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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
3. Results of Our Work
4. 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 Green’s Function between any pair of points is obtained using reciprocity and the Representation Theorem ? equation below
5. 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 Green’s Function between any pair of points is obtained using reciprocity and the Representation Theorem ? equation below
6. How virtual sensors are constructed:
Obtain Green’s 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
7. How virtual sensors are constructed:
Obtain Green’s 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
9. Results of Our Work
10. Illustration
18. Method
Results are consistent with theory
Essentially back-projects data recorded on real seismometers to a source location using empirical Green’s functions
But also converts sensitivity-to-particle-motion at the seismometers, to sensitivity-to-displacements-or-strains-that-created-the-original-energy-source
Implications
Non-invasive sensors in the Earth’s 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?