Metamaterial (MM)-based designs have tremendous applications in terahertz (THz) frequency regimes. THz metamaterial absorbers are a subclass of metamaterial-based designs that can absorb the incident THz electromagnetic radiations in the THz band. In this paper, four different designs of THz metamaterial absorbers are proposed which are based on split-relief (SR) design. The designs consist of a sun-shaped, SR sun-shaped, star-shaped and SR star-shaped resonators coated on top of a dielectric substrate. The resonance frequencies of the designs were found to be 0.70, 1.04, 0.41 THz and 0.60 THz, respectively. Results showed that the resonance frequency was independent on the incident and polarization angles, making a unique metamaterial absorber. The proposed absorbers were used to sense the thickness of the analyte and its refractive index. The thickness of the analyte can be sensed with a sensitivity of 73 GHz/um for the Sun design, 238 GHz/um for the SRSun design, 45.2 GHz/um for the Star design, and 133.4 GHz/um for the SRStar design. Similarly, the refractive index of the analyte can be sensed with a sensitivity of 1.581 THz/RIU for the Sun design, 4.053 THz/RIU for the SRSun design, 1.077 THz/RIU for the Star design, and 2.067 THz/RIU for the SRStar design when the analyte thickness was fixed at 3 μm. Further, the resonance mechanism has been explained with the help of electric and magnetic field distributions. Due to their high sensitivity, these designs can have profound applications in biomedical sensing.