Most of the current existing accessibility measures quantify the potential of reaching desirable opportunities across space and time. Nevertheless, these potential measurements only illus-trate the maximum possible accessibility a person can have, which may not accurately measure real-world transit accessibility in urban areas. This paper introduces a novel methodology to measure positive public transit accessibility based on multi-source big public transit data such as Smart Card Data (SCD) and Global Navigation Satellite System trajectory data, which embed rich travel information and real-world spatio-temporal constraints. First, we use multi-source transit data to reconstruct trip chains, which are used to extract popular destinations. A novel transit accessibility measure is defined to account for latent trip information such as mode/route preference, opportunity attraction, and travel impedance that are difficult to capture explicitly via traditional normative measures. Finally, we produce accessibility maps to visualize time-varying and heterogeneous accessibility patterns distributed over the study region. We performed an empirical evaluation on real-world transit data collected in Shenzhen City, China, demonstrating the applicability and effectiveness of the proposed method in mapping positive transit accessibility over large metropolitan areas. The results and findings of the empirical study demonstrate that the proposed positive accessibility measure can better capture travel behavior characteristics and constraints than traditional normative measures. The measure-ment method can be used as a practical high-resolution mapping tool for transit decision makers in evaluating public transit systems, supporting strategic transit planning, and improv-ing daily transit management.