Effect of Rock Structure on Seismic Wave Propagation
Abstract
1. Introduction
2. Methodology: Integrated Experimental and Analytical Framework
2.1. Experimental Equipment
2.2. Experimental Scheme
2.3. Signal Processing Methodology
- Pre-processing:
- 2.
- Analysis and Parameter Extraction:
3. Effect of Seismic Wave Characteristic Parameters by Rock Structure
3.1. Effect of Crack Angle to the Characteristic Parameters of Seismic Waves
3.2. Effect of Crack Width on Characteristic Parameters of Seismic Waves
3.3. Effect of Rock Interface on Characteristic Parameters of Seismic Wave
4. Difference in Characteristic Parameters of Seismic Wave Along Different Propagation Paths of the Same Rock Structure
5. Discussion
5.1. Limitations and Implications for In Situ Conditions
5.2. Practical Applications
5.3. Robustness of Time–Frequency Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No. | Structure Type | Crack Length, mm | Crack Width, mm | Angle of Crack, ° |
---|---|---|---|---|
1 | Crack | 30 | 1 | 35 |
2 | 2 | 35 | ||
3 | 3 | 35 | ||
4 | 1 | 55 | ||
5 | 1 | 75 |
Crack Angle, ° | Parameter | Excitation Source (Mean) | Receiving Source (Mean ± SD) | 95% CI | Decay (%) |
---|---|---|---|---|---|
35 | Amplitude (mV) | 10.0 | 2.36 ± 0.15 | [2.25, 2.47] | 76.35 |
Main Frequency (kHz) | 175.50 | 174.74 ± 0.52 | [174.37, 175.11] | 0.44 | |
Energy (a.u.) | 315.03 | 6.36 ± 0.41 | [6.06, 6.66] | 97.98 | |
55 | Amplitude (mV) | 10.0 | 1.36 ± 0.11 | [1.28, 1.44] | 86.42 |
Main Frequency (kHz) | 167.78 | 166.72 ± 0.65 | [166.25, 167.19] | 0.63 | |
Energy (a.u.) | 297.33 | 1.88 ± 0.23 | [1.71, 2.05] | 99.37 | |
75 | Amplitude (mV) | 10.0 | 0.60 ± 0.08 | [0.54, 0.66] | 94.04 |
Main Frequency (kHz) | 168.61 | 154.36 ± 1.21 | [153.49, 155.23] | 8.45 | |
Energy (a.u.) | 265.80 | 0.51 ± 0.07 | [0.46, 0.56] | 99.81 |
Equation | y = a + b × x | ||
---|---|---|---|
Parameter | Energy | Amplitude | Main Frequency |
Intercept | 10.95942 ± 2.56548 | 3.87283 ± 0.20106 | 193,287.29167 ± 3593.16331 |
Slope | −0.14625 ± 0.04472 | −0.04424 ± 0.0035 | −509.375 ± 62.62807 |
R2 | 0.91451 | 0.99376 | 0.98511 |
Symbol | Definition | SI Unit |
---|---|---|
RPP, TPP | Reflection and transmission coefficients for P-wave | Dimensionless |
RSS, TSS | Reflection and transmission coefficients for S-wave | Dimensionless |
KN | Normal specific stiffness | Pa/m (or N/m3) |
KT | Tangential specific stiffness | Pa/m (or N/m3) |
ω | Angular frequency (2πf) | rad/s |
ZP | P-wave acoustic impedance (pvP) | kg/(m2s) |
ZS | S-wave acoustic impedance (pvS) | kg/(m2s) |
P | Rock density | kg/m3 |
vP | P-wave velocity in the rock | m/s |
US | S-wave velocity in the rock | m/s |
i | Imaginary unit () | Dimensionless |
Crack Width, mm | Parameter | Excitation Source (Mean) | Receiving Source (Mean ± SD) | 95% CI | Decay (%) |
---|---|---|---|---|---|
1 | Amplitude (mV) | 10.0 | 2.36 ± 0.15 | [2.25, 2.47] | 76.35 |
Main Frequency (kHz) | 175.50 | 174.74 ± 0.52 | [174.37, 175.11] | 0.44 | |
Energy (a.u.) | 315.03 | 6.36 ± 0.41 | [6.06, 6.66] | 97.98 | |
2 | Amplitude (mV) | 10.0 | 0.74 ± 0.09 | [0.68, 0.80] | 92.56 |
Main Frequency (kHz) | 169.96 | 166.33 ± 0.71 | [165.82, 166.84] | 2.14 | |
Energy (a.u.) | 289.49 | 0.55 ± 0.08 | [0.49, 0.61] | 99.81 | |
3 | Amplitude (mV) | 10.0 | 0.49 ± 0.06 | [0.45, 0.53] | 95.08 |
Main Frequency (kHz) | 169.70 | 162.49 ± 0.88 | [161.86, 163.12] | 4.25 | |
Energy (a.u.) | 275.07 | 0.29 ± 0.04 | [0.26, 0.32] | 99.89 |
Equation | y = a·eb·x | ||
---|---|---|---|
Parameter | Energy | Amplitude | Main Frequency |
Fitting results | y = 11.8398·e−1.8848x | y = 4.5428·e−1.0287x | y = 167·e−0.0076x |
R2 | 0.9702 | 0.9822 | 0.9490 |
Parameter Type | Parameter Value | Experimental Attenuation (%) | Theoretical Prediction (%) |
---|---|---|---|
Angle (°) | 35 | 97.98 | 98.7 (DDM) |
55 | 99.37 | 99.5 (DDM) | |
75 | 99.81 | 99.94 (DDM) | |
Width (mm) | 1 | 97.98 | 98.1 (scattering) |
2 | 99.81 | 99.7 (scattering) | |
3 | 99.89 | 99.92 (scattering) | |
Interface (receiving source #6) | - | 99.89 | 99.82 (stiffness) |
No. | Peak Amplitude, mV | Peak Amplitude Time, ×10−4 s | Main Frequency, kHz | Energy Peak, a.u. |
---|---|---|---|---|
Excitation source 3 | 10 | 2.60 | 175.029 | 315.564 |
Receiving source 1 | −1.9189 | 3.24 | 171.528 | 4.178 |
Receiving source 2 | −1.2743 | 4.34 | 171.028 | 1.769 |
Receiving source 4 | 2.3388 | 4.18 | 174,529 | 5.794 |
Receiving source 5 | −5.8202 | 3.35 | 170,028 | 98.037 |
Receiving source 6 | 1.0058 | 3.96 | 169,028 | 1.110 |
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Kang, Z.; He, S.; Jiang, H.; Shen, F.; Quan, C. Effect of Rock Structure on Seismic Wave Propagation. Sustainability 2025, 17, 9325. https://doi.org/10.3390/su17209325
Kang Z, He S, Jiang H, Shen F, Quan C. Effect of Rock Structure on Seismic Wave Propagation. Sustainability. 2025; 17(20):9325. https://doi.org/10.3390/su17209325
Chicago/Turabian StyleKang, Zhongquan, Shengquan He, Huiling Jiang, Feng Shen, and Chengzhu Quan. 2025. "Effect of Rock Structure on Seismic Wave Propagation" Sustainability 17, no. 20: 9325. https://doi.org/10.3390/su17209325
APA StyleKang, Z., He, S., Jiang, H., Shen, F., & Quan, C. (2025). Effect of Rock Structure on Seismic Wave Propagation. Sustainability, 17(20), 9325. https://doi.org/10.3390/su17209325