## 3 Data Processing
### Autocorrelation Extraction of Reflected Wave  
The reflected P wave can be obtained by autocorrelation according to the vertical component of the continuous waveform recorded by the fixed station [21], but the calculation amount from this method is too large when extracting the reflected wave signal, resulting in low efficiency. In this article, the P wave, S wave and coda wave of the teleseismic events are used to extract the reflected wave, and the calculation efficiency is greatly improved. The core idea is that the reflection seismogram with a surface source and surface receiver can be obtained from the autocorrelation of the transmitted waves from the deep source and the receiver at the same position [22], that is, the autocorrelation of the vertically incident transmitted wave is equivalent to the reflected wave. The physical essence of this idea is to extract reflected waves from the multiples between a free surface and a discontinuity using autocorrelation [23]. In this way, the transmission problem of the teleseismic P wave and its coda is transformed into a reflection problem, and then the reflection coefficient of the layered media can be studied [24]. The process of constructing a station superposition autocorrelation map to extract the crustal reflection information can improve the consistency of the crustal reflection coefficient and suppress noise to a certain extent. Compared with an active source exploration, autocorrelation extraction technology, as passive source detection technology, makes up for the shortcomings of an active source exploration in cost and depth [25]. Compared with the traditional receiver function, the autocorrelation method can obtain deeper underground information [26; 27]. The teleseismic data recorded by a seismometer includes the source information, transmission path information from a source to discontinuity, reflection and transmission information of multiples from a discontinuity to a free surface, in which the source information is negligible, so a non-interference seismic channel teleseismic record can be expressed in the frequency domain by Equation (6):  
\[W(\omega)=P(\omega)C(\omega) \tag{6}\]  
From the relationship between autocorrelation and convolution, it can be seen that after autocorrelation:  
\[A(W(\omega))=\left[W^{T}(\omega)\right]*\left[W(\omega)\right]=C^{T}(\omega)* P^{T}(\omega)*P(\omega)*C(\omega)=C^{T}(\omega)*C(\omega) \tag{7}\]  
When the teleseismic \(P\) wave is vertically incident to the horizontal layer as the transmission wave, the source information as the point source can be ignored, and the  
Figure 4: Spectrum envelope of Shizuishan (SZS) station at 5:00 on 6 April 2015.  
relationship between the transmission response and reflection response can be expressed by Equation (8):  
\[\frac{T(t)*T^{T}(t)}{\Pi\text{det}}=(1+R(t)+R^{T}(t)) \tag{8}\]  
The autocorrelation method is used to obtain the seismic reflection wave with the station as the virtual source and receiving point. The processing flow mainly includes four steps: pretrending, autocorrelation, moveout correction and stacked, as shown in Figure 5.  
Because this method uses the P wave of the teleseismic seismic events recorded by the vertical component and the seismic phases, such as global seismic phases PKP and PKIKP and their coda, to construct the reflected wave, the most critical step is NMO correction, which is used to eliminate the travel time difference of the seismic reflection phase, caused by the incident slowness, and correct the time difference of the rays to make them incident vertically [28].