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Table 2 Computed seismic features in this study

From: Segmentation characteristics of deep, low-frequency tremors in Shikoku, Japan using machine learning approaches

ID

Expression

Description

1st family

1. EnvMean/Max

f1 = \(\frac{{\text{mean}} \, \text{(Env)}}{\mathrm{max}({\text{Env}})}\)

Ratio of the mean over the max of the envelope signal

2. EnvMed/Max

f2 = \(\frac{{\text{median}} \, \text{(Env)}}{\mathrm{max}({\text{Env}})}\)

Ratio of the median over the max of the envelope signal

3. EnvMax

f3 = \(\mathrm{max}\left({\text{Env}}\right)\)

Maximum envelope amplitude

4. EnvMaxTime

f4 = arg max(Env)

Time of the maximum envelope amplitude

5. RawKurt

f5 = \({(\frac{{\mu }_{\text{Raw}}}{{\sigma }_{\text{Raw}}})}^{4}\)

Kurtosis of the raw signal

6. EnvKurt

f6 = \({(\frac{{\mu }_{\text{Env}}}{{\sigma }_{\text{Env}}})}^{4}\)

Kurtosis of the envelope

7. RawSkew

f7 = \({(\frac{{\mu }_{\text{Raw}}}{{\sigma }_{\text{Raw}}})}^{3}\)

Skewness of the raw signal

8. EnvSkew

f8 = \({(\frac{{\mu }_{\text{Env}}}{{\sigma }_{\text{Env}}})}^{3}\)

Skewness of the envelope

9.\({\text{ACF}}_{1/3}\)

f9 = \({\int }_{1}^{3/T}{\text{C}}(\tau)\text{d}\tau\)

Energy in the first third of the autocorrelation function

10. \({\text{ACF}}_{2/3}\)

f10 = \({\int }_{\frac{\text{T}}{3}}^{\mathrm{T}}{\text{C}}\left(\tau\right)\text{d}\tau\)

Energy in the remaining part of the autocorrelation function

11. \({\text{ACF}}_{1/3}\)/\({\text{ACF}}_{2/3}\)

f11 = \(\frac{{f}_{9}}{{f}_{10}}\)

Ratio of the above two

2nd family

12. Max \({BP}_{2-8 Hz}\)

f12 = max(\({BP}_{2-8 Hz}\))

Maximum amplitude of the 2–8 Hz filtered signal

13. NPks \({BP}_{2-8 Hz}\)

f13 = length(findpeaks(\({\text{Env}}_{\text{BP}}\)))

Number of peaks in the envelope filtered by 2–8 Hz

14. \({ BP}_{0.1-1 Hz}\)

f14 = \({\int }_{0}^{\mathrm{T}}{BP}_{0.1-1 Hz}\left({\text{t}}\right){\text{dt}}\)

Energy of the signal filtered by 0.1–1 Hz

15. \({BP}_{2-8 Hz}\)

f15 = \({\int }_{0}^{\mathrm{T}}{BP}_{2-8 Hz}\left({\text{t}}\right){\text{dt}}\)

Energy of the signal filtered by 2–8 Hz

16. \({ BP}_{5-20 Hz}\)

f16 = \({\int }_{0}^{\mathrm{T}}{BP}_{5-20 Hz}\left({\text{t}}\right){\text{dt}}\)

Energy of the signal filtered by 5–20 Hz

17. Kurt \({BP}_{0.1-1 Hz}\)

f17 = \({(\frac{{\mu }_{\text{BP1}}}{{\sigma}_{\text{BP1}}})}^{4}\)

Kurtosis of the signal filtered by 0.1–1 Hz

18. Kurt \({BP}_{2-8 Hz}\)

f18 = \({(\frac{{\mu }_{\text{BP2}}}{{\sigma}_{\text{BP2}}})}^{4}\)

Kurtosis of the signal filtered by 2–8 Hz

19. Kurt \({BP}_{5-20 Hz}\)

f19 = \({(\frac{{\mu }_{\text{BP3}}}{{\sigma}_{\text{BP3}}})}^{4}\)

Kurtosis of the signal filtered by 5–20 Hz

3rd family

20. KurtDFT

f20 = Kurtosis(\(\underset{t=0\dots T}{\mathrm{max}}[\text{SPEC(}t,f\text{)}]\))

Kurtosis of the maximum of all DFT as a function of time

21. DFTmax/mean

f21 = mean(\(\frac{\underset{t=0\dots T}{\mathrm{max}}[\text{SPEC(}t,f\text{)}]}{\underset{t=0\dots T}{\mathrm{mea}n}[\text{SPEC(}t,f\text{)}]}\))

Mean ratio between the maximum and the mean of all DFT

22. DFTmax/med

f22 = mean(\(\frac{\underset{t=0\dots T}{\mathrm{max}}[\text{SPEC(}t,f\text{)}]}{\underset{t=0\dots T}{\mathrm{media}n}[\text{SPEC(}t,f\text{)}]}\))

Mean ratio between the maximum and the median of all DFT

23. NPks_DFTmax

f23 = length(findpeaks(\(\underset{t=0\dots T}{\mathrm{max}}[\text{SPEC(}t,f\text{)}]\)))

Number of peaks in the curve showing the temporal evolution of the DFT max

24. NPks_DFTmean

f24 = length(findpeaks(\(\underset{t=0\dots T}{\mathrm{mean}}[\text{SPEC(}t,f\text{)}]\)))

Number of peaks in the curve showing the temporal evolution of the DFT mean

25. NPks_DFTmed

f25 = length(findpeaks(\(\underset{t=0\dots T}{\mathrm{median}}[\text{SPEC(}t,f\text{)}]\)))

Number of peaks in the curve showing the temporal evolution of the DFT median

26. NPks_DFTmax/mean

f26 = \(\frac{{f}_{23}}{{f}_{24}}\)

Ratio between #23 and #24

27. NPk_DFTmax/med

f27 = \(\frac{{f}_{23}}{{f}_{25}}\)

Ratio between #23 and #25

28. Sum \({BP}_{2-8 Hz}\)/\({BP}_{5-20 Hz}\)

f28 = \(\frac{\mathrm{sum}(\underset{2\le f\le 8}{\text{[STFT}}\text{(}t,f\text{)]})}{\mathrm{sum}(\underset{5\le f\le 20}{\text{[STFT}}\text{(}t,f\text{)}])}\)

Ratio between the sum of energy in 2–8 Hz and the sum of energy in 5–20 Hz

29. Sum \({BP}_{2-8 Hz}\)/\({BP}_{5-50 Hz}\)

f29 = \(\frac{\mathrm{sum}(\underset{5\le f\le 20}{[\mathrm{STFT}}\text{(}t,f\text{)])}}{\mathrm{sum}(\underset{5<f\le 50}{[\mathrm{STFT}}\text{(}t,f\text{)])}}\)

Ratio between the sum of energy in 5–20 Hz and higher than 5 Hz