Sampling on the field: andesites, dacites and banded samples
Samples were collected in the pyroclastic deposits of the 2010–2013 eruption (Fig. 1a) during a three-week field mission which took place in August 2019. Samples coordinates can be found in Supplementary Table 2.
Sample preparation
The unaltered dacitic and andesitic samples were crushed (up to 3 mm). One half was then crushed again into fine powder for whole rock analysis while the other half was sieved into different size fractions (1 mm-710 µm, 710 − 500 µm, 500 − 355 µm, 355 − 250 µm, 250 − 125 µm). These fractions have been washed in ultrasonic bath and dried at 80°C for 48h. They were then observed under the binocular microscope to select the fractions in which the crystals were the more abundant and automorphic. Opx, plagioclase (plag), magnetites (mgt) and amphiboles (amph) were then handpicked under the binocular microscope in the different size fractions. They were mounted in epoxy resin and polished up to 0.3 µm to the middle part of the crystals. Opx were oriented with c-axis in a north-south direction as they have been used for intracrystalline diffusion modelling19,25,55. Before scanning electron microscope (SEM) or electron microprobe micro-analyzers (EPMA) investigations, selected mounts were all carbon-coated55.
Textural observations: Scanning Electron Microscope
Opx were observed under Scanning Electron Microscopes (SEM): Zeiss Supra 55VP (Sorbonne Université, Institut des Sciences de la Terre de Paris, ISTeP, Paris) and the Carl Zeiss EVO MA10 SEM at the PARI platform at the Institut de physique du globe de Paris (Université de Paris) using an acceleration voltage of 20kV and a beam current of 8 nA. An identification of possible chemical zonations in the crystals (grey levels of different intensities) was possible in order to position the rim-core profiles to be carried out with the electron microprobe for opx. Proportions of zoned/unzoned opx crystals have been determined on all the crystals mounted by looking closely at the SEM images.
Higher resolution images (mag x755) were taken for the diffusion modelling and intercalibration with chemical profiles of opx with the same parameters as mentioned above, a high integration line (N = 7, 7 integrations of each image line to reduce the impact of noise) and a dwell time per pixel of 48 µs.
Compositional analysis of crystals
Whole rocks
Whole rock major-element compositions were analyzed by ICP‐OES at Centre de Recherches Pétrographiques et Géochimiques (CRPG) in Nancy56.
Point measurements
Opx crystals have been analysed for major elements (Si, Al, Ca, Mg, Na, K, Ti, Fe, Mn et P) by electron microprobe micro-analyzers with an acceleration voltage of 15 kV, a beam current of 10 nA and a focused beam of 2 µm (CAMECA SX-Five and SX-100; Service Camparis, Paris). Counting time on peak and background for Fe and Mg was set at 80s and at 10s for the other elements. The core to rim compositional profiles in zoned opx had a 2 µm step and an average length of 100 µm (~ 4 hours per profile). Four points were measured across the unzoned crystals. They were acquired perpendicular to the long axes of the opx and away from the corners to avoid three-dimensional effects such as growth28,55,57,58.
For compositional analyses in magnetite/ilmenite pairs to estimate the temperature, the counting time was set at 30s for Fe, Ti and Al and 10s for the other elements.
Timescales of magmatic processes
To investigate the changes in crystallization conditions in time and date the magmatic processes, interdiffusion timescales are modelled following the shapes of the concentration’s profiles in opx and width of the diffusion zone between the plateaus. Using second Fick’s law, if the initial conditions, boundary conditions and diffusion coefficient of the elements are known, fitting of the profiles can be used to obtain the timescales. The diffusion coefficient depends on parameters such as chemical composition (Xi; molar fraction of the mineral constituent element), temperature (T in Kelvin), pressure (P in Pa), oxygen fugacity (fO2) and water fugacity (fH2O)6,7.
Modelling of the timescales associated to the zonations in the zoned crystals has been done by using the method developed in other studies57,59, using the parametrization of the interdiffusion coefficient D of Fe and Mg elements in opx60. The Fe-Mg interdiffusion profiles were modelled in one dimension, across the c-axis, parallel to the b-axis of the crystals57,59. D depends on the composition of the opx, temperature, pressure, oxygen fugacity and water fugacity6,25. The interdiffusion coefficient we used here is formulated for a temperature between 500 and 800°C, an oxygen fugacity of IW + 0.8 log units above the IW buffer (IW: Iron-Wüstite buffer) and XFe ~ 0.10-0.5060 (XFe is the molar fraction of the ferrosilite component). The parametrization of D in our model was done with a range of compositions of opx that includes those of this study (En44 − 73; XFe = 0.23–0.53; Supplementary Fig. 3)60, the temperature of the magmas are slightly above the range used in the parametrization of D, which is extrapolated at our temperatures. In the experimental study of D we used to model our timescales, they hypothesized an fO2 dependence similar to olivine with an exponent of 1/660. This fO2 dependence has been incorporated in the formulation of D in other works57,61 but this dependence has never been verified experimentally for opx with En contents of our dataset62,63. For En-rich opx of the mantle (En98 and En91), between 870–1100°C and oxygen fugacity controlled (fO2 = 10− 11-10− 7 Pa), an fO2 dependence of an exponent between 0 and 1/20 was found to be appropriate from their data63. The estimate for DFe−Mg used here60, when extrapolated to higher temperatures of the study on En-rich opx without considering any fO2 dependence appear to be consistent with their dataset63. The oxygen fugacity dependence on Fe-Mg interdiffusion coefficient is still under discussion as incorporating it can give longer timescales47 but no study has yet examined the appropriate En compositions of the opx and appropriate oxygen fugacity ranges. Therefore, the parametrization of the interdiffusion coefficient D used is the one determined on opx compositions close from our dataset without an fO2 correction60, as done in previous studies25,55. D is defined as follows in Eq. (1)60:
$$\begin{array}{c}logD=-5.54+2.6{\text{X}}_{Fe}-\frac{12530}{T}\#\left(1\right)\end{array}$$
The main assumption of the model is that the initial profile between two zones follows a step function, which is modified by diffusion to form sigmoidal concentration gradients64. This steep profile becomes broader with time, due to interdiffusion of the different elements. With the eruption, the diffusion is stopped. Maximum timescales are then estimated64. Profiles with smooth compositional variations of sigmoid shape are studied and those displaying growth dominant profiles are isolated. These profiles display linear trends or curves and bumps on the profiles and are not consistent with a diffusion sigmoid calculated for the given initial compositional contrast25 (Supplementary Fig. 5). The Al and Ca gradients are compared to the Mg#, as Al and Ca diffuse slower than Fe-Mg47,57,65,66 (Supplementary Data 1; Supplementary Fig. 5).
The model that we used consists in the intercalibration of chemical composition profiles of zoned opx, measured with an electron microprobe, with grayscale profiles on high-resolution north-south oriented images taken with SEM (spatial resolution of 755 nm)25,55, following the methodology developed in two other studies57,59. The Mg number is the parameter that seems to best control the grayscale of the images50,59. The ImageJ software (https://imagej.nih.gov/ij/; version 1.52a) is used to produce the grayscale profiles. They are averaged over a certain width to reduce the noise (between 20 to 50 µm, depending on the crystal rim size)25,55. After this intercalibration, the profiles are modelled to obtain the timescales of interdiffusion. As the diffusion coefficient used is composition-dependent, the curve shape of the profile is determined by the degree of compositional contrast but the curve width is dependent on time25,59 Based on a library of profiles of particular values of compositional contrasts, the shape of the curve that fits the best to the one obtained by intercalibration will be searched in this library according to the compositional data25. The curve will then be scaled in width to solve for time and the timescale corresponding to the zonation is obtained, as the scaling factor is an expression of crystal composition, the diffusivity used for the library of the profiles, the diffusivity in the crystal and the ratio between the timescales of the database and the timescale associated with the zoning in the crystal25 (with the timescale of the crystal being solved as the only unknown). The goodness of the fits is done by fitting the profiles by eye25,55.
The determination of the temperature, the diffusion coefficient and its measurement are the main sources of uncertainties6,64. Uncertainties on the calibration of measurements and point spacing during EPMA analyses, as well as the resolution of SEM images are also sources of uncertainties (pixel size, uncertainty on grayscale values defining a plateau)55. Overall, the measurement of the diffusion coefficient and temperature represent the main sources of uncertainty and have a logarithmic effect on final calculated timescales6,25,50 (Supplementary Fig. 4). Here, a Monte Carlo simulation was used to estimate the integrated time uncertainty from the different sources of uncertainty (T, on D0, Ea and resolution of grayscales values of SEM images), giving asymmetric uncertainties, with a larger error bar on the positive error and a smaller error bar on the negative error25.
Estimation of earthquake magnitudes
The Kamchatka Branch of Russian Geophysical Survey uses the following magnitude \(M\) scale in Eq. (2):
$$\begin{array}{c}M={log}_{10}U+f\left({t}_{S-P}\right)\#\left(2\right)\end{array}$$
With \(f\left({t}_{S-P}\right)\) expressed in Eq. (3):
$$\begin{array}{c}f\left({t}_{S-P}\right)=\left\{\begin{array}{c}1.42{ log}_{10}\left({t}_{S-P}\right)+0.72,{ t}_{S-P}<7s \\ 2.44 {log}_{10}\left({t}_{S-P}\right)-0.14,{ t}_{S-P}\ge 7s\end{array}\right.\#\left(3\right)\end{array}$$
where U is the maximum S-wave ground velocity in micron/sec and \({t}_{S-P}\) is the arrival time difference between S and P waves. The seismic moments \({M}_{0}\) (in N m) are approximately estimated from magnitudes based on the moment magnitude equation in Eq. (4):
$$\begin{array}{c}{M}_{0}={10}^{(1.5 M + 9.05)}\#\left(4\right)\end{array}$$