Stark, Philip 95-04410 Acoustic vibrations of the Sun contain information about the distributions of soundspeed, material density, and angular velocity within the Sun. Current methods for imaging these properties of the solar interior from helioseismic eigenfrequencies produce images that might resemble the Sun, but the formal uncertainties of the techniques do not accurately quantify possible differences between the models and the truth. Nor can the methods incorporate physical constraints that might reduce the uncertainty. The effects of data errors, choice of modeling algorithm, and theoretical approximations on the reliability of the images are largely unexplored; published uncertainties approximate the variability of the estimation method conditional on a particular parametric representation of the solar property and a host of other assumptions, without regard for possible biases. Dr. Stark will develop and apply methods to study both the variability and the bias of estimates of the distribution of soundspeed in the solar interior and the distribution of angular velocity in the solar interior, under less restrictive assumptions. The bias can be controlled using prior physical information about the Sun, such as bounds on either energy or observed rotationally-induced oblateness. The work will also lead to new methods to test hypotheses in the presence of infinite-dimensional nuisance parameters.
