A key challenge of 3-D seismic horizon tracking lies in effectively utilizing the appropriate seismic attributes to enhance tracking precision. Numerous existing horizon tracking methods based on models or deep learning (DL), hinge on mathematical or data-driven mapping relationships between seismic data and the target horizons.This mapping utilizes only seismic data or a single attribute, resulting in inaccurate horizon tracking across discontinuities. As an alternative approach, we propose a multiple attribute regression network (MARN) for 3-D seismic horizon tracking, which leverages multiple seismic attributes to achieve precise and robust tracking results. In this study, we initiate by formulating the problem as a multiple attribute regression model, subsequently the system state equation is introduced to establish temporal relationship. To address this nonlinear regression model, the deep convolutional autoencoder (DCAE), which possesses the capability to automatically learning spatial correlation from attributes, thereby extracting deep features. In this case, these features from DCAE serve as input sequences, enabling long short-term memory (LSTM) to effectively model the spatial-temporal relationships between multiple seismic attributes and target horizons. The proposed MARN is thoroughly compared with the single attribute regression network (SARN) on two real field 3-D datasets.

The volumetric local slope, which indicates the orientation of seismic events, plays a prominent role in the subsequent geological interpretation typically including horizon tracking, seismic facies analysis, and fault interpretation. Although numerous existing estimation methods are available, they still suffer from the challenge of reaching a balance between resolution preservation and resisting the heavy random noise. As an alternative, this letter proposes a seismic volumetric local slope estimation method named the multiscale gradient structure tensor (MGST), combining GST with the 3-D multiscale Gaussian pyramid (GP). In this regard, to preserve the details of the original resolution and fully exploit the unique information at different scales, the GP is reconstructed in 3-D space by decomposing the data into multiple scales. After that, we attempt to employ the GST to derive the local slopes in two directions at each scale, along with a corresponding quality metric. Finally, within the Kalman filter framework, the local slope of each scale is sequentially integrated using the quality metric as the weighting mechanism, resulting in an accurate and robust estimation. Experiments on both synthetic and real field datasets indicate that the proposed MGST method outperforms the traditional GST and plane-wave destruction (PWD) methods.

Random plus footprint noise provokes severe seismic image deterioration and makes it challenging for interpreters to recognize and analyze accurate subsurface responses. Thus, as an elementary and indispensable preprocessing step, diverse footprint removal approaches, including filtering in the frequency or time–frequency domain and dictionary learning (DL), have been documented to achieve promising results in tackling this challenge. However, the prevailing denoising methods tend to treat 3-D seismic data as images for processing, but such flattening or matricization operations inevitably obliterate the 3-D image structures concealed in noisy observational seismic data, which hinders the removal performance of these approaches. To resolve this issue, this article proposes a new tensor model for 3-D seismic random plus footprint noise suppression, and this model is based on unidirectional total variation regularized low-rank tensor approximation (UTV-LRTA). In this model, UTV regularization is imposed to obtain the innately structural and directional behavior of the acquisition footprint. In this way, the footprint is removed by effectively decomposing the footprint-contaminated seismic image into a footprint-free image and a footprint component by UTV. In contrast, random noise is mitigated by regularizing the low rankness of the third-order seismic tensors using the tensor nuclear norm. Moreover, a simple and powerful optimization algorithm based on the split Bregman iteration is introduced to resolve the proposed UTV-LRTA model. The suggested model is thoroughly assessed on synthetic and field datasets and significantly surpasses the state-of-the-art approaches quantitatively and qualitatively evaluated in the analyzed field examples.

Seismic acquisition footprints appear as stably faint and dim structures and emerge fully spatially coherent, causing inevitable damage to useful signals during the suppression process. Various footprint removal methods, including filtering and sparse representation (SR), have been reported to attain promising results for surmounting this challenge. However, these methods, e.g., SR, rely solely on the handcrafted image priors of useful signals, which is sometimes an unreasonable demand if complex geological structures are contained in the given seismic data. As an alternative, this article proposes a footprint removal network (dubbed FR-Net) for the unsupervised suppression of acquired footprints without any assumptions regarding valuable signals. The key to the FR-Net is to design a unidirectional total variation (UTV) model for footprint acquisition according to the intrinsically directional property of noise. By strongly regularizing a deep convolutional autoencoder (DCAE) using the UTV model, our FR-Net transforms the DCAE from an entirely data-driven model to a prior-augmented approach, inheriting the superiority of the DCAE and our footprint model. Subsequently, the complete separation of the footprint noise and useful signals is projected in an unsupervised manner, specifically by optimizing the FR-Net via the backpropagation (BP) algorithm. We provide qualitative and quantitative evaluations conducted on three synthetic and field datasets, demonstrating that our FR-Net surpasses the previous state-of-the-art (SOTA) methods.