  In this paper, we investigate the inverse problem on determining the spatial
component of the source term in a hyperbolic equation with time-dependent
principal part. Based on a newly established Carleman estimate for general
hyperbolic operators, we prove a local stability result of H\"older type in
both cases of partial boundary and interior observation data. Numerically, we
adopt the classical Tikhonov regularization to transform the inverse problem
into an output least-squares minimization, which can be solved by the iterative
thresholding algorithm. The proposed algorithm is computationally easy and
efficient: the minimizer at each step has explicit solution. Abundant amounts
of numerical experiments are presented to demonstrate the accuracy and
efficiency of the algorithm.
