The precise characterization of reservoir parameters is vital for future development and prospect evaluation of oil and gas fields. C-sand and B-sand intervals of the Lower Goru Formation (LGF) within the Lower Indus Basin (LIB) are proven reservoirs. Conventional seismic amplitude interpretation fails to delineate the heterogeneity of the sand-shale facies distribution due to limited seismic resolution in the Sawan gas field (SGF). The high heterogeneity and low resolution make it challenging to characterize the reservoir thickness, reservoir porosity, and the factors controlling the heterogeneity. Constrained sparse spike inversion (CSSI) is employed using 3D seismic and well log data to characterize and discriminate the lithofacies, impedance, porosity, and thickness (sand-ratio) of the C- and B-sand intervals of the LGF. The achieved results disclose that the CSSI delineated the extent of lithofacies, heterogeneity, and precise characterization of reservoir parameters within the zone of interest (ZOI). The sand facies of C- and B-sand intervals are characterized by low acoustic impedance (AI) values (8 × 106 kg/m2s to 1 × 107 kg/m2s), maximum sand-ratio (0.6 to 0.9), and maximum porosity (10% to 24%). The primary reservoir (C-sand) has an excellent ability to produce the maximum yield of gas due to low AI (8 × 106 kg/m2s), maximum reservoir thickness (0.9), and porosity (24%). However, the secondary reservoir (B-sand) also has a good capacity for gas production due to low AI (1 × 107 kg/m2s), decent sand-ratio (0.6), and average porosity (14%), if properly evaluated. The time-slices of porosity and sand-ratio maps have revealed the location of low-impedance, maximum porosity, and maximum sand-ratio that can be exploited for future drillings. Rock physics analysis using AI through inverse and direct relationships successfully discriminated against the heterogeneity between the sand facies and shale facies. In the corollary, we proposed that pre-conditioning through comprehensive petrophysical, inversion, and rock physics analysis are imperative tools to calibrate the factors controlling the reservoir heterogeneity and for better reservoir quality measurement in the fluvial shallow-marine deltaic basins.