Today

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Volcano Seismology - 16 March 2009

• Today
• Long-period earthquakes and complex frequencies
• Estimate fluid type from frequency-attenuation
  relationship of LP coda
• The Sompi method
• Deep Long period earthquakes
• Examples and case studies
• Midterm exam on Wednesday 18 March

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Sompi method

• LP earthquakes typically characterized by
  dominant frequency and decaying amplitudes
• The frequency and decay characteristics can be
  used to determine the type of fluid involved in
  the source

From Kumagai and Chouet, GJI, 1999
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Sompi method

• Sompi is from a Japanese word meaning
  existence?
• An application of an Autoregressive model
• AR typically used for prediction
• In this case, used for extracting complex
  frequencies
• Frequency and growth rate
• Complex frequency f-ig
• f - frequency
• i - sqrt(-1)
• g - growth rate
• Dimensionless measure of the increase in
  amplitude
• Negative values indicate decay
• So Sompi is used to extract the decay
  characteristics and dominant frequencies together

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How does the Sompi method work?

• Think of a simple regression technique, like
  least squares

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How does the Sompi method work?

• Think of a simple regression technique, like
  least squares
• You can fit the data with polynomials of
  different degrees (orders)
• Loop over many orders (from 20-60) and find
  parameters f and g for each
• Where many points are nearly the same (same f and
  g for different polynomial orders), the signal is
  stable for many different orders and there is
  some confidence that the parameters are
  significant

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Sompi method

• Attenuation quality factor, Q, estimated from
  complex frequency
• Large Q (small Q-1)- little attenuation
• Q-1 Qi-1 Qr-1
• Intrinsic Qi-1
• Energy lost through internal friction
• Conversion of seismic energy to heat
• Qr-1 from radiative losses
• Resonance
• Scattering
• Sompi method addresses only Qr-1
• Intrinsic Qi-1 also affected by crack and fluid
  properties, but may be less important
• The quality factor can be expressed in terms of
  the complex frequency
• Q-1 -2g/f

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Sompi method

• Sompi method estimates f and g for different AR
  orders
• Similar complex frequencies found for many orders
  indicate best estimates

From Kumagai and Chouet, GJI, 1999
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Sompi method

• Only the coda is used, not the inhomogeneous part
  at the beginning of he seismogram

From Kumagai and Chouet, GJI, 1999
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Sompi method

• Q varies from 10 at Redoubt to 1000 at
  Kusatsu-Shirane and Galeras

From Kumagai and Chouet, GJI, 1999
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Sompi method

• Q varies from 10 at Redoubt to 1000 at
  Kusatsu-Shirane and Galeras

From Kumagai and Chouet, GJI, 1999
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Sompi method

• One way to interpret Sompi results is to use
  numerical simulations (Kumagai and Chouet, JGR,
  2000)
• Assume crack (rock) properties
• Fix crack elastic parameters and dimensions
• Vary density and VP of fluid
• Generate synthetic LPs
• Identify dominant frequencies
• Estimate complex frequencies

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• Ranges of ?s and a for crack fluid
• Qr - Almost monotonically increases with
  increasing impedance contrast, Z (?s?/?fa)
• Dimensionless frequency decreases with increasing
  ?/a and ?f/?s

?/a
From Kumagai and Chouet, JGR, 2000
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Sompi method
From Kumagai and Chouet, GJI, 1999
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Sompi method
From Kumagai and Chouet, GJI, 1999
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Sompi method

• High Q is best explained by a dusty gas
• Dust 1 ?m
• Only tested fluid that can produce long-lived
  coda with Q significantly greater than 100
• Low Q results can be explained by a variety of
  fluid mixtures
• Frothy basalt
• H2O gas- CO2 gas
• Bubbly water
• Dominant frequencies are different!
• Crack dimensions are the same
• Only the fluid content has changed

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Sompi method

• Qi can not generally be neglected
• If Qi is low, there will be no resonance
• Qi can vary over several orders of magnitude
  depending on, e.g.,
• bubble radius
• bubble density (gas fraction)
• wavelength (frequency)
• Simply varying the bubble radius can explain
  changes in Q over two orders of magnitude (Nakano
  et al., JGR, 1998)

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Sompi method examples from Mt. Spurr, summer 2004

• Long duration LPs (up to 40 s)
• Sharp spectral peaks (.8 - 2.2 Hz)
• Dominant frequency and Q varied with time
• Generally declined
• Q from 100 to 25
• f from 2.2 to 0.8 Hz

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Sompi method examples from Mt. Spurr, summer 2004

• July, August, and Sept events on same two stations

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Sompi method examples from Mt. Spurr, summer 2004

• Sompi analysis of July, August, and Sept events

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Sompi method examples from Mt. Spurr, summer 2004

• Temporal variations of peak frequencies Q

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Sompi method examples from Mt. Spurr, summer 2004

• What caused temporal variation?
• increased volatile content (drying out of crack)
• Lower a and ?f
• higher impedance contrast
• Lower Qr
• Depending on relative decreases in velocity and
  density, could explain decrease in frequency
• Would lower bulk modulus of the fluid and lower
  crack stiffness
• Should increase frequency!
• Change in crack geometry
• As crack stiffness increases, frequency decreases
• Increased crack length or decrease in crack
  thickness would increase crack stiffness
• Many causes and effects are interlinked and some
  are probably not well understood!

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Characteristics of Deep Long Period Earthquakes

• Deep!
• lower crust or upper mantle
• 10-40 km
• P and S are both visible in some cases
• S is predicted for some resonating source models
  (cracks, vertical pipes), but not all (sphere)
• Sometimes have long, monotonic coda
• Often have emergent onset
• Observed in many areas
• Hawaii
• Alaska
• Long Valley
• Cascades
• Japan

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Characteristics of Deep Long Period Earthquakes

• Enigmatic, but presumed to be related to fluids
• sometimes related to eruptions, e.g.,
• Pinatubo 1991
• Spur 1992 (coincident)
• Mauna Loa 2002 (inflation, not eruption)

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Deep Long Period Earthquakes at Hawaii

• Swarms of similar events observed
• Swarm (31 events) preceded start of inflation of
  Mauna Loa
• Large swarm in 2004-2005 modulated by teleseismic
  waves
• Rate of occurrence declined following Sumatra
  MW9.3
• Strong evidence for relationship to magma
  transport
• Temporal relationship to inflation of Mauna Loa
• Relatively stationary, non-destructive source

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Deep Long Period Earthquakes at Hawaii
Okubo and Wolfe, JVGR, 2008
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Deep Long Period Earthquakes at Hawaii

• Subset of data from 2004-2005 swarm

Okubo and Wolfe, JVGR, 2008
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Deep Long Period Earthquakes at Hawaii

• Relocated earthquake locations
• 50 were tossed
• cross-correlation
• double-difference
• nearly identical source
• Directly below inflation source

Okubo and Wolfe, JVGR, 2008
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Deep Long Period Earthquakes in Aleutian Arc

• Occur under 11 volcanoes
• 10-45 km depth
• Emergent onset
• Extended coda
• Peak frequency 1-3 Hz
• Dominantly body wave energy
• Solitary or sequences of events

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Deep Long Period Earthquakes in Aleutian Arc
Power et al., JVGR, 2004
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Deep Long Period Earthquakes in Aleutian Arc
Power et al., JVGR, 2004
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Deep Long Period Earthquakes in Aleutian Arc

• Other observations/inferrences from Power et al.,
  JVGR, 2004
• Likely candidate for gas in magma is CO2
• Pressure is too great for other volatiles to come
  out of solution
• At Mammoth Mtn, CA deep (mid-crustal LPs)
  associated with increased CO2 flux at surface
• DLPs are generally within 15 km of summit, not
  directly beneath
• Mostly short period records
• Some LPs have characteristics of known VLPs seen
  on short period stations at other volcanoes

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Deep LP events at Mount Rainier
From Wendy McCausland, USGS
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Deep LP events at Mount Rainier
Depth 10 13 km Spatially distinct from
Volcano-tectonic (VT) events Similar depth to
deepest VT events Reflect injection of basaltic
magma into system? Result from Resonance of
fluid-filled crack? Unsteady non-linear flow in
irregular conduit? Another yet unknown
mechanism?
From Wendy McCausland, USGS
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DLPsFiltered for Low and High Frequencies
Deep LP events at Mount Rainier
From Wendy McCausland, USGS
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Comparing a Long Period with a High Frequency
Event
Deep LP events at Mount Rainier
From Wendy McCausland, USGS