*2.1. Noise Period Scanning*

The waveform of periodic noise is similar in a single trace. Based on the similarity, we scan the noise period from ambient noise, which exists in the records before the first arrivals. First, given the scanned period interval [*T*min, *T*max], the noise period *T* is changed from the initial scanned period *T*min to the final scanned period *T*max. The data *Sj* on the single trace *hj*(*j* = 1, 2, . . . , *m*) are split into many time windows *si*(*i* = 1, 2, . . . , *n*), denoted as

$$S\_{\rangle} = [s\_1, s\_2, \dots, s\_n] \tag{1}$$

where the length of time window *si* is equal to the scanned period *T*. The size of *Sj* is *N* × 1 (*N* ≥ *nT*). Next, the correlation coefficients for the adjacent two time windows *si* and *si*+<sup>1</sup> are calculated:

$$\text{Corr}(s\_i, s\_{i+1}) = \frac{\text{Cov}(s\_i, s\_{i+1})}{\sqrt{\text{Var}(s\_i)}\sqrt{\text{Var}(s\_{i+1})}} \tag{2}$$

where Cov(*si*,*si*+1) is the covariance of the two time windows and Var(*s*) is the variance of *s*. For accuracy, we average the correlation coefficients to obtain a coefficient to evaluate the similarity of all time windows.

$$\mathbb{C}(T) = \frac{1}{n-1} \sum\_{i=1}^{n-1} \text{Corr}(s\_{i\prime} s\_{i+1}) \tag{3}$$

Then, the scanned period *T* is increased and the former procedures are repeated until all periods in the interval [*T*min, *T*max] are scanned. The period which matches the maximum value of the correlation coefficients is our estimated period:

$$
\tilde{T} = \underset{T}{\text{argmax}} \{ \mathbb{C}(T) \} \tag{4}
$$

where *T* is the period of periodic noise on the trace *hj*.
