Gravitational Wave Bursts: Characterization of Transients in LIGO - - PowerPoint PPT Presentation

Gravitational Wave Bursts: Characterization

• f Transients in LIGO Interferometer Data

Ed Brambley Mentor: Dr. John Zweizig 19th August 2003

The Spectrum of LIGO Interferometer Output

Frequency (in kHz) Power (in dB Hz−1) 8 7 6 5 4 3 2 1

• 10
• 20
• 30
• 40
• 50
• 60
• 70
• 80

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Probability Distributions & Likelihood Ratios

• The probability distribution function (pdf) f:

P(a < X ≤ b) =

b

a f(x | θ) dx

(1)

• The hypotheses:

H0: Data x comes from a pdf f0(x | θ0), for some θ0. H1: Data x comes from a pdf f1(x | θ1), for some θ1.

• The log profile likelihood ratio statistic:

2 log

 supθ1

• f1(x | θ1)
• supθ0
• f0(x | θ0)
• 



(2)

2

Goodness of Fit of Different Distributions

99.99% Confidence Level Gamma Distribution Normal Distribution

Frequency (in kHz) Badness of Fit 8 7 6 5 4 3 2 1 20 18 16 14 12 10 8 6 4 2

3

Iterative Search Method

Time (in s) Power (in Units2 Hz−1) 10 8 6 4 2 0.6 0.5 0.4 0.3 0.2 0.1

4

Significance of the Signal Found

Frequency (in kHz) Log Profile Likelihood Ratio 8 7 6 5 4 3 2 1 200 180 160 140 120 100 80 60 40 20

5

Power Evolution in the 272–304Hz Frequency Band

Time (in s) Power (in Units2 Hz−1) 10 9 8 7 6 5 4 3 2 1 7e-05 6e-05 5e-05 4e-05 3e-05 2e-05 1e-05

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Results after Post-Processing

Transient 1: Start : 3.17969 End : 3.36719 Significance: 196.498 Power : 0.00265712 Frequency composition: 208 - 400: 1 Transient 2: Start : 6.42969 End : 6.55469 Significance: 81.7497 Power : 0.000221876 Frequency composition: 272 - 304: 1 Transient 3: Start : 6.88281 End : 7.11719 Significance: 86.5563 Power : 4.19208 Frequency composition: 48 - 80: 1

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Conclusions

• The algorithm created can detect transients — it did so in

the example presented. It can also indicate which frequency bands it believes the transients occurred in.

• It is susceptible to badness of fit and non-stationarity.
• General problems occurred in the 1–3kHz range, where there

is the least power.

• Specific, isolated problems occurred at 4320Hz and 7168Hz.

These frequencies correspond to dramatically higher power than the surrounding frequencies.

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