# Mechanisms of Noise Transmission in Velocity Broad-Band Seismometers: Modeling and Analysis
## 1 Introduction  
The velocity broad-band (VBB) seismometer is extensively used in fields such as seismic monitoring, subsurface velocity structure imaging, and mineral exploration, owing to its superior stability, wide frequency range, large dynamic range, and low self-noise levels [1]. Compared to accelerometers, it is typically applied for observing weak seismic motion signals. Currently, most VBB seismometers exhibit self-noise levels below the New Low Noise Model (NLNM) in the microseism frequency band [2]. However, in both ultra-low and high-frequency ranges, noise levels still surpass the NLNM, as illustrated in Figure 1.  
Reducing self-noise further remains essential for several reasons. First, weak seismic signals often carry critical information about dynamic processes within the Earth, such as its rotation and tidal effects. Reducing self-noise can improve the signal-to-noise ratio (SNR), enabling more accurate analysis of long-period Earth's free oscillation modes and thus providing deeper insights into the planet's internal structure and dynamics [3; 4; 5; 6]. Second, prior to major seismic events, extremely weak foreshock activities often occur. A higher SNR allows for better detection of these small-scale seismic activities, enhancing seismic monitoring and early warning systems while minimizing false alarms and missed events [7; 8; 9; 10; 11]. Lastly, for ambient seismic noise tomography, the seismometer's self-noise must remain below the background noise level of the Earth [12; 13; 14]. Numerous studies have focused on improving seismometer performance by altering internal noise sources or replacing specific modules. PMD Scientific Inc. has developed a novel seismometer that employs an electrolytic liquid instead of a spring suspension pendulum, achieving self-noise levels below NLNM in the 0.05-5 Hz range [15]. To mitigate Brownian noise from the suspension pendulum, researchers at the University of Tokyo designed a vibration pickup system using magnetic levitation technology, which achieves a noise level of \(10^{-9}\) m/s\({}^{2}\)/\(\sqrt{\rm Hz}\) @ 1 Hz; however, this prototype currently operates only for the vertical component [16]. Additionally, several studies have focused on developingnovel sensors utilizing optical methods in place of traditional electromechanical transducers. In 2010, [PERSON] et al. modified the transducer of the STS-1 seismometer to create a fiber-optic seismometer based on a Michelson interferometer, achieving displacement measurement accuracy of up to \(4\times 10^{-13}\) m. However, further improvements are necessary due to its open-loop design [17]. [PERSON] also developed a fiber Bragg grating-based seismometer, which achieved a self-noise level of \(2.7\times 10^{-7}\) m/s\({}^{2}\)/\(\sqrt{\text{Hz}}\) @ 0.1 Hz [18]. In contrast, VBB seismometers still offer unparalleled advantages in terms of stability, self-noise performance, and working frequency range. There is also some research on VBB seismometer noise modeling. [PERSON] and [PERSON] were among the first to begin analyzing seismometer self-noise [20]. [PERSON] discussed the levels of four significant noise sources in the feedback loop of leaf-spring suspension pendulum seismometers and suggested that the key to reducing suspension noise below seismic noise is ensuring that the mechanical pendulum's parameter MTQ exceeds 1 kg [21]. [PERSON] explored the theoretical model of self-noise in feedback seismometers, using the CMG-3 ESP seismometer as a case study. His research concentrated on suspension and electronic noise in the feedback system's forward path, concluding that electronic noise was the primary source of self-noise, while suspension noise could be neglected [22]. [PERSON] expanded on this by establishing a theoretical model for VBB seismometer self-noise, identifying eight noise sources in both the forward and feedback paths. His work, among the most complete in this field, provided a step-by-step method for calculating self-noise and proposed strategies to reduce forward-path electronic noise.