Techniques for detecting gravitational waves with a spherical antenna

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Abstract
We report the results of a theoretical and experimental study of a spherical gravitational wave antenna. We develop a number of techniques to deconvolve the data from a set of resonant transducers attached to the surface of a sphere to monitor the sphere’s five quadrupole modes. We show that by observing these modes, one can measure the five tensorial components of a gravitational wave. The inverse problem can then be solved and the direction of a gravitational wave can be determined. Asymmetries such as the nondegeneracy of the quadrupole modes and mistuning of the transducers are included in the model and their effects on the data analysis is studied. We develop a technique to compensate for these imperfections by measuring the response of the resonant transducers to the normal modes. These techniques were demonstrated on a room-temperature prototype antenna with which we verified that it is possible to determine the location of an impulse excitation applied to the prototype’s surface from the transducer outputs.
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