Petrographic analysis was done using an optical microscope, including phenocryst and groundmass observations to determine the textures and mineral associations of each sample.

All samples were ground to 200-mesh (<75 micron) powders. The freshness of samples was assessed using LOI (loss on ignition) measured on the dry powder samples using a Carbolite HTF High Temperature Chamber Furnace (Carbolite Gero, United Kingdom) at the Research Centre for Geotechnology, National Research and Innovation Agency of Republic Indonesia (Badan Riset dan Inovasi Nasional - BRIN). LOI measurements were carried out twice on each sample and averaged. About 1 G of sample was heated to 105°C–110°C and then placed in a porcelain bowl whose weight was already known. It was heated to 400°C for 30 min before the temperature was increased to 1,000°C and left for 20 min. Afterwards, the sample was cooled in a desiccator vacuum for 20 min, then weighed. Whole-rock geochemistry was analyzed using a PUMA S2 XRF (X-ray fluorescence) (Bruker Corp., Massachusetts, United States) with a high power 50-W X-ray tube with a maximum current of 2 mA and accelerating voltage of 50 kV at the Research Centre for Chemistry, BRIN.

Mineral and matrix-glass compositions of representative samples were analyzed with a JEOL JXA-ISP100 Super-probe EPMA in the Engineering Research Innovation Centre (ERIC), Engineering Faculty, Universitas Gadjah Mada, Indonesia. We obtained orthopyroxene, clinopyroxene, and matrix-glass compositions in the six representative samples listed. We used an accelerating voltage of 15 kV, probe current of 12 nA, and 1 μm beam diameter. Standard natural mineral samples of MAC 15298 and 15299 were used as standards for the quantitative chemical analysis. The results were processed with the ZAF correction method.

To estimate the crystallization pressures and temperatures of minerals, and hence to infer magma storage locations and conditions, we used the orthopyroxene-liquid and two-pyroxene thermobarometry of Putirka (2008). We performed orthopyroxene-liquid thermobarometry on samples SERT1, DN1, and SERT3, where the pressures were estimated from a simple barometer using global calibration model for felsic liquid (excel spreadsheet can be downloaded from https://csm.fresnostate.edu/ees/faculty-staff/putirka.html). The standard error of estimate (SEE) for the global calibration is 320 MPa. We also applied two-pyroxene thermobarometry to sample PJ3 and the 2020 sample, where the pressure and temperature estimates were obtained using equations 39 and 36 of Putirka (2008), respectively. The SEE of these pressure and temperature estimates is ± 280 MPa and ± 45°C, respectively. For sample RAK1, we used the clinopyroxene-liquid thermobarometry of Putirka (2008).

We obtained back-scattered electron (BSE) images of gold-coated and polished resin mount of all samples using a Phenom ProX Desktop Scanning Electron Microscopy (SEM) at Geostech, Puspiptek, BRIN to identify the texture and the abundance of magnetic minerals. The magnetic mineral abundances were estimated using Olympus Stream Software by analyzing BSE images with an image depth of 96 dpi, a resolution of 4096 × 4096, and minimum size for particle recognition of 10 pixels. The compositions of magnetic minerals were determined using energy dispersive X-ray spectroscopy (EDS) on the SEM operating with an accelerating voltage of 15 kV and a full Backscattered Electron Detector (BSD).

We measured two rock magnetism parameters using instrumentation available at our institution: 1) Specific mass magnetic susceptibility (MS) was measured using a Bartington MS2B and MS3 magnetic susceptibility system (Bartington Instrument Ltd., Witney, United Kingdom) at the Laboratory for Characterization and Modelling of Rock Physical Properties, Bandung Institute of Technology. This measurement for each sample was done for three sub-samples (e.g., sample-1A, sample-1B, and sample-1C) where each sub-sample was measured five times and then averaged and the standard deviation calculated; 2) Isothermal Remanent Magnetization (IRM) acquisition curves were obtained using a Dexing 250 Vibrating Sample Magnetometer (VSM) with an external magnetic of 100 Oe-21000 Oe at the Research Center for Physics, BRIN. The baseline of any deflection in the Magnetization (M) vs. Magnetic Field (H) curve was determined using the adjacent-averaging second derivative method with a specified smoothing window and threshold using OriginLab Software. Linear fitting of the baseline anchors clearly defines the saturated point where the curve and line intersect (saturation field).

Those methods can produce valuable data to identify the characteristics of magnetic minerals, especially to identify the type, composition, and amount of magnetic minerals (Chi and Dorobek, 2004; Liebke et al., 2011; Sakra et al., 2020; Kanamaru et al., 2022) because magnetic susceptibility and magnetic field saturation are dependent on those properties. The rock magnetism parameters come in to confirm the results of SEM-EDS observations, in order to get the comprehensive results regarding the detail of characteristics of magnetic minerals contained in the rock.

The six representative samples contain plagioclase, pyroxene, and Fe-Ti oxides as the most common minerals. The general petrographic features of Old Krakatau, Young Krakatau, and Anak Krakatau can be summarized as follows.

The products of Old Krakatau are represented by the samples of PJ3 (30% phenocrysts) and SERT1 (60% phenocrysts). Both samples have porphyro-aphanitic textures, with larger crystals in SERT1 than in PJ3. The maximum crystal sizes in PJ3 and SERT1 are 1 mm and 3 mm, respectively. The mineral association in Old Krakatau consists of plagioclase, clinopyroxene, orthopyroxene, and Fe-Ti oxides, while the groundmass in both samples is microlite-rich and consists of pyroxene, Fe-Ti oxides, plagioclase, and silica minerals. Although the mineral associations in both samples are similar, some differences are observed, including: 1) the Fe-Ti oxides in PJ3 consist of both magnetite and ilmenite, while those in SERT1 consist dominantly of magnetite; 2) silica minerals were observed in the matrix glass of PJ3 (Supplementary Figure S3A); and 3) unzoned plagioclase textures were dominantly observed in PJ3, while oscillatory zoning and sieve texture are often observed in SERT1. We also observed symplectite textures in some pyroxene phenocrysts in both samples, which are surrounded by small crystals of magnetite and orthopyroxene (Supplementary Figures S3B, C).

The Young Krakatau products are represented by two lava samples, DN1 (55% phenocrysts) and RAK1 (40% phenocrysts), and one pumice sample, SERT3 (5% phenocrysts). The lava samples have a porphyro-aphanitic texture, with phenocrysts reaching up to 4 and 5 mm in length in DN1 and RAK1, respectively. The pumice sample is dominated by volcanic glass and microphenocrysts <1 mm in length. Mineral associations in Young Krakatau lavas consist of plagioclase, pyroxene, and Fe-Ti oxides, while Young Krakatau pumice sample consists of plagioclase, orthopyroxene, and Fe-Ti oxides. Orthopyroxene and clinopyroxene are present as phenocrysts in DN1, but RAK1 is free of orthopyroxene, while SERT3 is free of clinopyroxene. Both magnetite and ilmenite exist in these three Young Krakatau samples. The groundmass of the lava samples is microlite-rich, consisting of plagioclase, pyroxene, Fe-Ti oxides, and silica minerals (predominantly in DN1), while the pumice is microlite poor. The silica minerals in Young Krakatau lava are less abundant compared to those found in Old Krakatau products. Normal zoning patterns in plagioclase dominate the Young Krakatau products. However, some oscillatory zoning and sieve textures are present in SERT3 and DN1. Symplectite textures occur in the pyroxene and magnetite phenocrysts in DN1, which are surrounded by small crystals of orthopyroxene.

Anak Krakatau is represented by recent lava that erupted in 2020, which also has porphyro-aphanitic texture with 60% phenocrysts with maximum lengths of 3 mm. The mineral association in Anak Krakatau consists of plagioclase, clinopyroxene, orthopyroxene, Fe-Ti oxides, and olivine. The matrix glass is rich in microlites consisting of pyroxene, Fe-Ti oxides, and plagioclase. Unlike older Krakatau products, no silica minerals were found in the AK groundmass. Fine and coarse sieve textures are common in the plagioclase crystals. Symplectite textures are infrequent in the pyroxene phenocrysts.

Whole-rock compositions and LOI values of all samples are shown in Table 2. The samples are mostly fresh (little-to-no apparent weathering) as shown by LOI values of <1% (Tugrul and Gurpinar, 1997; Pratama et al., 2018) except some Young Krakatau samples which are >4% LOI, in agreement with data obtained by Madden-Nadeau et al. (2021) in which they suspected the samples to be altered by seawater. However, we compare data from Mandeville et al. (1996) and Madden-Nadeau et al. (2021) with geochemistry data for our Young Krakatau samples.

The compositions of all Old Krakatau lava samples are dacitic, with SiO₂ contents of 63.6–68.5 wt%, while Young Krakatau lava samples (both RAK1 and DN1) are andesitic with SiO₂ contents of 61.2 wt% and 62.7 wt%, respectively, and all Anak Krakatau lava samples are basaltic in composition, with SiO₂ contents of ∼48.6–50.8 wt% (normalized) (Table 2; Figure 3). The Young Krakatau pumice samples are all dacitic with SiO₂ contents of 65.0–67.6 wt%. The mafic Anak Krakatau lavas are characterized by high Al₂O₃, FeO* (total iron as FeO), MgO, and CaO contents and slightly higher TiO₂ contents. In contrast, these major elements have low contents in Young and Old Krakatau lava samples (Supplementary Figure S4). However, the Young and Old Krakatau lavas can still be distinguished by their major element compositions. Figure 3 also shows that our Young Krakatau compositions are close to that of the 1883 pumice and olive obsidian presented by Mandaville et al. (1996), which are dacite to rhyolite, meaning that we obtained similar results despite our higher LOI values.

The matrix-glass major element compositions of representative samples from each period, normalized to 100% anhydrous, are listed in Supplementary Table S3. Matrix-glass compositions of these samples range from dacite to rhyolite, i.e., 66.3–78.8 wt% of SiO₂ (Figure 3). Despite being basaltic in composition, Anak Krakatau products have evolved matrix-glass compositions of 66.3–69.2 wt% SiO₂ (trachydacite). Young and Old Krakatau products have rhyolitic compositions, with SiO₂ contents of 70.6–78.8 wt% and 74.9–77.5 wt%, respectively. Binary plots of major element oxide contents of the matrix glasses of representative samples from each period show clear differentiation trends between Old Krakatau, Young Krakatau, and Anak Krakatau (Supplementary Figure S4).

The presence of two pyroxenes in all Krakatau products allows the application of the pyroxene geobarometer of Putirka (2008). Equilibrium tests between orthopyroxene and liquid and between the two pyroxenes are shown in Supplementary Figures S5, S6, respectively. Orthopyroxene-liquid thermobarometry yields good K_D (Fe-Mg) values for some pyroxene compositions with Old and Young Krakatau matrix-glass and whole-rock compositions, although not for all Anak Krakatau samples. To convert the pressure to the depth of magma storage, we used a density of 2.55 gcm⁻³, as also used by Mandeville et al. (1996) at Krakatau. The orthopyroxene-liquid geobarometer (Figure 6A) generally yields low pressures and shallow depths, i.e., 14–72 MPa (0.6–2.9 km) and 26–84 MPa (1.1–3.4 km) for Old Krakatau and Young Krakatau, respectively. Since we used the pressure from the global calibration of felsic liquids, which are not sensitive to temperature (T), we can only report the pressure data. For the Old and Anak Krakatau samples, we used two-pyroxene thermobarometry from Putirka (2008). We are unable to provide pressure and temperature estimates from the PJ3 sample due to the low Al₂O₃ content of the pyroxene (<1 wt%), which did not yield reasonable P and T values. Our Anak Krakatau samples are in equilibrium under subsolidus conditions, with K_D values close to 0.7. Two-pyroxene microphenocryst pairs yield pressures of 185–390 MPa (7.4–15.6 km; Figure 6B), with temperatures ranging of 916°C–956°C. Two-pyroxene phenocryst pairs yield high crystallization pressures, 428–665 MPa (17.1–26.6 km), with temperature ranging from 983°C to 1,034°C.

Fe-Ti oxides minerals have magnetic properties that will be discussed in the following section. Not only does the chemical composition of the Fe-Ti oxides differ in each period, their textures also vary across the eruptive period. In general, both titanomagnetite and ilmenite phenocrysts and microlites are anhedral to subhedral (Figure 7).

In Old Krakatau samples, the grain boundaries of titanomagnetite crystals are often corroded while being surrounded by pyroxene or plagioclase microlites (Figures 7A, D). Figure 7A also shows an example of an ilmenite inclusion in the rim of a titanomagnetite crystal. This texture could represent composite-type exsolution (Buddington and Lindsley, 1964; Haggerty, 1991; Tan et al., 2016). In addition, ilmenite also occurs in Old Krakatau samples as a trellis-like lamellae with the width of about <5 μm, occupying more than 60% of the host area (Figure 7B), and appears as an individual grain (Figure 7C).

In the Young Krakatau samples, particularly in the lava samples, the titanomagnetite grain boundaries also appear to be corroded (Figures 7E, F). In addition, Figure 7E shows ilmenite exsolution lamellae included as a trellis type with a width of about 7.5 µm and covering about 22% of the host area. In pumice samples (ST92 and SERT3), both titanomagnetite and ilmenite crystals are generally subhedral, have sharp or smooth edges, and sometimes are embayed (Figures 7G, H, I). Figure 7G also shows the different colors of titanomagnetite (Tmt) and ilmenite (Ilm) in BSE images, where the latter tends to be darker.

Unlike the Old and Young Krakatau samples, the Fe-Ti oxides in the Anak Krakatau samples tend to be more anhedral and have a variety of textures, including graphic textures or myrmekite-like titanomagnetite (Figure 7J), small skeletal or hopper titanomagnetite microlites (Figure 7K), and ilmenite exsolution lamellae in titanomagnetite hosts (Figure 7L). These lamellae are trellis-like (Tan et al., 2016), with widths of about 5 µm and covering about <10% of the host area. In addition, coarse magnetic minerals ( ≥ 2 µm) are more abundant in the Anak Krakatau sample (2020), while the Old Krakatau sample (ST91A) contained finer minerals ( ≤ 2 µm) (Supplementary Figure S7). The mean size of magnetic minerals in the Young Krakatau pumice (ST92) is difficult to identify due to their sparse presence regarding the field of view. However, measurement from several SEM images shows that their sizes are ranging from ∼10 to 200 µm. Overall, Anak and Old Krakatau samples contain magnetic minerals of 2.5% and 2% (by area fraction), respectively.

The rock magnetic analyses measured several parameters (Supplementary Table S7). The MS values of the Old Krakatau samples are lower than the Young and Anak Krakatau samples, between 273.33 × 10⁻⁸ m³/kg to 632.99 × 10⁻⁸ m³/kg, with a mean value of 443.05 × 10⁻⁸ m³/kg (Figure 8A) The Young Krakatau pumice samples (ST92, ST130, ST136, SERT3, and SERT4), erupted during the catastrophic 1883 eruption, yield MS values of <500 × 10⁻⁸ m³/kg (Figure 8A). The MS values of the Young Krakatau lava samples (DN and RAK1) are 765.57 × 10⁻⁸ m³/kg and 1438.06 × 10⁻⁸ m³/kg, respectively. The MS values of all AK samples are higher than 1,000 × 10⁻⁸ m³/kg, higher than those of the Young Krakatau and Old Krakatau samples.

The results of magnetic field saturation of all the samples are listed in Supplementary Table S6 and visualized in Figure 8B. Figure 9 shows the IRM acquisition curves of representative samples. Each sample was saturated at different values, indicated by the vertical dashed lines. For example, sample PJ4 (Old Krakatau) had the highest saturation value (∼576.77 mT). The Young Krakatau samples, represented by lava RAK1 and pumice ST92, were saturated at about 480.00 and ∼510.09 mT, respectively, lower than the Old Krakatau sample. Sample ST22 (AK) saturated early, at ∼404.52 mT. O’Reilly (1984) showed that the saturation magnetization field for pure magnetite is about 300 mT, whereas all our samples have saturation magnetization field values above 300 mT (Figure 8B, Supplementary Table S6). This indicates that the magnetic minerals in the samples are a mixture of Fe-rich and Ti-rich titanomagnetite or high coercivity magnetic minerals (Chi and Dorobek, 2004; Liebke et al., 2011; Pratama et al., 2018). Furthermore, the saturation magnetization fields of the Old Krakatau samples are higher than those of the Young and Anak Krakatau samples, indicating that the Old Krakatau samples contain more heterogeneous magnetic minerals.

Krakatau has experienced phases of growth and collapse of its edifice throughout its eruptive history (Francis, 1985; Bronto, 2000; Sutawidjaja, 2006). The collapse events were associated with caldera-forming eruptions (CFE) in 1883 and presumably 416 AD, as well as volcanogenic tsunamis (e.g., in 1883 and 2018). After the first CFE, eruptive activity resumed through the growth of Rakata island and subsequent formation of the new Danan and Perbuatan cones (Francis, 1985). This growth was then destroyed by the second CFE in 1883, which was followed by the growth of Anak Krakatau. Due to this cyclic activity involving CFEs, Krakatau can be classified as a polycyclic system, i.e., having formed more than one caldera (Bouvet de Maisonneuve et al., 2021). We focus our discussion on the chemical evolution of the melts and minerals (particularly titanomagnetite) in this cyclic system, excluding what triggered the Krakatau CFEs. Readers can refer to Madden and Nadeau et al. (2021) for the eruption mechanism of the 1883 CFE.

Stratigraphically, we suggest that our Old Krakatau samples preceded the first CFE (416 AD), with that CFE defining the end of the Old Krakatau period. The Young Krakatau lava samples were erupted before the second CFE in 1883 and belong to the Rakata and Danan series. The Young Krakatau pumice samples are products of the second CFE, which defined the end of the Young Krakatau period. Figure 12, adapted from Bouvet de Maisonneuve et al. (2021), shows the whole-rock and matrix-glass silica contents and the MnO, MnO/Al₂O₃, and TiO₂ contents of titanomagnetite crystals from our samples, which cover more than one caldera cycle. In one caldera cycle, there are three stages: pre-collapse activity, the caldera-forming eruption, and post-collapse activity. Detailed characteristics of each stage can be seen in Table 1 of Bouvet de Maisonneuve et al. (2021).

In Figure 12, stages a and c have similar whole-rock and matrix-glass compositions and titanomagnetite MnO contents and MnO/Al₂O₃ ratios. The liquid compositions are more evolved and the corresponding samples, the Old and Young Krakatau lava samples, have relatively high titanomagnetite MnO contents and MnO/Al₂O₃ ratios, implying that they were the most differentiated. In addition, magma was stored during these stages in shallow regions (Figure 11). These geochemical characteristics are indicative of the maturation phase or perhaps the beginning of the fermentation phase. For instance, Rabaul Caldera is currently in a mid-maturation phase, indicated by high SiO₂ contents (dacitic magma). In addition, the crystallization pressures estimated for the products of the August 2014 eruption are low (<100 MPa; Fabbro et al., 2020) indicating shallow magma storage. This is similar to the maturation phase of the Old and Young Krakatau lava samples, which record shallow magma storage (14–84 MPa).

Stages b and d were CFEs. It appears that the titanomagnetite MnO contents and MnO/Al₂O₃ ratios during the maturation phase (particularly shown by lava sample RAK1) are higher than those in the 1883 CFE event itself. This trend is clear at Rabaul Caldera, preceding the Rabaul Pyroclastics caldera collapse (1400 BP), and also observed at Campi Flegrei preceding the Neapolitan Yellow Tuff (∼14.9 ka) (Bouvet de Maisonneuve et al., 2021).

During the maturation phase, smaller magma reservoirs can grow and coalesce, forming larger, interconnected magma reservoirs at shallow depths. This will lead to an increase in the volume of silicic magma and volatile contents from continuing crystallization while the flux of mafic magma from the lower crust wanes (Degruyter and Huber, 2014; Pansino and Taisne, 2019; Bouvet de Maisonneuve et al., 2021). The geometry of this large shallow magma reservoir will change after a CFE due to the collapse of the roof of that reservoir (Bouvet de Maisonneuve et al., 2021).

Stage e in Figure 12 is the incubation phase, after the 1883 CFE, indicated by the mafic compositions of the Anak Krakatau products (Figure 3), which are less differentiated than the Young Krakatau and Old Krakatau magmas based on their lower titanomagnetite MnO/Al₂O₃ ratios, but generally hotter than the Young and Old Krakatau magmas. In addition, this phase is also indicated by frequent but small eruptions (Bouvet de Maisonneuve et al., 2021), as has been observed to date. Instead of a waning caldera cycle, Krakatau repeated the cycle after the two CFEs by growing and forming new cones, including Rakata, Danan, Perbuatan, and Anak Krakatau, with Anak Krakatau emerging from the sea in 1927. In addition, Abdurrachman et al. (2018) suggested that there is mantle upwelling beneath Anak Krakatau supplying new magma batches to the upper magma reservoir(s). As Krakatau has undergone two CFEs, it has potential to occur in the future, when the mafic magmas of the Anak Krakatau period continue differentiating and become more evolved: one of the characteristics of a system heading towards a CFE.

We compared the evolution of Krakatau with other calderas, i.e., Rinjani in Indonesia, Campi Flegrei in Italy, and Aso in Japan, in terms of the chemical changes from pre-, syn-, and post-CFE; regardless the time lapse from the previous event to the CFE and from CFE to post event as well as the composition and type of eruptive product. Since some of the volcanoes have experienced more than one caldera-forming eruption (i.e., Krakatau, Campi Flegrei, Aso), we take the last CFE event of each volcano for the comparison.

Krakatau and Rinjani have a similar trend of increasing SiO₂ content of whole-rock towards the CFE and decreased afterwards (Figure 13). The increase in SiO₂ in Krakatau and Rinjani from pre-to the CFE event could be resulted from an intense magma differentiation (e.g., Bouvet de Maisonneuve et al., 2021). Meanwhile, the decreased SiO₂ content of whole-rock post-CFE is due to an injection of basaltic magma, which feeds Anak Krakatau and Barujari (Dahren et al., 2012; Métrich et al., 2017). Similarly, Aso displays increasing SiO₂ content of matrix-glass towards CFE and decreasing SiO₂ content of whole-rock after CFE. On the contrary, Campi Flegrei shows decreasing SiO₂ content of whole-rock and matrix-glass towards the CFE, but these values, respectively, remain similar and continue to decrease after CFE. The decrease in SiO₂ content of magma in Campi Flegrei may be related to the continuous injections from deeper magma reservoirs (Pabst et al., 2008; Forni et al., 2018).

Krakatau, Rinjani, and Campi Flegrei display a similar trend of MnO and MnO/Al₂O₃ content titanomagnetite where it generally decreases after the CFE. The MnO content and ratio of MnO/Al₂O₃ titanomagnetite for Aso seems to increase during the CFE. As mentioned in the previous Section 5.2, higher MnO and MnO/Al₂O₃ ratio of titanomagnetite indicate higher degrees of differentiation and vice versa. The lower degree of magma differentiation is accompanied by the injection of less evolved magma. Lastly, the TiO₂ contents of titanomagnetite in the pre-, syn-, and post-CFE samples do not offer a unique signature, meaning that each volcano shows different trends.