Crosstalk Artifacts Research Articles

Efficient simultaneous migration of primary and free-surface related multiples using reformulated two-way wave-equation depth extrapolation scheme

The migration of free-surface related multiples can enhance subsurface illumination and improve overall imaging quality. However, this process encounters two main challenges: crosstalk artefacts resulting from the cross-correlation of non-reflection-related wavefields, and the increased computational burden of imaging different orders of multiples. We propose a novel method that simultaneously and efficiently migrates both primary and multiple reflections while mitigating crosstalk artefacts. The method employs a reformulated two-way wave-equation depth extrapolation scheme that simplifies up/down wavefield separation through straightforward summation and subtraction operations at each depth step. Two innovative algorithms are integrated into this scheme: a generalized up/down separation algorithm, and a simultaneous migration algorithm of primary and free-surface-related multiples. The up/down separation algorithm efficiently separates the up- and down-going wavefields into primary wavefield and multiple reflections of various orders at the measurement surface. The simultaneous migration algorithm then pairs these components as two-way quantities, allowing for efficient depth extrapolation using a unified propagator, followed by effective decomposition into corresponding one-way components for imaging. Numerical experiments conducted on synthetic models, including a two-dimensional two-layer model and the Sigsbee 2B model, as well as on real seismic data from a gas hydrates bearing zone, demonstrate that the proposed method simultaneously migrate both primary and multiple reflections with reduced crosstalk artefacts and limited computational overhead.

Image-domain least-squares imaging in an elastic vertically transversely isotropic medium: Multiparameter point-spread function deconvolution

By solving a linear inverse problem, least-squares migration (LSM) can provide higher-precision images of complex subsurface structures than traditional adjoint-operator-based migration. LSM can be conducted in the data domain and the image domain (IDLSM). IDLSM in acoustic media has been extensively studied, commonly using single-parameter point-spread function (PSF) deconvolution. For high-accuracy imaging of complex media, we develop an image-domain elastic least-squares imaging method using multiparameter PSF deconvolution for vertically transversely isotropic (VTI) media. The multiparameter PSFs, including P-P, P-S, S-P, and S-S components, are calculated on a sparse grid using elastic VTI wave equation Born modeling and migration. The traditional migration result is then decomposed into individual local results, each corresponding to the size of a single PSF, through unit partitioning. Finally, a set of filters is derived from four elastic VTI PSF components to approximate the Hessian inverse, which are subsequently assembled to reconstruct an entire deconvolved image. The numerical experiments confirm that our method can significantly decrease multiparameter crosstalk artifacts and improve spatial resolution and amplitude fidelity.

Advancing attenuation estimation through integration of the Hessian in multiparameter viscoacoustic full-waveform inversion

Accurate seismic attenuation models of subsurface structures not only enhance subsequent migration processes by improving fidelity, resolution, and facilitating amplitude-compliant angle gather generation but also provide valuable constraints on subsurface physical properties. Leveraging full-wavefield information, multiparameter viscoacoustic full-waveform inversion ( Q-FWI) simultaneously estimates seismic velocity and attenuation ( Q) models. However, a major challenge in Q-FWI is the contamination of crosstalk artifacts, where inaccuracies in the velocity model are mistakenly mapped to the inverted attenuation model. While incorporating the Hessian is expected to mitigate these artifacts, the explicit implementation is prohibitively expensive due to its formidable computational cost. In this study, we formulate and develop a Q-FWI algorithm via the Newton-conjugate gradient (CG) framework, where the search direction at each iteration is determined through an internal CG loop. In particular, the Hessian is integrated into each CG step in a matrix-free fashion using the second-order adjoint-state method. We find through synthetic experiments that our Newton-CG Q-FWI significantly mitigates crosstalk artifacts compared with the limited-memory Broyden-Fletcher-Goldfarb-Shanno method and the CG method, albeit with a notable computational cost. In the discussion of several key implementation details, we also determine the significance of the approximate Gauss-Newton Hessian, the second-order adjoint-state method, and the two-stage inversion strategy.

A method for extracting P‐SV‐converted wave angle‐domain common‐image gathers based on elastic‐wave reverse‐time migration

AbstractMulticomponent seismic technology utilizes the kinematic and dynamic characteristics of reflected P‐waves and converted S‐waves to reduce ambiguity in seismic exploration. The imaging and inversion accuracy of P‐SV‐converted waves are important in determining whether multicomponent seismic exploration can achieve higher exploration accuracy than conventional P‐wave exploration. Pre‐stack inversion of P‐SV‐converted waves requires precise input of P‐SV‐converted wave angle‐domain common‐image gathers. Consequently, the P‐SV‐converted wave angle‐domain common‐image gather extraction accuracy will significantly affect the P‐SV‐converted wave inversion accuracy. However, existing methods for extracting P‐SV‐converted wave angle‐domain common‐image gathers are constrained by issues such as the P‐ and S‐wave crosstalk artefacts, low‐frequency noises and inaccurate calculation of P‐wave incident angles, leading to poor imaging accuracy. We study an angle‐domain cross‐correlation imaging condition and address three key issues based on this condition: the decoupling of P‐ and S‐waves, the separation of up‐going and down‐going waves and the precise calculation of P‐wave incident angles. Our strategies facilitate high‐precision extraction of P‐SV‐converted wave angle‐domain common‐image gathers using elastic wave reverse‐time migration. In this paper, first, we employ the first‐order velocity‐dilatation‐rotation elastic wave equations to decouple P‐ and S‐waves automatically during source and receiver wavefield extrapolations. Second, we calculate the optical flow vectors of P‐ and S‐waves to ensure stable calculations of wave propagation directions. Based on this, we obtain up‐going and down‐going waves of P‐ and S‐waves. Meanwhile, we calculate the incident angle of the source P‐wave using geometric relations. Lastly, we apply the angle‐domain imaging condition to achieve high‐precision extraction of P‐SV‐converted wave angle‐domain common‐image gathers. Model examples demonstrate the effectiveness and advantages of the proposed method.

Pseudo-Helmholtz decomposition for an elastic VTI wavefield based on wavefront phase direction

P and S waves are coupled when propagating in anisotropic elastic media. The separation of P and S waves helps to study the characteristics of different types of seismic waves as well as mitigating crosstalk artifacts in elastic reverse time migration and elastic full-waveform inversion. At present, the methods of seismic wave mode separation in anisotropic media are mainly built on divergence- and curl-like operations, pseudo-Helmholtz decomposition, and low-rank approximation. We develop a new pseudo-Helmholtz decomposition operator based on eigenform analysis and the wavefront phase direction to decompose vertically transversely isotropic elastic wavefields. The corresponding P-/S-wave decoupling formulas are also derived in detail. Compared with the divergence- and curl-like methods, the new method does not change the phase of P and S waves. Compared with existing pseudo-Helmholtz decomposition methods based on eigenform analysis, our method achieves more accurate wavefield separation than the zero-order pseudo-Helmholtz decomposition operator. Our method requires solving one vector Poisson equation only, resulting in much less computational cost than the existing first-order pseudo-Helmholtz decomposition methods. In addition, the accuracy of our method is analyzed by providing homogeneous media with different parameter settings. Finally, the numerical examples demonstrate that the new pseudo-Helmholtz decomposition method is effective, efficient, and robust against random noise.

Least-squares reverse time migration of simultaneous sources with deep-learning-based denoising

Least-squares reverse time migration (LSRTM) is currently one of the most advanced migration imaging techniques in the field of geophysics. It uses least-squares inversion to fit the observed data, resulting in high-resolution imaging results with more accurate amplitudes and better illumination compensation than conventional reverse time migration (RTM). However, noise in the observed data and the Born approximation forward operator can result in high-wavenumber artifacts in the final imaging results. Moreover, iteratively solving LSRTM leads to one or two orders of computational cost higher than conventional RTM, making it challenging to apply extensively in industrial applications. Simultaneous source acquisition technology can reduce the computational cost of LSRTM by reducing the number of wavefield simulations. However, this technique also can cause high-wavenumber crosstalk artifacts in the migration results. To effectively remove the high-wavenumber artifacts caused by these issues, simultaneous source and deep learning are combined to speed up LSRTM as well as suppress high-wavenumber artifacts. A deep residual neural network (DR-Unet) is trained with synthetic samples, which are generated by adding field noise to synthesized noise-free migration images. Then, the trained DR-Unet is applied on the gradient of LSRTM to remove high-wavenumber artifacts in each iteration. Compared to directly applying DR-Unet denoising to LSRTM results, embedding DR-Unet denoising into the inversion process can better preserve weak reflectors and improve denoising effects. Finally, the proposed LSRTM method is tested on two synthetic data sets and a land data set. The tests demonstrate that the proposed method can effectively remove high-wavenumber artifacts, improve imaging results, and accelerate convergence speed.

Full-Wavefield Migration Using an Imaging Condition of Global Normalization Multi-Order Wavefields: Application to a Synthetic Dataset

In marine seismic exploration, seismic signals comprise primaries that undergo first-order scattering, as well as multiples resulting from multi-order scattering events. Surface-related multiples involve multi-order scattering at the free surface interface between seawater and air and exhibit a smaller reflection angle and broader illumination compared to primaries. Internal multiples, originating from multi-order scattering among stratified layers, provide additional illumination compensation beneath the reflecting interface. However, in conventional primary migration, different-order wavefields may result in crosstalk artifacts. To address this issue, we developed a least-squares migration (LSM) method based on the multi-order wavefield global normalization condition. This methodology investigates the illumination effects and crosstalk artifacts associated with different-order surface-related and internal multiples, and then modifies the global normalization condition by incorporating an illumination compensation perspective. Virtual sources, represented by surface-related multiples and internal multiples, are integrated into the source compensation term, ultimately yielding a multi-order wavefield normalization condition. This normalization condition is subsequently combined with least-squares full-wavefield migration (LSFWM). Numerical experiments demonstrate that the normalization condition of multi-order wavefields can resolve the problem of weak deep imaging energy and promote the suppression of multiple crosstalk artifacts in the least-squares algorithm.

Amplitude-preserving P-/S-wavefield separation with the discontinuous Galerkin method on unstructured meshes

The decoupling of P and S waves is an essential prerequisite for elastic reverse time migration, which effectively reduces crosstalk artifacts, but most wavefield separation algorithms are implemented on uniform rectangular grids. We develop an amplitude- and phase-preserving P- and S-wavefield separation approach on unstructured meshes, which can effectively decompose the original elastic wavefield into P and S wavefields. The isotropic case is considered. With the aid of viscoelastic theory, we choose to attenuate P or S waves and preserve the other wave mode, so as to achieve wavefield decomposition. Viscoelastic wave equations are first reformulated as decoupling wave equations with a selective strong attenuation. We then use the discontinuous Galerkin (DG) method to simulate decoupling P or S wavefield propagation on triangular and tetrahedral meshes. We adopt a quadrature-free DG approach and the arbitrary mesh is mapped into the reference mesh for numerical calculation, where no additional volume and surface integrations are involved. The amplitude and phase information of this vector decomposition agrees with that of the original elastic data. Four numerical examples are used to demonstrate the superior performance of this vector decomposition algorithm. The isotropic example indicates the applicability and correctness of our scheme and the second example displays superiority in handling strong velocity contrasts. The third example exhibits mesh flexibility in dealing with complex structures, such as caves, faults, and undulating surfaces. The last example indicates the effectiveness of our developed algorithm extended to a 3D case.

Deep-learning-based methods of attenuation correction for SPECT and PET

Attenuation correction (AC) is essential for quantitative analysis and clinical diagnosis of single-photon emission computed tomography (SPECT) and positron emission tomography (PET). In clinical practice, computed tomography (CT) is utilized to generate attenuation maps (μ-maps) for AC of hybrid SPECT/CT and PET/CT scanners. However, CT-based AC methods frequently produce artifacts due to CT artifacts and misregistration of SPECT-CT and PET-CT scans. Segmentation-based AC methods using magnetic resonance imaging (MRI) for PET/MRI scanners are inaccurate and complicated since MRI does not contain direct information of photon attenuation. Computational AC methods for SPECT and PET estimate attenuation coefficients directly from raw emission data, but suffer from low accuracy, cross-talk artifacts, high computational complexity, and high noise level. The recently evolving deep-learning-based methods have shown promising results in AC of SPECT and PET, which can be generally divided into two categories: indirect and direct strategies. Indirect AC strategies apply neural networks to transform emission, transmission, or MR images into synthetic μ-maps or CT images which are then incorporated into AC reconstruction. Direct AC strategies skip the intermediate steps of generating μ-maps or CT images and predict AC SPECT or PET images from non-attenuation-correction (NAC) SPECT or PET images directly. These deep-learning-based AC methods show comparable and even superior performance to non-deep-learning methods. In this article, we first discussed the principles and limitations of non-deep-learning AC methods, and then reviewed the status and prospects of deep-learning-based methods for AC of SPECT and PET.

An improved elastic wavefield separation method based on the Helmholtz decomposition

Elastic wave-mode separation plays an important role in elastic reverse time migration and elastic full-waveform inversion. It helps to remove crosstalk artifacts and improve imaging quality. A class of efficient methods for elastic wave-mode separation in isotropic elastic media is the Helmholtz decomposition technique. Although this kind of approach produces pure-mode vector wavefields with correct amplitudes, phases, and physical units, their computational costs are still high especially for 3D large-scale problems. By making use of the relationships among the divergence, curl, gradient, and exterior derivative operations, we develop an improved elastic wave-mode separation based on the Helmholtz decomposition. We also need to solve a Poisson equation, but the Laplace operator operates on a scalar function rather than a vector function. Thus, for multidimensional (2D or 3D) problems, the Poisson equation only needs to be solved once for the vector P and S wavefields. This allows us to reduce the computational cost of the conventional Helmholtz decomposition method by a factor of two for solving 2D problems. For a 3D problem, the computational cost can be reduced by a factor of three. To further reduce the computational cost, by introducing a smooth extension technique, we transform the problem into the wavenumber domain via the Fourier transform and use a fast solver for the Poisson equation. The resulting wavefield separation method not only produces P and S waves with the same phases and amplitudes as the input-coupled wavefields but also significantly reduces the computational cost. Numerical tests indicate the efficiency of the proposed method and confirm the theoretical results.

44‐2: Viewing Window Extension in Integral Imaging Based Head‐mounted Light Field Displays using Time‐Multiplexed Method

Conventional integral imaging based head‐mounted light field display systems suffer from a small viewing window to minimize crosstalk artifacts and achieve a balanced optical performance. In this paper, we present a method for expanding the eye‐box size through a time‐multiplexed scheme by using a liquid crystal aperture array.

15‐3: Crosstalk Compensation Method Using ELVDD Coupling Modelling in Mobile Active Matrix OLED Display

In this paper, a method of reducing horizontal crosstalk artifacts due to the coupling effect of data lines and ELVDD electrodes in each pixel of a mobile active matrix OLED display is proposed. In order to achieve this, this paper presents a method for calculating the compensation value through modeling that reflects the ELVDD coupling characteristics. The calculation is applied to find the exact amount of data transition and is controlled by the position of the pixel and the data coupling period. The experimental results show that the proposed method reduces the crosstalk artifact of the horizontal line luminance deviation from 11% to 2%.

2-D PP and PS imaging for VTI with weak equation-converted S-waves

For elastic reverse time migration (ERTM) in inhomogeneous isotropy (ISO), the key is to deal with conversions caused by media inhomogeneity. However, for ERTM in vertical transverse isotropy (VTI), researchers also need to handle equation-converted waves (such as S-wave generated with pure explosive source exciting) caused by undecoupling of elastic wave equation generated coincident with incident wave (such as P-wave generated with pure explosive source exciting) in homogeneous VTI, leading to crosstalk artifacts caused by unseparation of waves of the same mode. To analyze equation-converted waves, we define five pseudospatial differential operators and rewrite elastic wave equation of VTI into a form represented by Thomsen parameters. The rewrited equation shows the relationship between equation-converted wave and Thomsen parameters including three anisotropic parameters and two velocity parameters (α and β). Further studies indicate that when explosive source excites in homogeneous weak-anisotropy VTI with α/β = 1.73, the ratio between the energy of equation-converted S-waves and incident P-waves is generally <0.5 and we define equation-converted S-wave whose energy is less than the half of incident P-wave as weak equation-converted S-wave. On this basis, we propose an ERTM method for VTI with weak equation-converted S-waves and its effectiveness is demonstrated by the imaging results for two-layer models and Marmousi2 model.

Phase-encoding-based least-squares reverse time migration of controlled-order multiples

Reverse time migration of controlled-order multiples (RTM-CM) can significantly remove strong crosstalk artifacts in multiples imaging. However, the computational cost is demanding if all pairs of consecutive-order multiples are considered, and an RTM-CM image retains residual crosstalk. To address these issues, we have developed a phase-encoding-based migration approach. This approach first phase-encodes different-order multiples by randomly modifying time shifts and polarity reversals, and then blends the encoded data into supergathers. As a result of using supergathers, migrations of different-order multiples are simultaneously accomplished, which considerably improves computational efficiency. As the simultaneous migration inherits the advantages of RTM-CM and provides good gradients for least-squares migration (LSM), we introduced an iterative LSM to gradually attenuate residual crosstalks in our approach. Numerical experiments on synthetic and field data sets revealed that our approach can significantly enhance imaging quality by suppressing crosstalks, increasing spatial resolutions, and reducing computational costs.

Steeply dipping structure imaging with prismatic waves incorporating wavefield decomposition

AbstractPrismatic waves in seismic data can effectively delineate steeply dipping subsurface structures. However, the conventional migration of prismatic wave either requires the exact location of basement reflectors embedded in the accurate migration velocity model or the explicit isolation of prismatic wave from the recorded data to avoid crosstalk artefacts caused by mistaken imaging of primary reflections. Neither of the requirements is a trivial task for field data application with complicated subsurface structures. To image steeply dipping structures with an accurate but smooth enough migration velocity and without the need to extract prismatic waves from the recorded data, we analyse the prismatic imaging condition based on wavefield decomposition. In the up‐ and down‐going wavefield decomposition, the prismatic imaging condition can effectively remove the high‐wavenumber artefacts with incorrect polarity. However, the expected steeply dipping image is buried in low‐wavenumber noises. In contrast, the prismatic imaging condition based on left‐ and right‐going wavefield decomposition can accurately isolate the artefacts induced by the mistaken migration of primary waves from the steeply dipping interfaces in the image and is free of low‐wavenumber noises. Based on this analysis, we develop a reverse time migration workflow using the modified prismatic imaging condition to depict steeply dipping structures: First, we use the primary imaging condition based on the up‐and‐down‐going wavefield decomposition to obtain an image that can approximate the basement reflectors. Then, we use the modified prismatic imaging condition based on left‐ and right‐going wavefield decomposition to recover the steep interfaces. Finally, a combined subsurface image containing both basement reflectors and faults or steeply dipping structures is generated. We verify the feasibility and robustness of the modified prismatic imaging condition based reverse time migration method for delineating steeply dipping structures using several synthetic tests.

Seismic forward modeling of acoustic surface-related order-separated multiples

Seismic surface-related multiples have become a hot topic of great significance due to the buried geological information provided by broader illumination areas than primaries. In recent years, researchers attempt to extract the hidden hint of multiples rather than treating them as noise and eliminating them directly. The elimination methods, e.g., the surface-related multiple elimination (SRME) and the inverse scattering series free-surface multiple elimination (ISS-FSME), may be affected by the overlapping or proximity of primaries and multiples. Typical imaging methods, e.g., the reverse time migration (RTM) and the least-square reverse time migration (LSRTM), suffer severe crosstalk artifacts from multiples of inappropriate order and smooth migration velocities. To study the characteristics of primaries and surface-related multiples, whether for elimination or imaging, we propose a forward modeling method of acoustic surface-related order-separated multiples established on the areal/virtual source assumption. The free surface is replaced with an absorbing surface under the dipole source approximation and the ghost creation approach. We present two reflection operators to approximate the reflection at the free surface and apply them to the areal source to obtain ideal results. Numerical experiments on three models prove the effectiveness of the proposed forward modeling method of acoustic surface-related order-separated multiples.

Pre-stack elastic reverse time migration in tunnels based on cylindrical coordinates

Seismic forward-prospecting in tunnels is an important step to ensure excavation safety. Nowadays, most advanced imaging techniques in seismic exploration involve calculating the solution of elastic wave equation in a certain coordinate system. However, considering the cylindrical geometry of common tunnel body, Cartesian coordinate system seemingly has limited applicability in tunnel seismic forward-prospecting. To accurately simulate the seismic signal received in tunnels, previous imaging method using decoupled non-conversion elastic wave equation is extended from Cartesian coordinates to cylindrical coordinates. The proposed method preserves the general finite-difference time-domain (FDTD) scheme in Cartesian coordinates, except for a novel wavefield calculation strategy addressing the singularity issue inherited at the cylindrical axis. Moreover, the procedure of cylindrical elastic reverse time migration (CERTM) in tunnels is introduced based on the decoupled non-conversion elastic wavefield. Its imaging effect is further validated via numerical experiments on typical tunnel models. As indicated in the synthetic examples, both the PP- and SS-images could clearly show the geological structure in front of the tunnel face without obvious crosstalk artifacts. Migration imaging using PP-waves can present satisfactory results with higher resolution information supplemented by the SS-images. The potential of applying the proposed method in real-world cases is demonstrated in a water diversion tunnel. In the end, we share our insights regarding the singularity treatment and further improvement of the proposed method.

Elastic reverse time migration method in vertical transversely isotropic media including surface topography

AbstractCompared with acoustic seismic data, multi‐wave and multi‐component seismic data can offer some special media properties. Elastic reverse time migration is a high‐precision migration method to image multi‐wave and multi‐component seismic data. Anisotropy widely exists in the earth, and it is important to take anisotropy into account and correct the anisotropy effect for obtaining high‐quality image results during migration. However, accurate elastic reverse time migration in anisotropic media is still a challenging task, particularly for areas with irregular surface topography. To resolve these issues, a new elastic reverse time migration method is developed to correct the anisotropy effect in vertical transversely isotropic media with surface topography. We first use the modified pseudo‐acoustic wave equations of vertical transversely isotropic media to assist the elastic wavefield separation in vertical transversely isotropic media for suppressing the crosstalk artefacts between different wave modes and further generating high‐quality images. We then use a topography‐related filter to remove the influence of surface topography on the migration results of elastic reverse time migration. The advantage of the proposed topography‐related filter is that we do not need to make any changes to the conventional finite‐difference method based on regular grids but can calculate the wavefield in the areas with irregular surface topography efficiently. The synthetic examples with different surface topographies models demonstrate that our proposed elastic reverse time migration method can correct the anisotropy effect effectively, remove the influence of surface topography on elastic reverse time migration results, and generate high‐quality images.

Elastic reverse time migration without wavefield decomposition

In this paper, we provide a clear definition represented by a concise expression for seismic data migration that is a linear inversion of subsurface exploration targets using primary waves given a smooth migration model with accurate wave kinematics. Combining the definition with noncurl characteristic of P-wave and nondivergence characteristic of S-wave, we propose an elastic reverse-time migration approach without wavefield decomposition applied to heterogeneous isotropic media, in which decoupled P- and S-wave propagators independent of each other are derived. We obtain ideal imaging results when we apply the proposed migration approach to elastic synthetic seismic data of a simple four-layered model and the complex Marmousi2 model with pure P- or S-wave source exciting, demonstrating the validity of our method. Because the proposed method does not include wavefield decomposition in the backward extrapolation of recorded wavefield and demand less spatial derivative numbers in the forward extrapolation of source wavefield, it is capable of achieving high-efficiency computing. In the case of P/S composite source exciting, we suggest that although the recorded wavefield can be divided into P- and S-wave component, the P-wave component consists of primarily reflected waves PP plus primarily converted waves SP and the S-wave component consists of primarily reflected waves SS plus primarily converted waves PS. Because PP and SP or SS and PS cannot be further separated from each other by current decoupling methods, the crosstalk artifacts are unavoidable, which is verified by the migration imaging results of a two-layered model.

A new scheme of wavefield decomposed elastic least-squares reverse time migration

Elastic least-squares reverse time migration (ELSRTM) describes the reflectivity of the underground media more accurately than acoustic LSRTM in theory while suffering from the P- and S-waves crosstalk artifacts. We propose a new wavefield decomposed ELSRTM scheme to alleviate these crosstalk artifacts, which is different from conventional methods. In our new scheme, we implement the wavenumber domain elastic wavefield vector decomposition equivalently in the time-space domain to decompose source wavefield without Fourier transform, but with high precision. Then we decompose adjoint wavefield by constructing the shear component in a decoupled adjoint wave equation. Finally, based on elastic impedance parameterization, we derive the gradients with respect to elastic reflectivity in the wavefield-decomposed ELSRTM. Numerical examples show that our method is feasible even when applied to models with complex and uncorrelated P- and S-wave velocity structures.