  In this article, we consider the limited data problem for spherical mean
transform. We characterize the generation and strength of the artifacts in a
reconstruction formula. In contrast to the third's author work [Ngu15b], the
observation surface considered in this article is not flat. Our results are
comparable to those obtained in [Ngu15b] for flat observation surface. For the
two dimensional problem, we show that the artifacts are $k$ orders smoother
than the original singularities, where $k$ is vanishing order of the smoothing
function. Moreover, if the original singularity is conormal, then the artifacts
are $k+\frac{1}{2}$ order smoother than the original singularity. We provide
some numerical examples and discuss how the smoothing effects the artifacts
visually. For three dimensional case, although the result is similar to that
[Ngu15b], the proof is significantly different. We introduce a new idea of
lifting the space.
