Understanding the causes of sinkholes and determining the earth's subsurface properties will help Engineering Geologists in designing and constructing different kinds of structures. Also, determining of subsurface properties will increase possibilities of preventing expensive structural damages as well as a loss of life. Among the available health monitoring techniques, non-destructive methods play an important role. Full-waveform inversion together with the Gauss-Newton method, which we called as the regular method, able to determine the properties of the subsurface data from seismic data. However, one of the drawbacks of the Gauss-Newton method is a large memory requirement to store the Jacobian matrix. In this work, we use a different cell size approach to address the above issue. Results are validated for a synthetic model with an embedded air-filled void and compared with the regular method. HIGHLIGHTS• Full seismic waveform method based on Gauss-Newton method was used to detect embedded sinkholes in Earth's subsurface.• The difference cell size method is proposed to address the computational and memory requirements in Regular Full-wave inversion method.• Results are compared with regular full waveform inversion method• Less computational time is required for sinkhole detection with the proposed method.