In recent years, more and more oil-based mud is being used in middle to deep natural gas exploration of the Dengying and Longwangmiao formations in Sichuan basin. So only array induction instruments can be selected for bare hole resistivity logging. The dense carbonate rock commonly manifests as medium to high resistivity in the target layer in the region. The resistivity of typical gas layers is generally above 500 Ω·m and even up to 2000 Ω·m. The induction logging instruments measure the weak conductivity received signal and as well the influence of factors such as depth and high temperatures. So, the collected signal often shows negative values and software focused processing results often exhibit algorithm overlaps and flattens out. These cannot be used for reservoir identification and gas reservoir evaluation. We analyzed the influence of single factors such as mud resistivity, invasion radius and virgin zone resistivity on the array induction logging response and clearly defined the influence of various environmental factors on induction measurement signals with a finite element simulation algorithm. The results indicate that the contrast between formation and mud resistivity has a significant impact on the measurement signal when the contrast is close to 1, the error of each sub array is small and the depth of invasion is another important influencing factor. Overall, sub arrays with longer source distances are relatively less affected by various factors. Based on the characteristics of actual data, we propose a constrained correction method for raw conductivity signals based on the Archie formula which provides a software focus on the data after constraint correction and the results have been significantly improved.