**3. Discussion**

Whilst the migration in spectral peaks is very small compared to other well-known examples like Soufriere Hills [36] and Redoubt [38], the spectral gliding observed for White Island occurs over a much longer time period of ~3–4 months. This timescale is more comparable to the one observed at Villarrica volcano [43], although in that case the frequency changes were more abrupt. In all of these cases, the spectral changes can be linked to eruptive activity at the volcano. The gliding frequencies at White Island are unusual in two respects. First, they persisted over several months, starting with the onset of low-level ash eruptions in early September 2012, and the observation of a dome over 2.5 months later in late November. Second, while the gliding spectral lines observed prior to large eruptive events (e.g., Soufriere Hills [36]; Redoubt [38]) seem to have persistent monotonically increasing frequencies (concave upward trending spectral peaks) for fundamental frequencies and overtones, the observations here include increasing spectral peak-lines with a reduced rate of change over time (i.e., a concave downward increase in frequency). This observation might sugges<sup>t</sup> a di fferent mechanism for the two processes (Figures 3B and 5).

Harmonic features in seismic data are often regarded as part of three potential processes, including fluid-elastic [39,40,44–54], frictional-induced [38,41], and permeable flow-controlled resonance [42,46]. In the first source process (see Figure 2C label (1)), fluid-elastic resonance involves the vibrations of cavities as a result of the motion of fluids in response to short-term perturbations (e.g., possibly the superposition of hybrid earthquakes thought to occur as magma proceeds through the glass transition at shallow depth [55]. In such a case, the di fferent modes of vibration vary with the impedance contrast (i.e., with the properties of the fluid filling the cavity) and geometry [35,56–58]. In the second source process (Figure 2C label (2)), a frictional mechanism involves the generation of harmonic tremor by the superposition of highly regular repetition of mostly identical stick-slip earthquakes [41]. In such a case, the dominant frequencies vary with the elastic properties of the medium, stressing rates, and geometry, whereas overtones are the result of a Dirac comb e ffect. In the third source process (see Figure 2C label (3)), a permeable flow-controlled mechanism involves the spontaneous vibration of cavities while gas escapes toward the surface and is the result of the transient porous flow of magmatic/hydrothermal gases through the permeable medium that caps the cavity. In such a case, the pressure inside the cavity is governed by the equation of a non-linear oscillator, which reduces to a linear first-order harmonic oscillator for highly-fractured and thin (100 m) caps [42]; hence, the specific frequencies depend on the permeability and porosity of the cap, gas properties, supply, and geometry of the cavity. In particular, a harmonic tremor may emerge through a Dirac comb e ffect when gas feeds the cavity regularly (e.g., through bubble clouds or foam collapse, [59–61]. Alternatively, a harmonic tremor may arise as a non-linear e ffect [46] or for thick ( 100 m) caps as result of the high-order terms controlling the pressure oscillations of the cavities [42].

At White Island, the observation of the dome in late November 2012 and the lack of strong seismicity associated with its appearance is enigmatic and can provide some constraints regarding the governing tremor mechanism. Persistent steam obscured the back of the crater lake and this might imply that the dome had been emplaced much earlier, possibly around the 2 September ash venting period shown in Figure 4. If this did mark the dome emplacement, then the slow cooling of the dome and conduit may have contributed to the spectral gliding within the tremor. For example, the slow progressive cooling and degassing might provide both the required seismic trigger mechanism and the higher impedance contrast cavity to produce harmonic tremor through fluid-elastic resonance. If a magmatic root remained beneath the dome, such a feature could hold exsolved gases within a bubble-rich root structure; Neuberg and O'Gorman [58] have shown how such a conduit could produce resonant tremor. If this conduit became progressively further degassed or if progressive top down solidification occurred, this could produce a smaller conduit with time. The slowly evolving changes in tremor might then reflect variations of the resonant root structure.

As an alternative, the slowly evolving spectral features could be regarded as a feature of the emplacement process if the dome were emplaced shortly before its observation in late November. The 2–5 Hz tremor source process at White Island, thought to be dominantly within the hydrothermal system, is a long-term feature of the shallow volcanic system [1]. In this case, the modulation of the shallow seismicity might reflect a longer-term intrusion process at depth. If the sub-surface magma began its interaction with the shallow hydrothermal system about 2.5 months before the dome's observation, then the ascent rate of intrusion would have been very slow. We regard this alternative as less likely due to the apparent fluidity of the dome features, however it might be relevant to the spectral observations occurring prior to the 5 August explosive eruption (see Figure 3B).

Regarding the second source process (Figure 2), in order to produce clear overtones in the spectrogram, the repetition interval of seismic events must be very precise. However, we do not observe clear discrete earthquakes in the sequence (Figure 4A), so the application of a repeating clockwork pattern, and thus frictional-induced resonance, is not easy to invoke for White Island in this period. In any case, it might be possible for interactions of hydrothermal system fluids with the conduit walls to act as a source of persistent micro-seismicity. Whilst the occurrence of a regular clockwork pattern is not apparent in the waveform data (Figure 4A), it could still be part of the underlying tremor excitation process. This process might also be only weakly periodic but still interact with a nearby resonant cavity [62]. If, on the other hand, the dome was extruded immediately prior to its first observation in November, it is plausible that the tremor observed over the period September to November could be the result of interaction between the ascending magma column and the hydrothermal system through which it is moving. In Figure 2C labeled (3), we illustrate this process with the front of the ascending plug intruding into the overlying two-phase vapor–liquid region extant at the time. This process could explain the earlier June to September spectral features. Temperature gradients above the ascending magma are very high, ranging from an assumed sub-liquidus intrusion temperature of ~ 900 ◦C to the temperature of the vapour–liquid saturation curve. The overlying conduit, assumed to be a porous fractured medium, is two-phase over its entire length to the surface (see Figure 2C). This conduit could deliver non-condensable gas to an overlying compressible "gas pocket" created beneath a partial mineralogic seal. Such a seal system is argued to be present based on C/S ratios of vent emissions at the time [16].

Gas pockets trapped beneath permeable media or embedded in cracks within the dome may lead to spontaneous vibrations while gas escapes toward the surface [42] but also through thermal instabilities [54]. In these resonant gas pockets, gliding spectral behaviour results from changing lengths of the cavity, with shorter lengths generating progressively higher frequencies over the spectral range of 0.1 Hz to 15 Hz. It is possible that this could result from shortening of the conduit cavity during magma ascent, although this process cannot be definitively confirmed by the existing data. Whereas spectral gliding would be complete when the magma reaches the surface, a tremor would be ongoing during cooling and the ongoing interaction between the plug/dome with the hydrothermal system, as portrayed in Figure 2C.

We regard propagation and emplacement of the dome in early September as more likely due to the strong tremor and the relatively abrupt change of the spectral patterns (Figure 3). If so, then the perturbation of the hydrothermal system led to high levels of gas and steam discharge, which obscured the dome, and caused the observed spectral gliding. It also may have promoted the slow evaporation of the crater lake system, which was a central feature of the White Island crater vent for more than 10 years before the 2012–2016 eruption episode. Regardless of the timing and mechanism of emplacement and stabilisation, it is remarkable for a dome to be emplaced into an active wet hydrothermal system with such subtle changes of the observed tremor patterns.
