We present the results of an ongoing survey on the association between the muon flux variation at ground level (3m above sea level) registered by the Tupi telescopes (Niteri-Brazil, 229S, 432W, 3 m) and the Earth-directed transient disturbances in the interplanetary medium propagating from the Sun (such as coronal mass ejections (CME), and corotating interaction regions (CIRs)). Their location inside the South Atlantic Anomaly region enables the muon telescopes to achieve a low rigidity of response to primary and secondary charged particles. The present study is primarily based on experimental events obtained by the Tupi telescopes in the period from 2010 August to 2011 December. This time period corresponds to the rising phase of solar cycle 24. The Tupi events are studied in correlation with data obtained by space-borne detectors (SOHO, ACE, GOES). Identification of interplanetary structures and associated solar activity was based on the nomenclature and definitions given by the satellite observations, including an incomplete list of possible interplanetary shocks observed by the CELIAS/MTOF Proton Monitor on the Solar and Heliospheric Observatory (SOHO) spacecraft. Among 29 experimental events reported in the present analysis, there are 15 possibly associated with the CMEs and sheaths, and 3 events with the CIRs (forward or reverse shocks); the origin of the remaining 11 events has not been determined by the satellite detectors. We compare the observed time (delayed or anticipated) of the muon excess (positive or negative) signal on Earth (the Tupi telescopes) with the trigger time of the interplanetary disturbances registered by the satellites located at Lagrange point L1 (SOHO and ACE). The temporal correlation of the observed ground-based events with solar transient events detected by spacecraft suggests a real physical connection between them. We found that the majority of observed events detected by the Tupi experiment were delayed in relation to the satellite triggers. This result agrees with theoretical expectations. Our experimental data indicate that the Tupi experiment is able to add new information and can be complementary to other techniques designed to interpret the origin of some interplanetary disturbances observed by satellites.