Gaussian Beam Migration Research Articles

Adaptive focus beam migration method in visco-acoustic media

Abstract Owing to the prevalent viscosity in the subsurface medium, seismic waves experience amplitude attenuation effects during their propagation in visco-acoustic media. Therefore, it is crucial to develop a method that can compensate for wavelet amplitude attenuation and enhance imaging quality. In this paper, we derive an expression for corrected ray complex travel time by introducing the quality factor Q. Additionally, we modify the classical Gaussian beam propagation operator to an adaptive focus type propagation operator. Our research presents an adaptive focused beam migration imaging method specifically designed for viscous acoustic media, incorporating a combination of traditional Gaussian beam migration imaging methods. In comparison to traditional migration methods, the proposed approach achieves energy focusing along the phase axis and significantly improves imaging quality. The validity and effectiveness of our method are confirmed through the obtained imaging results.

Q-Compensated Gaussian Beam Migration under the Condition of Irregular Surface

The viscosity of actual underground media can cause amplitude attenuation and phase distortion of seismic waves. When seismic images are processed assuming elastic media, the imaging accuracy for the deep reflective layer is often reduced. If this attenuation effect is compensated, the imaging quality of the seismic data can be significantly improved. Q-compensated Gaussian beam migration (Q-GBM) is an effective seismic imaging method for viscous media, and it has the advantages of both wave equation and ray-based Q-compensated imaging methods. This study develops a Q-GBM method in visco-acoustic media with an irregular surface. Initially, the basic principles of Gaussian beam in visco-acoustic media are introduced. Then, by correcting the complex-value time of the Gaussian beam in visco-acoustic media, energy compensation and phase correction are carried out for the forward continuation wavefield at the seismic source of the irregular surface and the reverse continuation wavefield at the beam center, which effectively compensates the absorption and attenuation effects of visco-acoustic media on the seismic wavefield. Further, a Q-GBM method under the irregular surface is proposed using cross-correlation imaging conditions. Through migration tests for three numerical models of visco-acoustic media with irregular surfaces, it is verified that our method is an effective depth domain imaging technique for seismic data in visco-acoustic media under the condition of irregular surfaces.

Elastic common-receiver Gaussian beam migration of 4C ocean-bottom node data

Four-component ocean-bottom node (OBN) surveys allow for the imaging of subsurface elastic properties for oil and gas exploration in deepwater environments. However, sparse acquisition sampling for the high-quality imaging of OBN data is challenging. To alleviate this problem, a common-receiver domain 4C elastic Gaussian beam migration method based on elastic reciprocity transformation that considers the monopole/dipole characters of sources and receivers is developed. Common-receiver migration also is computationally efficient in an OBN survey wherein the number of shots usually exceeds the number of geophones. P/S and up-/downgoing wavefield decompositions are accomplished on the “virtual source side” during migration. A decomposition matrix and a wavefield extrapolation formula are derived from the elastic Kirchhoff-Helmholtz integral with the representation of the Green’s function as a superposition of Gaussian beams. The local slant stack is performed on the common-receiver recordings that are subjected to more optimized sampling, which is less sensitive to aliasing. The performance of the method on synthetic data is validated using the coarse sampling of OBNs in a deepwater and ultradeepwater environment.

A new implementation of the beam migration by using a model-driven variable grid strategy

Beam migration offers higher imaging accuracy, better flexibility, stability and adaptability than conventional ray migration, while the variable grid method achieves lower storage and higher efficiency under the same accuracy by means of different grid generation of the velocity model. However, the efficiency and accuracy of Gaussian beam migration are strongly affected by the algorithm used for Gaussian beam summation whose key step is to find the underground point at which the local beam contributes relevantly to the reconstruction of the Green's function. Conventionally, one uses Hale's recursive search method that firstly searches on a global coarse grid and then interpolated to a local fine one. Practical experience shows that this method can greatly improve the efficiency of the beam scanning, but causes some wavy discontinuities and imaging artifacts as well. To solve this problem, we present a new method called “model-driven variable grid strategy”. In this strategy, a key step is to establish a relationship between the vertical gradient of the velocity model and the local grid constants through local velocity gradient with respect to the global average velocity. Numerical tests on synthetic and field data show that the new method has a minimal need on computer resources and can largely improve the accuracy and efficiency of the beam migration in regions with complex geological structures.

2D Q-compensated multi-component elastic Gaussian beam migration

Elastic waves are affected by viscoelasticity during the propagation through the Earth, resulting in energy attenuation and phase distortion, in turn resulting in low seismic imaging accuracy. Therefore, viscoelasticity should be considered in seismic migration imaging. We propose a Q compensated multi-component elastic Gaussian beam migration (Q-EGBM) method to (1) separate the elastic-wave data into longitudinal (P) and transverse (S) waves to perform PP-wave and PS-wave imaging; (2) recover the amplitude loss caused by attenuation; (3) correct phase distortions caused by dispersion; (4) improve the resolution of migration imaging. In this paper, to accomplish (2), (3), and (4), we derive complex-valued traveltimes in viscoelastic media. The results of numerical experiments using a simple five-layer model and a sophisticated BP gas model show that the method presented here has significant advantages in recovering energy decay and correcting phase distortion, as well as significantly improving imaging resolution.

Adaptive Focused Beam Prestack Depth Migration Under the Condition of Rugged Topography

The complex topography is a challenging issue in onshore seismic exploration. The rugged terrain and lateral change of near-surface velocity pose a significant obstacle to the accurate imaging of seismic data. The adaptive focused beam migration method retains the good applicability of the ray methods for calculating the seismic wavefield under complex surface conditions. It can effectively solve the contradiction between the imaging accuracy of deep and shallow strata in traditional Gaussian beam migration. We extend the adaptive focused beam migration approach to the deep domain imaging of seismic data under complex surface conditions. Firstly, the basic principles of the adaptive focused beam are reviewed. Then, Green’s functions of the seismic source and the receiving point of rugged topography are characterized by the adaptive focused beam, and an adaptive focused beam prestack depth migration method based on cross-correlation imaging is proposed. The full-wave-arrival imaging strategy is applied to image all wave arrivals of subsurface imaging points. A single input seismic trace is adopted for imaging, which can directly emit the focused beam from the receiving point of rugged topography for wave field continuation, thus avoiding multiple focusing. As a result, the applicability of the migration approach to complex surface conditions was improved, and the imaging accuracy of the migration method was also effectively enhanced. The numerical model migration test of different rugged topography conditions and tectonic forms verified that the proposed method was an effective prestack depth migration applicable to accurately imaging seismic data under the rugged topography condition.

Iterative Reweighted Least-Squares Gaussian Beam Migration and Velocity Inversion in the Image Domain Based on Point Spread Functions

Amplitude-preserving migration is very important for reservoir characterization, which can faithfully provide information on the strength of the reflectors. However, conventional migration algorithms do not compensate for variable illumination effects and can hardly obtain true amplitudes of medium parameter. Least squares migration (LSM) is an effective method to address this issue. Unfortunately, there is a key problem with LSM methods: most LSM methods only consider illumination compensation but not consider the accuracy of migration velocity model. The accuracy of the migration velocity model directly affects the quality of migrated images. Moreover, changes in velocity are more indicative of reservoir properties than reflectivity. Therefore, it is necessary to incorporate velocity estimation into migration imaging to realize joint inversions. Based on these facts, we present an iterative re-weighted LSM method by approximating the local Hessian using point spread functions. Then, we related the LSM results to the scattering potential, simultaneously achieving velocity update with illumination compensation. Based on the gradually changing characteristics of rock properties, we adopted a sparse derivative constraint rather than requiring the result to be sparse. Consequently, this processing caused the results to contain broader bandwidths, giving the image a more continuous and textured appearance. Next, we evaluated the proposed method using the Marmousi2 model. The results had higher resolution and a more reliable amplitude than the initial migration images. Hence, we efficaciously completed the velocity model update, with our method achieving encouraging results under both relatively accurate migration velocity and highly smoothed migration velocity model tests.

Elastic Seismic Imaging Enhancement of Sparse 4C Ocean-Bottom Node Data Using Deep Learning

The ocean bottom node (OBN) seismic acquisition system is designed to gather high-fidelity, wide-azimuth, and long-offset four-component (4C) data, which includes shear waves and enables the use of the elastic assumption in imaging and inversion. However, deploying geophysical instruments on the seafloor is difficult and costly, leading to the usual adoption of sparse node spacing. This can, however, lead to poor illumination and imaging challenges, especially in the shallow subsurface near the seafloor. To address these issues in the context of 4C elastic imaging, we propose a deep learning-based method using a multi-scale convolutional neural network (Ms-CNN) to improve the imaging quality of OBN surveys with sparse data acquisition. As an alternative to interpolating the sparse seismic data in the data domain, which can be a challenging task due to the limitations attributed to sampling theorem and the often larger amounts of data compared to the image, we train an Ms-CNN in a supervised fashion to map from sparse data images of PP and PS sections produced by 4C Gaussian beam migration to the equivalent dense data images, allowing for the direct processing of sparse data to improve imaging quality. Here, we combine the mean absolute error and multiscale structure similarity index measure in the loss function to optimize the network’s training process, and to help improve the performance. The effectiveness of the method is demonstrated through experiments on synthetic and field data, resulting in improved event continuity and reduced noise in migration results from sparse OBN acquisitions.

Elastic Gaussian-Beam Migration for PP and PS Imaging Using Single-Component Seismic Data

Elastic Gaussian-Beam Migration for PP and PS Imaging Using Single-Component Seismic Data

True-Amplitude Gaussian-Beam Migration for Acoustic Transversely Isotropic Media With a Vertical Symmetry Axis

True-Amplitude Gaussian-Beam Migration for Acoustic Transversely Isotropic Media With a Vertical Symmetry Axis

A computational method for wide-azimuth 3D dip-angle gathers using Gaussian beam migration

The dip-angle-domain common-image gather (DDCIG) is a key tool to separate the diffraction and reflection imaging results. Reflectors with different spatial geometries produce different responses in DDCIGs. Compared with Kirchhoff migration, Gaussian beam migration (GBM) is more effective and robust to overcome the multipathing problem. As a ray-based method, it has explicit angle information naturally during the propagation. We have developed a 3D DDCIG computational method using GBM, which obtain both the imaging result and angle-domain gathers with only one pass of calculation. The angle-gather computation is based on geometrical optics, and multiple angle conversions are implemented under the rules of space geometry, which helps to avoid rounding errors and improve accuracy. Additionally, the multi-azimuth joint presentation strategy is proposed to describe the characteristic of omnidirectional dip angles using a finite number of gathers. After using a 2D model to illustrate application advantages of DDCIG, we apply the proposed method to two 3D models to test its feasibility and accuracy. A field data example further demonstrates the adaptability of our method to seismic imaging for a land survey.

A fast space-time-domain Gaussian beam migration approach using the dominant frequency approximation

The Gaussian beam migration (GBM) is a steady imaging approach, which has high accuracy and efficiency. Its implementation mainly includes the traditional frequency domain and the recent popular space-time domain. Firstly, we use the upward ray tracing strategy to get the backward wavefields. Then, we use the dominant frequency of the seismic data to simplify the imaginary traveltime calculation of the wavefields, which can cut down the Fourier transform number compared with the traditional GBM in the space-time domain. In addition, we choose an optimized parameter for the take-off angle increment of the up-going and down-going rays. These optimizations help us get an efficient space-time-domain acoustic GBM approach. Typical four examples show that the proposed method can significantly improve the computational efficiency up to one or even two orders of magnitude in different models with different model parameters and produce good imaging results with comparable accuracy and resolution with the traditional GBM in the space-time domain.

An Efficient and Stable High‐Resolution Seismic Imaging Method: Point‐Spread Function Deconvolution

AbstractBy fitting observed data with predicted seismograms, least‐squares migration (LSM) computes a generalized inverse for a subsurface reflectivity model, which can improve image resolution and reduce artifacts caused by incomplete acquisition. However, the large computational cost of LSM required for simulations and migrations limits its wide applications for large‐scale imaging problems. Using point‐spread function (PSF) deconvolution, we present an efficient and stable high‐resolution imaging method. The PSFs are first computed on a coarse grid using local ray‐based Gaussian beam Born modeling and migration. Then, we interpolate the PSFs onto a fine‐image grid and apply a high‐dimensional Gaussian function to attenuate artifacts far away from the PSF centers. With 2D/3D partition of unity, we decompose the traditional adjoint migration results into local images with the same window size as the PSFs. Then, these local images are deconvolved by the PSFs in the wavenumber domain to reduce the effects of the band‐limited source function and compensate for irregular subsurface illumination. The final assembled image is obtained by applying the inverse of the partitions for the deconvolved local images. Numerical examples for both synthetic and field data demonstrate that the proposed PSF deconvolution can significantly improve image resolution and amplitudes for deep structures, while not being sensitive to velocity errors as the data‐domain LSM.

Gaussian Beam Migration for Free-Surface Multiples in VSP

The vertical seismic profiling (VSP) Gaussian beam migration is a seismic imaging method with both computational efficiency and imaging precision. It can get high-resolution structural features near the well. However, the VSP migration based on primary reflection imaging is limited by the observation system, which makes it unable to image for the shallow structure at far offset. The free-surface multiples in VSP can expand the illumination range for far offset effectively. Therefore, Gaussian beam migration (GBM) for free-surface multiples imaging in VSP is proposed. Firstly, based on the ground Gaussian beam pre-stack depth migration, the method for decomposing the plane wave is improved and adapted into VSP geometry. We decompose the seismic records received by the well into plane waves in different directions according to different window centers and image the plane wave of each direction independently. Secondly, through the mirror image of both the velocity model and VSP receivers, the VSP free-surface multiples are converted into VSP primary reflections which are involved in the VSP Gaussian beam migration method, and thus, the method of the primaries is used to image the free-surface multiples. Finally, the effectiveness and robustness of the proposed method are verified by the theoretical model and practical data.

Two dimensional dynamically focused beam migration in weakly anisotropic media

Anisotropy exists widely in the earth medium. For anisotropic medium, the traditional isotropic migration will lead to the inaccurate images and unfocused energy. Especially for a deep target exploration, ignoring anisotropy will further affect the subsequent seismic data interpretation. As an improved ray method, Gaussian beam migration overcomes the imaging problems of caustics and shadow zones in Kirchhoff migration, and avoids the time-consuming problems of wave equation migrations. However, the imaging quality of the Gaussian beam migration is controlled by the initial beam width at the surface. In this paper, we extend Nowack (2011)’s algorithm to anisotropic media and present an anisotropic dynamically focused beam migration by modifying the propagator of the Gaussian beams. We use anisotropic kinematic and dynamic ray tracing with optimized coefficients to obtain travel times, trajectories and dynamic information. We then use dynamically focused beams for weakly anisotropic media to calculate the Green's function and the Claerbout imaging condition to obtain images. This strategy enables us to improve the imaging quality in the middle and deep layers without reducing the imaging quality in the shallow layers, which will help to overcome the limitation of the initial beam width in Gaussian beam migration. The results for a VTI fault model and the Shengli complex structure model show the accuracy and validity of the proposed method in this paper.

Research progress on seismic imaging technology

High-precision seismic imaging is the core task of seismic exploration, guaranteeing the accuracy of geophysical and geological interpretation. With the development of seismic exploration, the targets become more and more complex. Imaging on complex media such as subsalt, small-scale, steeply dipping and surface topography structures brings a great challenge to imaging techniques. Therefore, the seismic imaging methods range from stacking-to migration-to inversion-based imaging, and the imaging accuracy is becoming increasingly high. This review paper includes: summarizing the development of the seismic imaging; overviewing the principles of three typical imaging methods, including common reflection surface (CRS) stack, migration-based Gaussian-beam migration (GBM) and reverse-time migration (RTM), and inversion-based least-squares reverse-time migration (LSRTM); analyzing the imaging capability of GBM, RTM and LSRTM to the special structures on three typical models and a land data set; outlooking the future perspectives of imaging methods. The main challenge of seismic imaging is to produce high-precision images for low-quality data, extremely deep reservoirs, and dual-complex structures.

Elastic Least-Squares Gaussian Beam Imaging With Point Spread Functions

Elastic least-squares migration (ELSM) has the potential to produce high-resolution images. It can be implemented in either data-domain or image-domain but is much faster in the image domain. A critical step of image-domain ELSM is the calculation of the Hessian. However, it is impractical to directly calculate the Hessian due to its high storage and costs. In this letter, the Hessian is efficiently constructed with elastic point spread functions (PSFs) calculated by a combination of multicomponent Gaussian beam Born modeling (of scattering points with elastic parameters perturbation) and elastic Gaussian beam migration. Based on this, we propose a fast image-domain ELSM method. A hyper-Laplacian priori regularization is used to produce sparse solutions. We evaluate the proposed method with the Marmousi2 model, and the results demonstrate the capability of the method to image complex structures with improved resolution relative to the initial migrated image.

Reverse time migration with Gaussian beams using optimized ray tracing systems in transversely isotropic media

ABSTRACTPrestack depth migration is a key technology for imaging complex reservoirs in media with strong lateral velocity variations. Prestack migrations are broadly separated into ray‐based and wave‐equation‐based methods. Because of its efficiency and flexibility, ray‐based Kirchhoff migration is popular in the industry. However, it has difficulties in dealing with the multi‐arrivals, caustics and shadow zones. On the other hand, wave‐equation‐based methods produce images superior to that of the ray‐based methods, but they are expensive numerically, especially methods based on two‐way propagators in imaging large regions. Therefore, reverse time migration algorithms with Gaussian beams have recently been proposed to reduce the cost, as they combine the high computational efficiency of Gaussian beam migration and the high accuracy of reverse time migration. However, this method was based on the assumption that the subsurface is isotropic. As the acquired azimuth and maximum offsets increase, taking into account the influence of anisotropy on seismic migration is becoming more and more crucial. Using anisotropic ray tracing systems in terms of phase velocity, we proposed an anisotropic reverse time migration using the Gaussian beams method. We consider the influence of anisotropy on the propagation direction and calculate the amplitude of Gaussian beams with optimized correlation coefficients in dynamic ray tracing, which simplifies the calculations and improves the applicability of the proposed method. Numerical tests on anisotropic models demonstrate the efficiency and accuracy of the proposed method, which can be used to image complex structures in the presence of anisotropy in the overburden.

An Effective Acoustic Impedance Imaging Based on a Broadband Gaussian Beam Migration

The estimation of the subsurface acoustic impedance (AI) model is an important step of seismic data processing for oil and gas exploration. The full waveform inversion (FWI) is a powerful way to invert the subsurface parameters with surface acquired seismic data. Nevertheless, the strong nonlinear relationship between the seismic data and the subsurface model will cause nonconvergence and unstable problems in practice. To divide the nonlinear inversion into some more linear steps, a 2D AI inversion imaging method is proposed to estimate the broadband AI model based on a broadband reflectivity. Firstly, a novel scheme based on Gaussian beam migration (GBM) is proposed to produce the point spread function (PSF) and conventional image of the subsurface. Then, the broadband reflectivity can be obtained by implementing deconvolution on the image with respect to the calculated PSF. Assuming that the low-wavenumber part of the AI model can be deduced by the background velocity, we implemented the AI inversion imaging scheme by merging the obtained broadband reflectivity as the high-wavenumber part of the AI model and produced a broadband AI result. The developed broadband migration based on GBM as the computational hotspot of the proposed 2D AI inversion imaging includes only two GBM and one Gaussian beam demigraton (Born modeling) processes. Hence, the developed broadband GBM is more efficient than the broadband imaging using the least-squares migrations (LSMs) that require multiple iterations (every iteration includes one Born modeling and one migration process) to minimize the objective function of data residuals. Numerical examples of both synthetic data and field data have demonstrated the validity and application potential of the proposed method.

An illumination‐compensated Gaussian beam migration for enhancing subsalt imaging

ABSTRACTSeismic images of Earth's subsurface are essential for oil and gas exploration. Gaussian beam migration is popular for seismic imaging owing to its flexibility and efficiency of implementation. However, the practical use of classic Gaussian beam migration is limited for complicated structures such as subsalt because of poor seismic illumination in those areas. We propose an illumination‐compensated Gaussian beam migration under the framework of least‐squares migration, enhancing the subsalt imaging effectively. A novel scheme based on the Born modelling and migration of Gaussian beam is developed to estimate the point spreading function, with which the illumination compensation can be efficiently implemented in the local wavenumber domain. As the aim of least‐squares migration, the proposed illumination‐compensated Gaussian beam migration produces true‐amplitude images in subsalt areas, which facilitates the seismic interpretation of subsalt structures. The total computational cost of the proposed method includes one Born modelling process and two conventional Gaussian beam migrations, and thus it is much more efficient than the classic least‐squares migration which requires multiple iterations. Numerical examples have demonstrated the effectiveness of the adaptive strategies, manifesting applicable potential in oil and gas exploration of subsalt targets.