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2017

Patterns in eruptions at Fuego from statisticalanalysis of video surveillanceMonica Castro-Escobar

Copyright 2017 Monica Castro-Escobar

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PATTERNS IN ERUPTIONS AT FUEGO FROM STATISTICAL ANALYSIS OF VIDEO SURVEILLANCE.

By

Monica Castro-Escobar

A THESIS

Submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

In Geology

MICHIGAN TECHNOLOGICAL UNIVERSITY

2017

© 2017 Monica Castro-Escobar

This thesis has been approved in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE in Geology.

Department of Geological and Mining Engineering and Sciences

Thesis Advisor: Dr. Gregory P. Waite

Committee Member: Dr. Carol MacLennan

Committee Member: Dr. Thomas Oommen

Department Chair: Dr. John S. Gierke

iii

Table of Contents

Preface ........................................................................................................... iv

Abstract ........................................................................................................... v

1 Introduction ............................................................................................... 1 1.1 Fuego’s eruptive history ...................................................................... 5

2 Methodology ............................................................................................. 8 2.1 Video Monitoring .................................................................................. 8

2.1.1 Explosion onset and duration ....................................................... 9 2.1.2 Plume Height ................................................................................. 10 2.1.3 Thermal Time Series .................................................................... 14

2.2 Statistical Analysis of Repose Times ............................................... 16 2.3 Bulletins of Eruptive Activity ............................................................ 21 2.4 Average Seismic Amplitude, RSAM ................................................. 22

3 Results ..................................................................................................... 23 3.1 Video monitoring ................................................................................ 23 3.2 Statistical Analysis ............................................................................. 25 3.3 Eruptive cycles ................................................................................... 29 3.4 Thermal time series ........................................................................... 30 3.5 RSAM ................................................................................................... 33

4 Discussion .............................................................................................. 35 4.1 Statistical Analysis ............................................................................. 35 4.2 Eruptive cycles ................................................................................... 38 4.3 Video monitoring for volcanic hazard mitigation ............................ 39

5 Conclusion .............................................................................................. 41

6 References .............................................................................................. 43

Appendices ................................................................................................... 49 Appendix A. Authorizations for the use of figures .................................. 49 Appendix B. Results from KST .................................................................. 51

iv

PREFACE

This thesis is submitted in partial fulfillment of the requirements for the

Degree of Master of Science in Geology at Michigan Technological University.

The research describe herein was conducted under the supervision of

Professor Greg Waite in the Geological & Mining Engineering & Sciences

Department between May 2016 and June 2017. Greg Waite collected the data

that I worked with, I analyzed it and wrote this thesis which contains my

findings. This work to the best of my knowledge is original except when other

sources are credited. It is the intention of myself and my advisor to publish this

work in the near by future.

v

ABSTRACT

Fuego, a stratovolcano located in Guatemala, has had historic eruptions

ranging from strombolian to sub-plinian. Since 1999, it has been persistently

active, typically having multiple small strombolian to weak vulcanian eruptions

daily. With the aid of webcam surveillance, the activity for the period of March

2014 to October 2015 was investigated in detail to identify patterns in eruptive

behavior. A cycle of activity, which has paroxysmal explosion on a monthly

average, is a shorter and modified version of previously observed volcanic

behavior. In addition to investigating the monthly cycles, the patterns of daily

explosive eruptions were also investigated. Never before have statistical

models been applied to the eruption dynamics at Fuego to better understand

internal process. For each day, the time interval between successive

explosions was used to fit different probabilistic methods. A moving-average

test and correlation test assessed the stationarity and time-independence of

each data set. Results show a best fit for the log-logistic distribution suggesting

that there are competing processes driving eruptions at Fuego, and that these

processes are constant at least on a time scale of days.

1

1 INTRODUCTION

Advances in scientific equipment and detection systems in the last

several decades, have led scientists to better monitor volcanic activity. (Sparks

et al., 2012). Quantitative methods are sometimes used to explain the

nonlinear dynamics of complex systems such as volcanoes. In some cases, it

may seems that volcanic activity has no apparent pattern and that it is random,

but statistical models can uncover hidden cyclic behaviors and improve the

understanding of volcanic systems. (E De Lauro et al., 2009; Sparks, 2003;

Varley et al., 2006; Watt et al., 2007). A better understanding of magmatic

systems and better monitoring techniques enhances volcanic hazard mitigation

(Spampinato et al., 2011).

On a large scale, volcanoes undergo periods of unrest and dormancy.

Within the active phases, cycles of volcanic activity have been detected in

different volcanic systems. Some of the first important studies on cyclicity were

conducted at Soufriere Hills Volcano. Voight et al. (1999) described dome

growth between 1996 and 1998 using tilt and seismic data. In this model,

edifice inflation was attributed to a cycle that lasted hours to several days and

began when stiff magma with low gas content reduced flow in the upper

conduit. 1Degassing built pressure in the conduit, producing dome growth, and

1 The material contained in this chapter is in preparation for submission to a journal.

2

shallow seismicity. Denlinger and Hoblitt (1999), using data from Soufriere

Hills and Pinatubo volcanoes, compared the cyclic behavior to laboratory

experiments with industrial polymers. Silicic volcanic cycles were attributed to

the interaction between flow resistance and rate of pressurization produced by

magma supply.

More mafic volcanoes also appear to have cyclic activity. For example,

Allard et al. (2006), studied a twelve year cycle at Mt. Etna. The geochemical,

geophysical and volcanological techniques that were implemented to monitor

the cycle that started with the end of the 1991-1993 flank eruption, gave

scientists unprecedented insights about the behavior of the magmatic system.

Jaupart and Vergniolle (1988), describe the transition between lava fountain

and effusive activity as a cycle of collapse and growth of a gas foam layer in

the volcanic plumbing system.

Statistical analyses of eruption intervals provide a useful and relatively

simple tool for hazard evaluation (Connor et al., 2003; Varley et al., 2006).

They typically focus on the timing of eruption onsets; the analysis is based on

the time interval (repose time) between subsequent eruptions. A time series

analysis is done on eruption onsets. This analysis reveals trends or clusters in

the data. For steady state periods, probabilistic functions are applied and

different distributions functions are fitted to the data. The results obtained give

3

information such as variation in eruptive style, prediction of future explosion

timing, or probabilities of eruptive sequences ending.

Effective early warning systems have the potential of forecasting the

beginning of an eruption and tracking notable changes in one. Robust and

precise forecasts at volcanoes are done through analysis in real-time of

discrete-time data. The importance of volcanic monitoring lies in the capability

of decreasing the risks associated with volcanic hazards. The ability to

compose a catalog of volcanic activity allows the creation of “baseline

behavior” that can be used to interpret current changes in volcanic activity. The

data acquired by monitoring a volcano, knowledge of past volcanic history, and

models of how a volcano behaves are the only means of making short-term

forecast for volcanic eruptions. (Loughlin et al., 2015; Tilling, 2008)

Fuego volcano in Guatemala is part of the Central America Volcanic Arc

(Figure 1). Volcanic activity in this region is due to the subduction of the Cocos

Plate under the Caribbean Plate. This 3,800 m edifice is a basaltic to basaltic-

andesite stratovolcano. It represents the southern end of the Fuego-

Acatenango volcanic complex which is made of four craters: Yepocapa,

Acatenango, Meseta and Fuego from north to south (Rose et al., 1978)

4

Figure 1. Location of major volcanoes of Guatemala. https://upload.wikimedia.org/wikipedia/commons/0/04/Map_guatemala_volcanoes.gif

Fuego has been continuously active since 1999. In a detailed study of

eruptive activity between 2005 and 2007 Lyons et al. (2009) observed Fuego’s

activity on a regular basis. They proposed a three stage eruptive cycle: 1)

passive lava effusion and minor strombolian explosions; 2) paroxysmal

eruptions consisting of increased lava effusion and sustained columns of ash

and gas; and 3) degassing explosions with no lava effusion. The pattern

repeated five times in that order during the study.

This research aims to extend the idea of Lyons et al. (2009), that Fuego

has cyclic activity through a detailed statistical analysis of daily eruptions, as

well as the paroxysmal events. Between 2014-2016 there were so-called

5

paroxysmal eruptions about once per month; passive lava effusion in some

instances pyroclastic flows, and strombolian explosions. The increase in

frequency of occurrence of paroxysms compared to the period observed by

Lyons et al. (2009) suggests there have been some changes in the magmatic

system. Seismic data from Instituto Nacional de Sismologia, Vulcanologia,

Meteorologia e Hidrologia (INSIVUMEH) station FG3, a webcam at Fuego

maintained by Michigan Technological University (MTU) and INSIVUMEH, and

statistical analysis of these time series, will be used to investigate the style of

activity leading up to and following each paroxysm. This also helps to

contribute to a better understating of the long-lived activity at Fuego.

1.1 Fuego’s eruptive history

Since the 16th century, Fuego has erupted at least 60 times in a

vulcanian-subplinian style. These violent eruptions, which had have durations

of hours to days, have been characterized by the Volcanic Explosive Index

(VEI) (Table 1) between 3 and 4 (Rose et al., 1978). It also has strombolian

explosions (VEI between 1-2) for periods of months to years (Lyons et al.,

2009). In Fuego’s eruptive history three-quarters of its eruptions can be

clustered into four groups of 20-50 years (Rose et al., 1978) that occur every

80-170 years (Martin and Rose, 1981)

6

Table 1. Volcanic Explosive Index (VEI). Rank goes from 0 (lowest) to 8 (highest).

0 1 2 3 4 5 6 7 8

GeneralDescriptionNon-

Explosive | Small | Moderate | Moderate-large | Large | Verylarge | | |

VolumeofTephra(m^3) 1x104 1x106 1x107 1x108 1x109 1x1010 1x1011 1x1012

CloudColumnHeight(km) | | | | | | | |

Abovecrater<0.1

|0.1-1

|1-5

| | | | | |

Abovesealevel | | |3-15

|10-15

|>25

| | |

Qualitativedescription "Gentle" "Effusive"

Eruptiontype

<-----------------------------Vulcanian----------------------------->

<---------------------"Explosive"---------------------> <---------------------------------"Cataclysmic","paraxysmal","colossal"--------------------------------->

<----------------------------------------------------------"Severe","violent","terrific"---------------------------------------------------------->

<--------------------strombolian-------------------->

<-----------------Hawaiian--------------->

<------------------------------------------------------Plinian------------------------------------------------------>

<-------------------------------------Ultra-Plinian------------------------------------->

One of the latest clusters of vulcanian eruptions began with the 1932

eruption. Prior to this eruption Fuego had been dormant for over 50 years

(Martin and Rose, 1981). It seems that after the 1932 eruption, the intensity of

Fuego’s eruptions increases every ten years or so, as evidenced by the 1944,

1953,1964 and 1974 eruptions. Martin and Rose (1981) mentioned that there

were no records of eruption between the 1930’s and early 1940’s, but between

1944 and 1976, twenty eruptions occurred. The largest eruption from this

cluster happened in October 1974. An ash blanket of more than 0.2 km3 was

produced (Rose et al., 1978). Other volcanic activities that characterized this

eruption were lava flows and pyroclastic flows (Lyons et al., 2009). The high

volatile content leads to more explosive eruptions (Lyons and Waite, 2011).

7

Although the composition of older Fuego deposits were found to be more silicic

with some andesite and basaltic andesite, Fuego’s historic eruptions have

mostly been basalt (Chesner and Rose, 1984). Observations made in 1975

show that activity was characterized by ash-rich eruptions (Yuan et al., 1984).

In 1978 an intermediate-intensity eruption occurred and between 1977 and

1979, Fuego had minor level activity consisting of ash emissions on a regular

basis (Martin and Rose, 1981). From 1980 to 1999 a period of quiescence

dominated the volcano with only VEI 1 activity (Berlo et al., 2012) .

If the period of relative quiescence from 1980 to 1999 marked the end of

the activity cluster beginning in 1932 then a new cluster of activity began in

May 1999. This cluster is characterized by what Lyons et al. (2009) terms open

vent activity; daily minor eruptions that keep the main vent relatively

unconstricted. Eruptive activity for this cluster includes: recurrent small lava

flows, lahars, pyroclastic explosions, and paroxysmal eruptions. This latest

activity is the focus of our present study.

8

2 METHODOLOGY

2.1 Video Monitoring

Figure 2. Location of Panimiche (OVFGO) Webcam. http://ovfuego-norte.geo.mtu.edu/caminfo.php

Since early 2014, MTU and INSIVUMEH have maintained a webcam

(OVFGO) nearly continuously on Fuego. The Axis 1602E camera, sends an

image every 10 seconds from the INSIVUMEH observatory in Panimiche,

located 7 km southwest of Fuego’s summit (Figure 2). Images are transmitted

via cellular modem via FTP to a server at MTU where they are displayed online

9

and stored for later analysis. Routine processing produces time-lapse

animations of the images for analysis. With 10 seconds between images and

30 frames per seconds, sequences are speed up by a factor of 300. In some

cases, there are gaps in the videos due to telemetry problems or camera

malfunctions. In very low light conditions the camera also captures data in the

near-infrared allowing the capture of wavelengths up to 1 micron emitted by hot

material.

The images captured and videos produced, between March 2014 and

October 2015 were used to describe the volcanic activity of each day in terms

of: explosion onset, repose time or time between explosion onsets, number

and/or frequency of pulses, plume/jet height, and physical characteristics of

plume including the color and shape.

2.1.1 Explosion onset and duration

Explosions are defined as, “distinct eruptive jets” (Dominguez et al.,

2016) in individual images or visual records. The onset time was determined

from the time stamp on the webcam image associated with the first emission

from the vent. Given the 10 second time interval, this time has an uncertainty of

up to 10 seconds. For night time videos the end of an explosion was

determined by a lack of incandesce at the summit, once an explosion had been

detected. For daylight videos a technique that was employed was to look for

10

when an explosion column would detach from the vent. The number and

frequency of pulses were calculated using basic arithmetic operations on an

excel sheet where all the information was kept.

2.1.2 Plume Height

Similar to what was done in Arason et al. 2011, Fuego’s summit and a

prominent feature on the west flank of the volcano were used as reference to

calculate plume/jet heights (Figure 3). There is an approximately vertical

difference of 300m between these two reference points which correspond to 74

pixels per 1 km above the vent.

11

Figure 3. Webcam photo of February 20, 2014 showcases the prominent feature left of the summit and height in km above vent.

Using the definition of Mastin et al. 2009, plume height is the distance

between the vent and the top of the volcanic column; the top is where most of

the horizontal dispersion occurs. If there wasn’t any perceivable spread

laterally then the plume height was the elevation between the vent and the top

of the column, before the plume detached from the vent. If an explosion cloud

was detected the pixels between the summit, and the top of the plume were

counted. To verify the accuracy of counting pixels, an image with a vertical grid

was done in Adobe Illustrator (Figure 4), and on Matlab program a grid was

12

created on the same image by changing every 37th row and column to black;

37 pixels equal 500 m (Figure 5). Since both methods yielded the same results,

counting pixels was deemed appropriate and faster for calculations.

Figure 4. Grid made in Adobe Illustrator superimposed on an explosion cloud detected on March 22, 2014.

13

Figure 5. Grid create in Matlab superimposed on an explosion cloud detected on March 22, 2014. Every square is 500 m

The camera was not calibrated to compensate errors in measurements

such as, angle of view of volcano or the spreading direction of the plume

(Scollo et al., 2014). The pixel size was another error that was not accounted

for. Since the camera is at a lower elevation than the volcano, the angle of view

of the camera can affect the observed height of the plumes; only plumes that

were perceived as vertical were measured. Overcast weather days were

excluded and at night the measurement represents the height of the

incandescent jet.

14

2.1.3 Thermal Time Series

Using a Matlab code written by Rüdiger Escobar, the images for the

studied time period were processed to extract image brightness. The

brightness is extracted from the infrared images by summing all of the pixel

values inside a rectangular region of interest. The midpoint of the rectangle

window is given as input so that it captures the summit and area above the

summit. The code completes the rectangle by adding ±45 pixels to the X

coordinate and ±50 pixels to the Y coordinate (Figure 6). The output is a plot

of uncalibrated brightness vs. time (Figure 7). The rectangle encloses the

summit area of interest, because the uncalibrated brightness is associated with

the thermal output of each explosion.

15

Figure 6 Image from February 2015 showing the rectangle around the summit that it used to calculate pixel brightness.

16

Figure 7 .Unscaled thermal radiance for January 12, 2015. X-axis gives the time in 24hour format. Every peak represents an explosion, as detected by the code.

2.2 Statistical Analysis of Repose Times

In order to apply statistical models of renewal processes, the data need

to be stationary and time independent. This means that that each explosive

event has to be independent of the previous one, such that the system

recovers between each event (Dominguez et al., 2016). After establishing that

the data fit these criteria, we tested models that can be used to understand the

physical mechanisms underlying these eruptions.

17

An autocorrelation plot (Figure 8) was done to test the independence

property of each explosive sequence -daily sets of repose times. The autocorr

function in Matlab was used. The data is compared with an identical copy of

itself but the copy has been displaced by a fixed time known as the lag. For

repose times 𝑌!,𝑌!…𝑌! , at times 𝑋!,𝑋!…𝑋! , and a 𝑙𝑎𝑔 = 1, no correlation

exists between the data if the coefficient is zero or varies around zero. If the

autocorrelation coefficient exceeds ±2𝜎 of the mean, we mark the dataset as

not fully independent. Only datasets that did not exceed ±2𝜎 of the mean were

used for the statistical analysis.

Figure 8. Example of the autocorrelation plot for January 11, 2015. Blue lines are the mean ±𝟐𝝈. Values of zero or near zero demonstrate no correlation. Values of +𝟏 show positive correlations and values of –𝟏 show negative correlation.

18

To test for stationarity a moving average test was performed (Figure 9),

on each explosive sequence. The average is calculated every five data points

(Dzierma and Wehrmann, 2010) and a time series plot is done to determine

trends or clusters in the data. Data for time periods when the moving average

is within ± 𝜎 of the mean are considered sufficiently stationary (Dominguez et

al., 2016; Dzierma and Wehrmann, 2010).

Figure 9. Time series plot for January 11, 2015. Red line is the moving average test, blue lines are the upper and lower limits mean ±𝝈 and dotted blue line is the mean. Stationarity is established when the average test stays within the mean limits.

For those datasets that are independent and stationary, we compared

their distributions to a series of commonly used statistical distributions for

volcanic systems such as the exponential, Weibull, gamma and log-logistic

(Bebbington, 2013; Bebbington and Lai, 1996; Connor et al., 2003; Dominguez

19

et al., 2016; Dzierma and Wehrmann, 2010; E De Lauro et al., 2009; Varley et

al., 2006; Watt et al., 2007). Dominguez et al. (2016) used all these statistical

distributions to quantify unsteadiness and dynamics of pulsatory volcanic

activity. Fit to an exponential distribution suggests a homogenous Poisson

process. For example, repose times of explosions at Erebus volcano were

fitted by the exponential distribution and had a Cv = 0.99, suggesting that

dynamics are controlled by a Poisson process (E De Lauro et al., 2009). Both

Weibull and gamma are simple failure models. Watt et al. (2007) applied the

Weibull and log-logistic distributions to explosion repose intervals at Anak

Krakatau volcano in Indonesia. It was found that the data was fitted by two

Weibull distributions; the first half of the data was fitted by a Weibull distribution

and the second half of the data by another Weibull. Both of the lines

intersected at the mean which indicated two failure modes. The log-logistic

distribution was able to fit the data with just one line, modeling the multiple

competing processes. The log-logistic was also used to fit the distribution of

vulcanian explosions at Soufriere Hills Montserrat (Connor et al., 2003). They

concluded that competing process dominated explosion dynamics.

The repose times for explosions on a given day were examined in the

following way. First, a histogram of each eruptive sequence was plotted to

illustrate the distribution of explosions for the day. These were then plotted as

20

different distribution functions. The distribution of each eruptive sequence can

be described using the probability density function (PDF), a cumulative

distribution function (CDF) or the closely-related survivor function (SF). The

PDF describes the probability that a given repose interval will exceed some

time period t but will not exceed t + dt:

𝑓! 𝑡 = lim!"→!!(!!!!!!!")

!".

(1)

The CDF is the probability that the repose interval is shorter than the time

period t:

𝐹! 𝑡 = 𝑃 𝑇 ≤ 𝑡 = 𝑓!!! 𝑢 𝑑𝑢.

(2)

The SF is simply 1 minus the CDF and describes the probability of the repose

time, T, lasting for at least time, t:

𝑆! 𝑡 = 𝑃 𝑇 > 𝑡 = 1− 𝐹!(𝑡)

(3)

The maximum likelihood function (MLE) of Matlab was used to fit the

data to the following distributions: exponential, Weibull, gamma, and log-

logistic. The Kolmogorov-Smirnov Test (KST) was then used to evaluate the

21

goodness-of-fit. The KST is based on the maximum distance between two

curves evaluated at 5% confidence levels. A result of 1 rejects the null

hypothesis that the curves are from the same distribution; and a result of 0 fails

to reject the null hypothesis. The p-value result of this test indicates how likely

the proposed distribution generated the data (Bebbington, 2013). In addition to

the KST, the coefficient of variation 𝐶! was also calculated for each data set.

This technique can establish how clustered a data set is :

𝐶! = 𝜎∆𝑡∆𝑡

(4)

Where 𝜎∆𝑡 is the mean value of the repose times and ∆𝑡 is the repose

interval between events. For 𝐶! = 1 indicates a Poisson process, a clustered

process is given by 𝐶! > 1 and 𝐶! = 0 is periodic process (E De Lauro et al.,

2009; Varley et al., 2006).

2.3 Bulletins of Eruptive Activity

INVISUMEH publishes daily reports- Boletin Vulcanologico Diario- about

the activity at Fuego. The bulletins also provide other information such as

weather conditions, wind velocity and precipitation amounts at the observatory

in Panimache. When the volcano is in an effusive or explosive phase, they put

22

out special bulletins called: Special Volcanology Bulletin. Bulletins of the

current calendar year are published on the INSIVUMEH website

(http://www.insivumeh.gob.gt) by week and by month. INSIVUMEH sends their

daily bulletins to the Geology department of MTU. Unfortunately due to logistics

not all bulletins for the intended research period were obtained. These bulletins

aid with the identification of the onset of paroxysmal events.

2.4 Average Seismic Amplitude, RSAM

Although there are a number of ways to evaluate seismic data,

examining many months of data for comparison with long-term cycles of

activity is best done using a data product that distills and simplifies the signals.

We used 10 minute average absolute seismic amplitude, commonly called

RSAM (Realtime Seismic Amplitude Measurement), from the seismic station

FG3 between March 2014 and October 2015. The RSAM (Figure 16) was

plotted to visualized trends or cycles in the volcanic activity at Fuego. RSAM

correlates well with the level of volcanic activity (Endo and Murray, 1991).

23

3 RESULTS

3.1 Video monitoring

The webcam instrument at the Fuego Panimache observatory captures

an image every 10 seconds when the internet is available. These are then

processed into time-lapse videos each day. In addition to data gaps because of

telemetry problems, another source that produces gaps in the information

collected from the videos is weather. Overcast, cloudy, and foggy days don’t

allow for the proper timing of the onset of an explosion. If the volcanic activity

was dominated by puffing or constant gas emission, it was difficult to discern

the explosion cloud from background clouds or fog. If clouds were ‘sitting’ at

the summit of the volcano or they obscure the view of the summit, the starting

time of an explosion could not be properly determined. Is worth mentioning that

the dry season in Guatemala runs from November to April and the rainy season

from May to October. Better observations are done during the dry season

because the volcano tends to be less obscured by clouds. The visual

inspection of these videos provided the bulk of the data used in the analysis

here.

Even though the videos contain 24 hours of surveillance, in practice,

only between 10-14 hours were actually useable. As a general trend clouds

would obscure the summit after 16:00-UTC and the volcano was not clearly

24

visible before 2:00-UTC. Approximately between 00:00 UTC and 12:00UTC the

IR filter of the camera turns off and explosions were perceived as incandescent

jets of magma. Very rarely could one see the explosion cloud; this mostly

happened during a full moon. During the other twelve hours the IR filter would

be turn on and one could only see the explosion cloud. This sometimes

explains the discrepancy in explosion count during night-time vs day-time.

Table (2) shows an example of how the information was tabulated to be

later used in the statistical analysis. Although at times the onset of an explosion

could not be determined, the time when the explosion was detected was

recorded to have a more accurate count of daily explosions. The repose time

between explosions was only calculated for events whose onset was accurate.

Table 2. Excerpt of the tabulated data obtained from the videos. Times are given in UTC in a 24hour format (HH:MM:SS).

25

3.2 Statistical Analysis

The detailed statistical analysis was performed on the time period from

November 2014 to March 2015. There were only 100 videos available, 66% of

total days. Figure 10 shows (a) the daily explosion count, (b) daily mean

repose time for the available videos. A time series analysis of each explosive

sequence, regardless of explosion type (Watt et al., 2007), was done to test for

stationarity and independence. Figure 11 shows an example of the results

obtained for each day. Due to the lack of significant data for repose times, 17

videos out of the 100 available were not used for statistical analysis. Without

sufficient repose time intervals stationarity cannot be convincingly established.

All of the explosive sequences analyzed have repose intervals that are time-

independent as showed by the lack of correlating peaks in the correlogram,

and are stationary since the running average test does not go over the mean

± 𝜎 limits.

26

Figure 10 (a) Daily explosion count. Gaps in information are represented by lack of bars.(b) Open circles are the daily mean. Semi horizontal lines represent gaps in the information Vertical red lines with asterisk in all plots are the paroxysms events observed between November 2014 and March 2015.

Figure 11 (a) Plot of probability functions PDF, CDF and SF and fitted distribution. (b) Time series plot of explosions on December 05, 2014 showing stationarity. Blue lines represent the mean ±𝝈 and mean (middle), red line is the moving averege test. Data set also exhibits independence property as shown by the lack of correlation.

27

The KST was used to assess the fit of the data (repose times) to

different statistical distributions. The higher P values indicate that the best-

fitting distribution is the log-logisitc.

Table 3. Excerpt of the results of the KST P-value. This value expresses how good the data fits each distribution; the higher the P value the better the fit. The highest P values are cells highlighted in red with red numbers.

The Coefficient of Variation was a technique use to further analyzed the

results. As Figure 12 shows most of the data is between 0.05 and 1.5. A

𝐶! = 1, means the data exhibits a Poisson process.

28

Figure 12 Coefficient of Variation calculated for the 83 videos used for the statistical analysis. Vertical red lines with asterisk are paroxysmal eruptions.

The shape parameter of the Weibull distribution was also used to

analyze the data (Figure 13). The Weibull distribution is a special case of a

renewal process because it allows variable hazard rates. When its shape

parameter is one, the distribution reduces to a Poisson process. If the shape

parameter is greater than one, the failure rate increases over time, and if the

shape parameter is less than one the failure rate decreases with time.

(Bebbington, 2013; Bebbington and Lai, 1996; Cronin et al., 2001). As shown

in Figure 13, the Weibull shape parameter distribution oscillates between 0.8

and 1.6, but hovers around 1.2.

29

Figure 13 Weibull shape parameter distribution. A value of one points out to a Poisson process.

3.3 Eruptive cycles

For the period between March 2014 and October 2015 eight paroxysms

were observed, roughly one per month. There wasn’t any precursory activity

that signaled the start of paroxysmal activity although INSIVUMEH generally

noted an increase in activity in the day or days prior to the paroxysms. The

beginning of paroxysms was marked by lava effusion and explosions. Lava

flow would increase for an average of two days before ceasing and the

associated explosions were strombolian. White thin columns were observed

during daylight with what appeared to be a semi constant ash emission. The

30

February 7th and June 30th paroxysms seem to have more violent explosions

because clouds were thicker and darker than those of other paroxysms.

INSIVUMEH reports that pyroclastic flows developed for both of these

paroxysms.

In between paroxysms the volcanic activity didn’t have an apparent

pattern. Some days had minor vulcanian explosions, other days activity was

dominated by degassing. The months of November and December had the

most explosions (Figure 10). These two months were characterized by what

was termed as ‘incandescent pulsing’. At night these explosions were pulses of

magma that lasted seconds and were less than 100m in height, during the day

they were describe as puffs. Other months exhibit this behavior as well but it

was the main activity during November and December.

3.4 Thermal time series

An example of the results obtained with the thermal time series Matlab

code is shown in Figure 7. In general, the sharp peaks represent explosive

eruptions that produce hot ejecta that emit in the infrared. Although other

factors, such as clouds, can influence the brightness of pixels in the region of

interest, we can typically assume that higher peaks represent bigger

explosions. While low clouds can obscure or completely block the transmission

31

of light from the volcano, high clouds may actually intensify the brightness

values. In heavy fog, a street light near the camera appears at the lower left

corner of the camera interfering with the results. Figure 14 gives an example of

results obtain when the night is cloudy. The peaks in this thermal time series

plot don’t necessarily match the onset of explosions. Figure 15 is how lava

effusion is perceived by the code. In comparison with Figure 9 where the peaks

are more distinct and most of them do match the onset of explosion, there is

not much information that can be extracted when there are clouds or even

when explosion eject substantial amounts of ash. Eruption clouds have the

same effect as low clouds. The code certainly has its benefit and could even be

automated to do calculation every time an image is received but careful

consideration must be paid as to how results are interpreted.

32

Figure 14 Thermal time series plot for January 6, 2015. Peaks do not necessarily represent explosions since this was a cloudy night.

33

Figure 15 Thermal time series plot for February 7, 2015. Lava effusion had started this day.

3.5 RSAM

The RSAM is plotted with all the paroxysm events from January 2015 to

October 2015 (Figure 16). As results shows, the RSAM increases near the

paroxysm. This kind of plot is extremely helpful when trying to predict when

volcanic activity might increase. This tool can also be use to visualize a pattern

in the activity if any. Unfortunately Fuego’s seismic station is near a road within

a working farm and orchard. The daily activity of people walking and cars

34

passing by, is picked up by the station as noise. Although large scale events

are clearly seen in the RSAM, if some sort of small scale cycle is detected, it

would prove difficult to conclude if the cycle is due to volcanic active or

because of noise.

Figure 16 RSAM plot between January and October 2015 (blank line). Red lines with asterisk are paroxysmal eruptions.

35

4 DISCUSSION

4.1 Statistical Analysis

The only apparent limitation for the use of statistical analysis is lack of

data to convincingly establish stationarity. This tool can be applied to different

volcanic systems (eg. basaltic, andesitic, dacitic), exhibiting a range of volcanic

activity, over shorts periods of time (daily explosion) or longer periods of time

(historic eruptions) (Bebbington, 2013; Bebbington and Lai, 1996; Connor et

al., 2003; Dominguez et al., 2016; Dzierma and Wehrmann, 2010; E De Lauro

et al., 2009; Varley et al., 2006; Watt et al., 2007). For this research, all types

of explosions at Fuego were considered, and the statistical analysis was done

on daily datasets.

All data sets examined in detail show a lack of correlation, therefore they

are time independent. They are also stationary since the average test does not

go over the mean ±1𝜎 limit (Dzierma and Wehrmann, 2010). In a steady state

eruption there is a lack of memory in the volcanic system thus the onset of an

event is only dependent on the repose time from the previous event. The

driving force of an eruption will not change because the system resets after a

previous event (Bebbington, 2013; Dominguez et al., 2016).

If there are subsets in the data that do not show stationarity, this can be

36

interpreted as having missing events on the record or that the frequency in

events changed (Dzierma and Wehrmann, 2010). There are days at the

beginning or end of the data set, that show nonstationarity (Figure 17). This

part of the record correlates with days that either the video was not optimal;

either it had a lot of missing frames or the weather was not appropriate to count

explosions.

Figure 17 Statistical analysis for Novemeber 28, 2014. Running average test shows non-stationarity during the last five hours. This period correspond with a period of clouds.

The KST indicates the data is better fitted by the log-logistic

distribution as shown by the bigger 𝑃 values. Dominguez et al. (2016) suggest

that a lack of fit by the exponential distribution indicates that explosion

mechanisms are not control by a homogenous Poisson process therefore the

37

volcanic system is controlled by failure modes that are not random with variable

hazard rates. The Weibull distribution reduces to a Poisson process when its

shape parameter is one (Varley et al., 2006). Although the coefficient of

variation (Figure 12) and Weibull parameters (Figure 13) are suggestive of a

Poisson process – they both have a mean values near one – the variability of

failure rates discards this possibility; a Poisson process has constant failures

rates (Bebbington, 2013).

Lyons and Waite (2011) concluded that the viscosity of Fuego’s

magmas increase dramatically as they approach the surface due to

crystallization, water loss, and the exsolution of other gasses. This process

results in the creation of a magma plug that seals the conduit. Nadeau et al.

(2011) identified a secondary vent at Fuego that was not affected by the

plugged conduit and continued to have degassing explosions. The vents are

close enough that they cannot be discriminated form the webcam images 7 km

away, so the explosions observed in this study may have com form multiple

vents with somewhat different physical characteristics. Watt et al. (2007) and

Connor et al. (2003) both found that dominant competing process in the upper

conduit are modeled by a log-logistic distribution. Given the lack of fit by

exponential distribution one can assume that there is not one dominant process

at Fuego but instead several ones that control failure mechanisms.

38

4.2 Eruptive cycles

Here we describe the changes in longer-term, monthly, cycles of

eruptions over the last 10 years. Lyons et al. (2009) described the eruptive

activity at Fuego between 2005-2007 as dominated by cycles. Each cycle

consisted of 1) lava effusion with subordinate strombolian explosions, follow by

2) a paroxysmal stage where lava effusion was accompanied by more violent

explosions that persisted for 24-48 hours, and 3) the last stage of the cycle was

described as degassing explosions. After this the cycle would start again.

This cycle was attributed to a growth and collapse of a gas foam layer at

some location in the conduit. Paroxysmal eruptions were produce with the

collapse of the foam layer, following this the cycle goes into the degassing

phase, and passive lava effusion is produce as the foam layer grows. The

growth of the gas foam layer is controlled by gas flux or magma viscosity.

In 2014, the cycle has shortened and changed. Between March 2014

and October 2015 there were eight paroxysm, a cycle time about half as long

as the increment for the cycles observed between 2005 and 2007. The cycles

observed during 2014-2015 have other differences as well. Perhaps the most

notable difference is that the paroxysms are not preceded by lava effusion, but

are coincident with the start of lava effusion. In fact, there were very few

39

instances of active lava flows enduring for more than a few days during the

2014-2015 period. The nature of the explosions that accompanied the

paroxysms did not change in the 2014 to 2015 cycle. In some occasions the

activity would have more violent explosions, but for the majority of time activity

was dominated by strombolian explosions. The number of explosions counted

during paroxysmal eruptions was lower than at other times. This is due to the

fact that during daylight there was a semi constant emission of ash and thus

smaller explosions or puffing activity could not be visually detected. At night the

incandescence from the lava obscured the detections of smaller explosions

and only those that were more violent were accounted for. In between

paroxysms the activity changed yet there wasn’t an apparent cycle or pattern to

it. Video quality, missing videos, and weather sometimes made it difficult to

assess exactly how the volcanic activity changed before and after a paroxysm.

4.3 Video monitoring for volcanic hazard mitigation

A study conducted in developing countries revealed that out of 441

volcanoes, 380 or more have no monitoring or rudimentary monitoring,

including at least 60 volcanoes that were deem as a high risk for big

populations (Sparks et al., 2012). Limited resources at some locations in Latin

40

American countries restrict the monitoring of active volcanoes (Webley et al.,

2008). Cameras have become an important component of a volcano

observatory (Patrick et al., 2014). Most volcanic features can be observed with

such elementary and low cost equipment (Stoiber and Williams, 1990) allowing

monitoring in real-time by visually tracking ongoing activity (Patrick et al.,

2014). These observations provide meaningful knowledge of the condition of

an active volcano. They also ameliorate the quantitative assessment of

volcanic activity and are vital to confirm physical models that are proposed to

explain eruptive processes (Bertucco et al., 1999). Video monitoring does not

come without caveats. As discuss in previous sections noise sources such as

camera vibration, light sources outside area of interested, variable atmospheric

and light conditions can sometimes limit the analysis performed on visual

records. Nonetheless the accumulation of such robust data sets can aid in the

establishment of a baseline behaviors that allows interpretation of changes in

volcanic activity.

41

5 CONCLUSION

Statistical analysis can uncover hidden cyclic behaviors and improve the

understating of volcanic systems. The surveillance videos of a webcam located

7km away from Fuego Volcano were used to extract the onset time, describe

the styles and obtain a daily count of explosions. The onset and repose times

of explosions at Fuego were analyzed to confirm that the data was stationary

and time-independent. A lack of correlation among data sets confirms that

explosions at Fuego are time-independent. Time-independence also refers to

explosions only being dependent on the time that has passed since the last

event. A running average test was performed on the daily explosion time

sequences to determine stationarity. Having shown that the explosive events

during the period between November 2014 and March 2015 are stationary, it

can be said that after each explosion the system recovers and the probability of

having a certain type of explosion is the same for all events. Several

distributions were fitted to the data to explain explosion mechanisms. A lack of

fit by the exponential distribution means that Fuego’s explosion mechanisms

are not controlled by one dominant process. Instead there are several

dominant processes acting on Fuego as seen by the favorable fit for the log-

logistic distribution. This is evidence of the several processes known to cause

eruptions at Fuego such as crystallization, higher magma viscosity, gas

exsolution among others.

42

There have been significant changes in the activity levels of the cluster

that began in 1999. A three-stage cycle dominated the time period between

2005 and 2007; lava effusion with strombolian explosions, paroxysms, and

degassing. After four years of low volcanic activity, Fuego’s activity increased

tremendously after 2014. Between January and October of 2015, eight

paroxysms occurred on a monthly basis, a much shorter time than the 2005-

2007 cycle. This points to a change in the dynamics of explosions at Fuego. It

is evident that something about the previously proposed mechanism of growth

and collapse of a gas-foam layer at the conduit has changed, yet it is difficult to

fully assess what changes are occurring at Fuego’s magmatic system to cause

such increment in eruptions.

43

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49

APPENDICES

This thesis includes the following appendices with supplemental

information. Appendix A, contains the authorization for the figures use in this

thesis; appendix B, has the results from the Kolmogorov-Smirnov Test; and

appendix C, contains the results of the statistical analysis and it can be

downloaded from the online repository.

Appendix A. Authorizations for the use of figures

Figure 1: “Volcanoes of Guatemala” by USGS. Downloaded from

Wikipedia. The image is in the public domain in the United States because it

only contains material that originally came from the United States Geological

Survey, an agency of the United States Department of the Interior.

https://upload.wikimedia.org/wikipedia/commons/0/04/Map_guatemala_volcano

es.gif Access June 2017.

50

-------------------------------------------------------------------------------------------------------

Figure 2 to figure 6

51

Appendix B. Results from Kolmogorov-Smirnov Test

Table 1. The table below shows the results of the P value for each statistical distribution using the KST. This value expresses how good the data fits each distribution; the higher the P value the better the fit. Highlighted in red with red numbers, are the highest values for each day. Results show a better fit for the loglogistic distribution.

52

Table 2. (Continuation from the Table 1) The table below shows the results of the P value for each statistical distribution using the KST. This value expresses how good the data fits each distribution; the higher the P value the better the fit. Highlighted in red with red numbers, are the highest values for each day. Results show a better fit for the loglogistic distribution.

53

Table 3. (Continuation from Table 2) The table below shows the results of the P value for each statistical distribution using the KST. This value expresses how good the data fits each distribution; the higher the P value the better the fit. Highlighted in red with red numbers, are the highest values for each day. Results show a better fit for the loglogistic distribution.