monitor the deep dynamics of magmatic systems and the possible interference between them has remained limited due to the lack of techniques to follow transient processes. Here, for the first time, we use sequential data assimilation technique (Ensemble Kalman Filter) on ground displacement data to evaluate a possible interplay between the activities of Grímsvötn and Bárðarbunga volcanoes in Iceland. Using a two-reservoir dynamical model for the Grímsvötn plumbing system and assuming a fixed geometry and constant magma properties, we retrieve the temporal evolution of the basal magma inflow beneath Grímsvötn that drops by up to 85% during the 10 months preceding the initiation of the Bárðarbunga rifting event. We interpret the loss of at least 0.016 km3 in the magma supply of Grímsvötn as a consequence of magma accumulation beneath Bárðarbunga and subsequent feeding of the Holuhraun eruption 41 km away. We demonstrate that, in addition to its interest for predicting volcanic eruptions, sequential assimilation of geodetic data has a unique potential to give insights into volcanic system roots.

The description of the parameters, the corresponding values and references used in this study as well as 10 the results of the forward modeling are summarized in Table S2. Modeled displacements show that an 11 inflating source beneath Bárðarbunga can explain the displacements at DYNC station (Table S3 and 12 Figure S2) but not at GFUM station (Table S1 and Figure 2).

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Data assimilation using synthetic GPS data 14 We adopted the setup of ref.
[4] in generating the synthetic observations, except that in this case, we 15 only produce the radial component of a GPS time series measured at one station (i.e. at r = 3.5 km). 16 The frequency of incoming GPS observation is daily. Also, while generating the synthetic observations, 17 we assumed that after t step = 875 d, the value of Q in suddenly drops to zero such that the synthetic 18 displacement becomes constant afterwards (i.e. "Truth" in Figure S4). We considered a white In Figure S4, we demonstrate how the radial component of a GPS time series at one station 23 performs when tracking the sudden change of Q in using EnKF. For the context of data assimilation 24 experiments, we also presented the result of "Free-run" in Figure S4. Clearly, with EnKF we were 25 able to detect the sudden drop in Q in value, although it took time to approach zero.

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Testing different sets of uncertain model parameters as prior inputs to EnKF

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The set of best-fit values summarized in Table 1 and illustrated in Figure 4 is only one of the many 29 solutions that could satisfy the observed displacement we used for the inversion. The non-uniqueness 30 of the solution is a consequence of the poor spatial resolution of the dataset since we only have one GPS station at Grímsvötn with six uncertain model parameters to infer. However, our main goal is not 32 to find a unique solution to our inverse problem rather to obtain values that are consistent with the and ∆ρ are constant from one eruption to another so we adopted their values from case 1 and then 39 recalculated Q in , C and ∆P d,t0 using only the initial part of the 2011 radial displacement time series.
40 Figure S7 clearly shows that regardless of the set of prior values used as inputs to the EnKF scheme, 41 a sudden drop in the magma inflow rate is evident after the observed change of slope, ∼ 10 months 42 before the rifting event.    Note that the prior distribution of Qin used for the assimilation is also presented. Figure S5: The two-step strategy (i.e. inversion and data assimilation) implemented in this study. Note that step 2 (i.e. EnKF, enclosed in red box) is modified after ref.
[4]. The broken border and lines imply that the step is a tuning step for data assimilation.  Table 1 Figure S8C points at the deflected part of the surface displacement curve. This is similarly observed in the radial displacement contribution of the deep reservoir ( Figure S8B), implying that the measured radial displacement at 15km is mainly dominated by the deep reservoir. The black broken line marks the assumed change of slope prior to the start of the 2014 rifting event (tstep = 875 d). Table S1: Analyzed displacements at GFUM GPS station at the start of the rifting event (marked as the red broken line in Figure 2 in the main text). Linear Fit corresponds to the expected displacement value (black solid line in Figure 2 in the main text), and "Actual" means the actual displacement value.   Table S3: Analyzed displacements at DYNC GPS station at the start of the rifting event (marked as the red broken line in Figure S2). Linear Fit corresponds to the expected displacement value (black solid line in Figure S2), and "Actual" means the actual displacement value.
Linear Fit Actual Actual -Linear Fit