MA_W-Net-Based Dual-Output Method for Microseismic Localization in Strong Noise Environments

Abstract

With the continuous depletion of conventional oil and gas reservoir resources, the beginning of exploration and development of unconventional oil and gas reservoir resources has led to the rapid development of microseismic monitoring technology. Addressing the challenges of low signal-to-noise ratio and inaccurate localization in microseismic data, we propose a new neural network MA_W-Net based on the U-Net network with the following improvements: (1) The foundational U-Net model was refined by evolving the single-channel decoder into a two-channel decoder, aimed at enhancing microseismic event localization and noise suppression capabilities. (2) The integration of attention mechanisms such as the convolutional block attention module (CBAM), coordinate attention (CA), and squeeze-and-excitation (SE) into the encoder to bolster feature extraction. We use synthetic data for evaluating the proposed method. Comparing with the normal U-net network, our accuracy in seismic recordings with a signal-to-noise ratio of −15 is improved from 78 percent to 93.5 percent, and the average error is improved from 2.60 m to 0.76 m. The results show that our method can accurately localize microseismic events and denoising processes from microseismic records with a low signal-to-noise ratio.

1. Introduction

The microseismic monitoring technique is an important tool for monitoring the dynamic state of the formation and has been widely used in hydraulic fracturing [1,2,3] and geothermal development [4,5]. The key component of microseismic monitoring is the localization of microseismic events. Microseismic localization is the process of accurately reflecting the location of an earthquake source from microseismic signals recorded by geophones distributed on the surface or in wells. Accurately locating microseismic events is critical to better understanding rupture and fault behavior [6].

Microseismic events are relatively weak in energy, ranging in magnitude from −3 to 1 MW [7]. These events often exhibit a low signal-to-noise ratio (SNR) due to the influence of the complex monitoring environment (e.g., traffic noise, industrial interference, drilling interference), current noise, and spike-like noise. The interference of large amounts of noise makes subsequent microseismic localization extremely difficult. Denoising helps to localize microseismic events with low SNRs more accurately. Traditional denoising approaches have been employed to mitigate noise within microseismic data sets [8,9,10]. Furthermore, deep learning techniques, such as leveraging neural networks to construct mapping functions [11], have proven effective in addressing complex challenges. Specifically, in microseismic exploration, deep learning can solve the localization problem in the case of a poor SNR [12,13,14,15,16].

Recently, microseismic localization methods based on deep learning have become increasingly popular [17,18,19,20,21]. Trained networks can directly predict source locations from recorded microseismic data and have the potential to monitor microseismic events in real-time. Traditional deep learning approaches for localizing a singular source often struggle with accuracy, as they can only provide the location of one microseismic event, which may be compromised by the noise from concurrent events. Perol et al. [17] introduced ConvNetQuake, the inaugural convolutional neural network designed for earthquake detection and localization, aiming to tackle seismic monitoring challenges through supervised classification. Zhang et al. [18] crafted a deep neural network tailored to seismic source offset imaging, capable of identifying two distinct events within diffraction stacked images from continuous seismic records. Wang et al. [19] developed two convolutional neural networks for identifying multiple earthquake sources: one to categorize event counts and another to predict several epicenter locations. Vinard et al. [20] leveraged synthetic data to train a U-Net model, subsequently applying it to field data for microseismic event localization, demonstrating that real data can be effectively augmented with synthetic data for network training purposes. Feng et al. [21] unveiled a technique for microseismic source localization utilizing deep reinforcement learning.

In this study, we propose a novel neural network based on U-Net, named MA_W-Net, which combines low-resolution semantic information with high-resolution localized spatial information using skip connections. However, the existing U-Net architectural system has some limitations, such as the relatively small number of backbone layers and the feature extraction capability not being as good as that of other networks, which may lead to lower accuracy in localizing the earthquake source point. To solve these problems, we have made the following improvements: (1) We built a deep neural network with one encoder and two decoder structures based on U-Net, which is a multi-task learning based on the parameter hard-sharing mechanism to realize microseismic localization and denoising in a strong noise environment. Among them, the main task is to localize the microseismic source and the auxiliary task is denoising. The auxiliary task can help the network perform better in localizing microseismic events with a low SNR. And we define the label of the localization task as a Gaussian mixture model which contains the source location information of different microseismic events. (2) We have integrated multiple attention mechanisms into MA_W-Net, including CBAM in the encoder and the CA and SE modules in the decoder. The attention modules can learn to use global information to selectively emphasize useful information features and suppress useless features without increasing computational complexity, thus enabling better processing of input data.

2. Methods and Principles

Multi-task learning (MTL) is an important branch in the field of machine learning that aims to improve the generalization ability and efficiency of models by learning multiple related tasks simultaneously. Based on the assumption that all tasks, or at least some, are relevant, learning multiple tasks jointly has been found empirically and theoretically to lead to better performance than learning individual tasks independently [22]. The hard-sharing mechanism of implicit layer parameters is one of the most common approaches in multi-task learning. Multiple tasks share part of the hidden layer and learn some common low-level features while retaining the output layer for different tasks. Throughout the learning process, the tasks exchange beneficial information, thereby amplifying the efficacy of each task’s learning process, enhancing the model’s overall generalization capabilities, and diminishing the likelihood of overfitting.

U-Net is a model obtained by improving on the full convolutional neural network [23]. U-Net has low requirements on the size of training data, high segmentation accuracy, and is widely used in image segmentation tasks. U-Net and its variants have achieved remarkable results in the geophysical field due to good feature extraction capabilities [24,25,26]. The architecture of U-Net is inherently symmetrical, featuring a contraction path (encoder), dedicated to feature extraction, and an expansion path (decoder), which employs up-sampling through transposed convolution to restore the feature map to the original image’s dimensions. U-Net facilitates the transfer of features from the contraction to the expansion path via skip connections, effectively integrating surface-level high-resolution details with profound abstract features.

The input data to the network are low-SNR grayscale microseismic recording maps. The encoder first resizes the input data using a convolutional layer, followed by a Residual (RES) module and a maximum pooling operation. Decoder 1 outputs a Gaussian mixture distribution containing information about the location of the microseismic source after an up-sampling, convolution, and convolution and coordinate attention (CCA) module. Decoder 2 outputs a microseismic record after noise suppression after an up-sampling, convolution, and convolution and squeeze-and-excitation attention (CSEA) module.

The following section describes RES module, CCA module, CSEA module, and the overall architecture of the MA_W-Net network:

2.1. RES Module

Convolutional module attention module (CBAM) [27] can solve the problem of what and where the image features are utilizing a channel attention module and a spatial attention module. Therefore, we form an improved RES module by combining residual connectivity between three layers of convolution and CBAM. The RES module structure is shown in Figure 1.

The attention module, a pivotal data processing technique in machine learning, empowers neural networks to concentrate on specific local features within the input data for effective information extraction. CBAM contains two sequential sub-modules, namely the channel attention module (CAM) and the spatial attention module (SAM), as shown in Figure 2.

$$\begin{array}{c}{\mathrm{M}}_{\mathrm{c}}\left(\mathrm{F}\right)\begin{array}{c}=\sigma \left(MLP\right(AvgPool\left(\mathbf{F}\right))+MLP(MaxPool\left(\mathbf{F}\right)\left)\right)\end{array}\\ =\sigma \left({\mathbf{W}}_{\mathbf{1}}\left({\mathbf{W}}_{\mathbf{0}}\left({\mathbf{F}}_{\mathbf{a}\mathbf{v}\mathbf{g}}^{\mathbf{c}}\right)\right)+{\mathbf{W}}_{\mathbf{1}}\left({\mathbf{W}}_{\mathbf{0}}\left({\mathbf{F}}_{\mathbf{m}\mathbf{a}\mathbf{x}}^{\mathbf{c}}\right)\right)\right)\end{array}$$

(1)

CAM (Figure 3a) is used to learn by integrating the spatial information of the input feature maps after integrating them into a multilayer perceptron (MLP) through average pooling and maximum pooling operations, and the activation function is ReLU. The output features of the two MLPs are summed element-by-element to generate the channel attention value ${\mathrm{M}}_C$ through the Sigmoid activation function.

$$\begin{array}{c}{\mathrm{M}}_{\mathrm{s}}\left(\mathrm{F}\right)\begin{array}{c}=\sigma \left(f^{7\times 7}\right(\left[AvgPool\left(\mathbf{F}\right);MaxPool\left(\mathbf{F}\right)\right]\left)\right)\end{array}\\ =\sigma \left(f^{7\times 7}\left(\left[{\mathbf{F}}_{\mathbf{a}\mathbf{v}\mathbf{g}}^{\mathbf{s}}{;\mathbf{F}}_{\mathbf{m}\mathbf{a}\mathbf{x}}^{\mathbf{s}}\right]\right)\right)\end{array}$$

(2)

SAM (Figure 3b) takes the feature maps output from the CAM as input and performs channel-based global maximum pooling and global tie pooling operations on the feature maps to obtain two H × W × 1 feature maps, where H and W are the height and width of the feature map. The Concat operation splices the two feature maps, performs a convolution operation with a convolution kernel of 7 × 7, and reduces the number of channels to 1, i.e., we obtain a feature map of H × W × 1. Finally, a Sigmoid activation function generates the spatial attention value ${\mathrm{M}}_S$. This is then multiplied with the input feature map to obtain the final result.

2.2. CCA and CSEA Modules

In neural networks, the integration of an attention mechanism within the decoder enables the capture of feature correlations. Utilizing coordinate attention (CA) [28] and squeeze-and-excitation attention (SE) [29], we have developed two innovative attention modules, CCA and CSEA, to enhance the denoising ability and localization of the network. Attention mechanisms help networks to better handle complex tasks and data by optimizing resource allocation, improving model accuracy, enhancing flexibility and adaptability, and reducing redundant information interference. During the downward propagation of the neural network, there will be important information that may be lost due to the maximum pooling operation. To alleviate this problem, we adopt a U-Net-like framework for the joining process in the CCA and CSEA modules, which mainly performs time-consuming convolutional computations in low-resolution space. Among them, the fusion of shallow and deep features is widely used. Such feature fusion not only facilitates a seamless information flow from superficial to in-depth layers but also proves beneficial for maintaining features, supporting efficient gradient backpropagation, and minimizing information loss during subsequent propagation.

2.2.1. CCA Module

The structure of the CCA module is shown in Figure 4, which mainly consists of two 2D convolutions and CA. We can enhance the localization effect by adding CA.

CA reintroduces the channel attention mechanism along with the spatial attention mechanism, which embeds location information into the channel attention in the attention mechanism. The implementation of CA is shown in Figure 5 and can be divided into two main parallel stages. CA pools the input feature maps in both height and width directions with global average pooling to obtain the feature maps in both height and width directions, respectively. We enter the dimensions of the feature layer as [H, W, C], where H and W are the height and width of the feature map, respectively, and C is the number of channels. After the above operations, the feature had dimensions obtained in height and width are [1, W, C] and [H, 1, C], respectively. Afterward, the two parallel stages are merged to transpose the height and width to pass a dimension, and then stacking is performed to fuse the height and width features, at which point the feature layer size obtained is [1, H + W, C], followed by convolution, normalization, and ReLU activation function to obtain a feature layer size of [1, H + W, C/r], where r is the scaling factor.

The process is bifurcated into two parallel stages, where the dimensions of height and width are segregated into [1, W, C/r] and [1, H, C/r], respectively. Following this, a transpose operation is executed, yielding two distinct feature layers: [W, 1, C/r] and [1, H, C/r]. The application of a Sigmoid function then determines the attention distribution across both the vertical and horizontal dimensions. Finally, merging the original features through multiplication culminates in the implementation of the CA mechanism.

2.2.2. CSEA Module

The architecture of the CSEA module is shown in Figure 6, which mainly consists of two 2D convolutions and the squeeze-and-excitation attention (SE).

Figure 7 illustrates the structure of the SE module. This module has the capability to dynamically allocate weights across various channels, a process autonomously learned by the network with minimal human oversight. The SE module is adept at explicitly mapping the interrelations among convolutional feature channels, thereby enhancing the network’s representational power. It harnesses global information to judiciously highlight salient features while diminishing the less relevant ones. Incorporating the SE module significantly aids in the noise reduction process of seismic data.

2.3. Network Architecture

The MA_W-Net network introduced in this study based on an enhanced U-Net framework, shown in Figure 8. This architecture consists a single encoder and dual decoders. The two decoders are responsible for seismic source localization and noise suppression, respectively. They collaboratively utilize the encoder for the end-to-end parallel training of features extracted from noisy microseismic data. The encoder is tasked with isolating crucial features from these recordings. Utilizing these features, Decoder 1 constructs a Gaussian mixture model to provide the location details of microseismic events. Subsequently, Decoder 2 then attempts to reconstruct the clean microseismic record using the extracted features and outputs a noise-compressed microseismic record. In this study, it is assumed that microseismic events have been detected, and the input data are microseismic recordings with a low SNR received by geophones with a size of 512 × 64 × 1. In the encoder part, we first resize the input data using 4 convolutional layers, each with a filter of 64 and a convolutional kernel of 5 × 5. After two more RES modules, the output size is 64 × 64 × 64. The remainder of the encoder contains three down-sampling modules, each of which consists of a 2 × 2 max-pooling [30] and two RES modules. This configuration effectively doubles the channel count while reducing the feature map’s dimensions by half with each down-sampling iteration.

The decoder contains a series of up-sampling processes. In Decoder 1, each process is up-sampled using a 2 × 2 transposed convolution, doubling the size of the feature map and halving the number of channels. This process involves integrating feature maps from both the encoder and decoder, following a single convolution and two CCA modules. The final output of Decoder 1 has a size of 64 × 128 and represents a Gaussian mixture distribution containing information about the location of the seismic source. In Decoder 2, each process is up-sampled using a 2 × 2 transposed convolution, doubling the size of the feature map and halving the number of channels. Here, after merging encoder and decoder feature maps through one convolution and two CSEA modules, transposed convolution is then applied to revert the feature maps back to the original input dimensions. The final output size of Decoder 2 is 512 × 64, representing a microseismic record after noise suppression. Except for the two output convolutional layers, which use a Sigmoid activation function [31], all other convolutional layers are activated with a ReLU activation function.

3. Numerical Example

3.1. Data Organization

For microseismic source localization, we typically need a good understanding of the background velocity model of the study area. In this study, we assume that we could obtain a good velocity model of the study area using many velocity inversion methods. We selected the Marmousi [32] model as the background velocity model, which can simulate complex geological conditions. We assumed that the true velocity model is known. We assessed the model’s predictive performance across various SNRs. Then, a comparison was made with the single-task localization model.

We use the finite difference method to generate simulated microseismic records. Figure 9 shows the velocity model, which has an extent of 640 m × 1280 m and a grid spacing of 10 m: A total of 64 geophones were positioned at every other grid point on the velocity model’s surface. We use a Ricker wavelet with a sampling rate of 1 ms as a function of the source time, and the source location and excitation moment are randomly generated. Data were generated using one seismic source at a time, 4000 training data and labels were prepared, and the simulated data were divided into training and test sets in a 9:1 ratio.

Our computing device is NVIDIA Quadro RTX 4000, our neural network framework is TensorFlow-GPU 2.7.0, with 8 GB of video memory. We use ReLU as the activation function of the network, with the Sigmoid function applied in the final layer. We trained the network using Adam’s algorithm [33]. The entire training process was carried out for 600 iterations, the learning rate was set to 0.0001, and the number of training data in each batch was 32. This setting provides a basis for subsequent model evaluation and comparison.

3.2. Data Preprocessing

The input data to the neural network are noisy microseismic records, generated by adding Gaussian noise to clean microseismic records. The main task is to localize the source location of microseismic events from noisy data. Traditional deep learning approaches typically predict the exact coordinates of seismic sources, necessitating a predefined number of sources to structure the model’s output layer. However, with an increasing count of seismic sources, there arises a need for developing multiple models, each with a unique architecture. To address this, we employ a Gaussian mixture model to both represent the microseismic source locations and serve as the output label for this key task. The probability distribution of the source location of each microseismic event can be generated by a Gaussian distribution [34]:

$$f_i\left(x,z\right)=\mathrm{e}\mathrm{x}\mathrm{p}(-\frac{{(x-x_0)}^2+{(z-z_0)}^2}{2{\sigma }^2})$$

(3)

where $(x_0,y_0)$ are the coordinates of the epicenter point and $\sigma$ is the variance.

A Gaussian mixture model is essentially a composite of K Gaussian distributions. In scenarios where the microseismic record encompasses multiple events, this model is formulated by the linear aggregation of Gaussian distributions attributed to each event. Within the resultant Gaussian mixture model, the peak’s location signifies the microseismic event’s source location. To ensure high resolution across all sources, the standard deviation for the Gaussian distribution is uniform for each source.

For enhanced network learning, each composite Gaussian model undergoes normalization to a range of [0, 1].

Traditional deep learning approaches for denoising employ supervised learning, utilizing noisy data for input and pristine data for labels. However, this method faces significant challenges in the denoising of seismic data, primarily due to the difficulty in acquiring clean seismic data for labels. Lehtinen et al. [35] introduced a novel self-supervised learning technique for denoising that relies solely on noisy data for training. This method hinges on an L2 paradigm characteristic: the L2 norm remains constant for two vectors substituted with random numbers anticipated to be identical. Consequently, utilizing the L2 loss function for training ensures that network parameters remain stable, even in the presence of noise-contaminated label data. Thus, obtaining clean seismic data is not a prerequisite for effective denoising.

3.3. Model Training

The loss function serves as a metric to quantify the discrepancy between the model’s predicted outputs and the actual values. The value of the loss function directly affects the predictive performance of the model, the smaller the value of the loss function, the better the predictive performance of the model. The loss function consists of two parts: a weighted mean square error loss function for the main task and a conventional mean square error loss function for the auxiliary task. The overall loss is calculated as follows:

$$\mathrm{L}={\lambda }_1{L}_{main}+{\lambda }_2{L}_{aux}$$

(4)

where $L_{main}$ denotes the loss of the main task, $L_{aux}$ denotes the loss of the auxiliary task, and $\lambda$ denotes the weight of the two tasks.

The mean square error loss function finds the sum of the squares of the errors at the points corresponding to the predicted and true values.

$$L_{aux}=\frac{1}{N}\sum _{i=1}^N{\left({y^i}_{true}-{y^i}_{pred}\right)}^2$$

(5)

where N denotes the sample size, $y_{true}$ denotes the true value, and $y_{pred}$ denotes the prediction result. The smaller the value of the loss function, the more closely the model’s predictions align with the actual values.

This loss function gives equal weight to each pixel point. A lower standard deviation within the Gaussian mixture model for each dimension correlates with enhanced source resolution. There are only some higher values near the epicenter location, with most values close to 0. Due to the small percentage of pixels in the whole label, if the same weights are used, the loss of the network is small even if the seismic location is incorrectly predicted. This leads to a propensity for predicting non-seismic locations for most pixels, adversely affecting network convergence. Conversely, a larger standard deviation decreases the resolution but increases the convergence. To ensure higher resolution, a weighted mean-variance loss function is used to give higher weights to pixel points near the epicenter, which will be penalized by a larger gradient in case the network predicts incorrectly. The weighted loss function is calculated as follows:

$$L_{main}=\frac{1}{N}\sum _{i=1}^N\left[{\omega }_1{y^i}_{true}+{\omega }_2\left(1-{y^i}_{true}\right)\right]{\left({y^i}_{true}-{y^i}_{pred}\right)}^2$$

(6)

where N denotes the sample size, $y_{true}$ denotes the true value, and $y_{pred}$ denotes the prediction result.

3.4. Results

Microseismic records from geophones contain not only microseismic waveforms but also varying degrees of noise. Random noise with an SNR of −5, −10, and −15 were added to the training data to simulate the field data. An example of the input data is shown in Figure 10, where it can be seen that as the noise increases, the in-phase axis of the seismic record becomes less and less distinct and the continuity deteriorates. Seismic signals are barely visible at SNR = −15. We trained the network for 600 epochs. Figure 11 shows the loss curve of the network, which achieved convergence in the later stages of training.

$$\mathrm{S}\mathrm{N}\mathrm{R}=10\mathrm{l}\mathrm{g}\frac{P_s}{P_n}$$

(7)

where $P_s$ is the power of the signal, $P_n$ is the power of the noise, and lg denotes a logarithm with a base of 10.

After the network is trained, we verify its performance using a test set. To evaluate the proposed algorithm in different SNR scenarios, we add random noise with SNR of −5, −10, and −15 to the microseismic records in the test set, respectively. Figure 10 shows the seismic recordings at different noise levels. We input the test set into the model, with the primary task outputting microseismic locations and the secondary task outputting microseismic records after noise suppression. Figure 12 shows the localization results under different noises, from which it can be seen that the resolution of the source location imaging is high and the model-predicted source location almost exactly matches the real source location. Figure 13 shows the microseismic recordings after suppression noise. Each record is essentially free of noise residue, and the in-phase axis becomes clear and continuous. Since the denoising task is only an auxiliary task and the network focuses on extracting robust features of the microseismic recordings, it is less capable of recovering the local details of the microseismic waveforms, and some erroneous waveforms can be clearly seen below the in-phase axis. In

Table 1. Localization effects for different SNRs.

SNR	Average Error Distance	Accuracy	Accuracy (<10 m)	Accuracy (<20 m)	Accuracy (<50 m)
Original Record	0.03 m	99.75%	100.00%	100.00%	100.00%
SNR = −5	0.11 m	99.00%	99.75%	100.00%	100.00%
SNR = −10	0.29 m	97.50%	99.50%	99.75%	100.00%
SNR = −15	0.76 m	93.50%	98.50%	99.75%	100.00%

, the localization effects are summarized for different SNRs.

To show the superiority of the proposed method, we trained a localization model using an ordinary U-Net network. Both the training and test sets use seismic recording data with SNR = −15. Figure 14 shows a sample of events in the test set and their localization results. The localization results of the model did not accurately locate the source position of the single event and disturbances were observed in the surroundings. We randomly selected 400 events in the test set, and the average error distance of their localization results was 2.60 m, with an accuracy of 78% for an error of zero. Compared with the proposed model, the model still has a large gap between the average error distance and accuracy and is less noise-resistant. This suggests that auxiliary tasks are critical for improving the noise immunity of localization models.

To further analyze the predictive ability of the model, we generated microseismic records containing two and three events on the velocity model and added random noise with SNR = −10, as shown in Figure 15 and Figure 16. As shown in the figure, the model can successfully predict the location of the microseismic source, and the noise in the seismic record is well suppressed.

4. Conclusions

We propose a deep learning method for the localization of microseismic sources within noisy data environments. Based on multi-task learning, a decoder responsible for the auxiliary task is added in addition to the main task of seismic source localization, which improves the model’s localization accuracy at low SNRs. Furthermore, CBAMs were integrated into the encoder; CBAM effectively integrates both spatial and channel dimensions of the feature map, which can improve the generalization ability and performance of the model. CA and SE attention modules were also integrated into the decoder, and CA can enhance the localization of microseismic source locations. SE can learn to use global information to selectively emphasize informative features and suppress useless ones, enhancing the denoising capability of the network. We use a Gaussian mixture model to represent source location information for microseisms. To improve the stability and prediction ability of the network, the weighted mean square error is used as the loss function for the main task and different weights are assigned to the losses of the two tasks. The self-supervised assisted denoising task overcomes the difficulty of obtaining noise-free data as labels. Our method can improve the accuracy of seismic recordings with a SNR of −15 from 78% to 93.5% and the average error from 2.60 m to 0.76 m comparing with a normal U-net network. Experimental results show that our method can localize microseismic events with low SNRs and can keep the error within a small range. We plan to introduce real seismic data in future research to further validate the model’s effectiveness and generalization ability in practical applications.