Estimate of the regularly gridded 3D vector flow field from a set of tomographic maps

Abstract: Time--distance inversions usually provide tomographic maps of the interesting plasma properties (we will focus on flows) at various depths. These maps however do not correspond directly to the flow field, but rather to the true flow field smoothed by the averaging kernels. We introduce a method to derive a regularly gridded estimate of the true velocity field from the set of tomographic maps. We aim mainly to reconstruct the flow on a uniform grid in the vertical domain. We derive the algorithm, implement it and validate using synthetic data. The use of the synthetic data allows us to investigate the influence of random noise and to develop the methodology to deal with it properly.