A B S T R A C TThis paper presents a Lebedev finite difference scheme on staggered grids for the numerical simulation of wave propagation in an arbitrary 3D anisotropic elastic media. The main concept of the scheme is the definition of all the components of each tensor (vector) appearing in the elastic wave equation at the corresponding grid points, i.e., all of the stresses are stored in one set of nodes while all of the velocity components are stored in another. Meanwhile, the derivatives with respect to the spatial directions are approximated to the second order on two-point stencils. The second-order scheme is presented for the sake of simplicity and it is easy to expand to a higher order.Another approach, widely-known as the rotated staggered grid scheme, is based on the same concept; therefore, this paper contains a detailed comparative analysis of the two schemes. It is shown that the dispersion condition of the Lebedev scheme is less restrictive than that of the rotated staggered grid scheme, while the stability criteria lead to approximately equal time stepping for the two approaches. The main advantage of the proposed scheme is its reduced computational memory requirements. Due to a less restrictive dispersion condition and the way the media parameters are stored, the Lebedev scheme requires only one-third to two-thirds of the computer memory required by the rotated staggered grid scheme. At the same time, the number of floating point operations performed by the Lebedev scheme is higher than that for the rotated staggered grid scheme.

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This paper presents a new method to construct the optimal training dataset for the numerical dispersion mitigation network. The dataset is designed to preserve the prescribed maximal NRMSdistance between any seismogram from the entire dataset and those from the training dataset. So, the training dataset is constructed only using the precomputed coarse-mesh solution; thus, it does not require any additional simulations. Our numerical experiments illustrate that the suggested approach may reduce the number of common-shot gathers in the training set by the factor of four compared to the datasets using uniformly distributed shots. However, the areas with high model and seismograms variability are oversampled by the proposed approach without gaining extra accuracy, which requires further study.

Background and aim. The complexity of the structures of the Paleozoic deposits of Western Siberia requires the use of specialized methods for seismic data processing. However, the standard time processing procedures are still used in Western Siberia. Therefore, in this work, the goal is to study of seismic processing procedures for the construction of high-quality images of the pre-Jurassic complex in Western Siberia. Materials and methods. A comparative analysis of time and depth processing was carried out in the paper on realistic synthetic data and models from Western Siberia containing the pre-Jurassic complex. Numerical examples are calculated for synthetic data obtained from two realistic seismic models. To create the first model, various geological and geophysical data from the Tomsk region are used. The most difficult areas of the Paleozoic in this model are steeply dipping carbonate structures and intrusive formations with steep slopes and outcropping to the erosion surface. Another model was built based on the seismic data processing results in the area of the Maloichskoye and Verkh-Tarskoye fields in the Novosibirsk region. Based on these data, the main horizons and a system of sub-vertical faults, characteristic of the pre-Jurassic deposits of the Novosibirsk region, were identified. Seismic data processing was carried out with an emphasis on the possibility of object-oriented migration. Results. It is shown that the time processing of seismic data is insufficient and the need for deep processing to construct kinematically correct images of pre-Jurassic deposits. We also compared migration algorithms based on Gaussian beams and found that object-oriented migration gives the best quality results.

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