Frequency-Bessel Transform Based Microtremor Survey Method and Its Engineering Application
Abstract
:1. Introduction
2. Methodology
2.1. Frequency-Bessel (F-J) Transform
2.2. Construction of New Inversion Objective Function
3. Numerical Tests
3.1. Selection of Geological Model
3.2. Theoretical Synthesis of Microtremor Signals
3.3. Microtremor Signal Processing
3.4. Inversion of Multi-Mode Dispersion Curve
4. An Engineering Application Verification
4.1. Site Overview
4.2. Data Acquisition
4.3. Measured Microtremor Signal Processing
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Layer Serial Number | Layer Thickness (m) | Model 1 | Model 2 | Model 3 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
V1 | V2 | ρ | V1 | V2 | ρ | V1 | V2 | ρ | ||
1 | 5 | 1611 | 200 | 1.725 | 1611 | 200 | 1.725 | 1611 | 200 | 1.725 |
2 | 10 | 1695 | 300 | 1.784 | 1582 | 150 | 1.697 | 1743 | 350 | 1.809 |
3 | 15 | 1798 | 400 | 1.834 | 1798 | 400 | 1.834 | 1641 | 240 | 1.750 |
4 | ∞ | 1969 | 600 | 1.920 | 1969 | 600 | 1.920 | 1969 | 600 | 1.920 |
Layer Serial Number | Search Interval of Layer Thickness (m) | Search Interval of S-Wave Velocity (m/s) | ||
---|---|---|---|---|
Model 1 | Model 2 | Model 3 | ||
1 | 2.5~7.5 | 100~300 | 100~300 | 100~300 |
2 | 5~15 | 150~450 | 75~225 | 175~525 |
3 | 5~25 | 200~600 | 200~600 | 120~400 |
4 | ∞ | 300~900 | 300~900 | 300~900 |
Layer Serial Number | Model 1 | Model 2 | Model 3 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Err1 (%) | Err2 (%) | Err3 (%) | Err4 (%) | Err1 (%) | Err2 (%) | Err3 (%) | Err4 (%) | Err1 (%) | Err2 (%) | Err3 (%) | Err4 (%) | |
1 | 2.67 | 0.17 | 0.33 | 0.08 | 3 | 0.08 | 6.33 | 0.25 | 0.43 | 0.26 | 0.33 | 0.24 |
2 | 0.17 | 1.17 | 9.8 | 0.78 | 1 | 0.22 | 3.33 | 0.44 | 0.67 | 0.81 | 0.75 | 1.24 |
3 | 8.33 | 1.58 | 3.22 | 4.42 | 3.67 | 0.46 | 1.44 | 0.25 | 1.44 | 0.83 | 0.56 | 1.14 |
4 | --- | 0.5 | --- | 0.31 | --- | 0.61 | --- | 0.06 | --- | 1.00 | --- | 1.36 |
Inversion Serial Number | Calculation Time of Traditional Inversion Objective Function (s) | Calculation Time of Newly Proposed Inversion Objective Function (s) | ||||
---|---|---|---|---|---|---|
Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | |
1 | 6562.88 | 8963.45 | 6489.65 | 69.17 | 83.94 | 66.05 |
2 | 6462.36 | 9032.13 | 6875.24 | 67.81 | 83.30 | 66.08 |
3 | 6655.34 | 9268.64 | 6259.36 | 60.73 | 83.55 | 65.47 |
4 | 6034.07 | 9149.32 | 6387.68 | 61.58 | 83.70 | 64.94 |
5 | 6243.52 | 8989.64 | 6512.35 | 60.41 | 86.88 | 64.25 |
6 | 6368.43 | 9432.61 | 6659.84 | 62.19 | 86.36 | 65.06 |
Name | Model | Main Performance Indicators |
---|---|---|
Geophone | CDJ-S2C | Velocity type: |
three-component | ||
Natural frequency: 2 ± 10% Hz | ||
Voltage output sensitivity: 2 ± 10% V/cm/s | ||
Coil resistance: 6040 ± 5% KΩ | ||
Damping coefficient: 0.7 ± 10% | ||
Data Logger | LS-8800 | Number of data channels: 3 |
A/D conversion: 24 bits | ||
Sampling frequency: 100 Hz or 200 Hz | ||
Dynamic range: 128 dB | ||
Time correction: real-time GPS automatic correction | ||
Applicable temperature: −20~+50 °C |
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You, Z.; Xu, P.; Qian, J.; Cao, L.; Du, Y.; Fu, Q. Frequency-Bessel Transform Based Microtremor Survey Method and Its Engineering Application. Int. J. Environ. Res. Public Health 2022, 19, 13484. https://doi.org/10.3390/ijerph192013484
You Z, Xu P, Qian J, Cao L, Du Y, Fu Q. Frequency-Bessel Transform Based Microtremor Survey Method and Its Engineering Application. International Journal of Environmental Research and Public Health. 2022; 19(20):13484. https://doi.org/10.3390/ijerph192013484
Chicago/Turabian StyleYou, Zhiwei, Peifen Xu, Jing Qian, Lianpeng Cao, Yanan Du, and Qiang Fu. 2022. "Frequency-Bessel Transform Based Microtremor Survey Method and Its Engineering Application" International Journal of Environmental Research and Public Health 19, no. 20: 13484. https://doi.org/10.3390/ijerph192013484