Detection of Tectonically Deformed Coal Using Model-Based Joint Inversion of Multi-Component Seismic Data

Abstract

Tectonically-deformed coal (TDC) is a potential source of threats to coal-mining safety. Finding out the development and distribution of TDCs is a difficult task in coalfield seismic explorations. Based on the previous investigations, the P- to S-wave velocity ratio (α/β) is a stable parameter for the identification of TDCs and most TDCs have α/β values of less than 1.7. Here, a TDC detection method using a model-based joint inversion of the multi-component seismic data is proposed. Following the least square theories, the amplitude variation with offset gathers of the PP- and PS-waves are jointly inverted into the corresponding α/β values. The prior models generated from the P- and S-wave velocity and density logs are employed in the joint inversion to enhance the inversed models. Model test results show that the model-based inversion is of high anti-noise ability and has a good recognition ability of TDCs. The proposed method is applied to a work area of the Guqiao mine in China. The TDCs developed in coal seam 13-1 are effectively identified according to their inverted α/β values of less than 1.7. The detection result is verified by the well and tunnel excavation information.

1. Introduction

As a fractured and brittle medium, coal is easily broken and deformed under the action of tectonic stress [1]. In coalfields all over the world, tectonically-deformed coal (TDC) is one of the factors leading to coal mine disasters. TDC is considered to be associated with the coal and gas outbursts [2,3,4]. Usually, TDCs are prone to absorb more gas than undeformed coals due to the larger adsorption surface [5,6]. In China, a large proportion of coal mines are high-outburst [7]. Determining the TDC development and distribution before tunneling will help to avoid coal and gas outburst disasters. Seismic methods are often used in the engineering safety assessments [8]. In the coalfield seismic explorations, extracting the information related to the TDC development and distribution from seismic data has become a hot and difficult research topic.

Many scholars have done a great deal of research to detect the TDC based on the seismic exploration data. For some shallow coal seams, when the coal zone is deformed, it is possible to find the corresponding indications by means of the interpretation on the seismic stacking profiles [9]. These indications include phase anomaly, amplitude variation, and event discontinuity. However, in the coalfield seismology, the tectonic deformation is regarded as the intrinsic attribute of a coal seam, which is hard to identify directly. Therefore, some scholars tried to determine abnormal geological bodies developed in coal seams by seismic attribute analysis. Ge et al. used an in-seam seismic method to find the anomalies inside the coal mass [10]. Wang et al. applied extreme learning machine and principal component analysis to predict the TDC thickness [11]. Other scholars tried to identify the TDCs developed inside a coal mass by converting seismic data into the attribute data of stratigraphic lithology. Li et al. used only P-wave prestack inversion to derive the evaluation parameters as elastic impedance, acoustic impedance, and porosity for the TDC characterization [12,13].

As the target coal seams become deeper and thinner, only using P-waves in a seismic exploration leads to great uncertainties in the interpretation of the coal seam attributes [14]. In order to make up for the shortage of the conventional P-wave explorations, the coalfield multi-component seismic exploration has been tried [15,16]. Multi-component seismic explorations are feasible to provide reliable P- to S-wave velocity ratios (α/β values) for the reservoir prediction [17]. Stewart et al. pointed out that the purpose of multi-component seismic is to record and utilize both reflected P- and S-waves (PP- and PS-waves) for more information related to rock properties [18]. In the multi-component seismic methods, joint PP and PS amplitude variation with offset (AVO) inversion is a high-precision method for the rock property characterization. Compared with the conventional only PP-wave AVO inversion [19,20], adding PS-waves into the inversion will reduce multi-solution problems. Veire and Landrø applied least square theories to the joint PP and PS inversion [21]. Kurt proposed a generalized linear algorithm for the joint PP and PS AVO inversion [22]. Du and Yan applied joint PP and PS AVO inversion to detect fluid [23]. Lu et al. used the Taylor expansion method in the joint PP and PS AVO inversion [24]. In the field of coalfield exploration, Lu et al. demonstrated a successful case of the prediction of coal-bearing strata, in which joint PP and PS AVO inversion has played an important role [25].

However, reliable seismic inversion depends on the prior rock physical knowledge. Recently, the log curve and rock physics characteristics of coals have been investigated in depth. Li et al. evaluated the coal reservoir permeability through the analysis of log data [26]. Xu et al. systematically studied the logging curve characteristics of the TDCs [27]. The research on the rock physics tests of coals mainly focuses on the microstructure [28], mechanical properties [29,30,31], and elastic properties [32,33,34,35,36]. Nevertheless, for the seismic inversion, the empirical relationships related to the seismic wave velocities are most important. The rock physics tests of Wang et al. show that under the similar stratigraphic conditions, the acoustic velocity and bulk density of the TDCs are lower than those of the undeformed coals [34]. However, for the coal samples collected at different locations, it is difficult to find a definite threshold value to distinguish between the TDC and undeformed coal, regardless of the P- or S-wave velocity [34,36]. The correlation between the P- or S-wave velocities and densities is poor and the density difference between the undeformed and deformed coals is not obvious [34]. The test data of Morcote et al. on the dynamic elastic properties show that the α/β values of the coals are less affected by the pressure than the single P- or S-wave velocities [35]. Therefore, the α/β value is an effective and stable factor for the TDC detection. It can be found from the tests of Wang et al. that the α/β values of the most deformed coal samples are less than 1.7 [34]. From the experimental data of Chen et al. on the ultrasonic velocities of the TDCs, the same empirical relationship can be inferred [36]. This empirical relationship will be adopted in the proposed method.

This paper will propose a TDC detection method using model-based joint inversion of multi-component seismic data. Model-based inversion can link the high-frequency rock physics model to the seismic inversion results. Mallick applied model-based inversion to add the high-frequency log information into the AVO inversion results [37]. Spikes and Dvorkin used model-based inversion to derive the lithology and physical parameters [38]. However, the publications on the model-based theory for joint PP and PS AVO inversion are less found. The model-based joint inversion of PP and PS AVO datasets from the coalfield is the novelty of the proposed method. Most coal seams are thin layers. As pointed out by Stovas et al., the anomalies in the AVO responses caused by the property changes in thin layers are slight [39]. In order to highlight these slight anomalies in the inversion, we propose to use the model constraints from the two aspects. First, the well logs will be interpolated into the three-dimensional space as the prior initial models for the inversion. Second, to the inversion results, the inverted α/β values of the target coal seam will be graded according to the empirical relationship of Wang et al. [34]; the coals with α/β values less than 1.7 will be identified as the TDCs.

The following sections are organized as follows: in Section 2, the theories of the model-based joint PP and PS AVO inversion are given in detail. A multi-component seismic data processing strategy for the TDC detection is illustrated. The proposed inversion method will be tested on a theoretical model. In Section 3, the application results of the Guqiao mine in China are presented and discussed. In Section 4, some conclusions are made.

2. Theories and Methods

2.1. Model-Based Joint Inversion

In a multi-component seismic exploration, as shown in Figure 1, P-wave sources are often used to initiate seismic waves and multicomponent geophones are arranged on the ground to record the reflected waves. Usually, the multicomponent geophone has three components: a vertical component (Z) and two horizontal components (X and Y). The reflected PP- and PS-waves are recorded by the multi-component geophones on the ground, simultaneously. Most PP-wave energy is recorded by the Z-component because the polarization direction of the P-wave is parallel to its propagation direction. However, most PS-wave energy is received by X- and Y-components because the polarization direction of the S-wave is orthogonal to its propagation direction [40].

For an underground elastic interface (Figure 1), using α₁, β₁, and ρ₁ to denote the P-wave velocity, S-wave velocity, and density of the upper stratum and α₂, β₂, and ρ₂ to denote the P-wave velocity, S-wave velocity, and density of the lower stratum, the PP and PS reflection coefficients (R_PP and R_PS) are given by the Zoeppritz equations, respectively [41]:

$$R_{\mathrm{PP}}=[(b\frac{\cos i_1}{{\alpha }_1}-c\frac{\cos i_2}{{\alpha }_2})F-(a+d\frac{\cos i_1}{{\alpha }_1}\frac{\cos j_2}{{\beta }_2})H{p}^2]/D,$$

(1)

$$R_{\mathrm{PS}}=-2\frac{\cos i_1}{{\alpha }_1}(ab+cd\frac{\cos i_2}{{\alpha }_2}\frac{\cos j_2}{{\beta }_2})p{\alpha }_1/({\beta }_{1}D),$$

(2)

where i₁ denotes the incident (or reflected) P-wave angle, j₁ denotes the reflected S-wave angle, and i₂ and j₂ denote the transmitted P- and S-wave angles, respectively, and:

$$\{\begin{array}{l}a={\rho }_2(1-2{\beta }_2^2{p}^2)-{\rho }_1(1-2{\beta }_1^2{p}^2),\\ b={\rho }_2(1-2{\beta }_2^2{p}^2)+2{\rho }_1{\beta }_1^2{p}^2,\\ c={\rho }_1(1-2{\beta }_1^2{p}^2)+2{\rho }_2{\beta }_2^2{p}^2,\\ d=2({\rho }_2{\beta }_2^2-{\rho }_1{\beta }_1^2),\\ F=b\frac{\cos j_1}{{\beta }_1}+c\frac{\cos j_2}{{\beta }_2},\\ H=a-d\frac{\cos i_2}{{\alpha }_2}\frac{\cos j_1}{{\beta }_1},\\ D=F\left(b\frac{\cos i_1}{{\alpha }_1}+c\frac{\cos i_2}{{\alpha }_2}\right)+H{p}^2\left(a-d\frac{\cos i_1}{{\alpha }_1}\frac{\cos j_2}{{\beta }_2}\right),\\ p=\frac{\sin i_1}{{\alpha }_1}=\frac{\sin i_2}{{\alpha }_2}=\frac{\sin j_1}{{\beta }_1}=\frac{\sin j_2}{{\beta }_2},\end{array}$$

(3)

where p is the ray parameter [41]; however, the other parameters a, b, c, d, F, H, D have no specific physical meaning. They are only used to simplify the expressions of R_PP and R_PS. Using the P- and S-wave velocities and densities at all the samples within the time window for the inversion, the model parameter matrix E can be expressed as:

$$E={\left(\begin{array}{ccc}\alpha & \beta & \rho \end{array}\right)}^{\mathrm{T}},$$

(4)

where

$$\alpha =\left(\begin{array}{cccc}{\alpha }_1& {\alpha }_2& \cdots & {\alpha }_m\end{array}\right),$$

(5)

$$\beta =\left(\begin{array}{cccc}{\beta }_1& {\beta }_2& \cdots & {\beta }_m\end{array}\right),$$

(6)

$$\rho =\left(\begin{array}{cccc}{\rho }_1& {\rho }_2& \cdots & {\rho }_m\end{array}\right).$$

(7)

The matrices α, β, and $\rho$ are composed of the P-wave velocities, S-wave velocities, and densities at the time samples 1, 2, …, m within the time window for the joint inversion.

Based on Equations (1)–(3), considering each time sample as an interface, the PP- and PS-wave reflection coefficient matrices R_PP and R_PS can be calculated, respectively. Then, the synthetic amplitude variation with incidence angle (AVA) gathers of both the PP- and PS-waves can be derived by:

$$S_{\mathrm{PP}}=W_{\mathrm{PP}}{R}_{\mathrm{PP}},$$

(8)

$$S_{\mathrm{PS}}=W_{\mathrm{PS}}{R}_{\mathrm{PS}},$$

(9)

where

$$R_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}={\left(\begin{array}{cccc}{R}_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(1\right)}& R_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}& \cdots & R_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(m-1\right)}\end{array}\right)}^{\mathrm{T}}.$$

(10)

$R_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}$, …, $R_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(m-1\right)}$ are the PP- or PS-wave reflection coefficients at the time samples 1, 2, …, m − 1 within the time window. Since the calculation of the reflection coefficient on one time sample requires the elastic parameters of the two consecutive time samples, the element number in the matrix R_PP or R_PS is one less than that in the matrix α, β, or $\rho$. W_PP and W_PS are the PP- and PS-wavelet matrices, respectively, which have the form of:

$$W_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}=\left[\begin{array}{ccccc}{w}_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(1\right)}& 0& 0& \cdots & 0\\ w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(1\right)}& ⋮& ⋮& 0\\ ⋮& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(1\right)}& ⋮& ⋮\\ w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(n\right)}& ⋮& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}& \ddots & 0\\ 0& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(n\right)}& ⋮& \ddots & w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(1\right)}\\ ⋮& ⋮& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(n\right)}& ⋮& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}\\ 0& ⋮& ⋮& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(n\right)}& ⋮\\ 0& \cdots & 0& 0& w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(n\right)}\end{array}\right],$$

(11)

where $w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(1\right)}$, $w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(2\right)}$,…, $w_{\mathrm{PP}\left(\mathrm{or}\mathrm{PS}\right)}^{\left(n\right)}$ are the amplitudes of the PP- or PS-wavelet time samples (Figure 2). n is the maximum number of the wavelet time samples, which should be less than m. In a practical application, the PP- and PS-wavelets can be extracted through the construction of the amplitude and phase spectra in the frequency domain [42].

In the proposed inversion approach, the first step is to directly calculate the model parameter matrix E. Following the damped least-squares theories [43,44], the Gauss–Newton formulas are regularized as:

$$\Delta E^{\left(k\right)}={\left(H+\lambda I\right)}^{-1}{J}^{\mathrm{T}}\left(\begin{array}{c}{S}_{\mathrm{PP}}^{\left(k\right)}-S_{\mathrm{PP}}^{\left(k-1\right)}\\ S_{\mathrm{PS}}^{\left(k\right)}-S_{\mathrm{PS}}^{\left(k-1\right)}\end{array}\right),$$

(12)

$$E^{\left(k\right)}=E^{\left(k-1\right)}+\Delta E^{\left(k\right)},$$

(13)

$$J={\left(\begin{array}{cc}\frac{\partial S_{\mathrm{PP}}}{\partial E}& \frac{\partial S_{\mathrm{PS}}}{\partial E}\end{array}\right)}^{\mathrm{T}},$$

(14)

$$H=J^{\mathrm{T}}J,$$

(15)

where k denotes the iteration number and E^(k) is the updated model parameter matrix at the k-th iteration. ∆E^(k) is the k-th model modification matrix:

$$\Delta E^{\left(k\right)}={\left(\begin{array}{ccc}\Delta {\alpha }^{\left(k\right)}& \Delta {\beta }^{\left(k\right)}& \Delta {\rho }^{\left(k\right)}\end{array}\right)}^{\mathrm{T}}.$$

(16)

J and H are the Jacobian and Hessian matrices, respectively [45,46]. For the joint AVO inversion, if the incidence angles (i₁ in Equations (1) and (2)) of the PP or PS AVA gathers are θ₁, θ₂,…, θ_x, the Jacobian matrix J will have the form as:

$$J=\left[\begin{array}{ccc}\frac{\partial S_{\mathrm{PP}}\left({\theta }_1\right)}{\partial \alpha }& \frac{\partial S_{\mathrm{PP}}\left({\theta }_1\right)}{\partial \beta }& \frac{\partial S_{\mathrm{PP}}\left({\theta }_1\right)}{\partial \rho }\\ \frac{\partial S_{\mathrm{PP}}\left({\theta }_2\right)}{\partial \alpha }& \frac{\partial S_{\mathrm{PP}}\left({\theta }_2\right)}{\partial \beta }& \frac{\partial S_{\mathrm{PP}}\left({\theta }_2\right)}{\partial \rho }\\ ⋮& ⋮& ⋮\\ \frac{\partial S_{\mathrm{PP}}\left({\theta }_x\right)}{\partial \alpha }& \frac{\partial S_{\mathrm{PP}}\left({\theta }_x\right)}{\partial \beta }& \frac{\partial S_{\mathrm{PP}}\left({\theta }_x\right)}{\partial \rho }\\ \frac{\partial S_{\mathrm{PS}}\left({\theta }_1\right)}{\partial \alpha }& \frac{\partial S_{\mathrm{PS}}\left({\theta }_1\right)}{\partial \beta }& \frac{\partial S_{\mathrm{PS}}\left({\theta }_1\right)}{\partial \rho }\\ \frac{\partial S_{\mathrm{PS}}\left({\theta }_2\right)}{\partial \alpha }& \frac{\partial S_{\mathrm{PS}}\left({\theta }_2\right)}{\partial \beta }& \frac{\partial S_{\mathrm{PS}}\left({\theta }_2\right)}{\partial \rho }\\ ⋮& ⋮& ⋮\\ \frac{\partial S_{\mathrm{PS}}\left({\theta }_x\right)}{\partial \alpha }& \frac{\partial S_{\mathrm{PS}}\left({\theta }_x\right)}{\partial \beta }& \frac{\partial S_{\mathrm{PS}}\left({\theta }_x\right)}{\partial \rho }\end{array}\right].$$

(17)

In Equation (12), λ is a damping parameter and I is an identity matrix. These two parameters are used in sparse least-squares problems to ensure that a unique solution always exists [47]. Given the initial prior model matrix E⁽⁰⁾, matrices E^(k) and ΔE^(k) at the k-th iteration can be derived. To control the iteration, an objective function for the joint AVO inversion is built as:

$$Q^{\left(k\right)}=w\left({\Vert \frac{S_{\mathrm{PP}}^{\left(\mathrm{obs}\right)}-S_{\mathrm{PP}}^{\left(k\right)}}{S_{\mathrm{PP}}^{\left(\mathrm{obs}\right)}}\Vert }^2+{\Vert \frac{S_{\mathrm{PS}}^{\left(\mathrm{obs}\right)}-S_{\mathrm{PS}}^{\left(k\right)}}{S_{\mathrm{PS}}^{\left(\mathrm{obs}\right)}}\Vert }^2\right)+\left(1-w\right){\Vert \frac{E^{\left(0\right)}-E^{\left(k\right)}}{E^{\left(0\right)}}\Vert }^2,$$

(18)

where $S_{\mathrm{PP}}^{\left(\mathrm{obs}\right)}$ and $S_{\mathrm{PS}}^{\left(\mathrm{obs}\right)}$ are the input PP and PS AVA gathers, respectively; $S_{\mathrm{PP}}^{\left(k\right)}$ and $S_{\mathrm{PS}}^{\left(k\right)}$ are the synthetic PP and PS AVA gathers at the k-th iteration, respectively. The weight factor w ranks from zero to one. If w is larger than 0.5, seismic data are more involved in the constraint. Otherwise, the prior model contributes more to the constraint. When Q^(k) comes to a satisfied minimum or hardly changes, the iteration can be stopped and the corresponding E^(k) will be the outputted inverse model matrix.

2.2. TDC Detection

Using the α/β value for the TDC detection is based on the experimental data from Wang et al. [34] and Chen et al. [36]. Wang et al. [34] tested the TDC samples from Huainan, Pingdingshan, Hebi, and Jiaozuo coal mines in China under normal pressure and temperature conditions. The test results show that the average α/β value of the TDC samples is 1.702, which is far less than that of the undeformed coal samples. The tests of Chen et al. [36] came to the similar conclusion: in the primary environment, the α/β values of the coal seams are from 1.87 to 2.06, which are higher than those in the deformation environment. In the proposed method, the coals with the inverted α/β values less than 1.7 will be identified as the TDCs.

In a practical application, as shown in Figure 3, several data processing procedures are necessary to perform for the TDC detection. Because both the initial prior and inverse models are in the PP reflection time domain, the most important procedure is to compress PS AVA gather to the PP reflection time. The reliability of the inversion results will be greatly affected by the quality of the input AVA gathers. In order to improve the reliability of the attribute inversion in a thin coal seam, the initial prior models are derived by the extrapolation of the P- and S-wave velocity and density logs.

2.3. Model Test

In this section, a synthetic dataset is used to demonstrate the effectiveness of the proposed TDC detection method. The theoretical model of the coal-bearing strata is shown in Figure 4, in which layers 3–5 are the coal seams. From

Table 1. Theoretical model parameters of the coal-bearing strata.

Layer Number	α (m/s)	β (m/s)	α/β	ρ (g/cm3)	Thickness (m)
1	2800	933	3	2.3	50
2	3000	1500	2	2.32	30
3	3200	1684	1.9	2.4	30
4	1800	1000	1.9	1.9	4
5	1200	800	1.6	1.3	2
6	1800	1000	1.9	1.9	4
7	3400	1789	1.9	2.5	30
8	3600	1800	2	2.55	30
9	4000	2000	2	2.6	30

, it is seen that layer 5 is the TDC seam, which elastic parameters are far less than the undeformed coal seams (layers 4 and 6). The α/β value of layer 5 is smaller than the surrounding rocks. In the PP reflection time domain, the pure PP AVA gather (Figure 5a) and PS AVA gather (Figure 5b) are synthesized by the product of the seismic wavelet (30-Hz dominant frequency) matrix and the PP and PS reflection coefficient matrix, respectively. The corresponding incidence angles are from 5 to 30° with an interval of 5°. The pure AVA gathers are then added with 10% random noise (Figure 5c,d), respectively.

As shown in Figure 6, even though the coal seams are thin and the initial models deviate greatly from the real models, the model-based joint inversion can yield accurate results under the noise-free condition. The deformed coal is easily identified on any inverse model. When the 10% random noise is added to the synthetic AVA gathers, as shown in Figure 7, there are many anomalies in the inverse models. However, the inverted α/β model (Figure 7d) is still stable than other inverse models (Figure 7a–c) and the deformed coal seam is still clear.

3. Application Results and Discussion

3.1. Geologic Setting and Prior Model

The proposed method is applied in coal seam 13-1 of the Guqiao mine in the Huainan coalfield. The Huainan coalfield is located on the southern margin of the North China plate. Coal seam 13-1 is one of the main commercial coal beds, which is developed in Upper Shihezi Formation of the Permian strata. Due to the tectonic movement after the coal accumulation, the TDC development has become one of the main factors endangering the workers’ lives and the coal mine production [48,49].

The scope and coordinates of the multi-component three-dimensional seismic exploration area are shown in Figure 8, where it is seen that there is a large normal fault with an east–west strike in the north. The sampling interval for the seismic recording was 1 ms and the bin size was 20 × 20 m. Huainan Coal Mining Group has developed four mining tunnels (indicated by the blue lines in Figure 8) in the work area, where the TDCs were found during the excavation. The drill data of the five wells (4-56, 56bu3, 6bu1, 6bu2 and 6bu3) reveal that the thickness of coal seam 13-1 was stable, with an average thickness of 5 m. As shown in Figure 8, the floor depth of coal seam 13-1 varies from 700 m to 840 m. In the work area, only P-wave logs are recorded for all the five wells. The depth sampling interval of all the logs is 0.05 m.

Due to the lack of the measured S-wave and density logs in the work area, the S-wave and density logs used for the initial prior models are converted from the P-wave logs. However, for the sand and mudstone strata and coal seams, the conversion formulas are different. For the conversion of S-wave logs, the adopted empirical formula for the sand and mudstone strata is from Lu et al. [25]:

$$\beta =0.433\alpha +430.9,$$

(19)

and that for the coal seams is from Wang et al. [33]:

$$\beta =0.5208\alpha +110.67.$$

(20)

In the work area, there is no any empirical relationship on the P-wave velocity and density. Therefore, for the conversion of density logs for the sand and mudstone strata, a systematic relationship in sedimentary rocks given by Gardner et al. [50] is adopted:

$$\rho =0.31{\alpha }^{0.25}.$$

(21)

For the coal seams, a high-precision empirical formula on the P-wave velocity and P-wave impedance (ρα) is given by Wang et al. [33]:

$$\alpha =0.54\rho \alpha +350，$$

(22)

which is transformed for estimating the density logs as:

$$\rho =1.85-\frac{648.15}{\alpha }.$$

(23)

3.2. Inversion Results and Discussion

The model-based joint PP and PS AVO inversion is performed. The initial models are modified during the inversion. Well 6bu2 is located at line 341 and CDP 106. The PP and PS AVA gathers at line 341 and CDPs 106, 107, and 108 are shown in Figure 9, where the PS AVA gathers are compressed to the PP reflection time and both the PP and PS reflections of coal seam 13-1 are well matched. The dominant frequencies of the PP and PS AVA reflections near coal seam 13-1 are 50 and 25 Hz, respectively.

Under the constraints of well log models, the PP and PS AVA gathers are inverted into the α/β volume. As shown in Figure 10, from the α/β section across wells 6bu2 and 6bu3 at line 341, the following results of the stratigraphic lithology identification can be obtained:

(1)

As colored by bright violet, the strata with the α/β values close to 2 are sand and mudstone strata.

(2)

The stratum with the α/β values less than 1.75 (colored by dark purple) are discriminated as coal seam 13-1.

(3)

Inside coal seam 13-1, the TDCs are considered to have been developed in the positions with the α/β values less than 1.7 (colored by green-yellow).

(4)

The roof and floor of coal seam 13-1 are khaki-colored, with α/β values from 1.75 to 1.88.

It is found that the positions where the TDCs are developed are not continuous. In coal seam 13-1, the α/β values near well 6bu3 (CDPs 130–156) are close to 1.65, which are less than those near well 6bu2 (CDPs 99–116). Drill information provided by Huainan Coal Mining Group shows that coal samples from well 6bu3 are more broken than those from 6bu2. Therefore, near well 6bu3, the TDCs are more developed.

As shown in Figure 11, the α/β slice in the middle position of the top and bottom interfaces of coal seam 13-1 has been extracted and superimposed on the structural map of the floor of coal seam 13-1. In the khaki-colored fault zone, the α/β values (1.75–1.88) are relatively large due to the erosion of coal seam 13-1. The α/β values of coal seam 13-1 in the most areas (colored by dark purple) range from 1.7 to 1.75, where the TDCs are not developed. The areas where the TDCs (α/β < 1.7) are likely to be developed are marked with green-yellow and red-white.

The drill information obtained from wells 6bu2, 6bu3 and 56bu3 confirms that the 13-1 coals at these well locations are mainly crumbling and powdered. Only a small quantity of the 13-1 coals at well 6bu1 remain layered. Well 4-56 is located at the fault zone, so only a few residual coals are seen. In Figure 11, at the north of the big normal fault, there are some areas marked by green-yellow areas where the TDCs can be developed. In these areas, there are no any drill data can be adopted to verify whether the TDCS are developed. However, in these areas, the short distance to the large tectonic zone is likely to result in the TDC development.

From Figure 11, it is found that the variation of the α/β values in coal seam 13-1 is not sharp. Such slight anomalies are probably hard to identify because of the low seismic resolution or the noise disturbance. Therefore, in order to detect the TDCs, it is necessary to ensure that the seismic data are of high quality, and there are sufficient well data involved in building the initial prior models.

According to the excavation information in the mining tunnels (marked by the blue lines in Figure 11) from Huainan Coal Mining Group, coal seam 13-1 is confirmed to be soft and the TDCs are common. However, there were no outbursts of coal and gas to be reported. It is possible that the 13-1 coal mass has not reserved high strain energy under the high ground stress condition. Therefore, in order to forecast the outburst of coal and gas, it is necessary not only to find out the TDC distribution, but also to predict the rock burst and compression strength of coal-bearing strata. This also puts forward new requirements for the seismic exploration technology.

In the proposed method, the α/β value is the only parameter used for the TDC detection. In order to improve the detection accuracy, it is better to apply more geophysical attributes to the reservoir evaluation, but it depends on the results of rock physics experiments. The previous research has shown that the P- or S-wave attenuation factors of the TDCs and undeformed coals are obviously different [33,34]. It is still difficult to obtain highly accurate attenuation factors from the multi-component seismic data. However, comprehensively using the velocity ratios and attenuation factors of P- and S-waves for the TDC detection will be a potential research direction.

4. Conclusions

This paper proposes a TDC detection method using a model-based joint inversion of the multi-component seismic data. The α/β values are utilized to distinguish between the TDCs and undeformed coals. PS-waves and well log information are simultaneously used in the inversion. Thus, the prior knowledge of the TDC development revealed by the log data can be added into the inversion results. The model test results prove that the model-based joint inversion can help to effectively identify the TDC developed inside a coal seam even under the noisy condition. The application to the field multi-component seismic data from the Huainan coalfield located in East China is also successful. The inverted α/β values can clearly indicate the coal seam interfaces and TDC positions. In total, the α/β values of the undeformed coals of coal seam 13-1 are from 1.7 to 1.75. Inside coal seam 13-1, the TDCs have the α/β values less than 1.7. The drill and excavation information from Huainan Coal Mining Group support the findings. Therefore, the proposed TDC detection method has the potential to be a feasible and practical technique for coal mines to predict geological hazards.