Two-dimensional sonar tomography uses indirect data to image the structural boundaries of an underwater object by inverting the circular Radon transform. For data over circles with centers and radii in a compact set, i.e., a limited data set, it has been shown that visual reconstruction artifacts arise from points on the boundary of the data, making it relatively difficult to image the object due to the ill-posedness of the inverse problem. Yet, reconstruction artifacts for other limited sonar data scenarios have not been fully characterized; similarly, numerical methods to analyze unique limited sonar data sets and algorithms to reduce artifacts in tomographic reconstructions vary in usability and effectiveness. As such, we develop a clear pipeline that generates limited sonar data and numerically evaluates the resulting 2-D reconstruction for transceivers on both linear and curved paths. Using this, we determine a unique case in which visual artifacts occur independent of the object of interest which could potentially inform the microlocal context of the inverse sonar problem. Lastly, we develop a convolution algorithm that minimizes artifacts by selectively targeting singularities in the boundary of the data set.