Study on methods for all-particle energy spectrum and mean logarithmic mass of cosmic rays up to hundreds of PeV

The kilometer-square array (KM2A) of the Large High Altitude Air Shower Observatory (LHAASO, located at 4410 m above sea level with an atmospheric depth of 600 g/cm$^2$) can simultaneously measure air shower sizes of both electromagnetic particles and muon contents with high precision for cosmic rays. The LHAASO experiment has measured the cosmic ray spectrum and its mean logarithmic mass with high precision. This article focuses on the cosmic ray spectrum at the "second knee", using inclined incident events to measure the cosmic ray energy at the shower maximum and ensuring the accuracy of energy reconstruction. It optimizes the core position and zenith angle range of cosmic ray showers to expand the observation aperture and increase the statistical quantity. By integrating the information from the electromagnetic particle detectors and muon detectors of the LHAASO experiment, this study uses an energy reconstruction method independent of the composition of cosmic rays, eliminating the composition-dependent effects on the spectrum and achieving high-precision cosmic ray spectral measurement. Additionally, it utilizes the muon count in showers to accurately measure the mean logarithmic mass distribution of cosmic rays.