Identifying geofluids is vital for advancing geophysical exploration and enhancing reservoir forecasting. However, the accuracy and resolution of current methods are often compromised due to their dependence on linear amplitude variation with incident angle (AVO) approximation inversions. These inversions generate fluid indicators that are susceptible to influences from various factors, such as porosity and rock modulus. To overcome these challenges, we recognize that the pore fluid bulk modulus encapsulates the fundamental characteristics of pore fluids, effectively mitigating interference caused by the mixing effect and enabling highly precise fluid identification. Incorporating L0 and L1 norms as sparse regularization terms is crucial for enhancing inversion resolution. On this basis, we formulate a novel nonlinear elastic impedance (EI) equation specifically for pore fluid bulk modulus, utilizing the exact Zoeppritz equation. Additionally, we developed a new nonlinear EI inversion method, which incorporates L0 and L1 norms constraints and is grounded in a nonstationary convolution model. This innovative method not only circumvents the limitations of linear approximation but also significantly enhances the resolution and delineation capabilities for identifying reservoir fluids. The efficacy of this method is corroborated by precision analysis of the equation and field data inversions, underscoring its potential for practical application in geophysical exploration and reservoir prediction.