Deep Learning for Seismic Velocity Model Building: An Advanced Approach

A reliable subsurface velocity model is essential for high-resolution seismic imaging, which plays a crucial role in mapping oil and gas reservoirs and understanding their characteristics. While full-waveform inversion (FWI) is a high-accuracy velocity inversion method, it faces challenges such as human interference, strong nonuniqueness, and high computing costs. Deep learning (DL) has emerged as an efficient and accurate nonlinear algorithm for estimating velocity models. However, conventional DL methods often struggle to characterize detailed structures and retrieve complex velocity models.

To overcome these limitations, a hybrid network called AG-ResUnet is proposed, incorporating fully convolutional layers, an attention mechanism, and a residual unit to estimate velocity models from common source point (CSP) gathers. The attention mechanism extracts boundary information, serving as a structural constraint during network training. Additionally, the structural similarity index (SSIM) is integrated into the loss function to minimize the misfit between the predicted velocity and the ground truth.

Introduction to Seismic Imaging and Velocity Models

Seismic imaging is a cornerstone technique in seismic exploration, used to map the structure of oil and gas reservoirs. This mapping helps in inferring reservoir characteristics, such as lithology, fluid properties, and fracture properties. A reliable macro-velocity model is a prerequisite for accurate seismic imaging. Velocity inversion methods include stacking velocity analysis, migration velocity analysis, tomography, and full-waveform inversion.

The Role of Full-Waveform Inversion (FWI)

Full-waveform inversion (FWI) has become a promising method for estimating velocity models of complex structures. FWI aims to build an accurate model by matching the observed and modeled seismic data.

Challenges of FWI

Despite its potential, FWI suffers from strong nonlinearity, high computational cost, and inversion non-uniqueness. Tarantola's time-domain FWI, based on generalized least squares, addresses nonlinearity by linearization. Nonlinear optimization algorithms are used to establish the mapping between seismogram and velocity, acknowledging the nonlinear relationship between velocity and reflection coefficient.

Enhancements to FWI

To improve inversion efficiency, frequency-domain FWI was developed. Multi-scale analysis is used in frequency-domain FWI, where lower frequency information is used to estimate higher frequency components. Laplace-domain FWI addresses the non-uniqueness problem by obtaining the long-wavelength velocity model from a simple initial model.

The Need for Efficient and Robust Methods

The objective function of FWI is strongly nonlinear, leading to the need for efficient and robust methods for velocity inversion. Deep learning (DL) has been successfully applied in computer vision, demonstrating excellent nonlinear processability.

Deep Learning Applications in Seismic Data Processing

DL has been applied in seismic denoising, seismic data reconstruction, seismic data interpretation and attribute analysis, and velocity inversion. In velocity inversion, DL serves as an alternative to FWI with high precision, robustness, and efficiency.

Improving Inversion Resolution with Deep Learning

The loss function, network architecture, and data type are thoroughly studied to improve the inversion resolution of complex stratigraphic boundaries. Local structures and details are mainly impacted by the loss function. Novel loss functions combining structural similarity index (SSIM) and L1 norm improve inversion resolution.

The Significance of SSIM

The SSIM, suitable for the human visual system (HVS), evaluates the similarity of two images through lightness, contrast, and structure. In terms of network architecture, convolutional neural networks (CNN) with conditional random fields (CRF) precisely predict fault structures. Fully connected layers learn spatially aligned feature maps, improving the inversion accuracy of spatial locations of geological targets.

Input Data Considerations

Common source point (CSP) gathers are often used for training networks, but they have weak spatial correspondence with velocity models. Common-imaging point gathers (CIG) have been utilized for network training instead of seismograms, simplifying feature extraction and improving velocity model building.

Limitations of Modern DL Algorithms

Modern DL algorithms improve inversion efficiency and effect but are insufficient to characterize stratigraphic boundaries and geological structures. This study focuses on improving the construction boundary extraction ability of modern DL algorithms.

The AG-ResUnet Hybrid Network

The proposed hybrid network (AG-ResUnet) consists of Unet, residual units, and attention gates. SSIM is introduced to the loss function to precisely estimate geological structure details in the velocity model. Unlike other full reference image quality assessments (FR-IQAs) that focus on pixel value differences, SSIM pays more attention to local structural information, which is crucial in reconstructing structural details.

Training the Hybrid Network

The hybrid network is trained using a mix loss function consisting of mean square error (MSE) and SSIM to optimize each pixel and local patch velocity misfits simultaneously. The training effect of the mix loss function is compared with the MSE loss function to demonstrate the importance of the mix loss function in retrieving local structures.

Demonstrating the Strength of AG-ResUnet

Predictions of AG-ResUnet are compared with other methods (e.g., FWI and other conventional networks). Transfer learning and noisy data inversion experiments are conducted to demonstrate the generalization and robustness of the method. The synthetic examples indicate that the method can provide high-resolution recovery of the complex velocity model, thus significantly improving seismic imaging.

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Methodology: The AG-ResUnet Architecture

The AG-ResUnet network takes CSP gathers as input and outputs the predicted velocity model. It consists of the Unet frame, residual unit, and attention gate (AG).

Unet Architecture

In the Unet architecture, high-resolution features from the encoder combine with the decoder output, avoiding direct supervision and loss computation in high-level feature maps.

Residual Units

To tackle the degradation problem due to vanishing gradients, the residual skip connection is introduced between two non-adjacent layers in the encoder. Residual units allow the network to continue learning new features despite vanishing gradients.

Attention Gates (AG)

AG, an attention mechanism, is employed in feature fusion to adaptively focus on the boundaries between geological targets. This attention mechanism enhances the network's ability to discern and utilize important structural information. The value is higher at geological boundaries.

Loss Function: Combining MSE and SSIM

The loss function is a combination of mean square error (MSE) and structural similarity index (SSIM). MSE minimizes the pixel-wise distance between the output and target but ignores the texture structures.

Importance of Local Structures

Local structures and details are vital factors in recovering velocity models. SSIM is introduced to the loss function to make the network optimization focus on local structural information. It describes the similarity of the two models from the perspective of local structure. Evaluating model similarity with SSIM is known as full reference, meaning that a complete reference label (e.g., reference velocity models) is assumed to be known. The value of SSIM ranges from zero to one, with higher values indicating closer similarity between the predicted velocity model and the ground truth.

Quantitative Metrics for Evaluation

Besides the loss values, three additional metrics are used to evaluate the performance of inversion: SSIM, peak signal-to-noise ratio (PSNR), and coefficient of determination (R2). The range of R2 is generally zero to one. If the velocity inversion model and ground truth are the same, then the value of R2 would be 1.

Experiments and Results

Two kinds of datasets are used in this study: the synthetic salt dome dataset and the Society of Exploration Geophysicists (SEG) published salt dataset.

Data Preparation: Synthetic Salt Dome Dataset

The salt dome is a diapir structure typically associated with oil and gas. Imaging salt structures is necessary for studying reservoir structures. A strategy of random geological modeling is used to build P-wave velocity (Vp) models. An initial model with 5~8 flat layers is generated, and the Gaussian function is utilized to simulate the continuous fluctuation of the stratigraphic interface. The velocity of the first layer is randomly chosen from 1500~1600 m/s. The velocities of the remaining layers gradually increase, with the increment randomly assigned in the range of 150â250 m/s. Finally, a salt dome structure with a fixed velocity of 4000 m/s is added to the flat model. The model has 200 samples in both the x and z directions, with a sampling interval of 10 m.

Data Preparation: SEG Salt Dataset

The SEG data is a 3D pseudo-real salt model built by SEG and the European Society of Geologists and Engineers (EAGE) based on geological data. It is sliced to make 500 independent 2D stratigraphic models. The spatial size and grid interval are the same as those of the synthetic dataset. The velocity ranges from 1500 to 4482 m/s.

Seismic Data Generation

The Ricker wavelet is used as the source wavelet, where is the dominant frequency. The same parameters are used for both datasets. According to the workflow mentioned above, 3000 and 500 pairs of synthetic seismograms are generated from the synthetic and SEG velocity models, respectively.

Network Implementation

The neural network is implemented with PyTorch. Seismograms of six sources corresponding to a synthetic velocity model are fed into the network. The training parameters are documented in Table 2. All experiments are conducted with the same computer configuration. All network training in the study is performed on a GPU, model Tesla V100.

Training and Testing Data Splits

Three thousand pairs of synthetic data are randomly split into two groups: training and test sets, in which there are 2700 and 300 pairs, respectively. The trained AG-ResUnet serves as an initial model to continue training on the SEG dataset in transfer learning. Five hundred pairs of SEG data are randomly split into 400 pairs of the training sets and 100 pairs of test sets. The transfer learning parameters are the same as in Table 2, except the epoch is 100.

Results and Analysis

The experiments aim to demonstrate the effectiveness and efficiency of the proposed AG-ResUnet method for seismic velocity model building.

Optimized Performance of Loss Function

The network optimization effect of the mix loss function from the synthetic dataset is tested. Notice that ground truth is included as the reference. is close to the ground truth. For instance, the layered structure is clearly recovered. have more accurate salt dome boundaries. for the test set are shown in Figure 6.

Quantitative Analysis of Loss Functions

The R2 values of the two loss functions show the same change trend, both close to 1. , while training times for both loss functions are almost the same. improves the inversion accuracy without introducing extra computation. is also used to train other networks in this study.

Qualitative Comparison with Time-Domain FWI

The performance between DL and the traditional inversion method is analyzed by comparing AG-ResUnet and time-domain FWI. The forward parameters of FWI are assigned according to Table 1, and the conjugate gradient optimizer is employed. The inversion comparison based on the synthetic dataset is shown in Figure 7. Compared with the predictions and metrics of FWI, the proposed approach has a more remarkable performance.

Accuracy and Efficiency

The subsurface velocity models from AG-ResUnet are almost the same as the ground truth. The salt dome outline can be easily identified. Although FWI can also retrieve the stratigraphic structure, the resolution is low and structural boundaries are fuzzy.

Computational Efficiency

To compare the efficiency of velocity inversion between FWI and AG-ResUnet, the time consumed by FWI and AG-ResUnet for the training and inversion processes with the synthetic dataset is illustrated. Compared with FWI inversion time, the prediction time of the trained network is only 1.8 s, and the computational efficiency is much higher.

Visualizing Performance with Pseudo-Logging Data

To visualize the performance, the corresponding pseudo-logging data are plotted at the same position. The velocity profiles of AG-ResUnet are nearly identical to the ground truth, but FWI velocity profiles exhibit slight fluctuations. AG-ResUnet is capable of precisely capturing the sudden velocity change.

Comparison with Other Networks

To further demonstrate the superiority of AG-ResUnet for complex model inversion, the approach is compared with the other four DL algorithms, i.e., Unet, ResUnet, PSPnet, and DeepLab v3+, which have excellent ability in the segmentation field. The aforementioned network models are applied to perform network training on synthetic datasets. Predictions in the synthetic dataset are selected to comprehensively compare the performance of algorithms. Generally, the results inverted by each network show relatively uniform and accurate velocity distribution.

Conclusion

The AG-ResUnet hybrid network, incorporating fully convolutional layers, an attention mechanism, and a residual unit, effectively estimates velocity models from common source point (CSP) gathers. The attention mechanism extracts boundary information, serving as a structural constraint during network training. The integration of the structural similarity index (SSIM) into the loss function minimizes the misfit between the predicted velocity and the ground truth.

Advantages of AG-ResUnet

Compared with FWI and other networks, AG-ResUnet is more effective and efficient. Experiments on transfer learning and noisy data inversion demonstrate that AG-ResUnet makes a generalized and robust velocity prediction with rich structural details. The synthetic examples demonstrate that this method can improve seismic velocity inversion, contributing to guiding the imaging of geological structures. The proposed method provides high-resolution recovery of complex velocity models, significantly improving seismic imaging.

tags: #deep #learning #velocity #model #building #seismic