Smart card payment systems provide a convenient billing mechanism for public transportation providers and passengers. In this paper, a smart card-based transit log is used to reveal functionally related regions in a city, which are called zones. To discover significant zones based on the transit log data, two algorithms, minimum spanning trees and agglomerative hierarchical clustering, are extended by considering the additional factors of geographical distance and adjacency. The hierarchical spatial geocoding system, called Geohash, is adopted to merge nearby bus stops to a region before zone discovery. We identify different urban zones that contain functionally interrelated regions based on passenger trip data stored in the smart card-based transit log by manipulating the level of abstraction and the adjustment parameters.