Footprint Noise Research Articles

Improved Low-Rank Tensor Approximation for Seismic Random Plus Footprint Noise Suppression

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 three-dimensional 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.

Unsupervised Seismic Footprint Removal With Physical Prior Augmented Deep Autoencoder

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 \textcolor{black}{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.

Statistics-Guided Residual Dictionary Learning for Footprint Noise Removal

The footprint noise is a type of coherent noise that arises from the acquisition geometry. The footprint noise is commonly seen in 3-D seismic volumes and greatly affects the amplitude-based processing and interpretation steps in the seismic exploration workflow. Thus, removal of the footprint noise is necessary for warranting a reliable interpretation output of seismic data processing. However, because footprint noise is usually weak and also spatially coherent, it is inevitable to cause damages to useful signals during its removal steps. Here, we propose a dictionary learning (DL)-based method to effectively remove the footprint noise. We design an algorithm framework to effectively learn the dictionary atoms of the signal waveforms and separate the features of the footprint noise from the learned atoms. Considering the special features of the footprint noise in the dictionary atoms, we propose a statistics-guided way to separate the dictionary atoms into footprint-affected and footprint-free atoms. Then, the footprint-affected atoms are processed via a 2-D median filtering step. The combination between the untouched footprint-free atoms and filtered footprint-affected atoms result in a better dictionary of the signal waveforms and the footprint atoms. We use residual DL to encode the input data by a linear combination of signal atoms and footprint atoms. Removal of footprint atoms and their corresponding sparse coefficients leads to a successful footprint removal. We use both 3-D synthetic and field data examples to demonstrate the effectiveness of the proposed method.

Footprint removal from seismic data with residual dictionary learning

Dictionary learning (DL) is a machine learning technique that can be used to find a sparse representation of a given data set by means of a relatively small set of atoms, which are learned from the input data. DL allows for the removal of random noise from seismic data very effectively. However, when seismic data are contaminated with footprint noise, the atoms of the learned dictionary are often a mixture of data and coherent noise patterns. In this scenario, DL requires carrying out a morphological attribute classification of the atoms to separate the noisy atoms from the dictionary. Instead, we have developed a novel DL strategy for the removal of footprint patterns in 3D seismic data that is based on an augmented dictionary built upon appropriately filtering the learned atoms. The resulting augmented dictionary, which contains the filtered atoms and their residuals, has a high discriminative power in separating signal and footprint atoms, thus precluding the use of any statistical classification strategy to segregate the atoms of the learned dictionary. We filter the atoms using a domain transform filtering approach, a very efficient edge-preserving smoothing algorithm. As in the so-called coherence-constrained DL method, the proposed DL strategy does not require the user to know or adjust the noise level or the sparsity of the solution for each data set. Furthermore, it only requires one pass of DL and is shown to produce successful transfer learning. This increases the speed of the denoising processing because the augmented dictionary does not need to be calculated for each time slice of the input data volume. Results on synthetic and 3D public-domain poststack field data demonstrate effective footprint removal with accurate edge preservation.

Multiparameter deblurring filter and its application to elastic migration and inversion

Different types of model parameters, such as the P- and S-wave velocities, can be coupled to one another in multiparameter seismic inversion. This coupling effect is not taken into account by the conventional approximation to the Hessian inverse for a single type of parameter, and so it can lead to a slow rate of convergence by an iterative inversion method. To solve this problem, we have developed a multiparameter deblurring filter that approximates the Hessian inverse. This filter takes into account the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the different types of parameters. The filters are calculated by matching the reference multiparameter migration images to their reference reflectivity models. Numerical tests with elastic migration and inversion indicate that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude, and increases the resolution of the elastic migration images, but it also mitigates the crosstalk artifacts caused by the coupling effect. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.

Taking seismic acquisition artefacts beyond mitigation

Seismic acquisition footprint is an irritating noise type on the seismic data. This footprint noise is the dominated noise on the seismic stacked data; however, the common practice nowadays is removing them by filtering using 3D FKxKy frequency slice notch filter in pre-stack stage on OVT (offset vector tile) minimal data set in the orthogonal acquisition geometry in particular. Any acquisition footprint noise remnants will definitely hinder the accurate fault and fractures lineament seismic interpretation, since any discontinuities in the seismic might be treated as fractures or faults. Elimination, attenuation, or mitigation of this noise is some sort of compromise in this noise removal. Taking acquisition footprint beyond mitigation to be fully suppressed by applying alternative cascaded processing approach is the main goal of this study.

Exploring the seismic expression of fault zones in 3D seismic volumes

Mapping and understanding distributed deformation is a major challenge for the structural interpretation of seismic data. However, volumes of seismic signal disturbance with low signal/noise ratio are systematically observed within 3D seismic datasets around fault systems. These seismic disturbance zones (SDZ) are commonly characterized by complex perturbations of the signal and occur at the sub-seismic (10 s m) to seismic scale (100 s m). They may store important information on deformation distributed around those larger scale structures that may be readily interpreted in conventional amplitude displays of seismic data. We introduce a method to detect fault-related disturbance zones and to discriminate between this and other noise sources such as those associated with the seismic acquisition (footprint noise). Two case studies from the Taranaki basin and deep-water Niger delta are presented. These resolve SDZs using tensor and semblance attributes along with conventional seismic mapping. The tensor attribute is more efficient in tracking volumes containing structural displacements while structurally-oriented semblance coherency is commonly disturbed by small waveform variations around the fault throw. We propose a workflow to map and cross-plot seismic waveform signal properties extracted from the seismic disturbance zone as a tool to investigate the seismic signature and explore seismic facies of a SDZ.

Atenuación de huella de adquisición guiada por atributos sísmicos

Acquisition footprint, one of the major problems that PEMEX faces in seismic imaging, is noise highly correlated to the geometric array of sources and receivers used for onshore and offshore seismic acquisitions. It prevails in spite of measures taken during acquisition and data processing. This pattern, throughout the image, is easily confused with geological features and misguides seismic attribute computation. In this work, we use seismic data from PEMEX Exploración y Producción to show the conditioning process for removing random and coherent noise using linear filters. Geometric attributes used in a workflow were computed for obtaining an acquisition footprint noise model and adaptively subtract it from the seismic data.

Prestack migration deconvolution

Prestack migration in the time and depth domains is the premier tool for seismic imaging of complex structures. Unfortunately, an undersampled acquisition geometry, a limited recording aperture, and strong velocity contrasts lead to uneven illumination of the subsurface. This results in blurring the migrated image, sometimes referred to as acquisition footprint noise in the migrated image. To remedy this blurring partially, we introduce prestack migration deconvolution (MD). The MD filter is a layered-medium approximation to the inverse Hessian matrix that is applied locally to the migrated section. Both synthetic- and field-data results show noticeable improvements in reducing migration artifacts and increasing lateral spatial resolution by more than 10%. The computational expense for constructing the MD filter is related to the MD operator length. Its cost is about the same as that for migration, but opportunities exist for significantly reducing this cost. Results suggest that MD should be applied to migrated sections to optimize image quality.

High-resolution wave-equation AVA imaging: Algorithm and tests with a data set from the Western Canadian Sedimentary Basin

This paper presents a 3D least-squares wave-equation migration method that yields regularized common-image gathers (CIGs) for amplitude-versus-angle (AVA) analysis. In least-squares migration, we pose seismic imaging as a linear inverse problem; this provides at least two advantages. First, we are able to incorporate model-space weighting operators that improve the amplitude fidelity of CIGs. Second, the influence of improperly sampled data (footprint noise) can be diminished by incorporating data-space weighting operators. To investigate the viability of this class of methods for oil and gas exploration, we test the algorithm with a real-data example from the Western Canadian Sedimentary Basin. To make our problem computationally feasible, we utilize the 3D common-azimuth approximation in the migration algorithm. The inversion algorithm uses the method of conjugate gradients with the addition of a ray-parameter-dependent smoothing constraint that minimizes sampling and aperture artifacts. We show that more robust AVA attributes can be obtained by properly selecting the model and data-space regularization operators. The algorithm is implemented in conjunction with a preconditioning strategy to accelerate convergence. Posing the migration problem as an inverse problem leads to enhanced event continuity in CIGs and, hence, more reliable AVA estimates. The vertical resolution of the inverted image also improves as a consequence of increased coherence in CIGs and, in addition, by implicitly introducing migration deconvolution in the inversion.

Seismic array theorem and rapid calculation of acquisition footprint noise

The acquisition footprint noise in migrated sections partly consists of migration artifacts associated with a discrete recording geometry. Such noise can corrupt the interpretation of seismic sections for stratigraphic variations, AVO signatures, and enhanced oil recovery operations. We show that the point scatterer response of the far‐field Kirchhoff migration operator, which reveals acquisition footprint noise, is proportional to the stretched Fourier transform of the source and geophone sampling function. Using the array theorem developed by optical and electrical engineers, this Fourier transform for an orthogonal recording geometry can be calculated quickly by a product of 1‐D analytical functions. Thus, the acquisition footprint noise in migrated sections can be calculated efficiently for different recording arrays. By rapid trial and error or by an optimization method, the survey planner can use this theorem to help design a better recording geometry.

Least‐squares migration of incomplete reflection data

A least‐squares migration algorithm is presented that reduces the migration artifacts (i.e., recording footprint noise) arising from incomplete data. Instead of migrating data with the adjoint of the forward modeling operator, the normal equations are inverted by using a preconditioned linear conjugate gradient scheme that employs regularization. The modeling operator is constructed from an asymptotic acoustic integral equation, and its adjoint is the Kirchhoff migration operator. We tested the performance of the least‐squares migration on synthetic and field data in the cases of limited recording aperture, coarse sampling, and acquisition gaps in the data. Numerical results show that the least‐squares migrated sections are typically more focused than are the corresponding Kirchhoff migrated sections and their reflectivity frequency distributions are closer to those of the true model frequency distribution. Regularization helps attenuate migration artifacts and provides a sharper, better frequency distribution of estimated reflectivity. The least‐squares migrated sections can be used to predict the missing data traces and interpolate and extrapolate them according to the governing modeling equations. Several field data examples are presented. A ground‐penetrating radar data example demonstrates the suppression of the recording footprint noise due to a limited aperture, a large gap, and an undersampled receiver line. In addition, better fault resolution was achieved after applying least‐squares migration to a poststack marine data set. And a reverse vertical seismic profiling example shows that the recording footprint noise due to a coarse receiver interval can be suppressed by least‐squares migration.