In this work, we present a quantitative analysis model based on reference-free self-calibration to analyze scattered fields and approach curves on a dielectric substrate for terahertz scattering-type scanning near-field optical microscopy. The results of our model are compared with experimentally measured data and a fully numerical analysis based on a line dipole image method and a quasi-electrostatic approximation. The model is used to extract the effective radius of the tip and the relative permittivity of the silicon substrate to the near-field scattering signal. The measured approach curves on Au and silicon substrates show good agreement with the calculated approach curves, and the refractive index for silicon is precisely determined to be 3.42. For a tip-based THz scattering-type scanning near-field optical microscope, the proposed analysis model allows for the extraction of the effective probe radius and dielectric functions, thereby enabling conclusive measurements of geometric parameters and optical constants.