An Unsupervised Learning Method for Suppressing Ground Roll in Deep Pre-Stack Seismic Data Based on Wavelet Prior Information for Deep Learning in Seismic Data

Abstract

Ground roll noise suppression is a crucial step in processing deep pre-stack seismic data. Recently, supervised deep learning methods have gained popularity in this field due to their ability to adaptively learn and extract powerful features. However, these methods rely on a large amount of clean seismic records without ground roll noise as reference labels. Unfortunately, generating high-quality and realistic clean seismic records for training remains a challenge. To tackle this problem, an unsupervised learning method called WPI-SD (wavelet prior information for deep learning in seismic data) is proposed for ground roll noise suppression in deep pre-stack seismic data. This approach takes into account the distinct temporal, lateral, and frequency characteristics that differentiate ground roll noise from real reflected waves in deep pre-stack seismic records. By designing a ground roll suppression loss function, the deep learning network can learn the specific distribution characteristics of real reflected waves within seismic records containing ground roll noise, even without labeled data. This enables the extraction of effective reflection signals and subsequent suppression of ground roll noise. Applied to actual seismic data processing, this method effectively mitigates ground roll noise while preserving valuable reflection signals, proving its practical significance.

1. Introduction

In recent years, the conventional onshore oil and gas reserves have been declining, leading to a shift in research focus from conventional oil and gas to deep complex strata oil and gas exploration [1]. Consequently, seismic exploration technology has emerged as an indispensable tool for deep oil and gas exploration. Nonetheless, the intricate surface conditions and the absorption and attenuation effects of deep layers have led to the escalating complexity of low-frequency intense ground roll features, accompanied by a simultaneous weakening of the energy carried by real reflected waves. This deleteriously impacts the signal-to-noise ratio of seismic records and impairs the precision of subsequent data processing and interpretation. Furthermore, due to the ground roll and reflected waves having similar frequency characteristics and temporal forms, and their overlap in both the frequency and spatiotemporal domains, this blurs the boundary between ground roll and real reflected waves, increasing the difficulty of separating ground roll from reflected waves.

In order to meet the requirements of seismic exploration and improve the quality of deep pre-stack seismic records, experts and scholars have put forward various techniques for suppressing ground roll noise. These techniques can be classified into two main categories: model-based methods that suppress ground roll and deep learning algorithm-based methods that also target ground roll suppression. The first category, model-based ground roll suppression methods, mainly includes frequency domain bandpass filtering [2,3,4,5], F-K (Frequency–Wavenumber) fan filtering [6,7], wavelet filtering [8,9,10,11,12,13], curvelet filtering [7,14,15,16,17], the t-p transform (Travel-time and Slowness Transform) [18], singular value spectrum analysis [19], the hyperbolic interference method [20], morphological component analysis [21,22], and other methods [23,24,25,26]. The core idea is to utilize the differences in characteristics such as time, space, frequency, wave velocity, and morphology between ground roll and real reflected waves to design a ground roll prediction model and separate the ground roll from seismic records. However, these methods only consider the characteristics of ground roll in one aspect to establish mathematical models, which have limited expressive power and cannot describe the complex distribution of ground roll noise. This affects the accuracy of model assumptions and parameter settings, leading to the destruction of real reflected waves during the ground roll suppression process.

The second category, which relies on deep learning [27,28,29] algorithms for ground roll suppression, primarily involves training deep neural networks with extensive paired seismic data. In recent years, deep learning has been widely applied in the processing of seismic data [30,31,32,33,34,35,36,37,38,39,40,41]. However, its current focus primarily lies in suppressing random noise [42,43], while the application of deep learning algorithms for mitigating ground roll [44,45,46] remains limited. These networks learn the distinct features of seismic data and automatically distinguish between ground roll and real reflected waves, thereby successfully suppressing ground roll noise. The ground roll suppression methods based on the GAN (Generative Adversarial Network) studied by Si Xu [47] require the utilization of model-based ground roll suppression methods to suppress ground roll noise in actual seismic records as labeled data, followed by training deep learning networks to achieve ground roll suppression. However, in practical applications, it is impractical to obtain actual seismic data containing ground roll and corresponding denoised data. Due to the lack of high-quality training data, the above-mentioned two methods cannot fully achieve ground roll suppression. As a result of these limitations, deep learning-based ground roll suppression methods are gradually shifting from supervised methods that require annotated data to unsupervised methods that do not require labeled data. Nam Pham [48] proposed a combined unsupervised and supervised deep learning method to implement seismic ground roll attenuation. Dawei Li [49] studied an unsupervised ground roll suppression method based on NMO (Normal Moveout), which achieved ground roll suppression without using labeled data for the first time. This method first flattens the reflected waves through NMO correction, enhances the self-similarity of the reflected waves, and reduces the self-similarity of the ground roll. Then, by utilizing the multi-scale self-similarity feature extraction capability of the deep learning network, it prioritizes the extraction of strongly self-similar reflected waves. By selecting a specific number of iterations, the ground roll and reflected waves are separated, thus achieving ground roll suppression. However, this method can easily introduce phase shifts into the seismic records after ground roll suppression.

This paper proposes the WPI-SD (wavelet prior information for deep learning in seismic data) network, an unsupervised learning network that leverages prior information in deep learning and the distribution characteristics of seismic data for suppressing ground roll noise in deep pre-stack seismic records. The proposed method performs wavelet decomposition on the seismic records containing ground roll to obtain different wavelet components in different frequency bands with varying ground roll energy proportions. A loss function is then designed, which includes a sparse representation regularization term that controls the weight distribution of each sparse representation by modifying the coefficient difference between the input seismic records and the network output for each wavelet component. The loss function assigns smaller weights to wavelet components with strong ground roll and larger weights to wavelet components almost free of ground roll, leading to a higher weight for real reflected waves. By minimizing the loss function, the WPI-SD network model parameters are adjusted to extract reflected waves from the original seismic records, achieving ground roll suppression.

Compared to existing deep learning-based ground roll suppression methods, the WPI-SD network has two distinct features. Firstly, the method employs weighted processing of wavelet components based on the energy distribution characteristics of ground roll and effective signals in different frequency bands. This involves increasing the coefficients of wavelet components with almost no ground roll while decreasing the coefficients of those with ground roll. To achieve this, a ground roll suppression loss function is designed to prioritize the extraction of effective reflection signals during the deep learning network’s learning process. Secondly, the WPI-SD network does not require a large amount of paired training data. It leverages the ability of deep learning networks to automatically learn feature representations, optimize reconstruction loss functions, and learn data distribution characteristics. With a certain number of iterations, it can learn the features of different waveform signals from input data and separate ground roll from real reflected waves, without requiring a large amount of paired training data.

2. Materials and Methods

The actual seismic record $y$ collected in the field typically consists of three parts:

$$y=x+n+g$$

(1)

$y$ represents seismic records containing ground roll noise, $x$ represents clean seismic data, $n$ represents random noise, and $g$ represents ground roll noise. The methodological roadmap of the WPI-SD unsupervised learning-based deep pre-stack ground roll noise suppression method is illustrated in Figure 1. The WPI-SD based deep pre-stack ground roll suppression method first performs wavelet decomposition to obtain seismic wavelet components in different frequency bands. Then, a reconstruction loss function is designed to measure the difference between the network output and input wavelet components. The weight distribution is controlled by adjusting the coefficients of the differences in the loss function for each wavelet component. Finally, by minimizing the loss function, the parameters of the WPI-SD network model are adjusted to achieve ground roll suppression.

2.1. Network Architecture of WPI-SD

The WPI-SD network proposed in this article is built upon a six-layer skip connection network, as illustrated in Figure 2. The skip connection network incorporates cross-layer feature reconstruction, wherein the decoder combines high-level convolutional features with low-level convolutional features. This fusion process aims to retain crucial feature information from the higher-level convolutions, consequently enhancing the network’s accuracy in non-linear modeling and its ability to generalize.

Clearly, the upsampling process in deep learning networks requires filling in a lot of missing content, generating something from nothing, which lacks sufficient auxiliary information. Therefore, based on the encoder–decoder structure of the main pathway, we introduce the skip connection pathway. As the network propagates, with an increasing depth, the receptive field of the corresponding feature maps becomes larger, but the preserved detailed information decreases. For the task of extracting effective signals from seismic data, the rich detailed information preserved by high-level convolutions is very valuable. Based on the symmetrical encoder–decoder structure, we use concatenation layers to concatenate the feature maps extracted through downsampling in the encoding process with the new feature maps obtained through upsampling in the decoding process, corresponding one by one in the channel dimension. By introducing feature information at corresponding scales into the upsampling process, multi-scale and multi-level information is provided for the effective restoration of seismic signals, thereby improving the reconstruction quality and reducing information loss.

2.2. The Design of the Network Loss Function

To ensure the synthesis of real reflected waves and achieve the separation of ground rolls and useful signals during the training process of the unsupervised learning network, this paper proposes a total ground roll suppression loss function $L_{total}$. This loss function consists of two parts: weak ground roll loss $L_{low}$ and strong ground roll loss $L_{high}$. The function is represented as follows.

$$L_{total}={\lambda }_1\ast L_{low}+{{\lambda }_2\ast L}_{high}$$

(2)

In this case, ${\lambda }_1$ and ${\lambda }_2$ are hyperparameters of the total loss function, representing the scaling coefficients for the weak ground roll loss function and the strong ground roll loss function, respectively.

In this section, we will first introduce the characteristics of seismic records after wavelet decomposition and then provide a detailed explanation of each component of the loss function.

The wavelet transform is a time–frequency analysis method that can decompose signals into components of different scales and frequencies. In seismic records, by performing wavelet transform on the seismic signal, we can obtain wavelet coefficients at different frequencies. This allows us to concentrate the components and energy of the signal at different frequencies into different wavelet coefficients. Since ground rolls usually have lower frequency characteristics, while body waves in seismic signals often have higher frequency characteristics, we can filter out ground roll noise and retain the body wave signal by selecting appropriate wavelet basis functions and thresholds. Taking synthetic seismic records as an example, as shown in Figure 3, certain wavelet components (indicated by the blue box) exhibit strong ground roll energy, labeled as ${input}_{high}$, while other wavelet components (indicated by the green box) have weaker ground roll energy, labeled as ${input}_{low}$.

Next, let us delve into the individual components of the loss function.

(1) Weak ground roll loss $L_{low}$

The weak ground roll loss function aims to compute $MSE$ (the mean squared error) loss function between the network output and the wavelet decomposition of the input seismic records containing the weak energy ground roll components. It is defined as follows.

$$L_{low}=MSE({input}_{low}, {output}_{low})$$

(3)

Here, ${input}_{low}$ represents the wavelet component obtained through the wavelet decomposition of the original seismic records, which contains very few ground roll components. ${output}_{low}$ corresponds to the portion of the wavelet component obtained through the wavelet decomposition of the seismic records that does not contain ground roll components.

The significance of the weak ground roll loss function lies in its ability to help the network learn and preserve the information in the input data that is free from ground roll. By increasing the proportion of this component in the loss function and optimizing it, training the network can better suppress ground roll. This contributes to improving the overall performance of the network and the quality of the output results.

(2) Strong ground roll loss $L_{high}$

The strong ground roll loss function is designed to compute $MSE$ loss function between the network output and the wavelet decomposition of the input seismic records, containing the strong energy ground roll components. It is defined as follows.

$$L_{high}=MSE({input}_{high}, {output}_{high})$$

(4)

Here, ${input}_{high}$ refers to the wavelet component obtained through the wavelet decomposition of the original seismic records, which contains minimal ground roll components. ${output}_{high}$ corresponds to the section of the wavelet component obtained through the wavelet decomposition of the seismic records that does not contain any ground roll components.

The significance of the strong ground roll loss function is its ability to assist the network in learning and preserving the information in the input data that lacks ground roll. By decreasing the proportion of this component in the loss function and optimizing it, the network training can more effectively suppress ground roll, resulting in an improved overall network performance and output quality.

2.3. Training Process of the Network

The method proposed in this article utilizes unsupervised learning, eliminating the need for labels or target values and instead relying on prior information, such as input data and loss functions. By employing the ADAM (Adaptive Moment Estimation) optimizer to iteratively address optimization problems and reduce errors gradually, a superior network model is achieved. During each iteration, the network maps parameters to output data and trains the network model through minimizing the loss function without target outputs. This methodology enables the network to automatically discover data features and utilize them for data reconstruction.

Using the training of synthetic seismic records as an illustration, as depicted in Figure 3, we illustrate the training process of the WPI-SD network. Due to the unique structure of the loss function, the network can give priority to extracting features of multi-scale reflected waves and effectively reconstructing them.

Nevertheless, due to the relatively lower weight of ground waves in the loss function, the network may lag in extracting ground wave features. Initially, during the training phase, the network predominantly focuses on reconstructing reflected waves, shifting to ground waves after prolonged training. To tackle this issue, we introduce an early stopping strategy, selecting an optimal number of iterations within the red box in Figure 4 to ensure the network produces effective reflection signals. Specifically, monitoring changes in the loss function value throughout training and halting training once the value no longer decreases help prevent overfitting and improve the network’s ability to reconstruct seismic signals.

3. Results and Discussion

To test the feasibility and practicality of this method, we conducted a series of experiments, including synthetic seismic records and real seismic records. First, we conducted synthetic experiments to verify the meanings of different parts of the loss function and the impact of coefficients of each part on the experimental results. Next, we carried out real experiments to validate the effectiveness of this method and compared it with traditional F-K filtering and curvelet filtering methods to demonstrate the superiority of the method.

3.1. Synthetic Example

This section will first validate the effectiveness of the WPI-SD single model in suppressing synthetic surface wave noise.

To create the training set for synthetic seismic records, we utilized the hyperbolic event synthesis method from the crews toolkit. This approach generates data that include reflected waves simulated by hyperbolic common-midpoint gathers and surface waves simulated by linear common-midpoint gathers, leveraging the distinct morphological features of reflection signals and surface wave noise in the lateral–temporal domain. The process of generating seismic data with surface waves involves estimating amplitudes, frequency bands, and velocity ranges of surface waves and effective signals in the pre-stack seismic data of the target area based on actual seismic data. Random seismic signal velocities are then generated, followed by the random generation of fake seismic source wavelets with different dominant frequencies within the effective frequency band range. The observation system was set up based on the sampling interval and trace spacing. By employing the hyperbolic event synthesis method, a significant volume of targeted synthetic seismic data were generated using simulation parameters from the velocity model detailed in

Table 1. Synthetic seismic data parameter setting.

Parameter	Parameter Setting	Parameter	Parameter Setting
Model size	3000 samples × 240 traces	Time sampling interval	2 ms
Reflection wave velocity	800–1000 m/s	Ground roll wave velocity	200–500 m/s
Reflection wave source wavelet type	Ricker	Ground roll wave source wavelet type	Ricker
Reflection wave dominant frequency	25–35 Hz	Ground roll wave dominant frequency	5–15 Hz
Maximum amplitude of effective wave	2–5	Maximum amplitude of ground roll wave	4–10

.

The parameter settings used in this paper are as follows: the seismic model size is 3000 × 240, with 240 seismic traces. The time sampling interval is 2 ms, with a total of 3000 time sample points. The reflection wave velocity ranges from 800 to 1000 m per second, while the ground roll wave velocity ranges from 200 to 500 m per second. Both the reflection wave and ground roll wave source wavelets are of the Ricker type, with the dominant frequency of the reflection wave being 25–35 Hz and the dominant frequency of the ground roll wave being 5–15 Hz. The maximum amplitude range of the effective wave is 2–5, and the maximum amplitude range of the ground roll wave is 4–10. These highly realistic synthetic seismic data are crucial for further analysis and research purposes.

This section uses an example of synthetic seismic data composed of real reflected waves modeled by hyperbolic events and surface waves modeled by linear events to detail the situations of the loss function parameters ${\lambda }_1$ and ${\lambda }_2$ designed in this paper, as well as the classic traditional L2 loss function under different coefficients. With the increase in the number of iterations, the synthesis of real reflected waves and ground roll in the seismic records also evolves accordingly. As shown in Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9, synthetic seismic data were recorded during the iterative process of the network within 1000 iterations in the WPI-SD model, for the cases when ${\lambda }_1=1$ and ${\lambda }_2=1$, ${\lambda }_1=1$ and ${\lambda }_2=10$, ${\lambda }_1=1$ and ${\lambda }_2=40$, and ${\lambda }_1=40$ and ${\lambda }_2=1$, along with the L2 loss at iteration steps 0, 80, 100, 140, 160, 180, 340, 800, and 1000.

As illustrated in Figure 5, Figure 6, Figure 7 and Figure 8, irrespective of the values of ${\lambda }_1$ and ${\lambda }_2$, the WPI-SD model progressively converges towards the original seismic record by iteratively adjusting its network parameters with an increasing number of iterations.

In Figure 5, when ${\lambda }_1=1$ and ${\lambda }_2=1$, the WPI-SD network simultaneously reconstructs both the effective reflection signal and the ground roll, posing a challenge in distinguishing between the two. The difficulty arises from the values of ground roll and reflected waves, causing the network to struggle in discerning ground roll from reflected waves, leading to mutual interference during the recovery process and hindering complete separation.

In Figure 6 and Figure 7, in scenarios where ${\lambda }_1<{\lambda }_2$, the WPI-SD network prioritizes restoring the effective reflection signals. With the progression of iterations, it subsequently recovers the ground roll. Moreover, as the value of B increases, the disparity in the required number of iterations for recovering ground roll and reflected waves also grows. The preference for restoring effective reflection signals by the WPI-SD network stems from the distinct values of ${\lambda }_1$ and ${\lambda }_2$, resulting in varying reconstruction priorities for different signal types.

In Figure 8, when ${\lambda }_1>{\lambda }_2$, the WPI-SD network gives precedence to recovering the ground roll. As the iterations advance, it then proceeds to recover the reflected waves. The network’s inclination towards restoring the ground roll is influenced by the differing values of ${\lambda }_1$ and ${\lambda }_2$, prompting a higher priority for reconstructing ground roll over reflected waves.

According to Figure 9, when using the L2 loss function, deep learning networks tend to prioritize fitting the strong-energy, fast-wave, and smooth waveform of the reflected wave. However, during the iterative training process, due to the strong energy of the ground roll, the network also fits the strong-energy part of the ground roll while fitting the reflected wave, resulting in seismic data with strong-energy ground roll noise and a suboptimal fitting of the weak-energy part of the reflected wave. Additionally, the network’s fitting speed is too fast, making it difficult to find the optimal number of iterations to separate the ground roll and reflected wave. In conclusion, the suppression effect of the ground roll is far inferior when using the traditional classic L2 loss function compared to the loss function of the designed WPI-SD ground roll suppression network in this paper.

Therefore, when setting network parameters, in order to better extract effective reflection signals from actual seismic records, the value of parameter ${\lambda }_1$ should be greater than parameter ${\lambda }_2$.

Furthermore, to further verify the effectiveness and superiority of the method proposed in this paper, we conducted the following comparative experiments: We compared the ground roll suppression effects of the WPI-SD network with a six-layer skip connection network architecture when using the L2 loss function of ${\lambda }_1=0.07$ and ${\lambda }_2=1$, as well as when ${\lambda }_1=0.04$ and ${\lambda }_2=1$. Additionally, we also observed the mean square error (MSE) loss function curves between the network outputs within 1000 iterations and clean seismic records without ground roll for these four scenarios, as shown in Figure 10.

From Figure 10, it is evident in Figure 10a,e that when using the L2 loss function, the network tends to fit the reflected waves within a certain number of iterations. However, as the number of iterations increases, the network quickly starts fitting seismic records containing ground roll, leading to a rapid increase in the mean square error between the network output and clean seismic records without ground roll. Furthermore, it is also clearly observable from Figure 10 that when ${\lambda }_2$ is fixed, a larger ${\lambda }_1$ results in a faster fitting speed of the network; the more layers the network has, the faster the fitting speed.

In conclusion, from Figure 10, we can observe that in the initial iteration phase, the network tends to prioritize fitting the reflected waves, with the best fitting effect, as shown in Figure 10a–d. Particularly, the surface wave suppression effect in Figure 10c is the most effective, with a more coherent and clear waveform compared to Figure 10a–c while maintaining the mean square error within a smaller range. However, as the number of iterations increases, the mean square error of the network gradually increases and eventually stabilizes.

Therefore, when denoising actual seismic records, we selected the six-layer skip connection network with a faster processing speed as the overall structure of the WPI-SD ground roll suppression network. Additionally, when suppressing ground roll, it is important to choose appropriate loss function coefficients and optimal iteration numbers to achieve better ground roll suppression effects on seismic records.

3.2. Field Data Example

To further assess the applicability of WPI-SD, we applied it to field data processing in the Tarim Basin, located in western China. These field data were acquired from the Tarim Basin and consist of common-shot gathers, with each acquisition having a size of 3000 samples × 240 traces and a sampling rate of 2 milliseconds. We compared the results with those obtained using the F-K filtering method and curvelet transform method, and the specific findings can be seen in Figure 11.

Figure 11a,b display the original seismic records and their corresponding F-K spectra, respectively. Figure 11c–e illustrate the outcomes of ground roll suppression using the F-K filtering method, along with the difference between the original and the denoised data. Although the F-K filtering method effectively suppresses ground roll, some residual ground roll remains in the denoised profiles. Furthermore, Figure 11d’s denoised difference profile reveals the presence of numerous valid reflection signals. This occurs because F-K filtering is a global filtering method that unavoidably affects valid reflection signals while removing ground roll.

Next, Figure 11f–h demonstrate the denoising results obtained using the curvelet transform method, as well as the corresponding difference profiles and F-K spectra. Compared to the F-K filtering method, the curvelet transform method performs better in suppressing ground roll, resulting in minimal residual ground roll interference in the denoised profiles. However, as shown in Figure 11g, some strong energy valid signals still persist in the difference profile of the curvelet transform method. Therefore, further improvement is required to enhance the method’s ability to preserve valid signals.

Finally, Figure 11i–k showcase the denoising outcomes achieved with the proposed WPI-SD method, alongside the corresponding difference profiles and F-K spectra. The denoising results clearly indicate that this method significantly enhances the denoising effect compared to traditional methods, as it noticeably reduces the leakage of valid signal energy or residual ground roll in the difference profiles. By comparing the difference profiles (Figure 11d,g), it becomes evident that the proposed method minimizes the damage to high-frequency valid signals and strong energy valid signals, enabling the network to better preserve the detailed features of valid signals while suppressing strong ground roll.

The post-stack seismic data after ground roll suppression using F-K filtering, the curvelet transform, and the proposed method were obtained through conventional stacking processing without further denoising, as shown in Figure 12. The red box in Figure 12 indicates that compared to F-K filtering and the curvelet transform, the proposed method results in a clearer and more continuous seismic reflector after ground roll suppression.

To further validate the suppression effect of seismic ground roll, we employed the quality factor Q [50] to evaluate the analysis method of ground roll effects and conducted a quantitative analysis of the ground roll suppression effect of our approach.

$$Q=10{\log }_{10}\left(\frac{{‖d_{input}‖}_2}{{‖d_{input}-d_{clear}‖}_2}\right)$$

(5)

Here, $d_{input}$ represents the raw data, $d_{clear}$ represents the denoised data, and ${‖d‖}_2$ denotes the L2 norm of vector d. We calculated the Q values of the results after denoising with WPI-SD, the curvelet transform, and F-K filtering, as shown in

Table 2. Q values of different denoised methods.

Method	F-K	Curvelet	WPI-SD
Q	−0.771	−0.696	−0.801

. The results are consistent with qualitative understanding, indicating that WPI-SD exhibits a better suppression of ground roll waves.

4. Conclusions

This article introduces a method based on unsupervised deep learning, namely the WPI-SD ground roll suppression method, used to suppress ground roll noise. This method does not require high-quality paired training sets, only a seismic record containing surface waves is needed to train the network. By adjusting the coefficients of different parts of the loss function, we have designed a directional loss function to control the network’s priority in recovering effective reflection signals during the iterative training process, thereby achieving surface wave suppression. We also validated the necessity and effectiveness of the loss function design through synthetic seismic records and then verified the superiority and effectiveness of the proposed method through the processing results of pre-stack seismic data in western China.

In future research, we will further explore how to enhance the ability to extract weak effective signals to meet the demand for extracting weak signals from ultra-deep pre-stack seismic data in current western exploration.