A signal analysis of the sound of a propeller-driven unmanned aerial vehicle (UAV) shows that its acoustic signature comprises a set of strong narrowband tones superimposed onto a broadband random component. If such a UAV overflies an array of microphones, the projected and observed Doppler shifts in frequency of the narrowband tones may be compared and converted into effective sound speed values: 2- and 3D spatially varying atmospheric temperature and wind velocity fields may then be estimated using tomography. The technique has practical application in a number of research fields. In this paper, we examine the influence of UAV flight path and ground sensor geometry on the feasibility and usefulness of UAV-based atmospheric tomography. Realistic conditions for a weakly sheared daytime convective atmospheric boundary layer are synthesized through use of massively parallel large eddy simulation code that utilizes pseudo-spectral differencing in horizontal planes and solves an elliptic pressure equation. Particular attention is paid to the accuracy with which the surface layer (lowest 50 m of atmosphere) may be reconstructed using UAV-based acoustic tomography as this region typically experiences the greatest spatio-temporal variation in temperature and wind speed; and arrangements of UAV flight path and sensor geometry do not permit ray paths to intersect without the UAV flying very low and disturbing the atmosphere. The influence of meteorological observations obtained onboard the UAV and by ground sensors is also examined.