Exploration utilizing converted wave (PS) technology has garnered considerable interest in recent years owing to its ability to provide distinct insights into subsurface properties compared to compressional waves (PP). PS wave is particularly advantageous for accurately determining S-wave velocity (${V}_S$) and bulk density ($\rho $), whereas PP wave is better suited for assessing P-wave velocity (${V}_P$). Thus, theoretically, joint PP and PS AVA inversion can yield precise results for ${V}_P$, ${V}_S$, and $\rho $. However, a critical step before joint inversion is PP and PS registration, which is prone to causing lateral discontinuity in the inversion outcomes. To mitigate this issue, we present a simultaneous multi-trace joint inversion method. The method can improve the lateral consistency of inversion results by imposing lateral continuity constraints on the elastic parameters being inverted. Nevertheless, this simultaneous multi-trace inversion method inherently increases computational burden. To enhance algorithmic efficiency without sacrificing inversion precision, we implement an acceleration strategy. Synthetic and real data examples demonstrate that the proposed method offers remarkable performance in enhancing computational efficiency and lateral continuity compared to the conventional methods.