## 1 Introduction
The CNN component is responsible for precisely identifying and preserving the complex relationship between S-wave velocity and seismic data, while the GRU component extracts critical temporal characteristics of data. However, seismic inversion still faces two challenges. The first is the time-intensive process of inverting multiple elastic parameters individually. The second pertains to the limited labeled data available in supervised learning approaches, which can potentially result in network overfitting. Multi-task learning has been successful in various domains, including natural language processing [35], speech recognition [36], and computer vision [37]. Multi-task learning aims to empower the network to concurrently learn multiple tasks, enhance the generalization ability by leveraging diverse data from each task to extract more reliable features [38], improve the performances of individual tasks, and mitigate overfitting. Due to the interconnection between seismic data and elastic parameters [39], it is advantageous to integrate multi-task learning into the multi-parameter inversion of seismic data [40; 41; 42; 43; 44]. In the multi-task network, multiple tasks utilize a shared representation simultaneously. There are two common approaches used for sharing parameters of hidden layers in multi-task learning [45]. The first approach is hard parameter sharing, where hidden layers are shared among all tasks while individual task-specific output layers are retained. The second approach is soft parameter sharing, where different tasks operate with independent models and parameters, but constraints are imposed on the model parameters across tasks. In this work, our multi-tasking model utilizes hard parameter sharing. In addition, the results of traditional 1D trace-by-trace inversion methods often have lateral geological artifact [46]. The stable inversion results are difficult to guarantee and can easily be affected by noise. In this work, we leverage the structural information between adjacent seismic traces by converting multi-trace seismic data to single-trace elastic parameters during elastic parameter inversion. Based on the multi-trace to single-trace (M2S) strategy, we design an M2S multi-task FCRN and GRU hybrid network (M2S-MFCRGRU) for simultaneously inverting seismic elastic parameters, specifically Vp and density. M2S-MFCRGRU combines the capabilities of FCRN and GRU to learn data features across various scales. Moreover, the multi-task framework enhances inversion efficiency and takes advantage of the correlations between different tasks to improve the stability of inversion. At the same time, the M2S strategy ensures that the inversion results maintain structural horizontal continuity, enhances the inversion stability and reliability, and improves the anti-noise performance. As a supervised approach, the limited label data are expanded through data augmentation and transfer learning is evoked to enhance the inversion accuracy on field data implementations. Data augmentation artificially expands the labeled dataset, while transfer learning facilitates the transmission of knowledge from a pre-trained model to the specific seismic inversion task. The major contributions of the proposed method can be summarized as follows:  
1. The proposed M2S-MFCRGRU method combines the strengths of CNNs and RNNs for the accurate and reliable estimation of elastic parameters. The integration of FCRN and GRU allows capturing both local features and global temporal information, enhancing the inversion results. The multi-task framework enables the utilization of interconnections among the elastic parameters, resulting in an efficient and reliable inversion process. 2. As a supervised deep learning method, the M2S training strategy is employed to optimize the utilization of reliable seismic data while adhering to the structural constraints of seismic data.