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Sophie Butcher , Andrew Bell , Stephen Hernandez , Eliza Calder

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Sophie Butcher , Andrew Bell , Stephen Hernandez , Eliza Calder Comparing Q factor methods for the analysis of volcano seismic events Sophie Butcher1, Andrew Bell1, Stephen Hernandez2, Eliza Calder1, Mario Ruiz2 1 School of GeoSciences, The University of Edinburgh, 2Instituto Geofísico Escuela Politécnica Nacional, Quito, Ecuador Motivation Methods Results at Tungurahua 800 Decay: 푄 = 2휋푓0휏 where 푓0 is the peak frequency, and 휏 is the point at which the Decay amplitude of the waveform reaches 1Τ of the maximum.4,5 Bandwidth 푒 700 ARMA 푓0 Bandwidth: 푄 = ൗ훿푓 where 푓0 is the peak frequency, and δ푓 is bandwidth, where 3,6 600 the spectra is ½ the power at 푓0 (the corner frequencies). -2000 7 • 105 500 -1500 6 • 105 -1000 Q 400 5 • 105 -2500 4 • 105 300 -2000 PSD 3 • 105 2Amplitude -500 200 2 • 105 -1000 5 100 FIG 1. Tungurahua Volcano, looking east, February 2018. Baños, (population est. 14,000), pictured to the north. -1500 1 • 10 -2000 0 800 • Volcanic earthquakes are an important tool in understanding internal processes 0 5 10 15 20 25 30 3.0 3.2 3.4 3.6 3.8 4.0 26/11 27/11 28/11 29/11 30/11 and eruption forecasts.1 Vital for communities living near active volcanoes. Time (s) Frequency (Hz) Date FIG 4. Decay method to calculate Q, illustrated on an FIG 5. Bandwidth method. Dashed lines show corner FIG 9. All methods applied to one data set generates Q values in different orders of magnitude, with significant scatter. • Earthquake classification broadly determined by metrics like frequency and event from Tungurahua, November 2015. frequencies. Spectra from Tungurahua event. duration.2 • Three methods generate Q values in different orders of magnitude. • The quality factor (Q) is presented in a variety of ways across previous studies. It Auto-regressive moving average (ARMA): decomposes complicated signals with • Increase and decrease in event rate is not coincident with explosion and Q is a measure of waveform energy and can provide insights into driving and peaked spectra into components of harmonic decaying oscillations.7,8 Each remains unaffected. Overall slight increase in Q through the whole episode, in damping mechanisms.3 component is represented in the complex frequency space as frequency, 푓, and all three methods. −푓 9 10 growth rate, 푔, and 푄 = ൗ2푔. • ARMA results correspond best with previous findings. Still to investigate 4 11 10 • 10 similar periods of drumbeat activity for comparison. 4 8 • 10 FIG 10. Event rate and periodicity for LPs surrounding FIG 11. Q by the ARMA method at Tungurahua. Picked Data 6 • 104 26/11/2015 explosion at Tungurahua. LP events surrounding 26/11/2015 explosion. Drumbeat sequences – periodic repeating events that appear very similar to one PSD 4 • 104 2 • 104 Δt = 2.0hrs Periodicity Q calculated by ARMA – EC.RETU..SHZ.D.2015.329-333 120 4.0 40 another. A pre and post explosion sequence from Tungurahua, November 2015. ) 1 -0 - Explosion Explosion Explosion -1 3.5 35 00:00 100 -2 04:00 30 -3 t) 3.0 Δ 80 08:00 Growth rate, g(s -0 -2 -4 -6 -8 10 -Frequency (Hz) 25 12:00 2.5 FIG 6. ARMA method GUI. Poles from the decomposition of the waveform are plotted in complex frequency space. The 60 Local time 16:00 user selects the pole associated with the peak frequency and an average Q can be calculated. Q 20 2.0 20:00 40 15 0 60 120 180 240 1.5 Time (minutes) Rate of events (events/ Validating with Cayambe Data 10 FIG 2. Summary of activity at Tungurahua Volcano, November/December 2015. 20 1.0 Synthetic events – different styles of observed volcanic event types can be 80 0.8 55 generated synthetically for testing. Individual events with added random noise can 20 0.5 70 0.7 make analogous series. 50 26/11 27/11 28/11 29/11 30/11 26/11 27/11 28/11 26/11 29/11 30/11 27/11 28/11 29/11 2000 LP event – EC.RETU..SHZ.D.2015.331 Synthetic LP event 30/11 1500 60 0.6 1500 1000 1000 2500 2500 2000 50 2000 0.5 -500 -500 Amplitude -1000 References Amplitude -1000 -1500 -1500 Q 40 0.4 1Chouet & Matoza, J. Volcanol. Geotherm. Res., 2013, 252, 108-175 7Kumagai & Chouet, Geophys. J. Int., 1999, 138(2), F7-F12. f (Hz) f -2000 -2000 δ 2Lees et al, J. Volcanol. Geotherm. Res., 2007, 176(1), 179-190 8Lesage et al, J. Volcanol. Geotherm. Res., 2002, 114(3-4), 3 14 14 30 0.3 Rossing & Fletcher, Springer Pub, 2004 391-417 4 9 12 12 Elmore & Heald, Courier Corp, 1985 Kumazawa et al, Geophys. J. Int., 1990, 101(3), 613-630 5 10 10 10 Del Pezzo et al, Seismol. Res. Lett., 2013, 84(2), 190-198 Molina et al, Geophys. Res. Lett., 2004, 31(3) 20 6 11 8 8 0.2 Johnson et al, Geophys. Res. Lett., 2018, 45(11), 5436-5444 Bell et al, Earth Planet Sc Lett., 2017,475, 58-70. 6 6 4 4 10 0.1 Frequency(Hz) Frequency(Hz) 2 2 0 5 5 5 5 5 5 0 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 80 Get in touch 10 10 10 10 10 10 08/11 09/11 0.0 • • • • • • Time (s) Time (s) 01/11 02/11 03/11 04/11 05/11 06/11 07/11 10 10 20 30 40 50 60 70 80 6 4 2 4 2 6 Date τ (s) @sophie_butcher_ Check out my blog where I’ll be posting FIG 3. Waveforms, spectra and spectrograms for a real earthquake, and an example of a comparable synthetic event. FIG 7, 8. 200 manually picked events at station EC.CAYA, 2016 days 306-313. ARMA analysis on the left clearly updates from travel, conferences and Assorted data sets – as well as the periodic events at Tungurahua. Mixed separates distinguished event types. When considering the decay and bandwidth methods, the event types separate training across my PhD [email protected] sequences of VTs and LPs from Cayambe Volcano are used to validate methods. and are constrained by bandwidth and event duration https://blogs.ed.ac.uk/sophiebutcher/.
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