## 1 Introduction  
Crosswell seismic survey is a powerful method used in geophysics to obtain high-resolution geological profiles. It involves placing a seismic source in one well to generate seismic waves, while a geophone is placed in another well to capture the waves as they pass through the subsurface strata and reach the second well. By analyzing the recorded seismic data and performing inversion techniques, a detailed crosswell geological profile can be obtained [1]. Compared to traditional surface seismic surveys, crosswell seismic surveys offer significantly higher resolution, typically ranging from 10 to 100 times greater. This technique has found widespread applications in various geophysical fields, including subsurface rescoruit monitoring [2; 3; 4], CO\({}_{2}\) capture and sequestration [5; 6], and geothermal reservoir exploration and evaluation [7]. To effectively conduct crosswell seismic surveys, it is necessary to use an acoustic source capable of transmitting low-frequency and high-power signals in a compact size [8; 9; 10]. Currently, the acoustic source used in crosswell seismic surveys often consists of multiple piezoelectric circular tubes connected to form an elongated cylindrical liquid cavity with open ends. The radial vibrations of the piezoelectric circular tubes are utilized to drive the vibration of the liquid cavity, enabling low-frequency emission [8], as shown in Figure 0(a). However, this approach presents several challenges. Firstly, the acoustic source's reliance on the vibration of the elongated liquid cavity results in an excessively long axial size, occupying valuable space within the well. This limitation hampers the practical implementation of crosswell seismic surveys. Secondly, the current method only utilizes the radial vibrations of the circular tubes to drive the liquid cavity's vibrations. As a consequence, the sound power generated by the acoustic source within the well is insufficient, and the distance the seismic waves can penetrate through the strata between wells is limited. These limitations fall short of meeting the requirements of practical applications. To address these issues, innovative advancements are needed in the design and functionality of the crosswell seismic acoustic source. Such improvements should aim to reduce the axial size of the source while simultaneously increasing its sound power output. By doing so, the distance the seismic waves can effectively propagate between wells will be extended, resulting in enhanced performance that aligns with practical demands. To address these challenges, an innovative approach is proposed in this study, as shown in Figure 1b. Firstly, a rigid cover plate is introduced at one end of the piezoelectric circular tube. This modification changes the previous boundary condition, which had both ends of the liquid cavity open, into a new boundary condition with one end open and one end closed. By simulating a boundary condition where one end is rigid and the other end is free, the resonant frequency in the axial direction of the liquid cavity in the piezoelectric tube is effectively reduced [11]. This solution overcomes the limitation of relying solely on the excessive length of the axial dimension to achieve a lower resonant frequency in the acoustic source within the well. Additionally, a trilaminar bending ring with a central hole is incorporated at the other end of the piezoelectric circular tube. This design enables the utilization of both the bending vibrations of the trilaminar bending ring and the radial vibrations of the piezoelectric circular tube to simultaneously drive the vibration of the liquid cavity. This combination of vibration modes enhances the overall vibration response of the liquid cavity, resulting in improved performance of the acoustic source. By implementing these modifications, the proposed approach aims to optimize the design of the crosswell seismic acoustic source.