The direct P-wave and S-wave are first received in seismic records, subsequently, the direct channel wave also propagates to the receivers and is received. This three direct wave groups are the most obvious. When there is structural development in the working face (there is a wave impedance interface), which generated reflected channel wave [16], and the detection diagram is shown in Figure 1. Therefore, the development and distribution of the internal structure of the working face are detected by reflected channel wave.

In a certain time window, the covariance matrix is formed according to the amplitude value set of spatial data points, and the eigenvalues and corresponding eigenvectors of the covariance matrix are solved. The eigenvector corresponding to the maximum eigenvalue must be in the maximum polarization direction. According to the particle polarization and the relationship between the principal polarization direction and the propagation path direction, the filtering parameters

are set to separate the effective wave from the interference wave [17].

1) The constitution of covariance matrix

For three-component data acquisition, assume that there are m sampling points in the time window ( t 1 , t 2 ) , and the three-components on each receiving point correspond to X i , Y i , Z i (representing the amplitude value of the sampling point, respectively), and their average values in the time window ( t 1 , t 2 ) are as follows:

N x = 1 M ∑ i = M 1 M 2 X i , N y = 1 M ∑ i = M 1 M 2 Y i , N z = 1 M ∑ i = M 1 M 2 Z i (1)

where ( M 2 − M 1 ) ⋅ Δ t = t 2 − t 1 , M = M 2 − M 1 + 1 , Δ t is the sampling interval, and the above formula can be sorted into covariance matrix:

1 M [ ∑ i = M 1 M 2 ( X i − N x ) ( X i − N x ) , ∑ i = M 1 M 2 ( X i − N x ) ( Y i − N y ) , ∑ i = M 1 M 2 ( X i − N x ) ( Z i − N z ) , ∑ i = M 1 M 2 ( Y i − N y ) ( X i − N x ) , ∑ i = M 1 M 2 ( Y i − N y ) ( Y i − N y ) , ∑ i = M 1 M 2 ( Y i − N y ) ( Z i − N z ) , ∑ i = M 1 M 2 ( Z i − N z ) ( X i − N x ) , ∑ i = M 1 M 2 ( Z i − N z ) ( Y i − N y ) , ∑ i = M 1 M 2 ( Z i − N z ) ( Z i − N z ) , ] (2)

According to the covariance matrix, three eigenvalues, λ₁, λ₂ and λ₃ can be obtained. Through these three eigenvalues, the axis of the ellipsoid composed of the particle vibration track can be determined. The principal eigenvector V₁ corresponding to the maximum eigenvalue λ₁ is the long axis direction of the ellipsoid, which is called the principal polarization direction.

2) Parameter setting and selection of polarization filter

According to the eigenvalues λ₁, λ₂ andλ₃ obtained from the covariance matrix and the angle θ between the principal polarization direction and the propagation path direction, the polarization coefficient factor τ and the principal polarization direction factor φ are defined.

Polarization coefficient factor τ:

τ = ( 1 − λ 2 λ 1 ) 2 + ( 1 − λ 3 λ 1 ) 2 + ( λ 2 λ 1 − λ 3 λ 1 ) 2 2 ( 1 + λ 2 λ 1 + λ 3 λ 1 ) 2 (3)

principal polarization direction factor φ:

φ = { cos θ , P-wave sin θ , S-wave (4)

The filtering function is set as follows:

F ( t ) = τ p ( t ) φ q ( t ) (5)

where, the indexes P and Q are the weighted coefficients.

The original seismic record is the arrival time information about the spatial position and reflection phase of the excitation receiver. Generally, the reflection path information in these original records cannot directly represent the actual location of the underground geological body, so the subsequent migration and homing processing is needed [18].

If the S-coordinate of the source’s point is (x_s, y_s, z_s), the R-coordinate of the receiver’s point is (x_R, y_R, z_R), and the G-coordinate of the reflection point is (x_G, y_G, z_G), then the ellipsoid equation formed by the source-receiver and the travel path of the reflected signal is as follows:

x G 2 L G 2 − 4 z S 2 + y G 2 L G 2 − 4 z S 2 + z G 2 L G 2 = 1 4 (6)

According to the principle of pre-stack diffraction migration, each source-receiver can form an ellipsoid according to the travel length of seismic ray. Due to the multiple coverage technology in the actual detection, there are many pairs of source and check relations. At this time, each pair of source and check relations can construct the ellipsoid equation, and all the ellipsoid equations are combined to obtain the common section, which is the position where the reflection signal is generated.

According to the result of the three-dimensional seismic exploration showed that there may be a large collapse column about 90 m in diameter at the distance of 60m from the outside of a working face in actual engineering project. However, the surface terrain is complex and the fluctuations are large, which caused large restriction and low reliability of the three-dimensional seismic detection. In order to ensure the safety of the working face, detection work must be carried out in the coal mine. As the collapse column is located outside the boundary of the working face, there is only one roadway around it. Limited by the construction conditions, the working face transmission detection cannot be done, therefore, only the reflected channel wave detection is a suitable choice.

Taking into account the field conditions, a three-dimensional simulation was conducted based on high-order staggered-grid finite difference method [19], and a three-dimensional model of the collapse column containing the roadway was designed, as is shown in Figure 2, and the elastic parameters of the collapse column model are shown in Table 1. The physical parameters of this model meet the excitation conditions of Love channel wave [20]. A three-dimensional spatial coordinate system was established, X direction is vertical to the survey line, that is, the direction of coal seam side; Y direction is parallel to the survey line, that is, the direction pointing to the fault; Z direction is vertical downward, that is, the direction pointing to the floor. The size of the model in the X, Y and Z directions is 200 m, 400 m, 200 m, respectively. The width of air roadway is 4m, and the height is 5 m. The central position was located at the coordinate point 0 m, 2.5 m and 97.5 m in X, Y, and Z direction. The length is 400 m and the coal thickness is 2.5 m. The collapse column model boundary is located in

the X direction 302 m to 390 m, Y direction 67 m to 187 m, Z direction 85 m to 140 m. The size of the model grid is Δx = Δy = Δz = 0.2 m.

The observation system was arranged with 25 three-component receivers and the offset was 10 m. The receivers are arranged in a straight line in the direction of the collapse column. The position of NO1 receiver was located at the coordinate point 5 m, 5 m and 98 m in X, Y, and Z direction. There are 3 sources totally, and the position of source S1 was located at the coordinate point 390 m, 5 m and 98 m in X, Y, and Z direction. The position of source S2 was located at the coordinate point 350 m, 5 m and 98 m in X, Y, and Z direction. The position of source S3 was located at the coordinate point 300 m, 5 m and 98 m in X, Y, and Z direction. The numerical simulation is carried out using X-direction concentration source with a source frequency of 120 Hz and a sampling frequency of 10 kHz. The model boundary uses PML absorption boundary [21], and the free interface of roadway is processed by HA method to reduce the interference of artificial boundary [22].

Figures 3(a)-(c) respectively show the X component seismic records of S1 source, S2 source and S3 source. As is shown, Event 1, Event 2, Event 3 stand for

direct P-wave, direct S-wave, and direct channel wave. When the seismic wave propagates in the impedance interface of collapse column, it reflects back. Hence, Event 4, Event 5, and Event 6 stand for the reflected P-wave, reflected S-wave, and reflected channel wave. The seismic records of Y and Z components are shown in Figure 4.

Through comparison, it shows that the signal-to-noise ratio of the X component is higher than that of the Z component and Z component. Love channel wave is formed by SH wave interference [23], and SH wave is relatively developed in X component, so the energy of Love channel wave in X component is relatively stronger. At the same time, the reflected wave of S2 source is distinguished obviously, and the hyperbola is obvious. The signal-to-noise ratio is relatively higher.

According to the seismic records, the signal-to-noise ratio of X component is higher than that of Y component and Z component. Therefore, the wave field snapshot of X component of S2 source is selected to analyze the characteristics of seismic waves. Figure 5 shows the wave field snapshots of X component at 30 ms, 60 ms and 70 ms. At 30 ms, wave front 1, wave front 2 and wave front 3 are direct P-wave, direct S-wave and direct Love channel wave. when the seismic waves propagate to 60 ms, seismic waves meet the wave impedance interface of collapse column, and part of seismic waves propagate into the collapse column, wave front 4 is transmission P-wave, wave front 5 is transmission S-wave, and part of seismic wave generates reflected waves, wave front 6 is reflected P-wave propagating in the direction of roadway, and wave front 7 is reflected S-wave. At 70 ms, when the Love channel wave propagates to the impedance interface of the collapse column, a part of the Love channel wave propagates into the collapse column. Because there is no coal seam in the collapse column, the Love channel wave is converted into SH wave [24], and continues to propagate along the collapse column. As shown in wave front 8, wave front 9 is the reflected Love channel wave.

Figure 6 shows the wave field snapshots of X component at 90 ms, 100 ms

and 120 ms. When the seismic waves propagate to 90 ms, the reflected body waves and the direct waves are mixed, reflected S-wave and reflected Love channel wave, as shown in wavefront 8 and wavefront 9. The wave field snapshots at 100 ms and 120 ms are similar to that at 90 ms, but with the increase of propagation distance, reflected S-wave is mixed with direct Love channel wave.

To sum up, the source is excited near the roadway, the direct P-wave, S-wave and slot wave propagate along the roadway and are received by the receivers. When P-wave, S-wave and Love channel wave propagate to the collapse column interface, which generate reflected P-wave, reflected S-wave, and Love channel wave. But some reflected P-wave and reflected S-wave are easily mixed with direct channel wave, so it is difficult to distinguish them from the seismic record. Therefore, the reflection trough is reflected in the time domain. The wave is the characteristic wave of collapse column.

In seismic detection of working face by using the reflected body waves and the

reflected channel wave, when the source is excited in the coal seam, most of the energy will be confined in the coal seam [25], so the body waves energy is relatively weak, and the channel wave energy is relatively strong. At the same time, in the conventional reflection detection, the reflected body waves are easy to mix with the channel wave, which reduces the signal-to-noise ratio of seismic records. Relatively speaking, the energy of channel wave is strong and the wave train is wide, which is distinguished from other wave trains in time domain. Meanwhile, the high frequency signal of the channel wave is rich. Compared with the body waves, the imaging resolution of the channel wave is higher.

Channel waves can be divided into two types: Love channel waves and Rayleigh channel waves. The development condition of Love channel wave is relatively simple, but the formation condition of a Rayleigh channel wave is quite strict [26]. When the parameters of surrounding rock and coal seam do not meet the excitation conditions of Rayleigh channel wave, effective signals cannot be collected. The generation condition of Love channel wave (perpendicular to coal wall) is simple and more universal. From the perspective of actual construction, it is easier to operate the exciting and receiving in the left and right sides of the coal roadway than in the roof and floor.