# Mechanisms of Noise Transmission in Velocity Broad-Band Seismometers: Modeling and Analysis
## 4 Simulation
### Verification of the Amplitude-Frequency Characteristics of Noise Transfer Functions
#### 4.3.3 Results Analysis  
In Figure 6, the suspension pendulum noise PSD value is approximately \(-196\) dB, uniformly distributed across the spectrum. The EIN, represented by the orange line, equals the amplitude of the noise source in the frequency domain. As a result, the amplitude-frequency characteristic of its noise transfer function remains constant at 0 dB, consistent with the theoretical result for \(H_{ln}^{d_{l}}\) shown in Figure 5.  
In Figure 7, the forward path electronic Gaussian white noise PSD is approximately \(-149\) dB, also uniformly distributed across the spectrum. The EIN follows the amplitude-frequency characteristic of the transfer function \(H_{ln}^{d_{l}}\), as shown in Figure 5. For \(f<=0.77\) Hz, the gain remains constant at \(-80\) dB, while for \(f>0.77\) Hz, the EIN rises at a rate of 40 dB/dec. At \(f=80\) Hz, the gain reaches 0 dB, consistent with Equations (28) and (29).  
Figure 8: EIN caused by white noise of integrator.  
Figure 7: EIN caused by white noise in forward path.  
In Figure 8, the integrator white noise PSD is \(-130\) dB, and it is uniformly distributed across the spectrum. The EIN follows the transfer function characteristic of \(H_{n_{int}}^{a_{i}}\) shown in Figure 5, decreasing at a rate of \(-20\) dB/dec across the entire frequency range. According to Equation (39), the frequency point where the gain is \(0\) dB is \(1.8\times 10^{-6}\) Hz, which can be inferred from the figure. Thus, the integrator's noise transfer function exhibits a strong noise suppression effect within the measurement bandwidth, especially at higher frequencies.  
As shown in Figure 9, the force transducer noise PSD is around \(-180\) dB, uniformly distributed across the spectrum. The EIN behavior follows the transfer function characteristic \(H_{n_{fp}}^{a_{i}}\) shown in Figure 5. At low frequencies, the noise suppression is strong, while at higher frequencies, the suppression diminishes. Around \(100\) Hz, the PSD of the noise  
Figure 10: EIN caused by white noise of differential amplifier  
Figure 9: EIN caused by force transducer noise.  
source closely matches that of the EIN. Based on Equation (40), the gain reaches 0 dB at 175 Hz, confirming the alignment between the theoretical and simulation results.  
In Figure 10, the differential amplifier noise is approximately \(-147\) dB and uniformly spread across the spectrum. The behavior of the EIN aligns with the transfer function characteristic \(H_{n_{\mathrm{dB}}}^{a_{\mathrm{s}}}\) shown in Figure 5. At low frequencies, the noise transfer function exhibits an overall suppressive effect, decreasing at a rate of \(-20\) dB/dec until it reaches the corner frequency of 0.017 Hz. Beyond this point, it increases at a rate of 20 dB/dec. The transfer function gain at the corner frequency is \(-76\) dB, corresponding to Equation (44), and the frequency where the noise gain reaches 0 dB is 147 Hz, consistent with Equation (45).  
The simulation results presented above validate the proposed noise transfer mechanism model and confirm the accuracy of the analyzed noise spectral characteristics. The parameters used in our simulations and experiments are based on commercially available seismometers, which are widely used in industry and research. This ensures that the results are not only theoretically valid but also practically applicable in real-world scenarios.