In this study, we have developed a novel seismic data enhancement approach along with its corresponding software implementation that enables comprehensive processing of data in the 5D domain. The primary objective of this development is to establish a robust and computationally efficient methodology capable of producing optimal data enhancement results. Our approach is fundamentally based on the integration of two key techniques: seismic data super-grouping and non-linear beamforming. While each of these techniques individually operates using two spatial coordinates and one time coordinate, it is important to note that complete seismic datasets actually contain four spatial coordinates. To address this dimensionality challenge, we have developed an innovative integration of these techniques that effectively accounts for all four spatial coordinates simultaneously, thereby providing a more comprehensive and robust solution. A significant portion of our research has focused on systematically investigating the most suitable data domains for optimal performance when applying super-grouping and beamforming in combination. Through this investigation, we have identified and characterized several effective domain configuration options. The primary domain configuration employs the cross-spread domain for beamforming operations while utilizing its orthogonal counterpart for super-grouping. An alternative important configuration option utilizes the offset domain for beamforming while employing the central point domain for super-grouping operations. Furthermore, we have developed optimal data sampling strategies that are specifically tailored to different data geometries. Additionally, we have implemented several significant optimizations that enhance the standard application of non-linear beamforming, improving both its efficiency and effectiveness. To complete this comprehensive development, we have created specialized software that implements our enhanced methodology. The performance and capabilities of both our algorithmic approach and its software implementation have been rigorously evaluated through extensive testing. These evaluations have included both synthetic datasets and real seismic data acquired from the Arabian Plate. The results of these tests conclusively demonstrate the proposed methodology’s capabilities and effectiveness, validating its practical utility for seismic data enhancement applications.

This paper investigates the combined application of seismic inversion and migration for processing seismic data in the depth domain. Seismic inversion serves as a widely used practical tool allowing the derivation of detailed subsurface models from seismic data. In this study, we implement a constrained total variation inversion algorithm. The inversion input data comprise true-amplitude depth imaging results along with the depth migration velocity model. Furthermore, we develop and examine an iterative algorithm that jointly performs acoustic seismic inversion and depth migration. This approach aims to refine high-frequency and smooth low-frequency components of the depth velocity model. We validate our methods through numerical experiments using both synthetic data and a realistic Marmousi model.

In the paper we consider complex land near surface modeled as random clutter, and we study the depth imaging problem for such media. We consider synthetic clutter models, and we provide a numerical study using various realizations of the cluttered models. We propose and investigate a statistical imaging technique based on path summation allowing to get depth image without reconstruction of deterministic near-surface depth velocity model. Our results demonstrate that statistical imaging can significantly improve and recover reflectors, even with a limited number of realizations. The ability to achieve accurate images despite the absence of an exact velocity model underscores the robustness of this technique. We show that statistical imaging can average out phase distortions caused by near-surface clutter, enhancing the clarity and accuracy of the subsurface image. This method offers a promising direction for imaging in complex near-surface environments, effectively addressing the limitations of traditional deterministic approaches. We further explain why this technique works by leveraging the concept of "seismic speckle," analogous to optical and ultrasonic speckle noise, to account for phase distortions caused by small-scale heterogeneities. By estimating the statistical properties of the clutter, we generate ensembles of velocity models that perturb the phase of the depth-migrated arrivals symmetrically. In summary, our study highlights the potential of statistical imaging with path summation to significantly improve seismic imaging in challenging near-surface environments, offering a robust alternative to traditional deterministic methods and paving the way for future advancements in subsurface imaging.

A simple and numerically effective approach for calculating frequency dependent qP-rays in threedimensional TTI media is presented in this paper. Our method involves propagating a locally plane fragment of wavefront which is sensitive to the distribution of the model parameters in some subvolume of the medium near a ray. The width of the sensitivity area depends on the wavelength in each point on the ray. For numerical realization we apply approximate expressions for phase and group velocities which are valid for weak TTI media. Numerical experiment proves the effectiveness of the proposed approach

This study considers the Full Waveform Inversion (FWI) method in the image domain based on the asymptotic solution of the Helmholtz equation. The paper provides ray tracing and beam migration to get the images used to compute the tomographic part of the asymptotic FWI gradient. The comparison of asymptotic FWI and Common Image Point (CIP) tomography show that the computational time for both methods is similar while they provide reconstruction of different model parts. A series of numerical experiments show that CIP tomography is effective in reconstructing the low frequency model, while asymptotic FWI provides recovery of the details of complex velocity structure.

Данная работа посвящена исследованию возможностей применения сейсмической инверсии в связке с миграцией для глубинной обработки сейсмических данных. Сейсмическая инверсия используется на практике как инструмент для прогнозирования свойств коллектора. Она позволяет получить из сейсмических данных детальную модель. В данной работе реализован алгоритм сейсмической инверсии полной вариации с ограничениями. Входными данными для инверсии являются глубинные изображения в истинных амплитудах и миграционная скоростная модель. Также в рамках данной работы разрабатывается и исследуется итерационный совместный алгоритм акустической сейсмической инверсии и глубинной миграции для уточнения гладкой низкочастотной миграционной скоростной модели. Численно исследуются возможности совместного алгоритма для восстановления глубинной скоростной модели как для известной, так и для неизвестной модели плотности. Численные эксперименты проведены с использованием синтетических данных и реалистичной модели Marmousi. This paper is devoted to the study of the joint application of seismic inversion and migration for seismic data processing in depth. Seismic inversion is used in practice as a tool for predicting reservoir properties. It allows obtaining a detailed model from seismic data. In this work, constrained total variation inversion algorithm is implemented. The input data for the inversion are the depth image results in true amplitudes and the depth migration velocity model. Also, within the framework of this work, an iterative algorithm of joint acoustic seismic inversion and depth migration is developed and investigated to refine a smooth low-frequency migration velocity model. The capability of the joint algorithm to reconstruct the depth velocity model for both known and unknown density model is numerically investigated. Numerical experiments were carried out using synthetic data and a realistic Marmousi model.

This study investigates the challenges of imaging deep subsurface targets below complex near surface, described as random clutter. Our synthetic example, designed to simulate random clutter, reveals significant scattering distortions and defocusing effects, similar to those observed in complex field seismic data. We explore the use of statistical imaging through path summation as a heuristic method for achieving subsurface imaging without the need for an accurate velocity-depth model. This method utilizes an ensemble of random near-surface models that reflect the statistical complexity of the actual near-surface, without individually replicating the exact conditions. A statistical image is produced by summing the images obtained from the ensemble. We show that image traces undergo symmetric phase perturbations, which cancel out during the summation process, thus emphasizing true geological interfaces, albeit with a slight attenuation of higher frequencies. We establish an important connection between statistical imaging with small-scale heterogeneity and speckle scattering noise, highlighting the relationship between statistical imaging, small-scale heterogeneity, and speckle noise.

The paper provides a simple and numerically effective method to calculate frequency dependent rays of qP-wave in three-dimensional TTI media. Our method involves propagating a locally plane fragment of the wave front, which is sensitive to the distribution of the model parameters in some sub volume of the medium near a ray. The wave length in each point on the ray determines the width of the sensitivity area. For numerical realization we apply approximate expressions for phase and group velocities which are valid for weak TTI media. Numerical experiments demonstrate the effectiveness of the proposed approach.

The presented paper is devoted to the numerical study of the applicability of 3D inversion for fracture model reconstruction based on machine learning. In practice, geophysicists use seismic inversion for predicting reservoir properties. One-dimensional convolutional model lies in the basis of standard versions of inversion, but geology is more complex. That is why we provide implementation and investigation of the approach for 3D fracture model reconstruction based machine learning, which uses U-net neural network and 3D convolutional model. We provide numerical results for a realistic 3D synthetic fractured model from the North of Russia.

The presented paper is devoted to the numerical study of the applicability of 1D seismic inversion and 2D machine learning based inversion for fracture model reconstruction. Seismic inversion is used to predict reservoir properties. Standard version is based on a one-dimensional convolutional model, but real geological media are more complex, and therefore it is necessary to determine conditions where seismic inversion gives acceptable results. For this purpose, the work carries out a comparative analysis of one-dimensional and two-dimensional convolutional modeling. Also, machine learning methods have been adopted for 2D fracture model reconstruction. We use UNet architecture and 2D convolutional model to create a training dataset. We perform numerical experiments for a realistic synthetic model from Eastern Siberia and Sigsbee model.

Представленная статья посвящена исследованию возможностей применения сейсмической инверсии для глубинной обработки сейсмических данных. Сейсмическая инверсия используется на практике как инструмент для прогнозирования коллекторских свойств. Она позволяет выделить из сейсмических данных модель с высоким уровнем детализации, т.е. высокочастотную составляющую модели. При этом входными данными являются результаты временной обработки. В данной работе реализован алгоритм сейсмической инверсии полной вариации с ограничениями. Входными данными для инверсии являются глубинные изображения в истинных амплитудах и миграционная скоростная модель. Численно исследуются возможности сейсмической инверсии для уточнения высокочастотной составляющей глубинно-скоростной модели. Также в рамках данной работы разрабатывается и исследуется итерационный алгоритм совместной сейсмической инверсии и глубинной миграции для уточнения гладкой низкочастотной миграционной скоростной модели. Численные эксперименты проведены с использованием синтетических данных и реалистичной модели из Восточной Сибири, а также для модели Marmousi. The presented paper is devoted to the study of the seismic inversion possibilities for depth seismic data processing. Seismic inversion is used in practice as a tool for predicting reservoir properties. It allows one to extract a model with a high level of detail from seismic data, i.e. high-frequency component of the model. In this case, the input data are the time processing results. In this work, constrained total variation inversion algorithm is implemented. The input data for the inversion are the depth image results in true amplitudes and the depth migration velocity model. The possibilities of seismic inversion are numerically investigated to refine the high-frequency component of the model. Also, within the framework of this work, an iterative algorithm of joint seismic inversion and depth migration is developed, and we investigate its possibilities to refine the smooth low-frequency migration velocity model. Numerical experiments were carried out using synthetic data and a realistic model from Eastern Siberia, as well as for the Marmousi model.

We present a simple and robust approach for calculating frequency-dependent rays in three dimensional media. The proposed method simulates propagation of locally plane fragment of a wavefront. Ray properties depends on velocity distribution in some sub-volume around the ray and on wavelength in each point. Numerical experiment demonstrates the applicability of the proposed method to calculate travel-times and ray-based acoustic wavefields in complex 3D environments with the presence of slat intrusion.

In the paper, we describe an original 3D travel-time tomography approach. It is based on the new realization of the bending method which to some extent takes into account the band-limited nature of real seismic signals propagation. As a result, two-point ray tracing provides more reliable ray trajectories and travel times in complex media. Another original feature of the proposed tomography is that the model is represented using the Chebyshev polynomials. Such parameterization allows analytical calculation of travel times and their derivatives with respect to model parameters and significantly reduces the number of parameters to be recovered during inversion compared to more common grid tomography. In certain situations, the proposed approach provides significant computational advantages. Numerical examples prove its efficiency.

The work addresses the development of a statistical model of a discrete fracture network (DFN) using core, outcrop, and seismic data. We consider the DFN model defined by the fractal distribution of fracture centers and a power-law distribution of fracture lengths. We perform the statistical analysis of model realization on different spatial scales to investigate the possibility to evaluate the corresponding correlation fractal dimension and power exponent. Reproducing the statistical parameters estimated from seismic images is investigated by comparison with the parameters of the original model. We conclude that the analysis of the finite subdomain of the considered model of fractures system makes it possible to estimate the model's statistical characteristics with a decrease in the system's linear size by about one order of magnitude. On the other hand, the system built on the base of seismic images does not reproduce the power-law probability density of fracture length distribution. Also, the distribution of fracture centers in this system does not reflect the fractal nature and is uniform. The results obtained in this work show that data obtained from outcrops and core samples can be used to build a statistical DFN model. On the other hand, an explicit DFN model cannot be recovered based on seismic data.

Трехмерные лучи Ломакса для моделирования распространения широкополосных сигналов в сейсмике1 Институт нефтегазовой геологии и геофизики СО РАН, г.Новосибирск, Российская Федерация

Cейсмическая инверсия после глубинной миграции для восстановления высокочастотной составляющей модели1 Институт нетфегазовой геологии и геофизики СО РАН, г

The paper presents a simple and robust approach for calculating frequency-dependent rays in three-dimensional media. The proposed ray tracing procedure simulates propagation of locally plane fragment of a wave front. Ray properties depend on velocity distribution in some sub-volume around the ray and on wavelength at each point. We provide a numerical comparison of “fat” rays approach with the “exact” Helmholtz solver using complex 3D SEG salt model. This comparison show promise of using the concept of “fat” rays in 3D seismic data processing, i.e. comparison show that “fat” rays approach needs up to several orders less resources than Helmholtz solver, while the error between “fat” rays wave filed and “exact” solution does not exceed several percent.

This study considers the full waveform inversion (FWI) method based on the asymptotic solution of the Helmholtz equation. We provide frequency-dependent ray tracing to obtain the wave field used to compute the FWI gradient and calculate the modeled data. With a comparable quality of the inverse problem solution as applied to the standard finite difference approach, the speed of the calculations in the asymptotic method is an order of magnitude higher. A series of numerical experiments demonstrate the approach's effectiveness in reconstructing the macro velocity structure of complex media for low frequencies.