Stylization of a Seismic Image Profile Based on a Convolutional Neural Network

Abstract

Seismic data are widely used in oil, gas, and other kinds of mineral exploration and development. However, due to low artificial interpretation accuracy and small sample sizes, seismic data may not meet the needs of convolutional neural network training. There are major differences between optical image and seismic data, making it difficult for a model to learn seismic data characteristics. Therefore, a style transfer network is necessary to make the styles of optical image and seismic data more similar. Since the stylization effect of a seismic section is similar to that of most art styles, based on an in-depth study of image style transfer, this paper compared the effects of various style transfer models, and selected a Laplacian pyramid network to carry out a study of seismic section stylization. It transmits low-resolution global style patterns through a drafting network, revises high-resolution local details through correction networks, and aggregates all pyramid layers to output final stylized images of seismic profiles. Experiments show that this method can effectively convey the whole style pattern without losing the original image content. This style transfer method, based on the Laplacian pyramid network, provides theoretical guidance for the fast and objective application of the model to seismic data features.

1. Introduction

Seismic data interpretation is involved in most geological research fields [1], so the precision of results is of great significance for oil and gas and mineral exploration and development. Faults are characterized by low continuity or high discontinuity of cophase axes in seismic profiles. Seismic data are still interpreted manually or through human–computer interaction. Conventional interpretation [2] is based on the principle of wave group contrast, the results of which are obtained by seismic profile recognition and plane combination. The three-dimensional coherence technique [3,4,5] uses data volume slices to interpret faults. The variogram technique [6,7] calculates the optimum time window and sampling point of the variance values to reveal fault information. However, non-geological factors such as noise and seismic acquisition errors cause seismic cophase axis discontinuity, which makes the abovementioned methods very sensitive to them. While detecting faults, some information unrelated to faults will be highlighted. The ant colony algorithm [8,9] searches for fault lines based on a positive feedback mechanism. Edge detection [10,11] highlights continuous and discontinuous information in the profile. The optimal facet vote [12] selects the fault from the attribute image as the optimal path to search for the global maximum. These post-processing methods further strengthen the characteristics of faults in seismic attributes and suppress noise. In recent years, seismic fault interpretation has moved towards automation and artificial intelligence. Fault recognition [13] based on a convolutional neural network [14,15,16,17] continuously optimizes parameters and weights during cyclic training and continuously learns the shallow and deep characteristics of faults in seismic profiles [18]. Finally, the fault recognition model is trained and predicted to achieve the fault recognition effect. However, artificial intelligence still has limitations in its application to seismic data processing and interpretation: (1) Artificial interpretation of faults may be time-consuming and subjective, and inaccurate artificial interpretations may mislead the model learning process [19]. (2) Training and validation of models often require a large number of calibrated seismic images, but it is difficult to obtain large datasets with interpretation results using artificial interpretation. Therefore, the key problem of insufficient calibration datasets must be faced if artificial intelligence interpretation methods are to improve the efficiency of fault identification.

Style transfer can expand datasets by adaptively integrating the style of one image into another and converting the original content to a completely different style. It has been applied in medicine, aviation, remote sensing, animation, film, and television. In medicine, the WaveCT-AIN style transmission framework [20] guides optical image data to learn ultrasonic image data features. The fast style transfer model [21,22] makes optical image and fog data similar in style using a continuous background with no deformation of content. The style transfer network for SAR image conversion to optical images [23] solves the problem of insufficient sample sizes of artificial SAR images. In migrating animation style to optical image data [24,25,26], the generated cartoon image quality is high.

A style transfer network can eliminate huge differences in numerical distributions between optical and seismic image data styles and make them more similar. In this paper, a Laplacian pyramid network was selected to study the stylization of seismic sections. Through cosine similarity optimization, the image style of seismic data was transferred to a common objects in context (COCO) dataset, so that the whole dataset image had the image style of seismic data. At the same time, the distribution characteristics of stylized COCO datasets were similar to those for seismic data. Therefore, the style transfer method provided a richer calibration database for artificial intelligence interpretation algorithms.

2. Materials and Methods

This section mainly introduces the style transfer algorithms based on a convolutional neural network used in image seismic profile experiments and the necessary datasets.

2.1. Style Transfer Algorithm

In this section, we introduce some generative adversarial network (GAN)-based style migration algorithms, with CycleGAN, Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translation (U-GAT-IT) and Lapstyle as representative models. We also describe in detail the algorithmic principles of the models, the application formulas and the losses during training.

2.1.1. CycleGAN

First proposed by Jun-Yan Zhu (2017), CycleGAN [27], GAN is a generative adversarial network that realizes the function of image style conversion between two types of images without a corresponding relationship. As shown in Figure 1, a CycleGAN consists of two symmetric GANs that form a ring network that shares two generators while each carries a discriminator.

The loss included antagonism ${\mathrm{L}}_{\mathrm{GAN}}$ and cyclic consistency loss ${\mathrm{L}}_{\mathrm{cyc}}$. The former ensured that the generator and discriminator mutually evolved to produce more realistic images; the latter that the input and output images had the same content but different styles, because images must be converted between source and target domains. The antagonism is

$${\mathrm{L}}_{\mathrm{GAN}}\left(\mathrm{G},{\mathrm{D}}_{\mathrm{Y}},\mathrm{X},\mathrm{Y}\right)={\mathrm{E}}_{\mathrm{y}~{\mathrm{p}}_{\mathrm{data}}\left(\mathrm{y}\right)}\left[\log {\mathrm{D}}_{\mathrm{Y}}\left(\mathrm{y}\right)\right]+{\mathrm{E}}_{\mathrm{x}~{\mathrm{p}}_{\mathrm{data}}\left(\mathrm{x}\right)}\left[\log (1-{\mathrm{D}}_{\mathrm{Y}}\left(\mathrm{G}\left(\mathrm{x}\right)\right)\right]$$

(1)

During the mapping from X to Y, $\mathrm{G}$ stands for generator and tries to generate an image $\mathrm{G}\left(\mathrm{x}\right)$ that looks similar to the image in the target domain Y, and ${\mathrm{D}}_{\mathrm{Y}}$ distinguishes the generated image$\mathrm{G}\left(\mathrm{x}\right)$ from the real image $\mathrm{y}$. $\log {\mathrm{D}}_{\mathrm{Y}}\left(\mathrm{y}\right)$ is the probability that the discriminator recognized the true data as true data; and $\log (1-{\mathrm{D}}_{\mathrm{Y}}\left(\mathrm{G}\left(\mathrm{x}\right)\right)$ is the probability that the discriminator still recognized the false data generated by the generator as false data. The adversarial loss is the sum of the two. The cyclic consistency loss is

$${\mathrm{L}}_{\mathrm{cyc}}\left(\mathrm{G},\mathrm{F}\right)={\mathrm{E}}_{\mathrm{x}~{\mathrm{p}}_{\mathrm{data}}\left(\mathrm{x}\right)}\left[{\left|\left|\mathrm{F}\left(\mathrm{G}\left(\mathrm{x}\right)\right)-\mathrm{x}\right|\right|}_1\right]+{\mathrm{E}}_{\mathrm{y}~{\mathrm{p}}_{\mathrm{data}}\left(\mathrm{y}\right)}\left[{\left|\left|\mathrm{G}\left(\mathrm{F}\left(\mathrm{y}\right)\right)-\mathrm{y}\right|\right|}_1\right]$$

(2)

where $\mathrm{x}$ and $\mathrm{y}$ are two image domains, $\mathrm{G}$ is the generator of close $\mathrm{y}$ samples; and $\mathrm{F}$ refers to the generator of close $\mathrm{x}$ samples. When we fed $\mathrm{x}$ into $\mathrm{G}$, we got a fake $\mathrm{y}$ graph called $\mathrm{G}\left(\mathrm{x}\right)$. Then we fed $\mathrm{G}\left(\mathrm{x}\right)$ into $\mathrm{F}$ to get an even faker $\mathrm{x}$ graph called $\mathrm{F}\left(\mathrm{G}\left(\mathrm{x}\right)\right)$. This constituted a cycle. $\mathrm{F}\left(\mathrm{G}\left(\mathrm{x}\right)\right)$ was the generated $\mathrm{G}\left(\mathrm{x}\right)$ mapped back to X, and $\mathrm{G}\left(\mathrm{F}\left(\mathrm{y}\right)\right)$ was defined similarly.

2.1.2. U-GAT-IT

Based on CycleGAN, U-GAT-IT [28] adds an adaptive instance (AdaIN) regularization layer to control the style transfer process for image-to-image translation. As shown in Figure 2, the generator carries out image downsampling on the input terminal and combines it with residual blocks to enhance image feature extraction. The attention module is guided by AdaIN to obtain the transformed image by upsampling the residual block. The discriminator converts the decoding process into an authentication output.

The model’s objectives include four loss functions, including antagonistic loss, which are used to match the generated and target image distributions:

$${\mathrm{L}}_{\mathrm{lsgan}}^{\mathrm{s}\to \mathrm{t}}=\left({\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{t}}}\left[{({\mathrm{D}}_{\mathrm{t}}\left(\mathrm{x}\right))}^2\right]+{\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{s}}}\left[{(1-{\mathrm{D}}_{\mathrm{t}}\left({\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)\right))}^2\right]\right)$$

(3)

In the mapping process from source domain $\mathrm{s}$ to target domain $\mathrm{t}$, ${\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)$ refers to the false data generated from source domain $\mathrm{s}$. The probability that the discriminator will still determine the false data generated by the generator in the source domain as false data is given by $1-{\mathrm{D}}_{\mathrm{t}}\left({\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)\right)$. ${\mathrm{D}}_{\mathrm{t}}\left(\mathrm{x}\right)$ is the probability that the discriminator will determine the true data as true data, and the adversarial loss is the sum of the two. Cyclic consistency loss reduced the mapping path from the source to the target domain. Given an image x ∈ ${\mathrm{X}}_{\mathrm{s}}$, after the sequential translations of x from ${\mathrm{X}}_{\mathrm{s}}$ to ${\mathrm{X}}_{\mathrm{t}}$ and from ${\mathrm{X}}_{\mathrm{t}}$ to ${\mathrm{X}}_{\mathrm{s}}$, the image should be successfully translated back to the original domain:

$${\mathrm{L}}_{\mathrm{cycle}}^{\mathrm{s}\to \mathrm{t}}={\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{s}}}\left[|\mathrm{x}-{\mathrm{G}}_{\mathrm{t}\to \mathrm{s}}({\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)){|}_1\right]$$

(4)

where ${\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)$ refers to the false data generated from the source domain $\mathrm{s}$. We fed ${\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)$ into ${\mathrm{G}}_{\mathrm{t}\to \mathrm{s}}$ to get the false data ${\mathrm{G}}_{\mathrm{t}\to \mathrm{s}}({\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right))$, which ideally should be comparable to the $\mathrm{x}$. This constitutes a cycle. We applied an identity consistency constraint to the generator to preserve the consistency of the color composition of the input and output images. Given an image x ∈${\mathrm{X}}_{\mathrm{t}}$, after the translation of x using ${\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}$, the image should not change:

$${\mathrm{L}}_{\mathrm{identity}}^{\mathrm{s}\to \mathrm{t}}={\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{t}}}\left[{\left|\mathrm{x}-{\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)\right|}_1\right]$$

(5)

Class activation map (CAM) loss is the biggest difference between the source and target domain. The auxiliary classifiers ${\mathsf{\eta }}_{\mathrm{s}}$ and ${\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}$ help the generator and discriminator to evolve. For an image x ∈ {${\mathrm{X}}_{\mathrm{s}}$, ${\mathrm{X}}_{\mathrm{t}}$}, ${\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}$ and ${\mathrm{D}}_{\mathrm{t}}$ realize what makes the most difference between the two domains in the current state:

$${\mathrm{L}}_{\mathrm{cam}}^{\mathrm{s}\to \mathrm{t}}=-\left({\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{s}}}\left[\log \left({\mathsf{\eta }}_{\mathrm{s}}\left(\mathrm{x}\right)\right)\right]\right)+{\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{t}}}\left[\log \left(1-{\mathsf{\eta }}_{\mathrm{s}}\left(\mathrm{x}\right)\right)\right]$$

(6)

$${\mathrm{L}}_{\mathrm{cam}}^{{\mathrm{D}}_{\mathrm{t}}}={\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{t}}}\left[{\left({\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}\left(\mathrm{x}\right)\right)}^2\right]+{\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{s}}}\left[(1-{\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}{\left({\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)\right)}^2\right]$$

(7)

${\mathrm{L}}_{\mathrm{cam}}^{\mathrm{s}\to \mathrm{t}}$ refers to the CAM loss of the generator in the source domain. If x is the true data, the cross-entropy output is $-\left({\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{s}}}\left[\log \left({\mathsf{\eta }}_{\mathrm{s}}\left(\mathrm{x}\right)\right)\right]\right)$; if x is the false generated data, the cross-entropy output is ${\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{t}}}\left[\log \left(1-{\mathsf{\eta }}_{\mathrm{s}}\left(\mathrm{x}\right)\right)\right]$. In order to make the generator as false as possible, $-\left({\mathrm{E}}_{\mathrm{x}~{\mathrm{X}}_{\mathrm{s}}}\left[\log \left({\mathsf{\eta }}_{\mathrm{s}}\left(\mathrm{x}\right)\right)\right]\right)$ should be as small as possible. The higher the discriminator’s ability to judge true data and false data, the better. ${\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}\left(\mathrm{x}\right)$ refers to the probability that the auxiliary classifier ${\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}$ collaborated with the discriminator to judge true data as true data as true data, and $1-{\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}\left({\mathrm{G}}_{\mathrm{s}\to \mathrm{t}}\left(\mathrm{x}\right)\right)$ refers to the probability that the auxiliary classifier ${\mathsf{\eta }}_{{\mathrm{D}}_{\mathrm{t}}}$ collaborated with the discriminator to continue to judge false data from the generator in the source domain as false data. The sum of the two, ${\mathrm{L}}_{\mathrm{cam}}^{{\mathrm{D}}_{\mathrm{t}}}$, is the CAM loss in the discriminator from the source domain to the target domain.

2.1.3. Lapstyle

Lapstyle [29] transmits a low-resolution global style mode through a drafting network, revises local details with high resolution through a correction network, and generates image residuals according to the image texture and sketch extracted by a Laplace filter. Higher-resolution details can easily be generated by superimposing revision networks with multiple levels of the Laplacian pyramid. All pyramid-level output is aggregated to obtain the final stylized image, as shown in Figure 3.

The drafting network includes an encoder, several AdaIN modules and a decoder, as shown in Figure 4. The visual geometry group (VGG) encoder extracts corresponding granularity features at layers 2_1, 3_1, and 4_1, feeds them into an AdaIN module for aggregation, and merges them by jumping connection layers.

The revision network modified the rough stylized image by generating a residual detail graph ${\mathrm{r}}_{\mathrm{cs}}$ of the image, and combined it with the rough stylized image ${\stackrel{-}{\mathrm{x}}}_{\mathrm{cs}}$ to generate the final stylized image. As shown in Figure 5, the revision network has a simple, efficient codec architecture with only one undersampling and one upsampling layer. An image block discriminator helps the revision network capture fine block textures under adversarial learning.

During training, the drafting and revision networks optimized the content and style, and the revision network adopted the adversarial loss function. We described the style and content loss and introduced the goals of each network. The Laplacian pyramid network is a single style for a single model during training, keeping one ${\mathrm{x}}_{\mathrm{s}}$ and one set of ${\mathrm{x}}_{\mathrm{c}}$ from the content set ${\mathrm{X}}_{\mathrm{c}}$.

Following the STROTSS method, the rEMD and the commonly used mean-variance loss functions were combined into a style loss function. Given an image, we used the advance training VGG-19 encoder to extract a set of characteristic vectors for $\mathrm{F}=\left\{{\mathrm{F}}^{1\_1},{\mathrm{F}}^{2\_1},{\mathrm{F}}^{3\_1}{\mathrm{F}}^{4\_1},{\mathrm{F}}^{5\_1}\right\}$. The rEMD loss function measured the distance between the characteristic distribution of stylized images ${\mathrm{x}}_{\mathrm{s}}$ and ${\mathrm{x}}_{\mathrm{cs}}$. where $\frac{1}{{\mathrm{h}}_{\mathrm{s}}{\mathrm{w}}_{\mathrm{s}}}{\displaystyle \sum }_{\mathrm{i}=1}^{{\mathrm{h}}_{\mathrm{s}}{\mathrm{w}}_{\mathrm{s}}}\underset{\mathrm{j}}{\min }{\mathrm{C}}_{\mathrm{ij}}$ denoted the distance of fitting the style map with pixels of the image ${\mathrm{x}}_{\mathrm{s}}$ and of the $\frac{1}{{\mathrm{h}}_{\mathrm{cs}}{\mathrm{w}}_{\mathrm{cs}}}{\displaystyle \sum }_{\mathrm{j}=1}^{{\mathrm{h}}_{\mathrm{cs}}{\mathrm{w}}_{\mathrm{cs}}}\underset{\mathrm{i}}{\min }{\mathrm{C}}_{\mathrm{ij}}$ image. A smaller cosine distance term ${\mathrm{C}}_{\mathrm{ij}}$ means that ${\mathrm{x}}_{\mathrm{s}}$ and ${\mathrm{x}}_{\mathrm{cs}}$ are more similar. Assuming that ${\mathrm{F}}_{\mathrm{s}}\in {\mathrm{R}}^{{\mathrm{h}}_{\mathrm{s}}{\mathrm{w}}_{\mathrm{s}}\times \mathrm{c}}$ and ${\mathrm{F}}_{\mathrm{cs}}\in {\mathrm{R}}^{{\mathrm{h}}_{\mathrm{cs}}{\mathrm{w}}_{\mathrm{cs}}\times \mathrm{c}}$ to be the properties of ${\mathrm{x}}_{\mathrm{s}}$ and ${\mathrm{x}}_{\mathrm{cs}}$, respectively, their rEMD losses are calculated as

$${\mathrm{l}}_{\mathrm{r}}=\max \left(\frac{1}{{\mathrm{h}}_{\mathrm{s}}{\mathrm{w}}_{\mathrm{s}}}{\displaystyle \sum }_{\mathrm{i}=1}^{{\mathrm{h}}_{\mathrm{s}}{\mathrm{w}}_{\mathrm{s}}}\underset{\mathrm{j}}{\min }{\mathrm{C}}_{\mathrm{ij}},\frac{1}{{\mathrm{h}}_{\mathrm{cs}}{\mathrm{w}}_{\mathrm{cs}}}{\displaystyle \sum }_{\mathrm{j}=1}^{{\mathrm{h}}_{\mathrm{cs}}{\mathrm{w}}_{\mathrm{cs}}}\underset{\mathrm{i}}{\min }{\mathrm{C}}_{\mathrm{ij}}\right)$$

(8)

The content loss function is adopted between ${\mathrm{F}}_{\mathrm{c}}\in {\mathrm{R}}^{{\mathrm{h}}_{\mathrm{c}}{\mathrm{w}}_{\mathrm{c}}\times \mathrm{c}}$ and ${\mathrm{F}}_{\mathrm{cs}}\in {\mathrm{R}}^{{\mathrm{h}}_{\mathrm{cs}}{\mathrm{w}}_{\mathrm{cs}}\times \mathrm{c}}$ using normalized perceived loss and self-similarity loss.${\mathrm{h}}_{\mathrm{cs}}$ was equal to ${\mathrm{h}}_{\mathrm{c}}$, and${\mathrm{w}}_{\mathrm{c}}$ was equal to ${\mathrm{w}}_{\mathrm{cs}}$, because ${\mathrm{x}}_{\mathrm{c}}$ and ${\mathrm{x}}_{\mathrm{cs}}$ had the same resolution. Perceptual loss is defined as

$${\mathrm{l}}_{\mathrm{p}}={\left|\left|\mathrm{norm}\left({\mathrm{F}}_{\mathrm{c}}\right)-\mathrm{norm}\left({\mathrm{F}}_{\mathrm{cs}}\right)\right|\right|}_2$$

(9)

where $\mathrm{norm}$ represents the normalized channel direction $ℱ$. The purpose of self-similar loss is to maintain the relative relationship between the content and stylized images and is defined as

$${\mathrm{l}}_{\mathrm{ss}}=\frac{1}{{\left({\mathrm{h}}_{\mathrm{c}}{\mathrm{w}}_{\mathrm{c}}\right)}^2}{\displaystyle \sum }_{\mathrm{i},\mathrm{j}}|\frac{{\mathrm{D}}_{\mathrm{ij}}^{\mathrm{c}}}{{{\displaystyle \sum }}_{\mathrm{i}}{\mathrm{D}}_{\mathrm{ij}}^{\mathrm{c}}}-\frac{{\mathrm{D}}_{\mathrm{ij}}^{\mathrm{cs}}}{{{\displaystyle \sum }}_{\mathrm{i}}{\mathrm{D}}_{\mathrm{ij}}^{\mathrm{cs}}}|$$

(10)

where ${\mathrm{D}}_{\mathrm{ij}}^{\mathrm{c}}$ and ${\mathrm{D}}_{\mathrm{ij}}^{\mathrm{cs}}$ are the ${\left(\mathrm{i},\mathrm{j}\right)}^{\mathrm{th}}$ terms of self-similar matrices ${\mathrm{D}}^{\mathrm{c}}$ and ${\mathrm{D}}^{\mathrm{cs}}$, respectively. Here, ${\mathrm{D}}_{\mathrm{ij}}$ is the cosine similarity ${\mathrm{F}}_{\mathrm{i}},{\mathrm{F}}_{\mathrm{j}}$.

In the training stage of the revision network, the parameters of the drafting network were fixed and the training loss was based on ${\mathrm{x}}_{\mathrm{cs}}$. To better learn local fine grain textures, a discriminator was introduced, and a revision network with an antagonistic loss term was trained. The overall loss function is defined as

$$\underset{\mathrm{Rev}}{\min }{\mathrm{L}}_{\mathrm{base}}+\mathsf{\beta }\underset{\mathrm{Rev}}{\min }\underset{\mathrm{D}}{\max }{\mathrm{L}}_{\mathrm{adv}}\left(\mathrm{Rev},\mathrm{D}\right)$$

(11)

where $\mathrm{Rev}$ denotes the revision network, $\mathcal{D}$ denotes the discriminator, and β controls the balance between basic style transfer loss and antagonism loss. ${\mathrm{L}}_{\mathrm{base}}$ is the basic content loss, and ${\mathrm{L}}_{\mathrm{adv}}$ is the standard adversarial training loss.

2.2. Seismic Dataset Preparation

Herein, we discuss the required data, including seismic data, from a work area and the open-source COCO image instance segmentation dataset. The seismic profile classification dataset, shown in Figure 6, contains only seismic profiles and no artificial interpretations to avoid data leakage. These seismic profiles were selected because the faults were less developed, and the alignment of the in-phase axis was clear, thus avoiding ambiguity from the influence of geological structures or data processing. This avoided the influence of faults in the seismic profile classification dataset on the training of the Laplacian pyramid network. The seismic section classification dataset was only used in the image style migration network. We did not need to mark it, as it only provided the unique type, i.e., the seismic data class, used to pre-train the classification network in the style migration network, which this time was used to transfer the global style and local texture of the seismic section. Therefore, after migration, the image only had the sequence texture features of seismic data, and there were no obvious fault features to influence subsequent modeling.

Microsoft Common Objects in Context (MS COCO) is a large, rich, object detection, segmentation, and subtitled dataset that takes scene understanding as the target and is mainly extracted from complex daily scenes. The target in the image is calibrated by precise instance annotation. The dataset includes 91 categories of objects, 328,000 images, and 2.5 million labels. So far, the largest dataset with semantic segmentation has 80 categories and more than 330,000 images of which 200,000 are labeled. Some images are shown in Figure 7.

3. Results

This section focuses on how the three models CycelGAN, U-GAT-IT, and Lapstyle are network trained in seismic image profile stylization. We compared and analyzed the results after stylized mapping both subjectively and objectively and use them to evaluate the quality of the stylized images.

3.1. Network Training of Each Algorithm

In the experiments, CycleGAN and U-GAT-IT were trained on 256 pixels with the parameter batch size set to 1. The Lapstyle experiment had three stages: the drafting network trained on 128 pixels, the revision network trained on 256 pixels with a batch size of 14 and the revision network trained on 512 pixels, with a batch size of 5.

The training results of the drafting network are shown in Figure 8, from which it can be seen that the content and style of the resulting graph were retained globally under the premise of migrating the profile style, so the Lapstyle experiment could be continued.

In the second stage of the experiment, the training weight of the drafting network was added. Five groups of control experiments were set according to the proportional relationship between content and style weights. The style weight was 3.0, 2.0, 1.0, 1.0, 1.0, with corresponding content weights of 1.0, 1.0, 1.0, 2.0, 3.0, as shown in Figure 9.

Figure 9 shows the top part of a woman framed by a red box. From left to right, the shape of the top becomes gradually clearer and the color more prominent. The effect of (f) is similar to that of (e), but in principle the greater the degree of style change the better because the image content can be recognized by the naked eye. Therefore, the migration effect of content weight 2 and style weight 1 was the best for the first modified network training. The training weight was assigned to the second modified network training, and five groups of control experiments were set. Figure 10 shows a woman’s calf framed by a red box. In (c), the outline of the leg is not clear, while in (d), the details of the calf muscle can clearly be seen. Based on the above principles, the migration effect of content weight 1 and style weight 1 were the best in the second revision of network training.

Some of the experimental results are shown in Figure 11, where several representative images were selected to facilitate the comparison of the experimental results. On the whole, it can be seen that the image changed; however, the original content information style of the migrated images changed fundamentally, and their characteristics and backgrounds showed features of the in-phase axis of the seismic section. Figure 11c shows that all seismic profile styles were transferred at low resolution. The image is blurry, and the color of the image content is almost covered by that of the style image. Therefore, modification was carried out, and residual texture details were extracted at high resolution. In Figure 11d, on the basis of the successful migration of the seismic profile style, the color of the woman’s clothes in the beach figure is differentiated; the motorcycle figure is clearly outlined; and the letters in the stamp figure can be identified. The variety and quality of textures in Figure 11e are significantly improved, and the stylistic characteristics of the seismic sections were obtained while preserving the content. The image is clearer, and the overall artistic effect of the visual image has been improved.

Figure 12 shows changes in the mean value of the generator and discriminator loss functions in the training of each network with the MS-COCO dataset transformed by the seismic profile style. Iter is the number of iterations, The Lapstyle and U-GAT-IT algorithms recorded every 3000 steps, and trained 30,000 pieces of data in total. The CycleGAN network generation model was limited by a rate of only 6000 iterations. During the training, the loss function values of CycleGAN, U-GAT-IT and Lapstyle all oscillated within an acceptable range; the convergence was general, and the obtained style transfer model was stable.

3.2. Comparative Analysis of Results

We selected CycleGAN, U-GAT-IT, and Lapstyle for comparative experiments, using the VGG-19 model for network training. The selected target content images were from the COCO dataset, and the style images were from the Yinggehai seismic profile dataset.

Figure 13 shows the effect of the abovementioned style transfer method, and a comparison of the experimental results of sheep, beach, and food. The subjective visual effects of CycleGAN’s experimental results showed that the original content image color was completely covered, and the stylized image lost part of the original content color information, resulting in ambiguity. U-GAT-IT improved upon CycleGAN, and the quality of the generated image obviously improved. In contrast, the stylized images drawn by the Lapstyle method were transformed from the real world into the seismic profile style based on the premise that the original content color and detail information were not lost, and both the overall contour migration and texture detail processing significantly improved.

4. Discussion

It was necessary to evaluate the stylized image quality both subjectively and objectively. Visual observation showed that the Lapstyle style transfer effect was obviously better than that of the other two methods, but there was no unified index for objective evaluation. Therefore, we adopted the widely recognized Structure Similarity Index Measure (SSIM) and an image fusion quality evaluation index called ${\mathrm{Q}}^{\mathrm{AB}/\mathrm{F}}$ [30] to evaluate the quality of the stylized images objectively, and use the running time of an algorithm to evaluate the efficiency of the migration method.

The SSIM measures the similarity of image structures in brightness, contrast, and structure. ${\mathrm{Q}}^{\mathrm{AB}/\mathrm{F}}$ uses local metrics to estimate the performance of input style and content images in the fused image. A higher ${\mathrm{Q}}^{\mathrm{AB}/\mathrm{F}}$ indicates a fused image of better quality.

Figure 14 shows the SSIM, ${\mathrm{Q}}^{\mathrm{AB}/\mathrm{F}}$, and running time of stylized images generated by CycleGAN, U-GAT-IT, and Lapstyle. Compared with CycleGAN and U-GAT-IT, the stylized drawn image from Lapstyle had a higher fusion quality and greater structural similarity to the original image, indicating that its color information had been retained as much as possible and been transformed to the seismic profile style, which has the texture characteristics of the in-phase axis. The average running time of Lapstyle was 6.15 s, which was better than that of CycleGAN or U-GAT-IT (12.20 s and 20.21 s, respectively). Lapstyle also showed a better overall visual effect.

The COCO dataset was uniform in format, rich in content and variety, and suitable for training convolutional neural networks. The results of the seismic profiling style conversion based on the COCO dataset showed that features such as overall contour information and texture detail can be preserved better based on the selection of a suitable migration algorithm. Because the style migration method was based on the computer field of vision, it had a strong similarity to most of the fault interpretations carried out by seismic profiling. Similarly, this method is applicable to the interpretation of special geological phenomena, such as seismic facies or diapir identification, which are visually identified. After the style transfer of the COCO dataset was completed, the semantic segmentation model was trained for the COCO dataset with a stylized seismic profile. The training label maintained the label of the original COCO dataset. After training was completed, the front weight of the semantic segmentation model was frozen, and only the last two weights were retained as the training state. The model structure of the last two layers was modified, and the number of channels in the last layer was changed from 81 to 2. Next, the dataset was replaced by the fault dataset of the target work area from the stylized COCO dataset to reduce the learning rate and to retrain, meaning that only the weights of the last two layers were fine-tuned. After the loss value converged, the fault recognition model of the target work area based on the stylized COCO dataset was obtained. This method solved the problem of insufficient training samples of actual seismic data and provided a feasible solution that could expand the application of artificial intelligence methods in interpreting seismic data.

5. Conclusions

In this paper, we addressed the lack of sufficient training samples for artificial intelligence methods in seismic data interpretation applications, and proposed the use of style migration to convert the image recognition COCO dataset into a seismic profile format. We drew three main conclusions.

• Using a suitable style migration algorithm, the COCO dataset was well migrated into the seismic profile format, which retained the overall contour information and features such as texture details more completely. This result can be used to increase artificial intelligence seismic interpretation training samples and realize the application of artificial intelligence to visually discernable seismic geological interpretation tasks such as fault interpretation, seismic facies interpretation, and special morphological geological body interpretation.
• By comparing the effects of multiple style migration models, the Laplace pyramid network was preferred for carrying out seismic profile stylization research. It transmitted low-resolution global style patterns through the drafting network, corrected high-resolution local details through the correction network, and aggregated all pyramid layers to output a final stylized seismic profile image. Experiments showed that this method ensured that the overall style pattern was effectively transmitted without losing the original image content. It provided theoretical guidance for fast and objective application of the model to learn seismic data features.
• The quality of stylized images was objectively evaluated on two indexes, SSIM and ${\mathrm{Q}}^{\mathrm{AB}/\mathrm{F}}$ and the efficiency of the migration method was evaluated for algorithm running time. Thus, a quantitative evaluation of the good or bad quality of stylized images was achieved.

However, this study was limited to an analysis of the effect of stylized conversion, so further work and discussion are needed before implementing artificial intelligence algorithms combined with the training set of actual seismic interpretation data.