Seismic Diffraction Attribute Fusion for Geological Discontinuities in Hot Dry Rock Resources

Abstract

For the safe development and utilization of hot dry rock resources, it is essential to understand the distribution characteristics of underground faults. However, the commonly used reflection attribute analysis method has an insufficient resolution, and the diffraction attribute analysis method is affected by multiple solutions. Moreover, both are highly dependent on the interpreters’ experience and take a long time. Therefore, based on the classical U-Net model, a diffraction attribute fusion model (DAF-U-Net) with 27-layer convolution is proposed. The DAF-U-Net network takes four-channel diffracted attributes as an input and underground fracture distribution as an output. The new network adds a spatial attention and channel attention mechanism to improve the positioning and extraction ability of the U-Net model for the attribute characteristics of diffractions. After optimizing the diffraction attributes of hot dry rock slices in the Gonghe basin, Qinghai, the slices are input into the network to train the model. According to the prediction and identification results of the network model, the DAF-U-Net network has a high reliability in predicting fracture distributions. It has a specific reference role in the subsequent exploitation of hot dry rock.

1. Introduction

As a clean energy, hot dry rock geothermal resources do not emit carbon dioxide when providing energy, which has great potential to replace the traditional energy supply [1]. The primary method of exploiting hot dry rock is hydraulic fracturing. The shape of the hydraulic fracture determines the heat exchange volume and heat recovery efficiency. The formation of the hot dry rock is often accompanied by the development of faults and other structures, which will affect the expansion of hydraulic fractures and significantly affect the safe development and utilization of hot dry rock [2]. Therefore, it is of great significance for the secure development of hot dry rock to clarify the distribution of fractures in the hot dry rock.

In seismic exploration, the sudden interruption of the reflected wave and the generation of the diffracted wave represents the discontinuous fault. The seismic attribute method is crucial to helping the interpretation personnel understand the seismic data and analyze the underground structure [3]. Taner et al. (1979) proposed a complex seismic trace analysis method first [4]. Justice et al. (1985) used the multi-attribute combination method to locate the underground oil and gas reservoir [5]. Bahorich and Farmer (1995) employed the coherence attribute to interpret the underground fault [6]. Roberts (2001) used attribute prediction to describe the distribution of fractures [7]. Then, the seismic attributes developed rapidly. Now, the number of seismic attributes has exceeded 200 [8], and seismic attribute analysis technology is often used in identifying and engraving fractures [9,10,11].

Traditional seismic attribute analysis mainly uses seismic reflection imaging data. At the same time, the small-scale faults are primarily reflected in the attenuation of reflected wave energy and the generation of diffracted waves in the seismic data volume [12]. The shielding effect of the strong reflection interface overlying the hot dry rock will mask the change in seismic wave energy [13], which makes the identification accuracy of small-scale underground faults and fracture zones not high. Diffracted waves respond better to geological bodies smaller than one Fresnel zone and carry information about small-scale geological bodies, such as fault lines [14]. Therefore, this paper will separate and use the diffracted wave data in three-dimensional seismic data, study the analysis method of diffracted wave attributes, extract high-resolution seismic weak signal responses, and describe underground faults.

However, using a single seismic attribute that has multiple solutions to explain the underground faults will affect the accuracy [15]. Researchers use multiple seismic attributes to analyze underground structures to reduce the diversity of seismic attributes and improve their accuracy [8]. Kumar and Mandal (2018) studied the MLP (multi-layer perceptron) to analyze seismic attributes and realize structural interpretation of 3D seismic data volume [16]. Yue et al. (2019) exploited a support vector machine (SVM, support vector machine) to fuse seismic attributes and predict sand body boundaries and other information to optimize oil production results and production [17]. Dixit and Mandal (2020) provided important information for oil and gas exploration using multi-attribute analysis and artificial neural networks [18]. Li et al. (2022) proposed using the s-ae method to integrate seismic attributes to realize the interpretation of underground structures [19]. With the development and progress of computer technology, cyclic neural networks have also been widely used in seismic exploration (Zhao et al., 2019 [20]; Sheng and Zhao, 2022 [21]). Huang et al. (2017) realized the fusion of seismic reflection attributes using the CNN (convolutional neural network) method [22]. Di et al. (2019) used a CNN to analyze seismic attributes to complete the interpretation of underground structures [23]. Wu et al. (2020) employed a CNN to analyze seismic attributes and explain the distribution of underground karst caves [24]. Mężyk et al. (2021) investigated the content using a CNN [25]. Dou et al. (2022) studied the combination of seismic attributes and deep learning to explain underground structures [26].

Therefore, this paper proposes a DAF-U-Net model. The plane wave destructive filtering method is used to extract high-resolution seismic diffractions, and various diffracted attributes are calculated and obtained in diffraction image slices. After the attributes are optimized and normalized, they are input into the network to obtain a neural network model for identifying and predicting fractures in the hot dry rock reservoir.

2. Background

There are abundant hot dry rock resources in the Gonghe basin, Qinghai Province. The basement is granite, and the basement weathering crust is overlying sedimentary rock. The basin is adjacent to many faults, such as the Hunan Mountain fault and the Grande fault. To understand the fault distribution in the hot dry rock, we analyzed the geological structures including the underground fault structures by using the 3D seismic data of the 4 km² area in the Gonghe basin (Figure 1).

The top layer of hot dry rock in the seismic time domain data is determined by a well-seismic calibration and a comprehensive logging data analysis, as shown in Figure 2.

The time slice analysis method is one of the commonly used ways for researchers to interpret 3D seismic volume data at present. When extracting attributes from seismic data volume, the difficulty of obtaining slices varies with the type of slice, and their sensitivity to underground structures is also different. Currently, the commonly used seismic data slicing technology mainly includes stratigraphic slicing, time slicing, layer-by-layer slicing, and so on. Because hot dry rock is an intrusive rock mainly composed of granite, it has the property of non-stratification. The isochronous slices are obtained from diffraction and reflection data volume. After obtaining the slice, we perform attribute calculation on the reflection and diffraction data of the slice (Figure 3).

3. Materials and Methods

There are two difficulties in the analysis of the underground structures of the hot dry rock. The interpretation accuracy of its internal fractures is not high enough. The interpretation also depends on manual work, which requires high experience and takes a long time. Therefore, a diffraction attribute fusion network is investigated to solve these two issues.

3.1. Diffraction Separation Data

The diffractions are the seismic response when it passes through an inhomogeneous body smaller than a Fresnel zone. The diffraction attribute is the seismic attribute obtained using seismic-diffraction-aiming data volume. Similar to the reflection attribute, it is closely related to underground faults and other small structures, but its recognition accuracy is relatively higher. In order to obtain the diffraction data volume, it is necessary to separate the diffraction wave from the seismic data volume. The separation method used in this paper is the PWD (plane wave destruction) method, which was first proposed by Claerbout [28]; Fomel (2002) applied the improved plane wave destruction filter to many aspects of seismic data processing [29].

The PWD method defines a seismic section, m,

$$m={\left[m_1,m_2,\dots ,m_N\right]}^T$$

(1)

Therefore, the plane wave destruction operation in the linear operator could be expressed as

$$A=C\left(\sigma \right)m$$

(2)

$A={\left[a_1,a_2,\dots ,a_N\right]}^T$ in Equation (2) represents the destruction residual. $C\left(\sigma \right)$ can be expanded as

$$\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\\ \dots \\ a_N\end{array}\right]=\left[\begin{array}{ccccc}\mathrm{I}& 0& 0& \dots & 0\\ -C_{1,2}\left({\sigma }_1\right)& \mathrm{I}& 0& \dots & 0\\ 0& -C_{2,3}\left({\sigma }_2\right)& \mathrm{I}& \dots & 0\\ \dots & \dots & \dots & \dots & \dots \\ 0& 0& \dots & -C_{N-1,N}\left({\sigma }_{N-1}\right)& \mathrm{I}\end{array}\right]\left[\begin{array}{c}{m}_1\\ m_2\\ m_3\\ \dots \\ m_N\end{array}\right]$$

(3)

I is the identity operator, ${\sigma }_i$ is the local dip pattern, and $C_{i,j}\left({\sigma }_i\right)$ stands for an operator of trace j, which is the prediction from trace I by the dip pattern ${\sigma }_i$. According to the recursive operation of this method, it is easy to obtain the technique of predicting trace K from trace 1.

$$C_{j,k}=C_{k-1,k}\dots C_{2,3}{C}_{1,2}$$

(4)

After the linear predicted value of the reflected wave is obtained, it is eliminated, and the diffraction wave is retained as the prediction error. Thus, the diffraction wave data volume is obtained.

3.2. Seismic Attribute Calculation

Many studies have shown that the seismic reflection curvature attribute accurately reflects underground fractures. At present, the commonly used three-dimensional volume curvature attributes include average curvature (Km), Gaussian curvature (Kg), maximum positive curvature (Kpos), minimum negative curvature (Kneg), etc. Among them, K retains the underground fault structure when solving, so the maximum positive curvature attribute is calculated for the reflection attribute volume.

$$Z\left(x,y\right)=a{x}^2+b{y}^2+cxy+dx+ey+f$$

(5)

is used to represent the depth of the target layer. The coefficients d and e in the formula are the first-order derivatives of the surface function, and a, b, and c are the second-order derivatives of the surface function. A difference grid with a size of 3 × 3 is used to solve the difference, and K is calculated as follows (Yang et al.) [30]:

$$K_{pos}={\lambda }_1=\left(a+b\right)+{\left[{\left(a-b\right)}^2+c^2\right]}^{1/2}$$

(6)

For the weak energy of diffracted waves, more sensitive attributes should be selected when analyzing their attributes. After calculating and optimizing the variance volume attribute, average energy attribute, instantaneous phase attribute, and other attributes of diffraction slices, four diffraction attributes—namely, average energy attribute, instantaneous amplitude attribute, maximum gain rate attribute, and coherent attribute—which have the same geological significance and are more sensitive to fractures are selected to prepare for the subsequent attribute fusion.

The instantaneous amplitude attribute is the envelope function of seismic trace, and its primary function is to reflect the instantaneous change of energy during the propagation of seismic waves. Assume that the composite channel is:

$$F\left(t\right)=f\left(t\right)+ig\left(t\right)$$

(7)

where f(t) is the real consistent part used to record the data in the underground three-dimensional seismic data, and g(t) is the value of the real part f(t) Hilbert transform. Then, the numerical value of the instantaneous amplitude is [31]:

$$E(t)=\sqrt{f^2(t)+g^2(t)}$$

(8)

Since the high-density faults, fractures, and other structures in the underground will cause the scattering phenomenon of the propagating seismic waves, the distribution of the underground fracture development zone can be predicted according to the frequency attenuation characteristics of the seismic energy change and amplitude in the seismic data. If the amplitude value of each point in the seismic channel is x, the calculation formula of the average energy attribute is [32]:

$$E_{Avg}=\frac{({\displaystyle \sum _{i=1}^N{x}_i^2})}{N}$$

(9)

The coherence attribute describes the similarity of data between seismic channels in seismic data. It is obtained by concentrating all data results in the selected time window at the center of the time window, showing the continuity of the seismic waveform in the-phase axis. It is of great significance to highlight the horizontal discontinuity in underground structures, such as faults. We selected matrix D with size N × J in the longitudinal direction of the time window. If the sum of all eigenvalues of its full rank matrix is P and the maximum eigenvalue is Q, the calculation method of coherence coefficient in this paper is [33]:

$$C_3=\frac{Q}{P}$$

(10)

We can obtain the attributes of reflection curvature and diffraction data through the above methods.

3.3. Diffraction Attribute Fusion Network

(1)

Convolutional Block Attention Module

The cascade structure of the fusion network model used in this paper connects the up-sampling and the corresponding down-sampling features, which makes the depth learning accuracy higher and the positioning of pixels more accurate. Still, this jump connection will introduce noise to the up-sampling features. In order to improve the poor performance of this multi-scale fusion effectiveness judgment, this paper adds an attention mechanism (Figure 4) to the network cascade structure, controls the weight of each channel with an adaptive method, and automatically assigns the computing resources of the network model to more critical tasks, to strengthen the use of effective information and reduce the information confusion and redundancy caused by the direct splicing of high-level features and shallow features [34].

As shown in the above figure, the channel attention could be expressed as (Gao et al.) [35].

$$M_c=\sigma \left(MLP\left(Avgpool\left(F\right)\right)\right)+MLP\left(Maxpool\left(F\right)\right)$$

(11)

$\sigma$ represents the sigmoid function applied.

The spatial attention could be expressed as

$$M_s=\sigma \left(f\left(Avgpool\left(F^{’}\right),Maxpool\left(F^{’}\right)\right)\right)$$

(12)

(2)

Full Network

Using seismic attributes to interpret underground fractures is highly dependent on the interpreters’ experience and takes a long time. The U-Net network model can better analyze the hidden nonlinear relationship between data and can be used to establish the relationship between seismic diffraction attributes and underground fracture distribution. Therefore, based on U-Net, this paper proposes a DAF-U-Net model to predict the underground fracture distribution of hot dry rock.

To make the network model more suitable for seismic diffraction attribute data, this paper mainly discusses three aspects of U-Net: change from three-channel input to four-channel input; increase attention mechanism; change in output to single-channel output.

DAF-U-Net takes the seismic diffraction attribute slice data after optimization and batch normalization as the input and the slice fracture distribution as the expected output, which can be expressed as:

$$S=Net\left(cat\left(attr1,attr2,attr3,attr4\right)\right)$$

(13)

where s represents the neural network output; $Net(·)$ describes the process of the neural network; $cat(·)$ represents the splicing along the channel direction; and attr1, attr2, attr3, and attr4 represent four types of attribute data.

With the advancement of neural network training, according to the loss function, the network will constantly adjust the weights and errors of various parameters in the network. The traditional root means square error loss function will make the training time too long. In contrast, the binary cross entropy function (L(W)) divides the actual value into 0 and 1, which corresponds to the binary marking method of label data and is suitable for the in-depth learning evaluation of this paper. At the same time, according to the previous experience, if the binary cross entropy function is averaged, the learning and training process of the neural network can be accelerated. Therefore, this paper uses the average value of the L(W) as the loss function to evaluate the quality of the model of deep learning network training; that is:

$$loss=mean(L(W))=mean\left\{-{\displaystyle \sum _{i=0}^N[y_{i}log\sigma (x_i)+(1-y_i)log(1-\sigma (x_i))]}\right\}$$

(14)

After updating the parameters, the network could be optimized by using backpropagation and an ADAM (adaptive moment estimation) algorithm:

$$M_t=g_t\left(1-{\beta }_1\right)+{\beta }_1{M}_{t-1}$$

(15)

$$G_t=g_t^2\left(1-{\beta }_2\right)+{\beta }_2{G}_{t-1}$$

(16)

where T represents the number of iterations, M is the first moment of the gradient, and G is the second moment of the gradient. Generally, the moving average attenuation rate ${\beta }_1$ = 0.9, ${\beta }_2$ = 0.999.

When the initial values of M and G are zero, the value error calculated by the ADAM algorithm at the initial stage of iteration is significant, which can be corrected by the following formula:

$$\widehat{M_t}=\frac{M_t}{1-{\beta }_1^t}$$

(17)

$$\widehat{G_t}=\frac{G_t}{1-{\beta }_2^t}$$

(18)

After obtaining the correction value $\widehat{M_t}$ and $\widehat{G_t}$, the ADAM formula can be expressed as the following formula:

$${\theta }_t={\theta }_{t-1}-\alpha *\frac{\widehat{M_t}}{\sqrt{\widehat{G_t}}+\epsilon }$$

(19)

The default learning rate of α = 0.001, and $\epsilon ={10}^{-8}$ to avoid the divisor becoming 0.

The internal covariant displacement in the training process has an impact on the learning rate. This paper uses the batch normalization (BN) method to solve this problem. Its essence is to normalize the small batch data so that the input data of the nonlinear activation function are the normalized data in order to change the input data’s mean and variance. This method can avoid the disappearance of the gradient to a certain extent, increase the learning efficiency of the network, and improve the performance of the network. The process can be expressed as follows.

Introduce a small amount ε, and normalize it on the premise that the denominator is not zero:

$$\widehat{x_i}=\frac{x_i-{\mu }_B}{\sqrt{{\sigma }_B^2+\epsilon }}$$

(20)

where ε is a small quantity to avoid the denominator being zero; ${\mu }_B$ and ${\sigma }_B^2$ are the mean and variance of three-dimensional matrix data, respectively. For normalized data $\widehat{x_i}$, translate and zoom to obtain the input value $y_i$ of the nonlinear activation function:

$$y_i=\alpha \widehat{x_i}+\gamma$$

(21)

where α and γ are deep learning parameters.

The Figure 5 shows the complete DAF-U-Net network structure diagram.

In the coding path, the network model mainly uses the combination of a continuous convolution layer and a pooling layer to extract the characteristic data in the input data. Usually, the convolution layers have a convolution kernel with a size of 3 × 3, and the following pooling layer’s convolution kernel’s size is 2 × 2. After extracting the data, the nonlinear ReLU (rectified linear unit) activation function is used to activate it. Because the pooling layer of the model adopts the maximum pooling operation. The length and width of the characteristic map would be reduced to the half of the original after each pooling. The number of convolution kernels and distinctive maps of the convolution layer will be doubled, so the characteristic information will be mapped to the high dimension. The process could be represented as follows:

$$a_k=Down\left(\mathrm{Re}LU\left(BN\left(W_{k-1}·a_{k-2}+b\right)\right)\right)$$

(22)

where $a_k$ represents the characteristic diagram of the kth layer of the encoder; ReLU(∙) refers to the linear unit after correction; BN(∙) indicates batch normalization; Down(∙) indicates down-sampling operation;

In the decoding path, the network model uses the deconvolution method to map the high-dimensional features to the low-dimensional features. That is, two convolutional layers with a convolutional kernel of 3 × 3 and a deconvolutional up-sampling operation with a size of 2 × 2 are utilized, which causes the number of feature maps to be halved and the scale to be doubled. In the convolution process, feature stitching is carried out using skip connection, so the deep learning accuracy is higher. The process can be expressed as follows:

$$a_t=\mathrm{Re}LU\left(BN\left(W_t·Cat\left(a_{t-1}+a_{t-1}^{encoder}\right)\right)\right)$$

(23)

where $a_t$ represents the characteristic diagram of the t layer of the decoder; $a_{t-1}^{encoder}$ represents the characteristic diagram with the same number of encoder channels; Cat(∙) Indicates a splicing operation.

4. Experiment

4.1. Network Training

Before using DAF-U-Net to fuse seismic diffraction attributes, the diffraction attribute data should be normalized so that their value is mapped between 0 and 1 [35], and the formula is expressed as:

$$x_{0-1}=\frac{x-X_{\min }}{X_{\max }-X_{\min }}$$

(24)

where $x_{0-1}$ is the normalized data, $X_{\min }$ is the minimum value in the sample, and $X_{\max }$ is the largest value in the sample.

Normalization can promote the smooth convergence of the model and improve the generalization ability of the model on the premise of preserving the original characteristics of the data.

In addition, in order to expand the training data and improve the generalization ability of the data set, data augmentation is carried out. In our experiment, geometric augmentation method is used for labeling data, which includes turning, rotation, and clipping. After data augmentation, the data set was expanded to 7200, and we input the processed attribute and label data into the network for training. Figure 6 shows part of the slice attribute and labels dataset.

When the model’s loss function converges to a small value, oscillates in a small range, and no longer rises, we stop the model-training process and obtain the corresponding fracture solution model (Figure 7).

4.2. Example

The model trained by deep learning is used to predict the faults and fractures of the test set data. The prediction results of the DAF-U-Net network are as follows (Figure 8):

It is observed that they are generally parallel and oblique and develop more, which is conducive to extracting heat from the complex fracture network during hydraulic fracturing. However, in the description of large-scale faults, the reflection attribute is more continuous.

In order to analyze the accuracy of the DAF-U-Net network in identifying underground fractures in hot dry rocks, we compare our obtained results to the manual annotation label (Figure 9), refection attribute (Figure 10), and single diffraction attributes (Figure 11). Compared to the manual annotation result in Figure 9, the prediction result of the DAF-U-Net network is relatively accurate. In terms of overall characteristics, it conforms to the characteristics that the underground faults and fractures of the hot dry rock in the Gonghe basin are generally in the NW (northwest) and NNW (north–northwest) directions.

Compared to the reflection attribute in Figure 10, the network prediction results are more accurate for describing small faults, such as secondary faults. The exit area of red coil is a typical area in which the fusion result of diffraction attributes is better than that of traditional reflection attributes. The arrow indication in Figure 8 has higher accuracy and better effect than the arrow indication in Figure 10.

Compared to the single diffraction attribute (Figure 8), the prediction results of the DAF-U-Net model better combine multiple diffraction attributes.

The network prediction results synthesize the fracture characteristics represented by the four attributes and show certain performance for the fractures in the middle and surrounding areas of the work area, reducing the multiplicity of solutions.

5. Discussion

As illustrated in the field data application, it can be seen that the DAF-U-Net network can predict the distribution of fractures in the hot dry rock better than the traditional single-reflection attribute method. The DAF-U-Net’s has good accuracy and can reduce the multi-solution interpretation problems. Our proposed method can predict the fractures distributions in the hot dry rock and reduce the dependence of artificial experience. Of course, similarly to the general artificial intelligence method, the prediction results are affected by the training data set, network parameters, and structures.

The limitation of this model is mainly reflected in the influence of the training dataset on the final results. First, the training data of this model are the two-dimensional slice data of hot dry rock, which has a certain impact on the continuity of faults and a negative impact on the identification of fractures. Second, the larger the data volume of the training data set, the more the fracture diffraction information characteristics in the hot dry rock and the better the prediction ability of the model. However, increasing the number of datasets will increase the training time of the model.

The advantages of the DAF-U-Net model mainly lie in the better prediction results and the reduction of manpower. The prediction results are reliable and close to the manual labeling results. The problem that the reflection property is not sensitive to small fractures is solved. The high diffraction resolution to small fractures is achieved, and the problem of multiple solutions of a single diffraction property is greatly solved. In addition, the traditional fracture labeling method is highly dependent on human experience and takes a long time, while the DAF-U-Net network only needs to manually label the fractures in the training data, which can save interpretation time and workforce.

6. Conclusions

Based on the classical U-Net model, the DAF-U-Net model is proposed, and a deep learning method is used to predict the fracture distributions of underground hot dry rock. The following two conclusions are obtained:

(1)

In the research area of the Gonghe Basin, the fractures in the underground hot dry rock are mainly NW- and NNW-trending, and small faults—including secondary faults—are relatively developed, which is conducive to hydraulic fracturing to extract heat from the complex fracture network;

(2)

Using the DAF-U-Net to predict and identify small- and medium-scale fractures in underground hot dry rock has high reliability, high accuracy, and few multi-solutions. It can better realize the exemplary description of deep small-scale fractures, can reduce the dependence of manual interpretation on experience and time-consuming problems, and is more efficient and intelligent than traditional methods.