Virtual Seismic Strain Sensors

1
Virtual Seismic Strain Sensors

• Andrew Curtis
• Heather Nicolson, David Halliday, Jeannot
  Trampert, Brian Baptie
• Edinburgh Seismic Research
• www.geos.ed.ac.uk/seismic
• University of Edinburgh
• ECOSSE
• www.geos.ed.ac.uk
• University of Utrecht
• www.geo.uu.nl

2
Rationale

• Traditionally seismology analyses earthquake
  waves
• Seismic Interferometry freed us (to some extent)
  from bias due to the spatial distribution of
  earthquakes
• Receivers assume the role of sources
• Dominant remaining bias is due to seismometer
  distribution

3
Results of Our Work

• Any well-recorded energy source can be turned
  into a receiver
• ? Reciprocal of passive noise interferometry

4
Seismic Interferometry

• How standard interferometry works
• Define volume V surrounded by either
  independently-recorded impulsive or uncorrelated
  noise sources on the bounding surface S
• Sources on S radiate energy into volume V
• Homogenous Greens Function between any pair of
  points is obtained using reciprocity and the
  Representation Theorem ? equation below

x
A
V
S
Apply source-receiver reciprocity...
5
Seismic Interferometry

• How standard interferometry works
• Define volume V surrounded by either
  independently-recorded impulsive or uncorrelated
  noise sources on the bounding surface S
• Sources on S radiate energy into volume V
• Homogenous Greens Function between any pair of
  points is obtained using reciprocity and the
  Representation Theorem ? equation below

x
A
V
S
Apply source-receiver reciprocity...
6
Seismic Interferometry

• How virtual sensors are constructed
• Obtain Greens function between two impulsive
  sources if both are recorded on surrounding
  receivers on S
• ? One source acts as a Virtual Reciever
• If sources are represented by Moment Tensors MA
  and MB ? similar formula with left side

x
A
V
S
7
Seismic Interferometry

• How virtual sensors are constructed
• Obtain Greens function between two impulsive
  sources if both are recorded on surrounding
  receivers on S
• ? One source acts as a Virtual Reciever
• If sources are represented by Moment Tensors
  MA and MB ? similar formula with left side
• If sources A and B have source time functions
  represented by WA and WB, we obtain the above
  multiplied by WB WA (cross-correlation)
• ? Phase may be shifted relative to real
  seismometers

x
A
V
S
8
Seismic Interferometry

• How virtual sensors are constructed
• Obtain Greens function between two impulsive
  sources if both are recorded on surrounding
  receivers on S
• ? One source acts as a Virtual Reciever
• If sources are represented by Moment Tensors
  MA and MB ? similar formula with left side
• If sources A and B have source time functions
  represented by WA and WB, we obtain the above
  multiplied by WB WA (cross-correlation)
• ? Phase may be shifted relative to real
  seismometers

x
A
V
S
9
Results of Our Work

• Any well-recorded energy source can be turned
  into a receiver
• ? Reciprocal of passive noise interferometry
• Virtual Receiver spatio-temporal sensitivity
  function matches that of the original source
  mechanism
• Earthquake Virtual Receivers are seismic strain
  sensors
• They record closer to zero phase than normal
  seismometers
• These record locally in the subsurface of areas
  of tectonic activity

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Illustration

• We chose Virtual Receiver earthquakes that
• Had moment tensor estimates available
• Were shallow and close to a seismometer (for
  comparison)
• Were low magnitude
• ? higher spatio-temporal concentration of source
  pulse, again for comparison with a
  point-particle motion seismometer

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East West Pair, Strike-Slip Virtual Receiver
A
B
Radial component results. (A) interferometry
(solid) inverted, real event time derivative
(dotted). (B) envelope functions of
interferometry (solid) and inverted, real event
time derivative (dotted). Amplitudes are
normalised and all traces are band-passed between
15 and 33 seconds.
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East West Pair, Normal Virtual Receiver
A
B
Vertical component results. (A) interferometry
(solid) inverted, real event (dotted). (B)
envelope functions of interferometry (solid) and
inverted, real event (dotted). Amplitudes are
normalised and all traces are band-passed between
15 and 33 seconds.
15
East West Pair, Normal Virtual Receiver
A
B
Radial component results. (A) interferometry
(solid) inverted, real event time derivative
(dotted). (B) envelope functions of
interferometry (solid) and inverted, real event
time derivative (dotted). Amplitudes are
normalised and all traces are band-passed between
15 and 33 seconds.
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North South Pair, Normal Virtual Receiver
A
B
Vertical component results. (A) interferometry
(solid) inverted, real event (dotted). (B)
envelope functions of interferometry (solid) and
inverted, real event (dotted). Amplitudes are
normalised and all traces are band-passed between
15 and 33 seconds.
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Conclusions

• Method
• Results are consistent with theory
• Essentially back-projects data recorded on real
  seismometers to a source location using empirical
  Greens functions
• But also converts sensitivity-to-particle-motion
  at the seismometers, to sensitivity-to-displacemen
  ts-or-strains-that-created-the-original-energy-sou
  rce
• Implications
• Non-invasive sensors in the Earths subsurface
• Earthquake Virtual Sensors are concentrated
  directly within areas of tectonic and geological
  interest
• ? Intra-fault zone subsurface monitoring
• Direct sensitivity to strain seismic
  triggering?