High Resolution Array Detector

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High Resolution Array Detector

• Design of Infrasound Detection and Parameter
  Estimation Systems
• Hein Haak Läslo Evers
• June-September 2003

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Design of the Infrasound network

• Bulletin
• Localization
• Association to events
• Parameter estimation
• Signal detection
• Array layout
• Instruments

System design
Bulletin production, build-up, from IMS to IDC
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Detectors / Estimators

• Several detectors available
• F- detector
• PMCC, MCCM
• PWS phase-weighted stacks
• LTA/STA
• Generally the detailed descriptions of the
  detectors could be improved, clear determination
  of ROCs could be added, black boxes are
  undesirable, transparency is needed
• What is the relation between detector and array
  design

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Basic design considerations

• Hardware is hard to adjust, software is more
  flexible
• Frequency wave number analysis is the standard
• High resolution methods (Capon) are less robust
  at low S/N
• Coherency detectors are used Fisher,
  correlation, semblance throughout the network of
  arrays
• Small arrays, higher resolution, lower costs
• Detection without some parameter extraction or
  estimation is meaningless

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What is Performance

• Low missed event and false alarm rates (detection
  part of the problem)
• Event parameters with small error bars
  (estimation part of the problem)
• Low investment and operation costs leading to
  small dimensions of the array (cost efficiency)

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Practical array design (1)

• Suppose an array of 8 elements is confined to a
  100 ? 100 grid, then the system has 2.5 10 27
  independent realizations
• A year contains 31.5 10 9 milliseconds
• Brute force array design is not realistic
• Even with only 50 independent positions there are
  536,878,650 possible configurations
• Alternative solutions are needed like genetic
  algorithms or Monte Carlo techniques
• Only an approximate solution are possible
• Symmetric approaches are generally not helpful

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Practical array design (2)

• If most of the array is fixed, for instance
  because of infrastructural circumstances
  additional elements can be placed strategically,
  to achieve a secondary optimum
• With isotropic response
• Angular resolution conform array diameter
• Low side lobe amplitudes

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Side lobes reducers
Side lobes can be reduced through
Hardware

• Small diameter of the array
• Many array elements
• Optimal array design in detail

Software

• Broad frequency band in analysis
• Use of Fisher statistics

Conclusion side lobes should not be a problem
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Resolution of arrays theory

• Consider Cramér-Rao Lower Bound
• Separation of a signal/noise component and array
  geometry
• Maximize moment of inertia
• Isotropic condition
• Resolution
• Leads to circular arrays with constant radii, the
  central element is not contributing to the
  resolution
• In sparse arrays non-max-R elements contribute to
  lower side lobes

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• Main lobe / side lobe
• amplitude vs.
• number of elements
• S-range 0.005 sec/m
• and 0.0075 sec/m
• Resolution conform
• diameter of 1200 m
• The product
• Smax?B ? Const.

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Array response 8 elements at 1 s period
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Array response 8 elements at 4 s period
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Array response 8 elements at 1 s period with side
lobe penalty function
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Array response 8 elements at 4 s period with side
lobe penalty function
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F

• Calculation of the F-statistic from multiple
  time series Xct

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F

• F in terms of coherent signal-to-noise power
  ratio

• Power is defined as the square of the amplitude

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F

• Calculation of the F-response

• FKResp. is the normalized FK-array response

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F

• Side lobe suppression if any measured F-value is
  larger than Fside lobe then it is originating
  from the main lobe

For R 2.0, Fside lobe ? 7 with C 8
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Pentagonal array six elements

• Relative small array in CTBT context
• Radius 100 m
• Small side lobes
• S/N-power ratio 5.5
• 3 Hz, ? ? 110 m

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F-K and F-plot, S/ Np 5.5, 3 Hz
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FK and F-plot, S/ Np 0.2, 3 Hz
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F-K, F-plot, 1/f, S/ Np 5.5, 1 Hz
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F-K, F plot, 1/f, S/ Np 0.2, 1 Hz
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Resolution with F- estimator
This plot is made for white, Gaussian noise
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A New CTBT Infrasound Array?

• Smaller array diameter
• More array elements
• Optimal detailed design
• Better adjusted to the detector

?