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groups:homestake:radiometer [2014/02/18 12:24]
ethrane created
groups:homestake:radiometer [2014/06/12 09:56]
mandic
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-**Radiometer Planning Page**+====== ​Radiometer Planning Page ======
  
-Action items+ 
 +**Action items**
   - Code for generation of stochastic S and P waves.   - Code for generation of stochastic S and P waves.
   - Code for \vec{d}_i(t) given simulated sky map of S and P waves.   - Code for \vec{d}_i(t) given simulated sky map of S and P waves.
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   - Work out formalism for Rayleigh waves (covariant S+P waves).   - Work out formalism for Rayleigh waves (covariant S+P waves).
   - Investigate the relevance of refraction / turning depth for radiometric measurements.   - Investigate the relevance of refraction / turning depth for radiometric measurements.
-  - +  - Investigate depth dependence of surface (Love) waves.
  
-Seismology for astrophysicists+**Seismology for astrophysicists**
   * Love waves are just a subset of S waves. ​ However, they are surface waves, so their amplitude varies with depth.   * Love waves are just a subset of S waves. ​ However, they are surface waves, so their amplitude varies with depth.
   *  When an S or P wave interacts with a surface, boundary conditions require that it reflects as a *coherent* combination of S *and* P wave.  These combined SP waves are Rayleigh waves, and the fact that S and P are coherent violates the assumption in Eq. 5 in Vuk's note, where S and P are assumed to be uncorrelated. Further, the fraction of power that gets converted from S into P and vice versa is O(1).  The good news is that there'​s a very predictable phase relationship between S and P in Rayleigh waves.   *  When an S or P wave interacts with a surface, boundary conditions require that it reflects as a *coherent* combination of S *and* P wave.  These combined SP waves are Rayleigh waves, and the fact that S and P are coherent violates the assumption in Eq. 5 in Vuk's note, where S and P are assumed to be uncorrelated. Further, the fraction of power that gets converted from S into P and vice versa is O(1).  The good news is that there'​s a very predictable phase relationship between S and P in Rayleigh waves.
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   * Inhomogeneities. ​ Any features characterized by a size of lambda/4 can probably be safely ignored. ​ At 1 Hz, Victor thinks this corresponds to a length scale of ~700m, and the rock should appear very uniform at that length scale. ​ However, at 10 Hz, Victor thinks that the length scale will be ~20m (note v depends on f in rock), and we might see significant inhomogeneity at this scale.   * Inhomogeneities. ​ Any features characterized by a size of lambda/4 can probably be safely ignored. ​ At 1 Hz, Victor thinks this corresponds to a length scale of ~700m, and the rock should appear very uniform at that length scale. ​ However, at 10 Hz, Victor thinks that the length scale will be ~20m (note v depends on f in rock), and we might see significant inhomogeneity at this scale.
  
-Previous questions/​investigations/+**Previous questions/​investigations**
   * Investigate 2D version of radiometer. ​ If we were only interested in surface waves (intrinsically a 2D problem), then we could model the change in surface waves as a function of depth with a simple formula. ​ The angular power spectrum for surface waves is the same at all depths up to an overall factor which decays exponentially with depth. ​ However, we're interested in 3D.   * Investigate 2D version of radiometer. ​ If we were only interested in surface waves (intrinsically a 2D problem), then we could model the change in surface waves as a function of depth with a simple formula. ​ The angular power spectrum for surface waves is the same at all depths up to an overall factor which decays exponentially with depth. ​ However, we're interested in 3D.
 +
 +**Slides**
 +  * [[http://​www.ligo.caltech.edu/​~ethrane/​stoch/​tmp.pdf|turning depth]] (April 3, 2014)
 +  * [[http://​www.ligo.caltech.edu/​~ethrane/​stoch/​turning_depth2.pdf|more on refraction]] (April 17, 2014)
 +  * {{groups:​homestake:​diagnostics_noah_20140612.pdf|Noah'​s Update on P-wave Radiometer Simulations}} (June 12, 2014)
groups/homestake/radiometer.txt · Last modified: 2014/06/12 09:56 by mandic