The prime focus of Singh's researches were on designing methodologies for the quantification of geological processes.[8] During his days at NEERI, he worked on introducing mathematical modeling for use in developing environmental technologies and evolved models of several geophysical and environmental processes such as the models of heat conduction processes in stratified crust, linear surface heat flow and surface heat generation using Thomson-Haskell matrix method which helped in quantifying the lithospheric geodynamics.[6] The Cuddapah basin, south Indian high grade metamorphic terrains, Afanasi Nikitin seamount, Carlsberg Ridge, and fracture zones in the Indian Oceanic lithosphere are some of the other models developed by him. He is credited with using rheological laws of rock forming minerals for the first time in India which he used for profiling the Indian continental lithosphere.[3] His studies have been detailed in over 150 peer-reviewed articles;[9][note 1]ResearchGate, an online article repository has listed 110 of them.[10] Besides, he co-edited a text, Magmatic and Allied Processes,[11] which contains three chapters written by him.[12][13]
Singh delivered a series of lectures in the 1970s propagating the inverse theory in geophysics and was involved in the coordination of more than one hundred environmental impact and risk assessment reports.[6] He was involved in the development of CSIR Centre for Mathematical Modelling and Computer Simulation during his early years and sat in the editorial boards of the Journal of Earth System Sciences of Indian Academy of Sciences and Proceedings of the Indian National Science Academy (Physical Sciences). He was also a member of the council of the Indian National Science Academy during 2000-02 and was the guide for nine scholars in their doctoral studies.[3]
Santosh Kumar; Rishi Narain Singh (13 June 2014). Modelling of Magmatic and Allied Processes. Springer. ISBN978-3-319-06471-0.
Chapters
R. N. Singh, A. Manglik (June 2014). "Parameterized Mantle Convection Analysis for Crustal Processes". Modelling of Magmatic and Allied Processes. Society of Earth Scientists Series. pp. 75–88. doi:10.1007/978-3-319-06471-0_4. ISBN978-3-319-06470-3.
R. N. Singh, Jibamitra Ganguly (June 2014). "Modelling Paleogeotherms in the Continental Lithosphere: A Brief Review and Applications to Problems in the Indian Subcontinent". Modelling of Magmatic and Allied Processes. Society of Earth Scientists Series. pp. 89–108. doi:10.1007/978-3-319-06471-0_5. ISBN978-3-319-06470-3.
Singh, Rishi Narain (1974). "A method of the calculation of the mantle-electrical conductivity by the inversion of the geomagnetic secular variation data". Pure and Applied Geophysics. 112 (1): 149–152. Bibcode:1974PApGe.112..149S. doi:10.1007/BF00875929. S2CID122013990.
Rai, Shivendra Nath; Singh, Rishi Narain (1981). "A mathematical model of water table fluctuation in a semi-infinite aquifer induced by localized transient recharge". Water Resources Research. 17 (4): 1028–1032. Bibcode:1981WRR....17.1028R. doi:10.1029/WR017i004p01028.
^R. N. Singh, A. Manglik (June 2014). "Parameterized Mantle Convection Analysis for Crustal Processes". Modelling of Magmatic and Allied Processes. Society of Earth Scientists Series. pp. 75–88. doi:10.1007/978-3-319-06471-0_4. ISBN978-3-319-06470-3.
^R. N. Singh, Jibamitra Ganguly (June 2014). "Modelling Paleogeotherms in the Continental Lithosphere: A Brief Review and Applications to Problems in the Indian Subcontinent". Modelling of Magmatic and Allied Processes. Society of Earth Scientists Series. pp. 89–108. doi:10.1007/978-3-319-06471-0_5. ISBN978-3-319-06470-3.