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[SCG40-P03] Classification of tilt changes before volcanic eruptions in Japan
Keywords:Volcanic eruption, Precursor, Tilt change, Slow to fast
Volcanic eruptions are sometimes preceded by tilt changes. A majority of the tilt changes show acceleration (slow to fast), although deceleration (fast to slow) is not rare, and is followed by an eruption that is an even faster phenomenon. Therefore, these signals are considered to be a kind of slow-to-fast phenomenon. Maeda (2023, J. Volcanol. Geotherm. Res.) examined the tilt changes before all monitored eruptions in Japan. The study showed that approximately half of the eruptions were preceded by tilt changes, and classified them into acceleration, linear, and deceleration types. However, further quantification of the characteristics of the signals was difficult because of complicated waveforms.
To address the characteristics of the waveforms, this study classified the signals of the pre-eruptive tilt changes based on the similarity of the waveforms. The catalog of Maeda (2023) was used, which consisted of the start and end times (1-s resolution) of 3749 pre-eruptive tilt changes. To enable a quantitative comparison of the waveforms, the time and amplitude axes for each signal were normalized to a range from 0 to 1 (or -1 for signals with negative polarity), and the data were resampled at every 0.01 of the normalized time axis scale by linear interpolation. Note that the signals of the pre-eruptive tilt changes were monotonic; the normalized waveforms monitonically increased or decreased from 0 to ±1.
The waveforms of these monotonic signals were difficult to classify using correlation coefficients. To understand this, consider three functions: f1(t) = t, f2(t) = t2, and f3(t) = t0.5, where t is the normalized time. The three functions show linear, acceleration, and deceleration patterns from t = 0 to 1, respectively. Despite the different shapes, the correlation coefficients between f1(t) and f2(t), f2(t) and f3(t), and f1(t) and f3(t) are as high as 0.9682, 0.9798, and 0.9035, respectively. This simple example shows that the differences in the shapes of monotonic waveforms are difficult to quantify based on correlation coefficients. A trial classification of the waveforms using high thresholds (0.98 or 0.99) for the correlation coefficients did not show good performance.
Therefore, this study used an waveform misfit M = {∫[f(t) - g(t)]2dt / (1/2)∫[f(t)2 + g(t)2]dt}0.5 as a measure of the similarity of two waveforms f(t) and g(t); M = 0 if f(t) = g(t), M = 20.5 if f(t) ≠ g(t) = 0, and M = 2 if f(t) = -g(t). The classification method was as follows: (1) M was calculated for every pair of waveforms; (2) the pairs of waveforms with M less than a threshold value were labeled as similar pairs; (3) the waveform with the largest number of similar pairs was selected as the master waveform for group 1; (4) all waveforms that were labeled as similar to the master were classified into group 1; and (5) procedures (3) and (4) were repeated for all remaining (unclassified) waveforms to sequentially define groups 2, 3, 4, and later groups. This approach was the same as that used by Green and Neuberg (2006, J. Volcanol. Geotherm. Res.) except that M was used instead of the correlation coefficients.
This procedure with 0.05 for a threshold value of M yielded reasonable classification results (Figure). The features of the waveforms in each group are examined and quantified in the future (possibly before presentation at JpGU).
This study used continuous waveform records from V-net (National Research Institute for Earth Science and Disaster Resilience), Japan Meteorological Agency, and the University of Tokyo. This work was supported by JSPS KAKENHI Grant Number JP21H05203.
(Figure) The waveforms classified into 1st to 12th groups with positive polarity.
To address the characteristics of the waveforms, this study classified the signals of the pre-eruptive tilt changes based on the similarity of the waveforms. The catalog of Maeda (2023) was used, which consisted of the start and end times (1-s resolution) of 3749 pre-eruptive tilt changes. To enable a quantitative comparison of the waveforms, the time and amplitude axes for each signal were normalized to a range from 0 to 1 (or -1 for signals with negative polarity), and the data were resampled at every 0.01 of the normalized time axis scale by linear interpolation. Note that the signals of the pre-eruptive tilt changes were monotonic; the normalized waveforms monitonically increased or decreased from 0 to ±1.
The waveforms of these monotonic signals were difficult to classify using correlation coefficients. To understand this, consider three functions: f1(t) = t, f2(t) = t2, and f3(t) = t0.5, where t is the normalized time. The three functions show linear, acceleration, and deceleration patterns from t = 0 to 1, respectively. Despite the different shapes, the correlation coefficients between f1(t) and f2(t), f2(t) and f3(t), and f1(t) and f3(t) are as high as 0.9682, 0.9798, and 0.9035, respectively. This simple example shows that the differences in the shapes of monotonic waveforms are difficult to quantify based on correlation coefficients. A trial classification of the waveforms using high thresholds (0.98 or 0.99) for the correlation coefficients did not show good performance.
Therefore, this study used an waveform misfit M = {∫[f(t) - g(t)]2dt / (1/2)∫[f(t)2 + g(t)2]dt}0.5 as a measure of the similarity of two waveforms f(t) and g(t); M = 0 if f(t) = g(t), M = 20.5 if f(t) ≠ g(t) = 0, and M = 2 if f(t) = -g(t). The classification method was as follows: (1) M was calculated for every pair of waveforms; (2) the pairs of waveforms with M less than a threshold value were labeled as similar pairs; (3) the waveform with the largest number of similar pairs was selected as the master waveform for group 1; (4) all waveforms that were labeled as similar to the master were classified into group 1; and (5) procedures (3) and (4) were repeated for all remaining (unclassified) waveforms to sequentially define groups 2, 3, 4, and later groups. This approach was the same as that used by Green and Neuberg (2006, J. Volcanol. Geotherm. Res.) except that M was used instead of the correlation coefficients.
This procedure with 0.05 for a threshold value of M yielded reasonable classification results (Figure). The features of the waveforms in each group are examined and quantified in the future (possibly before presentation at JpGU).
This study used continuous waveform records from V-net (National Research Institute for Earth Science and Disaster Resilience), Japan Meteorological Agency, and the University of Tokyo. This work was supported by JSPS KAKENHI Grant Number JP21H05203.
(Figure) The waveforms classified into 1st to 12th groups with positive polarity.