What’s the big fuss about
Harmonic Tremor on Volcanoes?
Jonathan M. Lees
New Mexico Tech, 2009
Where is it observed?
Karymsky, Kamchatka
Arenal, Costa Rica
Sangay, Ecuador
Reventador, Ecuador
Tungurahua, Ecuador
*Santiaguito, Guatemala
(Semeru, Merapi…others?)
Typical VT event at Mt. Merapi,
Indonesia
a) typical example of a VT-B type event recorded during a high
activity phase at Mt. Merapi. Note that the overall frequency
content is mainly between 1 — 10 Hz with a dominant
frequency at roughly 3 Hz. b) zoomed out version of the same
event in its three components. Whereas the P-wave arrival is
clearly visible, no clear S-wave arrival can be seen. The circle
marks the wavelet that has the approximate S-wave travel time
for the estimated source location
http://www.seismo.com/msop/nmsop/13 volcano/volcano2/volcano2.html
Low Frequency Events
a) example of a LF-wave group
recorded at Mt. Merapi. Clearly the
dominant frequency is around 1
Hz. b) shows an example of a LF
event recorded at two different
sites located at Redoubt volcano,
Alaska (courtesy of S. McNutt,
Alaska Volcano Observatory; AVO).
The spindle shaped signal is also
known as Tornillo.
Harmonic tremor signal recorded at Mt. Semeru, Indonesia. Up to six overtones can be
recognized starting with a fundamental mode located at roughly 0.8 Hz.
Typical Karymsky Chugging Event, 1997
Initial explosion
Chugging
Acoustic
Vertical
North-South
East-West
Simple Harmonic Motion
Sinusoid : 5 Hz (sample rate = 0.001)
Sinusoids with 4 frequencies, 5,10, 15, 20
Ten harmonics, 5 through 50 Hz
10 Random Frequencies
10 frequencies around the harmonics randomly perturbed
10 frequencies around harmonics with slight perturbation
Harmonic Tremor
• Common on Volcanoes
• Provides Constraints for Conduits:
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Geometry
Composition
Density
Visco-elastic parameters
Many researchers have contributed
to the study of Harmonic Tremor
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K. Aki & M. Fehler
B. Crosson
B. Chouet
B. Julian
S. McNutt
M. Ripepe
V. Schlindwein
M. Hellweg
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E. Gordeev
T. Ohminato
M. Garces
M. Yamamoto
H. Kumagai
T. Nishimura
R. Leet
K. Konstantinou
(review)
In this presentation we are concerned with tremor that is accompanied by
infrasonic emission
Note Tremor on Seismic
?
Reventador tremor
Reventador tremor
Reventador tremor
Reventador tremor
Seismo-Acoustic Tremor:
Chugging
• Observed when seismic and acoustic waves are
discerned and correlated
• Examples:
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Arenal (Benoit & McNutt, 1997; Garces, 1998; Hagerty et al. 2000)
Karmysky (Johnson & Lees, 1999; Lees et al. 2004)
Sangay (Johnson & Lees, 1999; Lees & Ruiz, 2008)
Reventador (Lees et al., 2008)
Tungurahua (Ruiz et al., 2005)
Fuego (Lyons et al.)
Santiaguito (Lees et al.)
Slow
Fast
Video
Infrasound Chugging at Karymsky, 1997
While there are similarities between these
chugging sequences, there is also
considerable variability.
Examples of Chugging at Sangay Volcano
Chugging Spectrum
Gliding
Chugging Sound:
Karymsky Infrasound, 1997
Fundamental Mode….and Harmonics?
Karymsky Infrasound, 1997
Numerous episodes of seismo-acoustic tremor exhibit
fundamental frequencies ranging between 0.7 to 1.4 Hz.
21 chugging events at Karymsky
Karymsky, tremor (chugging)
Santiaguito Explosion from 2009
V = vertical
I = Infrasound
Zoom of Santiaguito explosion, 2009
What is the best model
to explain these
physical phenomena?
Active vent
V. Schlindwein
M. Garces
S. Mcnutt
Others…
M. Hellweg
M. Hellweg
J. Johnson
J. Lees
Possible Physical Models
• Harmonic Oscillations –
Organ Pipe Modes?
• Periodic Bubble/Slug Formation?
• Flow Past Small Obstruction?
• Cork/Viscous Plugging –
Pressure Cooker Modes
Milton Garces’ Model:
Organ Pipe Modes
Arenal Volcano, Costa Rica
1  g1
2
 g1 
2
c
2
1
t
2
1  g2
2
 g2 
2
c2 t
2
2
0
 
 Q  (t )  ( R  R ' )
Garces Approach: Model Fourier Spectrum
Organ Pipe Mode Explanation of Volcano Chugging
Rijke Tube
Excitation of fundamental modes
And harmonics in a column of fluid
Resonating Cylindrical Conduits
Integer Harmonics
Open-Open
L 

f n  nf 1
2
f1 
v
2L
Odd Integer Harmonics
Open-Closed
L
n  2, 3, 4,K
f1 
Closed-Closed

f n  nf 1
4
v
4L
Integer Harmonics
L 

2
n  3, 5, 7,K
f1 
v
2L
Correlation of interval time and amplitude:
indication of non-linear, feed back mechanism
Sangay
Linear Trends
Karymsky
Slope Analysis: Amplitude vs Time Delay
Positive slopes
Sangay, Ecuador
Multiple Chugging Events
Chugging at Santiaguito: Linear
amplitude-repose time until
change in vent modifies
relationship in time.
Pressure Cooker Model
Steam Vent
Set of coupled, non-linear
Differential Equations
Lees and Bolton (1999)
Damping
Acceleration of plug
3Q m
( x  xc ) / xc
A
A
x  (( P  P )  g )(1  ce
)  2  x 
m  4a
1
2 m
n





Non-negative
RT
B  n  Q 
P 
m
0
V 
n  A  B T
in B
Qs
P a n3  P x 3
2
P  0
1
a n3  x 3
Pressure in Pot
Number of Molecules in Pot
Pressure in Vent
Ram effect





2
Back of the envelope calculation
plug
Cone plug, radius R=20m, height h=20m
Force = .2×109N
Pressure = .1 MPa
 3Q
( x  xc ) / xc

A
A
m
x  (( P  P )  g )(1  ce
)  2  x 
m   4 a
1
2 m
n

RT

B  n  Q 
P 
m
0
V 
n  A  B T
in B
Qs
P a n3  P x 3
2
P  0
1
a n3  x 3
Pressure Cooker,
Lees and Bolton, 1999





2
Karymsky
Volcano,
1997
1998
Active vent
No Chugging
1999
Moderate Chugging
Lots of Chugging
Karymsky Volcano, Infrasound, 1997
f
t
 Derivative of Frequency w.r.t Time
BLUE=Derivative
RED=spectral line
Take time derivative of each
line to estimate variations in
rate of change of frequency
with respect to time
Karymsky Volcano, Infrasound, 1997
Checking for Harmonics
BLUE=Predicted = N*f0
RED=Observed
For times when there are
many harmonics, predict
the harmonics as integer
multiples of the
fundamental frequency.
Time Domain Analysis: Precise timing of individual events