# Mechanisms of Noise Transmission in Velocity Broad-Band Seismometers: Modeling and Analysis
## 6 Discussion and Conclusions  
This paper provides a comprehensive analysis of noise transmission pathways in VBB seismometers, presenting a detailed noise transmission model and identifying key factors that influence the noise transfer function. Using this model, we analyzed the spectral characteristics of noise transfer functions across the forward path, feedback path, and data acquisition stages, focusing on critical parameters such as gain and corner frequencies. Figure 13: Measured, theoretical, and simulated self-noise values. NLNM and NHNM curves represent [PERSON]’s Earth noise model [2]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency(Hz)** &
\begin{tabular}{c} **Measurement Uncertainty** \\ **(dB)** \\ \end{tabular} & **Confidence Interval (dB)** \\ \hline
0.01 & 3.3939 & \([-178.51,-165.2]\) \\
0.1 & 1.6529 & \([-192.58,-186.1]\) \\
1 & 0.31204 & \([-185.71,-184.48]\) \\
10 & 0.96385 & \([-165.27,-161.49]\) \\
100 & 2.0388 & \([-141.74,-133.75]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measurement uncertainty and confidence interval of results. Theoretical analysis and numerical simulations showed excellent agreement, confirming the accuracy of the proposed noise transfer model and noise optimization strategy. The primary findings are as follows:  
* The noise transfer function of the suspension pendulum is constant, determined by the input mechanical constant. Optimizing its mechanical design effectively reduces the noise transfer gain. * The forward path noise transfer function exhibits attenuation at low frequencies and amplification at high frequencies. Increasing input mechanical constant or enhancing the forward path gain--such as improving the suspension pendulum sensitivity, capacitive bridge gain, or preamplifier gain--lowers the noise transfer gain. * The integrator noise transfer function demonstrates higher attenuation at higher frequencies. Reducing integrator gain, force transducer gain, and the mechanical feedback constant, or increasing the integration resistance and input mechanical constant, can lower this gain. * The force transducer noise transfer function behaves similarly to the forward path noise, with low-frequency attenuation and high-frequency amplification. Reducing the force transducer gain and feedback mechanical constant, or increasing the input mechanical constant, can help lower the noise transfer function gain. * The noise transfer function of the differential amplifier follows the same trend, with low-frequency attenuation and high-frequency amplification. Lowering the feedback loop gain (e.g., PID controller gain, force transducer gain, and feedback mechanical constant) and increasing the input mechanical constant can reduce the gain. * Optimizing the input mechanical constant or feedback mechanical constant has a full-band effect and can improve all noise transfer functions. It is also important to note that the optimization methods described above may sometimes impact other performance metrics of the seismometer, requiring case-by-case analysis to balance noise reduction with the preservation of other critical parameters. Although the conclusions in this study were validated using a commercially available seismometer, the proposed noise optimization methods and formulas based on transfer path analysis are applicable to other VBB seismometers. The underlying principles are generalizable, making the conclusion applicable to other real-world seismometers. This research fills a critical gap in the understanding of noise transmission mechanisms in VBB seismometers, especially regarding feedback path noise transmission. This systematic approach, which has not been explored in previous studies, establishes a solid theoretical foundation for optimizing seismometer noise within specific frequency ranges by improving transmission paths. Conceptualization, Y.S. and Z.Z. ([PERSON]); methodology, Y.S., B.C. and L.Y. ; software, Y.S. and Z.Z. ([PERSON]); validation, Y.S. ; formal analysis, Y.S. and Z.Z. ([PERSON]); investigation, Y.S. ; resources, Y.S.