**1. Introduction**

White Island (Whakaari in Te Reo Maori) is a frequently active and hazardous composite cone volcano with most of its relief lying below sea level within the south-eastern Bay of Plenty (Figure 1A). While White Island produces only small eruptions by global standards, the tragic 9 December 2019 event illustrates the possible societal impacts that relate to small eruptions at volcanoes that are frequented by tourists. Such eruptive activity was also present during the 2012–2016 period (Figure 1) which proceeded from the onset of unrest in mid-2011 [1,2], produced several well documented explosive eruptions [1,3,4] through 2012 and 2013, and culminated in April 2016 with a small phreatomagmatic event [2,5,6].

**Figure 1.** Map of White Island, located in the south-eastern Bay of Plenty (the topographic contour is 40 m). The single seismic station WIZ (blue triangle) and dome eruption vent (red circle) and south east eruption vent (red square) shown in (**A**). Ash venting during the 5 August post eruption ash venting period is shown for 9 August. The dome is shown in (**C**) and was taken 12 December. Note the remainder of the crater lake in the foreground. Photo (**B**) is unattributed courtesy of GeoNet, while (**C**) is by Brad Scott courtesy of GeoNet.

Eruptions at White Island are driven by persistently active magmatic degassing that is evident over the historical record [7]. This degassing requires long-term magmatic injection into shallow portions of the volcanic edifice, which may be accomplished via convective overturn within a conduit [8–10] or persistent injection of small batches of magma [11,12].

A small effusive dome was also emplaced on the back wall margin of the active lake filled eruption vent system, and hence this is an excellent example of magmatic propagation through a 'wet' volcano hydrothermal system. The dome effusion had significant consequences for the evolution of the hydrothermal system, promoting the drying of the lake, and a switch to persistent and well documented mud/sulphur eruption activity [13–16]. Dome forming eruptive activity is a frequent occurrence in volcanic systems with viscous magmas and have drawn significant scientific interest due to their persistent medium- to long-term hazards. These hazards are greatest when the domes are perched at elevation on unstable slopes of a volcanic edifice such as at volcanoes like Soufriere Hills, Montserrat [17]; Redoubt, Alaska [18]; or Merapi, Indonesia [19]. Domes may also form within positions of lower relief (e.g., Mt. St. Helens [20–22]), and in such cases, the eruptions can be emplaced through well-developed hydrothermal systems.

The hydrothermal system at White Island results from the interaction between magmatic heat and juvenile fluids with water from meteoric and oceanic sources that percolates into the crust [16]. Heat and fluids from the magma drive convective circulation that establish fluid phase transitions below the surface and a hydrostatically controlled phase equilibrium with its enclosing hydrothermal brine. In particular, at the magma-hydrothermal system interface, a single-phase gas enveloped by a two-phase fluid composed of liquid and gas bubbles dominates, whereas a single-phase liquid will eventuate at shallow levels and within the crater lake. These conditions are generally stable but can evolve in different ways depending on the position of magma within the system and externally modulating effects like rainfall (Figure 2).

**Figure 2.** Schematic cross section depicting (**A**) the pre- and (**B**) post-extrusion scenarios for the dome. Acidic brine fluids underlie meteoric water/condensate lenses (both depicted green) and encapsulate the magmatic/fumarolic vent system (blue and grey). Magma ascends along the main conduit (designated by the red line in (**B**), preceded by increased heat and gas flow which evaporates the two-phase vapour-liquid region to single-phase vapor along its way (grey). Three possible resonant systems are portrayed in the inset diagram (**C**). The bubble filled cavity (1). A clockwork stick-slip rupture mechanism (2), or the frothed expanding boiling front (3 and its inset) may produce harmonic signals discussed. The arrows in B show the expanded two-phase system that results from the propagating magma injection. See text.

From a seismological perspective, the shallow hydrothermal system may produce the full range of seismic observations seen at White Island and its global analogues like Kawah Ijen volcano, Indonesia [4,23]. Examples include discrete long-period (LP) [24], volcano-tectonic (VT) [2,25], very long period (VLP) seismicity [2], and persistent volcanic tremor [1]. Tremor is an important feature of volcanic seismicity [26]. It is characterised by a continuous, banded, or spasmodic signal, which is detectable only when exceeding the background seismic energy level [26]. Several data reduction methods [27] have been proposed to characterize its short- and long-term time evolution, that can lead to the identification of significant transitions between volcanic processes [28], sometimes triggered by external or internal events such as tectonic or volcano-tectonic (VT) seismic events [29]. Volcanic tremor can also occur precursory to an eruption [30–33]. However, the origins of tremor may vary at different volcanoes, and are often poorly understood; moreover, many different seismic sources can act at the same time and combine to produce the signal of interest [27].

Harmonic tremor, consisting of a fundamental frequency and evenly spaced overtones, is a common occurrence at volcanic systems worldwide [34,35], and is important both to determine possible source processes and as a monitoring tool. Changing spectral patterns in harmonic tremor (e.g., migration of the spectral lines, i.e., so-called gliding) is increasingly recognised at volcanoes [36–38] as an important short-term precursor that may occur several minutes prior to explosive activity. Systematic evolution of spectra over longer time periods are less common; however, an assessment of such slowly evolving systems may also be important from a process and hazard standpoint [39].

It is surmised that movement of magma below or within a hydrothermal system should produce significant changes in seismic observations [40–42] (Figure 2). Hence, the extrusion of magma through a well-established hydrothermal system and onto the surface provides an excellent opportunity to re-examine remote monitoring data for hazards implications. The dome forming eruption at White Island is interesting in this context because its discovery was truly enigmatic. It was first documented by GeoNet on 11 December 2012 but was observed by White Island tour operators possibly a fortnight earlier (Volcanic Alert Bulletin WI-2012/16; https://www.geonet.org.nz). Surprisingly, its emplacement occurred without dramatic seismicity revealed on the permanent White Island seismic station (Figure 1A). Likewise, an evaluation of the White Island web camera system did not reveal the appearance of the small dome, mostly due to persistent obscuring steam plumes for the period from the initial onset of eruption activity on 5 August 2012 [1]. It also appeared to have been quite effusive, based on the smooth lumpy texture of the surface (Figure 1C). The dome, with an extent of 20–30 m in diameter and a height of 10–15 m, has a volume on the order of 1−7 × 10<sup>3</sup> m3. Below, we retrospectively document the pre-eruption seismicity from the onset of eruptive activity from August to the observation of the dome in December 2012.

#### **2. Seismic Data and Results**

White Island seismic monitoring was composed of a single broadband seismic sensor at site WIZ (Figure 1A), which is comprised of a Guralp 3ESP seismometer and a Quanterra Q330 digitiser, sampling at 100 Hz and telemetering data in real time to the GeoNet data center. The archived seismic data were processed in two ways: (1) calculation of the real-time seismic amplitude measurement value (RSAM) by taking the time-series data from the vertical component sensor, correcting it to velocity, and computing the root mean square (RMS) amplitude within one minute long, non-overlapping windows (Figure 3A); and (2) computing the spectra via the fast-Fourier transform (FFT) for each one-minute window (Figure 3B). For the latter, we visualised the data by picking the peak amplitude from the spectra and monitoring that over the period of interest (before the first eruption to the end of the dome forming phase).

**Figure 3.** Real-time seismic amplitude measure (RSAM) computed from one-minute moving windows (**A**) and the maximum spectral peak amplitude (**B**) from Fast Fourier Transform of the same one-minute window. The 6 August 6 eruption and 2 September ash venting episode and the dome emplacement are marked ( **A**) and the inferred injection of magma into the deeper hydrothermal system and emplacement of the dome are shown in (**B**).

The one-minute RSAM observations (Figure 3A) show the first eruption on 5 August 2012 (RSAM~2800 nm/s), as well as a persistent high amplitude signal in early September (~2100 nm/s), followed by sustained moderate level tremor (500–1000 nm/s) through the time of the dome observation in late November 2012. The spectral analysis (Figure 3B) shows that the peak frequency of tremor is generally focused within the ~1.0–4.0 Hz band, with specific and persistent peaks and notable evolutionary patterns. We note with particular interest the spectral changes associated with high amplitude tremor periods, including (1) a shift from broader spectrum tremor to 2.5–3.5 Hz in mid-June 2012; (2) the onset of a migration of the spectral peaks (termed gliding spectral lines in the literature [36]) in mid-July; (3) the onset of broader spectra tremor with slowly gliding spectral lines in early September; and (4) establishment of stable (non-gliding) persistent spectral peaks in late December (see red dots in Figure 4). These spectral changes of tremor are linked in time to specific aspects of volcanic activity, including: (A) Rapid volcanic lake fluctuations of about 4 m and minor geysering (observed in June/July); (B) the onset of the first strong eruption on 5 August; (C) persistent ash venting in early September; and (D) the first observation of the dome in late November.

**Figure 4.** Example waveforms (**A**) and spectra (**B**) for a subset of the seven-month period of interest. The examples are extracted from the continuous seismic data and include one minute from the start of each Julian day (UT HH:MM 00:00 to 00:01). The initial eruption occurred on 5 August 2012 at NZST 04:55, and the waveforms are not shown. Note the change in peak frequency around the time of the secondary ashing on 2 September 2012 NZST. Also note the slow migration of peak frequencies until the observation of the dome (note red marks for peak spectral frequency). The crater was largely obscured by steam from the period of ashing to the observation of the dome.

To aid in interpreting the seismic observations, example waveforms (Figure 4A) and spectra (Figure 4B) are plotted from the first minute of each day for the period 1 July to 31 December 2012 (Figures 3 and 4 are presented in UTC). Although we realize that this procedure potentially produces an aliasing e ffect, the individual sample waveforms and spectra match closely a denser spectral analysis and confirm the observations in Figure 3. Hence, we regard the observations in Figures 3 and 4 as robust, illustrating both the longer-term features of the tremor and the slowly evolving migration from lower to higher spectral frequencies.

Specific spectral peaks become well established in late August 2012, which then perceptibly migrate towards higher frequencies over a three-month period. On ~ 29 August 2012, the specific peaks of interest are at 2.1 Hz (Figure 4B). These peaks shift to a stable frequency of 2.3 Hz by 30 November 2012 (Figure 4B), about the same period that the dome must have been emplaced based on the tremor and the first observation of the dome. A subsidiary peak is also observed, which weakly emerges at ~2.9 Hz after the ashing episode and persists after the first dome observation at a modestly higher frequency of ~ 3.2 Hz. There are also stationary spectral peaks observed at other specific frequencies (Figures 3 and 4B) as part of a possible harmonic pattern which began in early September and evolved until the dome was observed.

To assess possible harmonic patterns, we computed spectrograms using two-minute-long windows. Each time window is detrended with a mean and a linear function before tapering using a Hanning window (10% on each side). The frequency resolution is 0.0083 Hz. For each column of the spectrogram the resulting FFT amplitudes are color-coded and shown in Figure 5. After smoothing the results with a median of five days, we picked the central frequencies of continuous spectral lines: 1.4, 1.6, 1.8, 2.0, 2.2, 2.3, 2.7, 2.9, 3.2, 3.5, 4.9 Hz. We note that 2.2 Hz and 2.3 Hz seem to merge in September.

**Figure 5.** Spectrogram computed using two-minute-long windows after removing the mean, the trend and applying a cosine taper in each window. Yellow colours correspond to high amplitudes, whereas blue colours correspond to low amplitudes.

We then assess if the data were consistent with a harmonic tremor source. In fact, although peaks often appear to be equally spaced in frequency, the dominant frequency is rarely seen. We therefore developed an algorithm to automatically compute this possibly buried dominant frequency.

For each column of the spectrogram (i.e., 2 min), the algorithm determines all the peaks by looking for local maxima in the column. An histogram of these peaks is then built over a wider time window (e.g., 4 h or 12 h) by counting for each frequency how many times a peak is detected. Finally, we search for our dominant frequency in the 0.3–1.3 Hz range, and cumulate histogram values not only for that candidate dominant frequency but also for its potential harmonics. The cumulated value is then normalized (i.e. divided by the number of harmonics) because lower frequencies may yield higher numbers of harmonics and higher cumulated values.

For each column, we determine the potential dominant frequency, and we superimpose it, together with all its harmonics, on the spectrogram to assess its coherency with time. The results (Figure 6 for time windows of 4 h, and in Figure 7 for time windows of 12 h) are consistent with a harmonic oscillation over a narrow frequency band, hence confirming that the tremor could originate from a harmonic process. We must acknowledge that the observation is based on the sole single station observation and hence may include other influences such as path and structural effects in this complex volcanic edifice.

**Figure 6.** Same as Figure 5, but with potential dominant frequency and corresponding harmonics overlaid (red dots in 4-hr time windows).

**Figure 7.** Same as Figure 6, but with potential dominant frequency and corresponding harmonics overlaid (12-hr time windows).
