Based on the optical coherent theory, the non-Kolmogorov spectrum of atmospheric turbulence and the extended Huygens-Fresnel integral, correlated imaging with Gaussian Schell beams through the horizontal turbulence channels of z-tilt aberration correction has been studied and the theoretical models of ghost-imaging have been derived. Based on these formulas, we find that the image quality is influenced by the turbulence strength, the propagation distance, the fractal constant of the non-Kolmogorov power spectrum of atmospheric turbulence and the coherent parameters of the partially coherent light.