Noise Tomography of the Sun and Earth

Solar Oscillations, similar to Earth noise, are excited stochastically. Statistical averages of cross correlations of the surface velocity field of the Sun, observed at nearly 16 million points, show the presence of seismic signals, allowing us to measure wave travel times and amplitudes. I will describe techniques of PDE-constrained optimization that are applied to retrieve the gradient of the measurement misfit and show examples of sensitivity kernels. These developments render possible the accurate imaging of sub-surface magnetic fields and convection in the Sun and show recent work along these lines. I will also present results on an inversion for the distribution of noise sources in Southern California.