With the development of unconventional shale gas in the southern Sichuan Basin seismicity has increased significantly in the region in recent years. Though the existing regional sparse seismic stations can capture most earthquakes with M_L≥2.5, a great number of smaller earthquakes are often omitted due to the limited detection capacity. With the advent of portable seismic nodes, many dense arrays for monitoring seismicity in the unconventional oil and gas fields have been deployed, and the magnitudes of those earthquakes are key for understanding the local fault reactivation and seismic potentials. However, the current national standard for determining the local magnitudes was not specifically designed for monitoring stations in close proximity, and it uses a calibration function with a minimal step of 5 km in the epicentral distance. That is, the current national standard tends to overestimate the local magnitudes for stations in short epicentral distances, and can result in discrepancy in magnitude measurement for dense arrays. In this study, we propose a new local magnitude formula which corrects the overestimated magnitudes in shorter distances, and yields accurate event magnitudes for small earthquakes in the Changning-Zhaotong shale gas field in the southern Sichuan Basin monitored by dense seismic arrays in close proximity. The formula is used to determine the local magnitudes of 7,500 events monitored by a two-phased dense array with several hundred 5 Hz 3C nodes deployed from the end of February 2019 to early May 2019 in the Changning-Zhaotong shale gas field. The magnitude of completeness (M_C) using the dense array is -0.1, compared to M_C 1.1 by the sparser Chinese Seismic Network (CSN). In addition, using a machine learning detection and picking procedure, we successfully identify and process some 14,000 earthquakes from the continuous waveforms, a ten-fold increase over the catalog recorded by CSN for the same period, and the M_C is further reduced to -0.3 from -0.1 compared to the catalog obtained via manual processing using the same dense array. The proposed local magnitude formula can be adopted for calculating accurate local magnitudes of earthquakes monitored by dense arrays in the shale gas fields in the southern Sichuan Basin in the future, and help to better characterize the local seismic risks and potentials.