We investigate the validity of three theories of seismic tomography by numerical comparison of cross-correlation travel time shifts of acoustic waves with their theoretical predictions in 3-D heterogeneous random media. Whenever the characteristic heterogeneity scale length is shorter than half of the first Fresnel zone width, ray-theoretical travel times yield large discrepancies from the cross-correlation measurements. Born-Fr¿chet kernel theory is valid for small-scale structures but restricted to weak velocity perturbations. With increasing perturbation strength, neglecting the nonlinearity due to wave path bending in linearized ray and Born theories is no longer eligible. General ray theory accounts for the detour least-time paths in strongly heterogeneous media, which prominently improves the predicted travel times for intermediate to large scale velocity variations.