ALBERT

Description: State-of-the-art next-generation sequencing, transcriptomics, proteomics and other high-throughput ‘omics' technologies enable the efficient generation of large experimental data sets. These data may yield unprecedented knowledge about molecular pathways in cells and their role in disease. Dimension reduction approaches have been widely used in exploratory analysis of single omics data sets. This review will focus on dimension reduction approaches for simultaneous exploratory analyses of multiple data sets. These methods extract the linear relationships that best explain the correlated structure across data sets, the variability both within and between variables (or observations) and may highlight data issues such as batch effects or outliers. We explore dimension reduction techniques as one of the emerging approaches for data integration, and how these can be applied to increase our understanding of biological systems in normal physiological function and disease.

Description: 〈span〉〈div〉Summary〈/div〉Full waveform inversion (FWI) is a nonlinear waveform matching procedure, which suffers from cycle skipping when the initial model is not kinematically-accurate enough. To mitigate cycle skipping, wavefield reconstruction inversion (WRI) extends the inversion search space by computing wavefields with a relaxation of the wave equation in order to fit the data from the first iteration. Then, the subsurface parameters are updated by minimizing the source residuals the relaxation generated. Capitalizing on the wave-equation bilinearity, performing wavefield reconstruction and parameter estimation in alternating mode decomposes WRI into two linear subproblems, which can solved efficiently with the alternating-direction method of multiplier (ADMM), leading to the so-called iteratively refined wavefield reconstruction inversion (IR-WRI). Moreover, ADMM provides a suitable framework to implement bound constraints and different types of regularizations and their mixture in IR-WRI. Here, IR-WRI is extended to multiparameter reconstruction for VTI acoustic media. To achieve this goal, we first propose different forms of bilinear VTI acoustic wave equation. We develop more specifically IR-WRI for the one that relies on a parametrisation involving vertical wavespeed and Thomsen’s parameters δ and ε. With a toy numerical example, we first show that the radiation patterns of the virtual sources generate similar wavenumber filtering and parameter cross-talks in classical FWI and IR-WRI. Bound constraints and TV regularization in IR-WRI fully remove these undesired effects for an idealized piecewise constant target. We show with a more realistic long-offset case study representative of the North Sea that anisotropic IR-WRI successfully reconstruct the vertical wavespeed starting from a laterally homogeneous model and update the long-wavelengths of the starting ε model, while a smooth δ model is used as a passive background model. VTI acoustic IR-WRI can be alternatively performed with subsurface parametrisations involving stiffness or compliance coefficients or normal moveout velocities and η parameter (or horizontal velocity).〈/span〉

Description: 〈span〉〈div〉ABSTRACT〈/div〉Seismic velocity analysis is one of the most crucial and, at the same time, the most laborious tasks during seismic data processing. This becomes even more difficult and time-consuming when nonhyperbolicity has to be considered in the velocity analysis. Nonhyperbolic velocity analysis provides very useful information during the processing and interpretation of seismic data. The most common approach for considering anisotropy during velocity analysis is to describe the moveout based on a nonhyperbolic equation. The nonhyperbolic moveout equation in vertically transverse isotropic (VTI) media is defined by two parameters: normal moveout (NMO) velocity VNMO and anellipticity η (or horizontal velocity Vhor). We have developed a new approach based on polynomial chaos (PC) expansion for automating nonhyperbolic velocity analysis of common-midpoint (CMP) data in VTI media. For this purpose, we use the PC expansion to approximate the nonhyperbolic semblance function with a very fast-to-simulate function in terms of VNMO and Vhor. Then, using particle swarm optimization, we stochastically look for the optimum NMO and horizontal velocities that provide the maximum semblance. In contrary to common approaches for nonhyperbolic velocity analysis in which the two parameters are estimated iteratively in an alternating fashion, we find VNMO and Vhor simultaneously. This approach is tested on various data including a simple convolutional model, an anisotropic benchmark model, and a real data set. In all cases, the new method provided acceptable results. Reflections in the CMP corrected using the optimum velocities are properly flattened, and almost no residual moveout is observed.〈/span〉

Description: 〈span〉〈div〉ABSTRACT〈/div〉Given the ill-conditioned nature of Dix inversion, the resultant Dix interval-velocity field is often unrealistic, noisy, and highly dependent on the quality of the provided root-mean-square velocities. While the classic least-squares regularization techniques, e.g., various forms of Tikhonov regularization, lead to somewhat suboptimal stability, we formulated the Dix inversion as a new constrained optimization problem. This enables one to incorporate prior knowledge as soft and/or hard bounds for the optimization, effectively treating it as a denoising problem. The solution to the problem is achieved by a bound-constrained total variation (TV) regularization. TV regularization has the advantage of being able to recover the discontinuities in the model, but it often comes with a large memory and compute requirements. Therefore, we have developed a simple and memory-efficient algorithm using iterative refinement strategy. The quality of the new algorithm is also cross-examined against different strategies, which are currently used in practice. Overall, we observe that the proposed method outperforms classic Dix inversion methods on the synthetic and real data examples.〈/span〉

Description: Residual statics estimation in complex areas is one of the main challenging problems in seismic data processing. It is well known that the result of this processing step has a profound effect on the quality of final reconstructed image. A novel method is presented to compensate for surface-consistent residual static corrections based on sparsity maximization, which has proved to be a powerful tool in the analysis and processing of signals and related problems. The method is based on the hypothesis that residual static time shift represents itself by noise-like features in the Fourier or curvelet domain. Residual time shift corrections are then retrieved by optimizing the sparsity in these domains. Here, the statics model is considered as a maximizer of $${\ell }_{p}$$ -norm ( $$p 〉 2$$ ) of the data coefficients in the sparse domain, and a fast and efficient algorithm is presented to iteratively solve the corresponding nonlinear optimization problem. Applications on synthetic and real data show very high performance of the presented algorithm.

Description: 〈span〉〈div〉SUMMARY〈/div〉Full-waveform inversion (FWI) is a waveform matching procedure, which can provide a subsurface model with a wavelength-scale resolution. However, this high resolution makes FWI prone to cycle skipping, which drives the inversion to a local minimum when the initial model is not accurate enough. Other sources of non-linearities and ill-posedness are noise, uneven illumination, approximate wave physics and parameter cross-talks. All these sources of error require robust and versatile regularized optimization approaches to mitigate their imprint on FWI while preserving its intrinsic resolution power. To achieve this goal, we implement bound constraints and total-variation (TV) regularization in the so-called frequency-domain wavefield reconstruction inversion (WRI) with the alternating direction method of multipliers (ADMM). In the ADMM framework, WRI relies on an augmented Lagrangian function, a combination of penalty and Lagrangian functions, to extend the FWI search space by relaxing the wave-equation constraint during early iterations. Moreover, ADMM breaks down the joint wavefield reconstruction plus parameter-estimation problem into a sequence of two linear subproblems, whose solutions are coordinated to provide the solution of the global problem. The decomposability of ADMM is further exploited to interface in a straightforward way bound constraints and TV regularization with WRI via variable splitting and proximal operators. The resilience of our regularized WRI formulation to cycle skipping and noise as well as its resolution power are illustrated with two targets of the large-contrast BP salt model. Starting from a 3Hz frequency and a crude initial model, the extended search space allows for the reconstruction of the salt and subsalt structures with a high fidelity. The TV regularization filters out the imprint of ambient noise and artefacts associated with multiscattering and Gibbs effects, while fostering large-contrast reconstruction. Compared to other TV-regularized WRI implementations, the proposed method is easy to tune due to its moderate sensitivity to penalty parameters and does not require a prior guess of the TV-norm ball.〈/span〉

Description: Different types of regularization have been developed to obtain stable solutions to linear inverse problems. Among these, total variation (TV) is known as an edge preserver method, which leads to piecewise constant solutions and has received much attention for solving inverse problems arising in geophysical studies. However, the method shows staircase effects and is not suitable for the models including smooth regions. To overcome the staircase effect, we present a method, which employs a local-order difference operator in the regularization term. This method is performed in two steps: First, we apply a pre-processing step to find the edge locations in the regularized solution using a properly defined minmod limiter, where the edges are determined by a comparison of the solutions obtained using different order regularizations of the TV types. Then, we construct a local-order difference operator based on the information obtained from the pre-processing step about the edge locations, which is subsequently used as a regularization operator in the final sparsity-promoting regularization. Experimental results from the synthetic and real seismic traveltime tomography show that the proposed inversion method is able to retain the smooth regions of the regularized solution, while preserving sharp transitions presented in it.

Description: Permeability is a key parameter associated with the characterization of any hydrocarbon reservoir. In fact, it is not possible to have accurate solutions to many petroleum engineering problems without having accurate permeability value. The conventional methods for permeability determination are core analysis and well test techniques. These methods are very expensive and time consuming. Therefore, attempts have usually been carried out to use artificial neural network for identification of the relationship between the well log data and core permeability. In this way, recent works on artificial intelligence techniques have led to introduce a robust machine learning methodology called support vector machine. This paper aims to utilize the SVM for predicting the permeability of three gas wells in the Southern Pars field. Obtained results of SVM showed that the correlation coefficient between core and predicted permeability is 0.97 for testing dataset. Comparing the result of SVM with that of a general regression neural network (GRNN) revealed that the SVM approach is faster and more accurate than the GRNN in prediction of hydrocarbon reservoirs permeability.