The wavelet transform converts microseismic signals from the time domain to the frequency domain, offering excellent time-frequency localization capabilities. This ability enables multi-scale refinement analysis and represents the signal as different frequency components, aiding in the extraction of fine features of the microseismic signal. The Transformer model, with its advantages in capturing long-range dependencies, further improves the signal’s representational capability. This study proposes a Wavelet Transform-Transformer Block (WTTB), with the specific structure shown in Figure 1. The block first performs DWT using Haar wavelets, decomposing the signal into low-frequency components (Low) containing the main information and high-frequency components (High) containing detailed information. Both components then undergo feature transformation through convolution layers with a kernel size of 1 × 1 , where the transformed low-frequency and high-frequency components form a Full feature map containing the entire frequency-domain information. In the self-attention mechanism, the Full feature map is used as both the query and value vectors, while the high-frequency components are used as the key vectors. The rationale is that high-frequency components often contain more noise and fine details, while low-frequency components carry the main signal structure. Using high-frequency components as keys allows the Transformer to focus on distinguishing between noise and fine signal features. The full-frequency features as queries and values provide a comprehensive context for this discrimination process. The model generates a new feature map that integrates both global and local information through multi-head self-attention. This feature map is then processed with IDWT to reconstruct the full-frequency domain information back into the time domain. Finally, the feature map is further refined through a convolution layer with a kernel size of 3 × 1 , generating the final output feature map. This block effectively combines the excellent time-frequency localization and multi-scale analysis capabilities of wavelet transform with the powerful long-range dependency capture of the Transformer, thereby significantly enhancing the feature representation and denoising performance for microseismic signals.

As shown in Figure 2, the proposed model is composed of three key components: a shallow feature extraction module (SFEM), a deep feature extraction module (DFEM), and a reconstruction module.

The SFEM begins with a standard convolutional layer, followed by a depthwise separable convolution (DSConv). Initially, a 3 × 1 convolution projects the input from a single channel to 64 channels. The DSConv structure, depicted in Figure 2a, includes a depthwise convolution, a pointwise convolution, and a non-linear activation. The depthwise convolution, using a 3 × 1 kernel, performs spatial convolutions independently on each input channel. The pointwise convolution ( 1 × 1 kernel) then integrates the outputs along the channel dimension. To accelerate convergence, stabilize training, improve non-linearity, and reduce overfitting, Batch Normalization and GELU activation are applied after both convolution stages. The shallow feature extraction process is represented as Equation 3: F s = D S C o n v C o n v y , (3) where y is the noisy signal and F s denotes the extracted shallow features.

The DFEM consists of four deep feature extraction blocks (DFEB), as illustrated in Figure 2b. Each DFEB contains four DSConvs, a WTTB, and residual connections. The DSConvs are configured identically to those in the shallow feature extraction module. Each DSConv layer processes the input data through depthwise spatial convolutions, effectively extracting local temporal information. By stacking multiple DSConv layers, the model incrementally abstracts features, allowing it to capture increasingly complex signal characteristics. The WTTB further strengthens the model’s capacity to extract informative features through a multi-scale attention mechanism. Additionally, the multi-level residual architecture promotes stable training of the deep network. The deep feature extraction process is defined as Equation 4: F d = D F E B 3 ⋯ D F E B 0 F s , (4) where F d represents the learned deep features.

The reconstruction module comprises two 3 × 1 convolutional layers followed by GELU activations. This module integrates the deep features with the original input signal, preserving key characteristics while reconstructing the denoised signal x ̃ . The reconstruction process is outlined as Equation 5: x ̃ = C o n v G E L U C o n v F s + F d . (5)

The mean absolute error (MAE) is used as the loss function: l = | x ̃ − x | . (6) In Equation 6 x ̃ denotes the denoised signal and x is the clean signal.

The number of DWT levels in WTTnet was set to five, a choice grounded in the dominant frequency distribution of typical microseismic signals and the spectral characteristics of noise. Too few decomposition levels would fail to adequately separate low-frequency useful signals from low-frequency noise, whereas too many levels would produce excessively sparse high-frequency sub-bands, impairing the preservation of fine details. A five-level decomposition sufficiently covers the main frequency range of microseismic signals while providing a structurally clear multi-scale representation for the subsequent attention mechanism. The model adopts an eight head self attention mechanism to balance computational efficiency with sufficient feature interaction. Each attention head can be regarded as an independent feature discriminator that simultaneously examines different frequency band subspaces or distinct time frequency regions, thereby modeling signal noise relationships. For a microseismic sequence length of 2000 samples, eight heads effectively capture long-range dependencies across scales while avoiding the parameter redundancy and overfitting risks associated with an excessive number of attention heads. The dimensionality of each attention head in the Transformer was set to 64. When combined with eight attention heads, the resulting total hidden dimension achieves an optimal trade-off between modeling the full signal length and maintaining computational efficiency.

The proposed WTTnet framework exhibits strong potential for cross platform generalization to other geophysical data modalities, owing to its core design that addresses universal challenges in geophysical signal processing: multi scale decomposition, non stationary feature representation, and noise signal separation in the time frequency domain. By adjusting the core parameters of WTTnet based on the dominant frequency distribution, spectral concentration of noise, sequence length, and other characteristics of the target data, the model can be adapted to meet the demands of various tasks ranging from natural earthquake monitoring to exploration seismology. For instance, in natural earthquake monitoring, the same architecture could enhance weak phase arrivals obscured by cultural or oceanic noise. In exploration seismology, the model could be retrained to suppress coherent noise in reflection seismic data, where the wavelet based frequency separation and attention based spatial temporal modeling would help distinguish between primary reflections and noise trains.

The model is optimized using the Adam optimizer. The initial learning rate is set to 1 × 1 0 − 3 and is adaptively reduced by a factor of 0.1 whenever the validation loss fails to decrease after 10 epochs, until it reaches a minimum value of 5 × 1 0 − 7 . The total number of training epochs is set to 200. All experiments are conducted on an NVIDIA RTX 4090 GPU (24 GB) and a Xeon Gold 6430R CPU.

To assess the effectiveness of the proposed method, we first conduct evaluations on synthetic seismic data. A portion of the Marmousi velocity model is chosen to simulate a microseismic monitoring region, as shown in Figure 3. The model spans 1280 m × 1280 m with a grid resolution of 10 m. Synthetic events are generated using a 50 Hz source frequency, with 500 randomly selected grid points serving as event origins. A total of 128 receivers are uniformly distributed across the surface, spaced 10 m apart, and the data is sampled at 1 m intervals for 2000 time steps per trace. The data are normalized to the range of [-1, 1], and a microseismic dataset is created by randomly adding Gaussian noise, colored noise, electromagnetic interference (EMI) noise, and mixed noise to the signals. Gaussian noise obeys a zero mean normal distribution, where the standard deviation is determined by a randomly drawn SNR value within [-10,5] dB. Colored noise is generated by passing Gaussian white noise through a 1/f spectral shaping filter. The fundamental frequency of 50 Hz is adopted as the EMI noise source. Its amplitude varies randomly between 0.1 and 0.3 times the amplitude of the clean signal to simulate the fluctuating intensity of interference in real-world environments. Mixed noise is produced by randomly selecting two or three of the above noise types and superimposing them with random relative energy ratios, where each constituent noise contributes (20%)–(60%) of the total noise energy. The resulting dataset consists of 64,000 one-channel waveform samples, each 2000 time steps in length. The 64,000 samples were evenly distributed across the four noisy signal categories. The selection of 2000 time steps per trace was determined based on a trade-off between capturing sufficient waveform duration for microseismic events and maintaining computational efficiency during training. This length not only covers the complete event window in our synthetic setup but also helps reduce the model’s computational complexity and improve overall efficiency. The data are randomly divided into training (75%), validation (15%), and test (10%) sets.

We input the test set into the trained model to obtain experimental results. Figure 4a presents a microseismic signal contaminated with Gaussian random noise, and Figure 4b shows its corresponding frequency spectrum. As illustrated, the original noisy signal exhibits significant overlap between signal and noise in both domains, with the frequency spectrum completely dominated by the flat Gaussian noise. After processing with WTTnet, the time-domain waveform becomes clear and coherent, with virtually no residual noise visible. In the frequency domain, the signal spectrum is well-recovered, closely matching the clean signal’s spectral characteristics. Gaussian noise is stationary and exhibits a flat spectrum, which allows wavelet transforms to effectively separate the signal from the noise in the frequency domain. The self-attention mechanism of the Transformer can capture global dependencies, further suppressing noise. By decomposing the signal into different frequency bands using wavelet transform, WTTnet can then model the relationships between these frequency bands using the Transformer, effectively removing Gaussian noise.

Figure 5 illustrates a microseismic signal contaminated by colored noise and its corresponding frequency spectrum. The introduced colored noise is concentrated below 50 Hz, directly overlapping with the dominant frequency band of the effective microseismic signal. This presents a particular challenge as the noise shares spectral content with the signal of interest. The original noisy signal displays obvious contamination in both time and frequency domains, with the low-frequency colored noise obscuring the fundamental components of the microseismic signal. WTTnet effectively restores the signal’s original waveform, producing a clean time-domain trace with minimal distortion. The processed frequency spectrum shows successful separation, with the low-frequency noise components significantly attenuated while preserving the signal’s spectral integrity. Colored noise typically exhibits specific frequency distribution characteristics, which wavelet transform can separate into low- and high-frequency components. WTTnet processes the low- and high-frequency components separately and uses the self-attention mechanism to learn the correlations between them. This enables the model to specifically reduce the impact of noise at certain frequencies while retaining the useful frequency components of the signal.

Figure 6 shows a microseismic signal with EMI noise and its corresponding frequency spectrum. EMI noise typically manifests as narrow-band interference or periodic spikes, often originating from electrical equipment in field environments. The original signal is heavily corrupted, with the EMI components distorting both the amplitude and phase characteristics of the underlying seismic event. After WTTnet processing, the time-domain waveform appears clean with the oscillatory interference removed, and the signal’s natural morphology is well-preserved. The frequency spectrum becomes organized, with the narrow-band EMI peaks effectively suppressed. EMI noise is challenging due to its structured nature and potential similarity to genuine signal features. Wavelet transform provides multi-resolution analysis to localize these frequency-specific interferences, while the attention mechanism of the Transformer helps to distinguish between persistent EMI patterns and transient seismic signals. Through this combined approach, structured EMI noise can be effectively identified and removed.

In Figure 7, a microseismic signal is contaminated with a mixture of the three aforementioned types of noise. Figure 7b displays its corresponding frequency spectrum. The complex noise mixture creates severe signal distortion in both domains, making it difficult to distinguish the original microseismic event. WTTnet successfully recovers the signal’s essential features, producing a clean time-domain waveform with excellent fidelity. The denoised frequency spectrum exhibits a clear, organized structure that facilitates accurate event analysis. Mixed noise contains various noise characteristics, and WTTnet’s multi-scale processing capabilities and self-attention mechanism enable it to handle different types of noise simultaneously. The wavelet decomposition separates the signal into different frequency bands, allowing the model to process noise in each band independently, while the Transformer integrates information from multiple bands, providing a more comprehensive denoising solution.

The algorithm restores the denoised signal with high accuracy, effectively suppressing common types of noise encountered in field operations, such as Gaussian random noise and various environmental noises. The shape and amplitude characteristics of the predicted signal exhibit a high degree of similarity to the original signal, with the overall frequency spectrum remaining clean and clear, ensuring excellent fidelity. This high fidelity in signal reconstruction is crucial for ensuring that the restored signal retains the essential features of the original, which is vital for accurate analysis and interpretation of microseismic data in practical applications.

Subsequently, the SNR of the original noisy data and the denoised data is calculated. The formula for calculating the SNR is as Equation 7: S N R = 10 l o g 10 P s P n = 10 l o g 10 ∑ i = 1 N s c 2 i ∑ i = 1 N s c i − s d i 2 , (7) where P s and P n denote the signal and noise power, respectively. s c is the clean signal, and s d is the denoised signal.

As shown in Figure 8, the noisy signals are primarily distributed in the −7 to 4 dB range, reflecting signals buried at the noise threshold. In contrast, the denoised outputs predominantly lie between 5 and 17 dB. The proposed method boosts the average SNR from −0.225 dB to 11.556 dB, highlighting its strong denoising capability.

The proposed method is compared to WT and Swin Transformer (Sun et al., 2025; Li et al., 2024). For WT, we employ the Haar wavelet with 5 decomposition levels. Swin Transformer was implemented as a 1D version comprising 4 stages, each containing 2 Transformer blocks, with a window size of 8, 8 attention heads, and a hidden dimension of 64. To ensure a fair comparison under identical conditions, Swin Transformer was trained using the same experimental setup as WTTnet. The Adam optimizer was employed, and the MAE was adopted as the loss function. The model was trained for 200 epochs on the same hardware platform as WTTnet, using the same learning rate schedule and batch size. The results are shown in Figure 9. For the original noisy signal, the time-domain waveform clearly displays significant distortion and confusion, with a heavy overlap between the signal and noise. In the frequency domain, this overlap is also quite evident in the spectrum. When comparing the denoising performance of the three methods, it becomes apparent that the WT method performs the worst. While it does reduce noise to some extent, the improvement in SNR is relatively modest. The Swin Transformer demonstrates improved performance; its denoised time-domain waveform shows minimal visible noise. However, residual high-frequency noise is still present in the frequency domain. In contrast, WTTnet shows a clear advantage over the other methods in both signal recovery and noise reduction. The time-domain waveform is notably clean and coherent, with almost no remaining noise. The frequency spectrum is also organized and well-defined, with high-frequency noise completely removed, facilitating more accurate event detection. From the frequency domain comparison, it is evident that the Swin Transformer’s self-attention mechanism, which struggles to effectively distinguish different frequency components, leaves some high-frequency noise in the denoised signal. On the other hand, WTTnet leverages DWT to decompose the input signal into both high-frequency and low-frequency components. It then applies a multi-head self-attention mechanism to model the interdependencies between cross-scale features, allowing for more effective extraction of low-frequency signals while efficiently removing high-frequency noise. This significantly enhances the overall denoising performance.

To further evaluate denoising performance, we employ three metrics: SNR, MAE, and the structural similarity index (SSIM). While the SNR formula was introduced in the previous section, the MAE and SSIM formulations are provided Equations 8, 9: M A E = 1 N ∑ i = 1 N | s c i − s d i | , (8) S S I M = 2 μ c μ d + C 1 + 2 σ c d + C 2 μ c 2 + μ d 2 + C 1 σ c 2 + σ d 2 + C 2 , (9) where μ c and μ d are the means of the clean and denoised signals, σ c 2 and σ d 2 are their variances, σ c d is the covariance, and C 1 and C 2 are stabilization constants.

As shown in Figure 10, the proposed denoising method outperforms both the Swin Transformer and WT methods. Compared to the other two approaches, WTTnet achieves the greatest improvement in SNR. The average improvement is 7.604 dB over traditional wavelet denoising and approximately 4.382 dB over the Swin Transformer method. The higher SSIM values in Figure 10b further indicate that the signal processed by WTTnet maintains greater similarity to the original clean signal, suggesting that the method introduces minimal waveform distortion during the denoising process. The lowest average MAE value in Figure 10c demonstrates that WTTnet produces the least overall deviation during signal reconstruction. This not only reflects the effectiveness of the denoising but also highlights its exceptional performance in signal reconstruction accuracy. The lower error indicates that the denoised signal is closer to the true seismic waveform, providing a reliable data foundation for subsequent precise analysis and interpretation.

Improving signal quality has a profound and widespread impact on subsequent microseismic data processing. The accurate determination of the P-wave arrival time is a fundamental step in the localization of microseismic events and the calculation of source parameters. The precision of this key parameter directly determines the reliability of all subsequent analyses. Additionally, the presence of non-seismic signals significantly increases the false positive detection rate. These interfering signals, which may stem from mining equipment operation, vehicle vibrations, electrical interference, or other human activities, often share similar characteristics with microseismic signals, making it difficult for traditional detection methods to effectively distinguish them.

In Figure 11, we showcase two typical examples demonstrating the superior performance of the WTTnet model in enhancing the STA/LTA characteristic function. Traditional STA/LTA methods face significant challenges when processing noisy signals, as noise interference can create false peaks in the characteristic function, making accurate identification of the true P-wave arrival time difficult. Meanwhile, weak signals hidden under noise are prone to being missed, with this issue being particularly evident in low SNR environments. In the first example, a weak useful signal was originally submerged in strong background noise, and the STA/LTA algorithm failed to produce a clear triggering signal. However, after enhancement with WTTnet, the SNR of the signal was significantly improved, and the characteristic function showed a distinct upward slope at the P-wave arrival time, providing a reliable basis for automatic detection. In the second example, noise in the signal caused fluctuations in the STA/LTA ratio, generating multiple false peaks that severely disrupted accurate identification of the P-wave. After processing with WTTnet, these non-seismic noise components were effectively suppressed, and the characteristic function curve became smooth and clear, with the peak corresponding to the true P-wave arrival time standing out and being easily identifiable.

To further evaluate the method’s generalization and field applicability, we test it on field microseismic data from the 2018 hydraulic fracturing experiment at the Grimsel Test Site, as reported by Gischig et al. (2018). The monitoring system includes 28 piezoelectric sensors and 4 accelerometers, with 20 sensors installed along the tunnel wall and four accelerometers co-located. An 8-channel borehole array with 1 m spacing is placed in borehole SBH-1, which consistently records all events due to its low-noise environment. The shortest sensor-to-source distance is approximately 9 m (from HF1), while the furthest sensors (S1-S5) are 55–72 m away. Data acquisition uses a 32-channel digitizer, with band-pass filters at 1000 Hz and 50 Hz. A representative trace containing a microseismic event is preprocessed, and the model trained on synthetic data is directly applied.

The trained model was directly applied to field data for denoising. As shown in Figures 12, 13, the original microseismic recordings are heavily contaminated by various types of complex noise, with the effective signals largely buried, making it difficult to directly identify microseismic events. The WT method exhibits relatively poor denoising performance, failing to effectively separate signal from noise. The denoised waveform in the time domain still contains significant interference components, and the frequency domain features show no notable improvement. The Swin Transformer demonstrates better performance in the denoising task. Its denoised waveform in the time domain shows minimal visible noise components. However, frequency domain analysis reveals that some low-amplitude residual noise remains in the waveform following the end of the microseismic event. WTTnet delivers the most impressive results in both signal recovery and noise suppression. It not only effectively restores the original waveform characteristics, maintaining continuity and clarity in the time domain, but also demonstrates strong noise suppression capabilities in the frequency domain. The resulting spectral distribution becomes more focused and structured, significantly enhancing the feasibility of subsequent event extraction and precise analysis.

In terms of computational efficiency, the Transformer’s self-attention mechanism has a time complexity of O ( n 2 ) , which results in significantly higher computational costs compared to CNN-based parallel sliding window methods during training. However, compared with traditional methods, deep learning models can perform rapid inference once trained, which offers a significant advantage for real-time microseismic monitoring applications that require low-latency response. Nevertheless, optimizing real-time processing latency on edge computing devices, such as downhole microseismic acquisition instruments, remains a key direction for future research. Another important consideration relates to the model’s generalization capability across diverse geological settings.

Although the proposed method performs well on both synthetic data and the Grimsel test site dataset, its generalizability across diverse geological and acquisition conditions requires further validation. The training data in this study are primarily based on synthetic velocity models and a single field dataset, which possess specific noise characteristics, signal frequency content, and geological responses. In practice, factors such as varying lithology, fracture density, depth, and acquisition systems can significantly alter microseismic signal patterns and noise structures, potentially leading to degraded model performance. Future work should test and fine-tune the model on broader and more diverse field datasets, or explore the integration of physics-based constraints to enhance its robustness and applicability in unseen geological and noisy environments.