“sicut in caelo et in terra”
TRANSCRIPT
![Page 1: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/1.jpg)
Coalescence of two black holes (credits: SXS)
“Sicut in caelo et in terra”As in heaven and on earth
Data representations for
seismic and gravitational waves
Eric Chassande-Mottin
Astroparticule et Cosmologie APC CNRS/IN2P3 Univ Paris Diderot
![Page 2: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/2.jpg)
Birth of wavelet analysis
Collaboration with Jean Morlet with application to seismic data
I. Daubechies, Where do wavelets come from? A personal point of view
![Page 3: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/3.jpg)
From earth- to spacetime- quakes
● Seismic wavesdensity perturbations propagating as sound waves in the rock bed
Produced e.g., in Earth-quakes or by man-made explosions for oil exploration
● Gravitational wavespropagating space-time metric perturbations
Consequence of General Relativity
Produced by accelerated masses, e.g., mergers of compact stars
![Page 4: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/4.jpg)
“Cycle-octave” transform & oil exploration
Goupillaud, Grossman, Morlet, Cycle-Octave and related transforms in seismic signal analysis, Geoexploration, 1984
● Objective: higher resolution in the detection and localization of thin layers of oil reservoirs preserve high frequencies of the seismic echo
● Attenuation due to scattering by successive layers follows a constant-Q lawlarge low freqs from small high freqs
![Page 5: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/5.jpg)
“L-transform”
Voice transf: log scales
Cycle-octave transf: rescaled time
Goupillaud, Grossman, Morlet, Cycle-Octave and related transforms in seismic signal analysis, Geoexploration, 1984
● Standard data recording: low-pass filter for the “noise-dominated” high freqs
● Change to recording in separate frequency bands → 2D time-frequency representation
● Issues: size of data set/memory, signal recoverydiscretization, inversion
● Connected to coherent state rep of quantum mech.
![Page 6: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/6.jpg)
Simulated signature of a sediment layer
time
octave
time
octave
Analysis ReconstructionReconstruction error
![Page 7: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/7.jpg)
From earth- to spacetime- quakes
● “Wavefront” reconstruction using a sensor array● Spatial localization of the source of the wave
– Timing measurement → importance of high frequencies
● Signal identification using time-frequency patterns
Similar signal analysis problems → similar solutions
![Page 8: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/8.jpg)
A primer on gravitational waves
![Page 9: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/9.jpg)
Alain Brillet Thibault Damour
![Page 10: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/10.jpg)
1915● Space-time is a deformable and dynamical object
● Gravity is a geometrical effect that emerges from space-time curvature
« Spacetime tells matter how to move; matter tells spacetime how to curve
JA Wheeler
![Page 11: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/11.jpg)
Gravitational waves (1)
Einstein's equations → wave equation !for small perturbations of flat space-time metric
There are waves of space and time
Those waves are transverse
![Page 12: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/12.jpg)
Gravitational waves (2)
here
time
+
x
General Relativity predicts two polarizations
Gravitational wave amplitude h(t) has no dimension
![Page 13: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/13.jpg)
Black hole binary mergerinspiral merger ringdown
Chirp!
Characteristic waveform signature
![Page 14: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/14.jpg)
How do we detect gravitational waves?
![Page 15: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/15.jpg)
Michelson interferometer
![Page 16: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/16.jpg)
Michelson interferometer
![Page 17: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/17.jpg)
LIGO (Etats unis) Virgo (Italie)
Radius of atomic nuclei (x 1000)
![Page 18: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/18.jpg)
LIGO Handford H1 LIGO Livingston L1 Virgo V1
Quasi-omnidirectional(no pointing, see below)
~3000 km (10 light-ms)
~10000 km (30 light-ms)
Sensitivities during O2H1: 60 Mpc
L1: 80 Mpc
V1: 25 Mpc
BNS range
![Page 19: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/19.jpg)
2015 2016 2017 2018 2019
O14 months~50 days
coincident
O26 months
~ 100 dayscoincident
VirgoO31 yr from Apr 2019
LIGO Handford H1 LIGO Livingston L1 Virgo V1
LIGO only LIGO & Virgo
~5 TB of science data product
~15 millions segments
![Page 20: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/20.jpg)
How do we search LIGO and Virgo data?
![Page 21: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/21.jpg)
What do we search for?Tr
ansi
ent
Per
man
ent
![Page 22: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/22.jpg)
What do we search for?Tr
ansi
ent
Per
man
ent
With a model“parametric”
Matched filtering
Without a model“non-parametric”
Time-frequencyWavelets
![Page 23: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/23.jpg)
Compact binary mergers
● We have accurate waveform models
15 parameters: masses & spins + geometry
To leading order, the phase is determined by
then by mass ratio, spins, …
– … except in extreme region of parameter space, for instance: high-mass ratio, misaligned spins (→ precession), …
Can be used as “template”
Correlate data with the templates (matched filtering)
chirp mass
![Page 24: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/24.jpg)
Compact binary mergersMatched filtering
Cover expected scenarios(parameter space coverage)
1 point = 1 waveform = 1 filter400 000 filters !
Retain events that occur in coincidence on two or more detectors and come from the
same filter
Dal Canton & Harry, https://arxiv.org/abs/1705.01845
![Page 25: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/25.jpg)
Main difficulties
Non-stationarity Non-Gaussianity
“glitches” regularly appearing
![Page 26: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/26.jpg)
Time-frequency searchesTransient signals =
outliers in time-frequency representation
Time (sec)
Fre
quen
cy (
Hz)
Excess power !
Time-frequency representation
![Page 27: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/27.jpg)
Time-frequency searchesCoherent WaveBurst (1)
S. Klimenko et al., arXiv:1511.05999
Time-frequency map• A collection of Wilson transforms at multiple scales• Using the Meyer scaling function
Signal identification by pattern matching ● Clusters of “bright” time-frequency pixels● General relativity is not required – Can detect
unexpected sources
![Page 28: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/28.jpg)
Time-frequency searchesCoherent WaveBurst (2)
S. Klimenko et al., arXiv:1511.05999
H1
L1
V1
data mixing signal noise
mixing(beampattern)
● Network of detectors● They all receive the same gravitational
wave h+ and hx
● Seek phase-coherent signals ● Likelihood → Inverse problem
● Mixing: beampattern, propagation delays● Similar to beamforming (radar, radioastro)
● Compensate time delays → Can be done efficiently in the time-frequency plane using Wilson transforms (orthonormal basis)
● Source localization and waveform reconstruction using “bright” pixels● Small scales, high-frequency pixels are important!
![Page 29: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/29.jpg)
Gravitational wave polarizations
● Polarization reconstruction– Bivariate signal h+ and hx
● Polarized AM-FM signal– Can be characterized by Stokes params
(through quaternionic embedding) See posters by F Feng & P Chainais
Precession of the orbital plane!
![Page 30: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/30.jpg)
LIGO and Virgo observations so far...
![Page 31: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/31.jpg)
Sep 14, 2015
7 ms
![Page 32: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/32.jpg)
Sep 14, 2015
![Page 33: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/33.jpg)
![Page 34: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/34.jpg)
GWTC#1● 10 binary black hole mergers
including Virgo
arXiv:1811.12907, https://www.gw-openscience.org/catalogs/
● population hidden to conventional astronomy
![Page 35: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/35.jpg)
Aug 17, 2017
![Page 36: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/36.jpg)
https://www.gw-openscience.orgLecture videos, Jupyter notebooks, challenge data set available online – Run on Google Colab cloud
https://indico.in2p3.fr/2/gw-odw2
![Page 37: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/37.jpg)
LIGO at ~120 Mpc (L1) and 100 Mpc (H1)Virgo at ~50 Mpc (x ~2 wrt O2) ~90 % duty cycleVery promising start! 14 alerts
https://gracedb.ligo.org/latest/
~ 1 alert/week
Science run O3
![Page 38: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/38.jpg)
May 2019 April 2019
BBH: binary black holeBNS: binary neutron starNSBH: neutron star black hole binary
Last BBH on Jun 02 !
?
Science run O3 – current status
![Page 39: “Sicut in caelo et in terra”](https://reader031.vdocuments.pub/reader031/viewer/2022011921/61d8679beadf3f7ac3059e04/html5/thumbnails/39.jpg)
Prompt gravity signal from earthquakes
JP Montagner et al, Nature Comm. 7, 13349 (2016)
2011 Tohoku-Oki earthquake
M. Vallée et al, Science, 358, 6367, pp. 1164-1168 (2017)Gravity signals could speedily warn of big quakes and save lives [doi:10.1038/nature.2017.23045]