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groups:homestake:radiometer

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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