Two-dimensional seismic data reconstruction using patch tensor completion

The 3-D seismic data reconstruction can be understood as an underdetermined inverse problem, and thus, some additional constraints need to be provided to achieve reasonable results. A prevalent scheme in 3-D seismic data reconstruction is to compute the best low-rank approximation of a formulated Hankel matrix by rank-reduction methods with a rank constraint. However, the predefined Hankel structure is easily damaged by the low-rank approximation, which leads to harming its recovery performance. In this article, we present a structured tensor completion (STC) framework to simultaneously exploit both the Hankel structure and the low-tubal-rank constraint to further enhance the performance. Unfortunately, under the assumption of elementwise sampling used by existing methods, STC is intractable to be solved since Hankel constraints cannot be expressed as linear tensor equations. Instead, tubal sampling is proposed to describe the missing trace behavior more accurately and further build a bridge between tensor and matrix completion (MC) to overcome the solving issue in two aspects: through the bridge from tensor to MC, STC can be solved efficiently using MC from random samplings of each frontal slice in the Fourier domain. Through the bridge from matrix to tensor completion, various tensor models within the framework can be developed from noise-specific MC to meet the need for data reconstruction in changeable noise environments. Moreover, alternating-minimization and alternating-direction methods of multipliers are developed to solve the proposed STC. The superior performance of STC is demonstrated in both synthetic and field seismic data.

High‐quality seismic data are crucial for interpreting subsurface structures. Due to economic costs, geological obstacles and other factors, the acquired seismic data are often sampled regularly or irregularly along spatial coordinates. Such incomplete data pose significant challenges to subsequent seismic data processing workflows, making seismic data reconstruction one of the most cost‐effective and critical techniques to address this issue in seismic exploration. While deep learning has yielded promising results in data reconstruction, supervised methods rely heavily on large volumes of labelled seismic data – a resource that is scarce in practical applications. To tackle this limitation, this study proposes a self‐supervised learning method for seismic data reconstruction, incorporating a global‐aware blind‐trace mask mapper and squeeze‐and‐excitation (SE) attention blocks. First, we introduce a global‐aware blind‐trace mask mapper, which mitigates the identity mapping problem in self‐supervised learning frameworks and leverages global information to enable efficient reconstruction. This mapper samples all traces at the blind‐trace positions on the interpolated volume and maps them to the same channel, allowing the loss function to optimize all blind traces simultaneously. Second, we adopt a nested U‐Net (UNet++) architecture integrated with SE attention blocks as the interpolation network, enhancing the model's capacity to capture key features. Third, we guide network training using a hybrid loss function combining mean absolute error and structural similarity index, which captures both fine‐grained details and global structural information to ensure reconstruction quality. Experiments on synthetic and field datasets demonstrate that our method outperforms existing approaches in interpolation accuracy.

The principal objective of seismic exploration is to determine three geologic parameters, the structural top, the bottom, and the lateral extent of an oil and gas reservoir. Conventional (100%) data is very efficient in locating the structural top and bottom of reservoirs. Two-dimensional (2D) common depth point (CDP) seismic data provides an immense improvement in seismic data quality over conventional (100%) data. This improvement enables the explorer to better visualize and map the reservoir in each direction of the seismic line. Three-dimensional (3D) seismic technology provides even more mappable data and capability. The explorer may visualize every imaginable direction and subtlety of a reservoir. This talk compares conventional (100%), two-dimensional (2D), and three-dimensional (3D) seismic data from the Midcontinent. Case histories of the Douglass (Upper Pennsylvanian) in Texas, the Morrow (Lower Pennsylvanian) in Colorado, the {open_quotes}Chat{close_quotes} (Mississippian) and the Hunton (Silurian-Devonian) in Oklahoma, and the Simpson (Ordovician) in Kansas will be discussed. Major and independent operators can maximize their exploration efforts by integrating existing data with three-dimensional (3D) technology and a solid geologic interpretation.

Seismic data incorporation in reservoir simulation models history matching (HM) studies has been continuously growing. 4D seismic data, in contrast with well production data, can provide a very good scenario of fluids arrangement along reservoir. In this work we describe how 3D and 4D seismic data gathered in acquisitions performed in Campos Basin was incorporated in Marlim Sul deep water field geological model reconstruction and in assisted HM (AHM). It is taken advantage of both 3D and 4D seismic data in several stages of the study, for instance, in the construction of a new porosity – most influential in impedance – model by using a methodology based on the inversion of synthetic seismic (calculated by petro-elastic model) in porosity through an optimization process that aims to reduce the difference between observed and synthetic impedance, and when defining influential parameters based on fluids displacement registered by seismic signal, by using a technique based on the creation of transmissibility multipliers parameters regions that considers the fluids displacement shown in 4D signal. Another relevant point is the use of information from reservoir and 3D seismic data when weighting the 4D data in the objective function. Combining the above mentioned techniques with the knowledge of the field – supported by the 3D seismic data – which allowed, for instance, identification of faults – where fault transmissibility multipliers were used as parameters in the HM process – a fairly good agreement on the observed well and seismic production data was achieved. HM studies using AHM tools have been shown a much more time-efficient technique when compared to manual HM. The incorporation of 4D seismic data can considerably improve the HM quality by improving the reservoir description, once it increases the ability of describing fluids arrangement and pressure distribution. The techniques successfully applied in the Marlim Sul field HM support these conclusions.

Relevance of the work. The paper considers challenging problems related with outlining of intervals with oil and gas presence in the mature Khylly field by use of latest 3D seismic survey techniques in order to gain larger crude resources base. The purpose of this research is to discover the most promising intervals of target horizons with relatively high reservoir properties outlined by 3D seismic data. The subjects of research are 3D seismic survey data, downhole seismic survey – Vertical Seismic Profiling (VSP) and well logging diagrams. The object of research is the Khylly deposit. The paper describes in brief geological and geophysical characteristics, stratigraphic and lithological features of rocks making the section. It is noted that despite repeated surveys by use of various geological and geophysical techniques, the field setting is not thoroughly studied and it has been covered by 3D seismic survey in 2012. Research results. 3D seismic survey applied across Khylly area is resulted in drawing of 4 structural maps for III and I horizons of Productive Series (PS), Akchagyl and Lower Absheron suites. Taking into account the relevance of structural planes of various stratigraphic levels and III horizon of PS being one of the major reference horizons the paper gives description of structural map drawn for this horizon. The detailed velocity model is designed based on VSP data with wide use of velocity analysis data. It has been made clear that Khylly area has block structure and each block has been described in detail. Based on acquired data it has been recommended to drill exploratory well R-1. Conclusion. Processing and interpretation of seismic data are aimed at solving some geological problems; the main task was to obtain results that ensure the study of the geological structure in the seismic survey area, including tracing of seismic horizons, faults and outlining the areas and section intervals which may be of interest due to possible oil and gas presence. VSP data acquired in well 2012 and velocity analysis made it possible to design velocity model of the section under the study, with the use of which the temporary 3D cube was transformed into a depth cube. The quality of seismic data is good and made it possible to solve the tasks set for this research.

Tensor completion via multi-shared-modes canonical correlation analysis

The Canning Basin is a largely unexposed and underexplored frontier basin, formed mostly in the Paleozoic. Geological knowledge of this basin is based predominantly on sparse regional “vintage” two-dimensional seismic and small three-dimensional (3-D) seismic surveys and less than 230 exploration wells. Following seismic interpretation, an integrated interpretation was completed on airborne gravity gradiometer (AGG), magnetic, seismic, well, and complementary data along the southwestern margin of the Fitzroy trough and Gregory subbasin. Seismic data were reinterpreted using AGG data to produce a better constrained geological model. A basement structure map, two intrasedimentary structure maps, and a formation distribution map were produced. The interpretation of seismic profiles, validated through 2.5-dimensional gravity gradiometer modeling, is essential to this workflow. Repeatedly reactivated west–northwest and northwest structural trends, inherited from Proterozoic orogenies, respectively delineate the Fitzroy trough and the Gregory subbasin with its northwestern structural extension into the Fitzroy trough, the Gregory subbasin trend. Subsidence occurred during two periods of extension. An asymmetric extensional system of the Fitzroy trough controlled Ordovician–Silurian deposition of the Carribuddy Group. Devonian–Carboniferous subsidence defines the Gregory subbasin trend. This Pillara extension reactivated structures in the east of the Fitzroy trough. Simultaneous activity of both extensional fault systems and growth faulting controlled the facies and thickness distribution of carbonates and clastics of the early Carboniferous Fairfield Group. The Meda and Fitzroy transpressional phases inverted faults of the Gregory subbasin trend and Fitzroy trough, producing prospects by structural interference. The improved understanding of tectono-stratigraphic relationships, including the 3-D distribution of carbonate reservoirs, benefited the planning of seismic surveys, prospect evaluation, drilling, and acreage relinquishment.

Monitoring the performance of a large network would involve a high measurement cost. To reduce the overhead, sparse network monitoring techniques may be applied to select paths or time intervals to take the measurements, while the remaining monitoring data can be inferred leveraging the spatial-temporal correlations among data. The quality of missing data recovery, however, highly relies on the specific inference technique adopted. Tensor completion is a promising technique for more accurate missing data inference by exploiting the multi-dimensional data structure. However, data processing for higher dimensional tensors involves a large amount of computation, which prevents conventional tensor completion algorithms from practical application in the presence of large amount of data. This work takes the initiative to investigate the potential and methodologies of performing parallel processing for high-speed and high accuracy tensor completion over Graphics Processing Units (GPUs). We propose a GPU-accelerated parallel Tensor Completion scheme (GPU-TC) for accurate and fast recovery of missing data. To improve the data recovery accuracy and speed, we propose three novel techniques to well exploit the tensor factorization structure and the GPU features: grid-based tensor partition, independent task assignment based on Fisher-Yates shuffle, sphere facilitated and memory-correlated scheduling. We have conducted extensive experiments using network traffic trace data to compare the proposed GPU-TC with the state of art tensor completion algorithms and matrix-based algorithms. The experimental results demonstrate that GPU-TC can achieve significantly better performance in terms of two relative error ratio metrics and computation time.

Abstract. Seismic oceanography is a new cross-discipline between geophysics and oceanography that uses seismic reflection data to image and study the oceanic water column. Previous work on seismic oceanography was largely limited to two-dimensional (2D) seismic data and methods. Here we explore and quantify temporal and spatial variations in three-dimensional (3D) seismic oceanography to address whether 3D seismic imaging is meaningful in all directions and how one can take advantage of the variations. From a 3D multichannel seismic survey acquired for oil and gas exploration in the Gulf of Mexico over a 6-month period, a 3D oceanic seismic volume was derived. The 3D seismic images exhibit both temporal and spatial variations of the ocean, and theoretical and data analyses were used to quantify their contribution. Our results suggest that temporal variation is more prominent in the crossline direction than in the inline direction, causing discontinuities in crossline images. However, a series of 3D inline images can be seen as snapshots of the water column at different times, capturing temporal variation of thermohaline structures induced by ocean dynamics. Our findings suggest the potential uses of marine 3D seismic data in studying time-evolving mesoscale ocean dynamics.

Seismic impedance inversion is a geophysical technique that transforms seismic data into quantitative subsurface properties, primarily acoustic impedance. This process enables the identification of rock boundaries, hydrocarbon reservoirs, and lithological variations, thus supporting informed drilling decisions and reducing exploration risks. However, conventional inversion methods face limitations such as noise sensitivity, low resolution, and reduced effectiveness in geologically complex areas, often resulting in oversimplified subsurface models. This study addresses these challenges by employing deep learning approaches, specifically LeNet, AlexNet, and conventional CNN architectures, to improve seismic resolution and synthetic seismogram generation. The methodology involves preprocessing seismic and well-log data, calculating acoustic impedance and reflection coefficients, and applying Continuous Wavelet Transform (CWT) for feature extraction. The models are trained using synthetic seismograms and validated against real seismic data. Among the models evaluated, AlexNet demonstrates superior performance in seismic data reconstruction, achieving the lowest MSE (0.0031), RMSE (0.0557), and MAE (0.052), along with the highest R2 score (0.993). The proposed technique demonstrates superior predictive accuracy, refined subsurface characterization, and reduced geological risk, thereby establishing a robust benchmark for advanced geophysical data analysis.

In some oilfield where 3D seismic survey has been done, the deeper structure cannot be discovered for poor deep seismic data. Layer stripping technique applied both seismic and gravity data is a solution, but it cannot get satisfied processing effect because the horizontal variation of formation density is ignored. To improve the gravity survey effect in 3D seismic survey area, this paper presents the formation separation technique. Based on 3D seismic depth data and the transformed density data from 3D seismic velocity data, the upper formation's gravity effects are calculated and removed from Bouguer gravity and then the formation‐separated gravity‐anomaly was obtained, which mainly reflects the deeper geological structure. In block XX, the seismic data of shallow formations are excellent but that of top of basement are poor. The formation‐separated gravity‐anomaly processed under the control of 3D seismic data fits well with the known seismic interpretation and wells. It makes the geological interpretation more reliable

With the advance of acquisition techniques, plentiful higherorder tensor data sets are built up in a great variety of fields such as computer vision, neuroscience, remote sensing and recommender systems. The real-world tensors often contain missing values, which makes tensor completion become a prerequisite to utilize them. Previous studies have shown that imposing a low-rank constraint on tensor completion produces impressive performances. In this paper, we argue that low-rank constraint, albeit useful, is not effective enough to exploit the local smooth and piecewise priors of visual data. We propose integrating total variation into low-rank tensor completion (LRTC) to address the drawback. As LRTC can be formulated by both tensor unfolding and tensor decomposition, we develop correspondingly two methods, namely LRTC-TV-I and LRTC-TVII, and their iterative solvers. Extensive experimental results on color image and medical image inpainting tasks show the effectiveness and superiority of the two methods against state-of-the-art competitors.

The growth, interaction and controls of gravity-driven normal faults is somewhat understudied. Using three-dimensional (3D) and two-dimensional (2D) seismic reflection data, located at the present-day shelf-edge break and into the deepwater province of the Otway Basin, southern Australia, we aim to temporally and spatially constrain the development of a normal fault system and determine the controls on growth. The Otway Basin is a Late Jurassic to Cenozoic age, rift-to-passive margin basin. The seismic reflection data images a gravity-driven fault array, consisting of ten fault segments, striking NW-SE (128-308), located within Upper Cretaceous clastic sedimentary rock. We analyse the growth of a gravity-driven hard-linked fault assemblage interacting with basement normal faults. Our analysis shows that the fault assemblage is linked to major basement faults and displays Turonian-Santonian nucleation, continued growth until the latest-Maastrichtian and a maximum throw of 1.74 km. High variability of throw along-strike and down-dip of the fault assemblage indicates growth via lateral and vertical segment linkage. We interpret that the spatial and temporal evolution of the fault assemblage is the result of rifting basement fault control during Upper Cretaceous resumed crustal extension in the Otway Basin. The control of the rifting basement faults on these gravity-driven normal faults has implications towards the growth and petroleum prospectivity of gravity-driven normal faults on passive margins such as the Niger Delta and Gulf of Mexico, but also towards gravity-driven normal faults developed in supra-salt sedimentary rock in rift basins, such as the North Sea and Suez Rift.

Low-rank tensor completion (LRTC) has gained significant attention due to its powerful capability of recovering missing entries. However, it has to repeatedly calculate the time-consuming singular value decomposition (SVD). To address this drawback, we, based on the tensor-tensor product (t-product), propose a new LRTC method-the unified tensor factorization (UTF)-for 3-way tensor completion. We first integrate the tensor factorization (TF) and the tensor nuclear norm (TNN) regularization into a framework that inherits the benefits of both TF and TNN: fast calculation and convex optimization. The conditions under which TF and TNN are equivalent are analyzed. Then, UTF for tensor completion is presented and an efficient iterative updated algorithm based on the alternate direction method of multipliers (ADMM) is used for our UTF optimization, and the solution of the proposed alternate minimization algorithm is also proven to be able to converge to a Karush–Kuhn–Tucker (KKT) point. Finally, numerical experiments on synthetic data completion and image/video inpainting tasks demonstrate the effectiveness of our method over other state-of-the-art tensor completion methods.

Seismic data offer valuable spatial information that contributes to the development strategy, such as drilling decisions and well planning. Inverting 3D seismic reflectivity data to impedance unlocks the potential of using seismic data to estimate the lateral variability and to predict reservoir geomechanical behaviour. The geomechanical model contributes for the evaluation of wellbore stability, frackability and drilling direction. The objective of this work is to illustrate the use of seismic derived models for reservoir and geomechanical properties, such as total porosity, total organic carbon (TOC) and rock rigidity. These properties are instrumental to characterize tight reservoirs and useful tools for defining a horizontal well trajectory.The study area has an exploration potential of unconventional reservoirs, targeting tight carbonates from Upper Jurassic. To date, only one well has been drilled in the area of the interest and high quality 3D seismic data is available. The process consists of conducting seismic inversion, using the well and the 3D PSTM seismic data, and resulting in the generation of 3D subsurface impedance model. The well-log relationships between impedance and reservoir quality (effective porosity, source richness) and completion quality (brittleness) were determined and showed high correlation. Hence, 3D rock quality and geomechanical volumes were derived to characterize the behaviour of the reservoir target.Seismic derived properties models yield a better description of the reservoir heterogeneity than using seismic reflectivity data only. The horizontal well trajectory was planned taking into account the observed and significant lateral variability revealed by the 3D models estimated based on seismic inverted data.The results obtained using this methodology demonstrate the importance of integrating geophysical characterisation as a relevant supporting factor in the drilling decision making process. In particular, it validates the use of seismic derived reservoir and completion quality models as an additional tool in the definition of a horizontal well trajectory in a tight/unconventional deep gas target.