The wave equation inversion method is based on the theory of spherical wave propagation and utilizes seismic shot-gather data for inversion. It exhibits high fidelity in inversion results and possesses unique technical advantages in the identification of strongly heterogeneous reservoirs. The acoustic wave equation inversion method assumes the underground elastic medium as an acoustic medium, considering only the P-wave component. Therefore, the inversion results only provide P-wave velocity, which cannot meet the demand for multi-parameter reservoir identification. Currently, the status of land-based single-component seismic data acquisition is insufficient to satisfy the needs of elastic wave equation inversion. For land-based collected data, seismic wave propagation in the low-velocity zone can be approximately regarded as propagation in an acoustic medium. To predict the elastic parameters of the underground medium using single-component data, we consider the stress continuity conditions and displacement continuity conditions at the coupled interface. By combining the acoustic wave equation with the elastic wave equation, we establish a coupled wave equation of acoustic and elastic media, serving as the theoretical foundation for forward modeling and residual backpropagation to achieve elastic wave inversion. Practical techniques are studied based on the characteristics of actual data, enabling the practical application of the inversion method in the heterogeneous sandstone reservoir development area of the eastern exploration region, with satisfactory application results achieved.