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In the past decade, deep learning algorithms gained a remarkable interest in the signal processing community. The availability of big datasets and advanced computational resources resulted in developing efficient algorithms. However, such algorithms are biased towards the training dataset. Thus, the transferability of deep-learning-based operators are challenging, especially when the goal is to apply the learned operator on a new dataset/domain. Lack of transferability of learned operator across domains hinders the applicability of deep learning algorithms in processing seismic data. Unlike camera images, the comprehensively labeled seismic datasets are not available. Moreover, from one task to another, the training parameters should be tuned. To remedy this shortcoming, we have developed a workflow that transfers the learned operator from the camera images to the seismic domain, without modifying its training parameters. The similarities in the algorithms and optimization methods in camera and seismic data processing allow us to do so. Accordingly, by incorporating feed-forward de-noising convolutional neural networks (DnCNN) in regularization by de-noising regularizer, we formulate two transferable optimization problems for de-noising and compressive sensing recovery of seismic data. Simulated and real-world data examples show the efficiency of our proposed workflow., Comment: 8 pages, 5 figures, one table

Least-squares migration can, in theory, reduce the acquisition footprint and improve the illumination of the subsurface structures. It can also recover the amplitudes of the events to some extent. However, the migration operator is not complete. In other words, the operator does not span the full range of the model and the portion of the model that is in the null space of the operator will not be recovered even by posing imaging as an inverse problem. In geophysical terminology, in complex subsurface structures, rays or the wave energy will penetrate poorly in some regions, e.g., subsalt region, and that region will be a shadow zone to our acquisition system. The shadow zone is in the null space of the migration operator and the subsurface information in that region will not be recovered. Accordingly, in this research, we aim at using another set of data whose ray paths are different from the surface seismic. Seismic-while-drilling (SWD) dataset are complementary to surface data, and it brings an opportunity to address seismic illumination issue by adding new measurements into the imaging problem. After considering the correlative and non-impulsive nature of the SWD source signature, the prestack least-squares depth migration of the SWD dataset can be achieved. We study the feasibility of the least-squares reverse time migration of the SWD dataset and its potential in imaging the parts of the model which are in the shadow zone of the surface seismic acquisition., Comment: CSPG CSEG CWLS Convention

Recursive estimates of large systems of equations in the context of least squares fitting is a common practice in different fields of study. For example, recursive adaptive filtering is extensively used in signal processing and control applications. The necessity of solving least squares problem via recursive algorithms comes from the need of fast real-time signal processing strategies. Computational cost of using least squares algorithm could also limits the applicability of this technique in geophysical problems. In this paper, we consider recursive least squares solution for wave equation least squares migration with sliding windows involving several rank K downdating and updating computations. This technique can be applied for dynamic and stationary processes. One can show that in the case of stationary processes, the spectrum of the preconditioned system is clustered around one and the method will converge superlinearly with probability one, if we use enough data in each windowed setup. Numerical experiments are reported in order to illustrate the effectiveness of the technique for least squares migration., Comment: CSPG CSEG CWLS Convention

This paper develops a Statics Preserving Sparse Radon transform (SPSR) algorithm.The de-coloration power of Radon basis functions depends on different factors. The most important one is statics. Statics decrease the sparsity of Radon models. To tackle this problem, it is necessary to include statics into the Radon bases functions. SPSR algorithm includes statics into the Radon bases functions, allowing for a sparse representation of statics contaminated data in the Radon domain. SPSR algorithm formulated as an $L_2- L_1$ optimization problem and solved via alternating minimization method. Real data examples used to test the performance of the proposed method in multiple and noise attenuation in the presence of statics., Comment: CSPG CSEG CWLS Convention

Seismic waves bring information from the physical properties of the earth to the surface. Full waveform inversion (FWI) is a local optimization technique which tries to invert the recorded wave fields to the physical properties. An efficient forward-modelling engine along with local differential algorithm, to compute the gradient and Hessian operators, are two key ingredients of FWI approach. FWI can be done in time or frequency domain. Each method has its own pros and cons. Here, we only discuss frequency domain method with Krylov subspace solvers for time-harmonic wave equation. Nonlinearity of the problem requires good initial macro model of the physical properties and low frequency data. Macro models are built based on the kinematic information of the recorded wave fields. Another difficulty is the data modelling algorithm which is hard to solve especially for high wavenumbers (high frequencies). Without incorporation of high frequencies in the FWI algorithm we are not going to be able to update the macro models to high resolution ones. In the companion paper we showed that efficient forward modelling algorithms can be reached via proper preconditioners. Here, we will use the preconditioned data modelling engine in the context of local optimization method to solve for model parameters. The results show that we yield better convergence of the method and better quality of the inverted models after using the preconditioned FWI., Comment: CSPG CSEG CWLS Convention

In several geophysical applications, such as full waveform inversion and data modelling, we are facing the solution of inhomogeneous Helmholtz equation. The difficulties of solving the Helmholtz equa- tion are two fold. Firstly, in the case of large scale problems we cannot calculate the inverse of the Helmholtz operator directly. Hence, iterative algorithms should be implemented. Secondly, the Helmholtz operator is non-unitary and non-diagonalizable which in turn deteriorates the performances of the iterative algorithms (especially for high wavenumbers). To overcome this issue, we need to im- plement proper preconditioners for a Krylov subspace method to solve the problem efficiently. In this paper we incorporated shifted-Laplace operators to precondition the system of equations and then generalized minimal residual (GMRES) method used to solve the problem iteratively. The numerical results show the performance of the preconditioning operator in improving the convergence rate of the GMRES algorithm for data modelling case. In the companion paper we discussed the application of preconditioned data modelling algorithm in the context of frequency domain full waveform inversion. However, the analysis of the degree of suitability of the preconditioners in the solution of Helmholtz equation is an ongoing field of study., Comment: CSPG CSEG CWLS Convention