| dc.description.abstracteng | This dissertation aims at developing a theoretical framework for the signal and noise in helioseismic holography which is mathematically rigorous and physically meaningful. A main focus of this dissertation is modeling the Porter-Bojarski (PB) integral, a well-established method used in the field of acoustics to locate subsurface sources and scatterers. We test and validate the potential application of the PB integral to probe the Sun's internal structure and dynamics.
In the first study, we compare the PB integral with the `egression', the current imaging technique used in helioseismic holography, in a homogeneous medium. This proof of concept shows that the two imaging methods can locate subsurface sources of acoustic waves, which have a similar spatial resolution. However, the egression suffers from artificial signals located away from the source, whereas the PB integral does not. This suggests that the PB integral can potentially improve the current imaging capability of helioseismic holography.
The next study implements the PB integral for a realistic solar model, and a theoretical framework is developed to investigate its signal and noise.
Solar oscillations are formulated into the solution of a scalar Helmholtz equation with the background sound-speed and density taken from a standard solar model, and are excited by a stationary and spatially uncorrelated random source function. We then apply the first-order Born approximation to relate scatterers such as sound-speed heterogeneities, density, and flows to PB integrals. The example computations show that PB holographic measurements are diffraction limited, i.e., the spatial resolution is half the local wavelength. We also investigate noise due to the random nature of wave excitation. We find large variations in both signal and noise at low frequencies due to contributions from individual long-lived modes of solar oscillations, and low signal-to-noise ratios for measurements above the frequency cut-off.
With the theoretical framework in hand, we then investigate the optimal flow-measuring strategy for helioseismic holography. Two different approaches are investigated and compared, the traditional method that measures directional phase shifts using pupils in a quadrant geometry (method #1); a new method that correlates the estimated wave field at two nearby locations in the solar interior using all observed waves (method #2).
We find that method #2 is consistently superior to the traditional method. Specifically, it reaches the diffraction limit of acoustic waves (half the local wavelength) and has a much higher signal-to-noise ratio than the traditional method. Furthermore, it is much less susceptible to the leakage from the solar surface. Therefore, we conclude that method #2 will improve the imaging of solar subsurface flows using heliosemic holography, and hence should be used in future applications. | de |