Receiver Wavefields Research Articles

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.

Elastic reverse time migration based on nested triangular mesh in 2D isotropic media

Abstract Reverse time migration (RTM) based on two-way wave equation is an important imaging tool, which has been widely used in exploration geophysics. It offers distinct advantages in handling complex geological structures. Moreover, elastic reverse time migration (ERTM) can produce more physically meaningful images for subsurface and has received increasing attention in recent years. However, rugged topography presents challenges in the reconstruction of subsurface structures for ERTM. To overcome this problem, we introduce the grid method for topography ERTM, which is an unstructured mesh based algorithm. However, the conventional gird method for RTM is implementing by discretizing model into small meshes, leading to high computational cost. To address this problem, we introduce the grid method based on nested unstructured meshes to implement ERTM with complex surface topography. Low-order small meshes, due to their fine scale, can accurately depict complex surface topography. However, their generation process is relatively time-consuming. In contrast, high-order large meshes contain many similar small meshes internally, which can be processed in parallel, resulting in higher computational efficiency. Therefore, we propose the following strategy: for the receiver wavefield, several layers on surface discreted by the small meshes are used to place receivers and remaining layers discreted by the large meshes to improve computational efficiency. For the source wavefield, only the large meshes are used because the spacing of shot is relatively large. In this way, we ensure the accurate description of complex surface topography for the implementation of ERTM with high computational efficiency. Finally, the effectiveness of our method is validated through experiments on three models with complex topography.

An efficient ultrasonic full-matrix imaging method for industrial curved-surface components defect detection

Curved-surface components are ubiquitous in various industries. However, defects inside the components badly degenerate the mechanical properties and lead to premature failure. Ultrasonic full-matrix imaging is a prominent method in nondestructive testing, but there is still a lack of efficient imaging methods for cases with curved interfaces. To amend this problem, this article proposes an efficient ultrasonic full-matrix imaging method to detect the defects in the industrial curved-surface components. The wavefield extrapolation for full matrix capture (FMC) dataset is taken as the combined effect of the downward migration of the source and receiver wavefields in the wavenumber-frequency domain. Compensation terms corresponding to the source and receiver wavefields act on the wavefield of FMC in the spatial-frequency domain to make up for lateral variations of the sound speed. After the wavefield reconstruction, an efficient imaging condition is implemented to transform the wavefield into the defect image. The best compensation term is determined and the influence factors is investigated in the simulation experiments. Laboratory experiments furtherly validate the superiority of the proposed method over the existing methods, especially for the imaging efficiency which is twice of the phase shift migration (PSM) based method.

Strain field reconstruction from helical-winding fiber distributed acoustic sensing and its application in anisotropic elastic reverse time migration

Optical fiber-based distributed acoustic sensing (DAS) technology has been a popular seismic acquisition tool due to its easy deployment, wide bandwidth, and dense sampling. However, the sensitivity of straight optical fiber to only single-axis strain presents challenges in fully characterizing multicomponent seismic wavefields, making it difficult to use these data in elastic reverse time migration (ERTM). The helical-winding fiber receives projecting signals projected onto the fiber from all seismic strain field components and has the potential to reconstruct those strain components for ERTM imaging. Here, we give detailed mathematical principles of helical fiber-based DAS with crucial parameters such as pitch angle, gauge length, and rotating angle. At least six points of DAS responses are required in one or several winding periods to rebuild the strain fields within the seismic wavelength. The projecting matrix of conventional regular helical-winding fiber is singular and ill conditioned, which results in computation challenges for the inverse of the Hessian matrix for strain component reconstruction. To tackle this problem, we develop a nonregular variant pitch-angle winding configuration for helical fiber. Our winding design is validated using the rank and condition number of the projecting matrix, which is proven to be an important tool in the reconstruction of the original seismic strains. The recovered strain components from the DAS response are then used to backward propagate the receiver wavefields in ERTM with an efficient P/S decoupled approach. To summarize, we develop a novel winding design of helical fiber to recover the strain fields and then develop an efficient 3D anisotropic P/S wave-mode decomposition method for generating vector P and S wavefields during their propagation. Both methods are applied to build an anisotropic DAS-ERTM workflow for producing PP and PS images. Two synthetic examples demonstrate the effectiveness of our approach.

Generative adversarial network-enhanced directional seismic wavefield decomposition and its application in reverse time migration

Reverse time migration (RTM) is an accurate method for imaging complex geologic structures without imposing any dip limitations. However, a large amount of high-amplitude low-frequency noise, which is mainly generated by the crosscorrelation of source and receiver wavefields propagating in the same directions, seriously contaminates the image quality. The causal imaging condition with separated up- and downgoing wavefields is an effective approach to reduce these low-frequency artifacts. Explicit up- and downgoing wavefield decomposition based on the Hilbert transform is computationally expensive due to additional wavefield extrapolation and storage for the imaginary parts. Directionally propagating wavefields have distinctive kinematic patterns such as traveltime and wavefront curvature, which provide us an opportunity to implement the wavefield decomposition using the statistical neural network method. Using extrapolated wavefields as the input and the decomposed up-, down-, left-, and rightgoing wavefields as the labeled data, we train a pair of generative adversarial networks to predict the directional wavefields. The training data sets are generated using seismic full-waveform modeling and explicit wavefield decomposition based on the Hilbert transform. Then, the decomposed directional wavefields are incorporated into a novel imaging condition that depends on the subsurface dip angles to compute the reflectivity perpendicular to the reflectors. Numerical experiments demonstrate that our method can produce accurate directional wavefield decomposition results and high-quality reflectivity images without low-wavenumber artifacts.

Multi-image, reverse time, and Kirchhoff migrations with compact Green’s functions

Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image and no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well established in the literature (low-frequency noise separation and turning wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a postmigration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Furthermore, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using these methods.

Monochromatic wave equation reflection traveltime inversion

Wave equation reflection traveltime inversion (WRTI) is a fundamental method for interrogating the deep subsurface macrovelocity model. The time-domain WRTI calculates the gradient through the crosscorrelation of the source background and receiver scattered wavefields and the crosscorrelation of the source scattered and receiver background wavefields. During the backward propagation of the adjoint source, access to the source background and scattered snapshots of the entire propagation time is required. Because the source and receiver wavefields are extrapolated in opposite temporal directions, these source background and scattered wavefields are either stored in memory or reconstructed by additional wavefield extrapolation. This leads to a heavy memory burden and/or high computational cost. To address these challenges, we develop a new frequency-domain WRTI that is based on a monofrequency. By using the wavenumber coverage and gradient analyses, we prove that the monochromatic WRTI can produce comparable wavenumbers with time-domain and multifrequency-based WRTI. Our method directly stores monochromatic wavefields in memory because only one frequency is used for the gradient calculation. Therefore, our method significantly outperforms the conventional time-domain implementation in terms of memory requirement and computational cost. The accuracy of the monochromatic WRTI method is validated by gradient and result comparisons of several models with different complexities. Finally, we determine the effectiveness of our method by applying it to offshore streamer data.

Crosswell frequency-domain reverse time migration imaging with wavefield decomposition

Abstract Crosswell seismic technique can provide high-resolution imaging and monitoring of the subsurface. However, compared to the surface seismic, crosswell data contain more complex wave components, which increases the difficulty of seismic processing and migrations. Conventional acoustic reverse time migration (RTM) mainly uses the cross-correlation of the source forward and the receiver backward wavefields. The redundant information generated by cross-correlation may undermine the imaging reliability in the crosswell models. Thus, we develop a novel wavefield decomposition imaging condition and only used cross-correlation information of incident and reflection waves in the same propagation directions, which eliminates the artifacts generated from the cross-correlation of wave information unrelated to reflections in the crosswell image. We perform RTM in the frequency domain to maintain efficiency in multi-shot problems. A mono-frequency wavefield decomposition method is applied to separate and process the seismic data. The forward and backward wavefields are reclassified into the up- and downpropagating components. The L1 norm is introduced to enhance the robustness of the proposed imaging method. We then use this method to synthesize data from layering models and analyze the imaging results generated from each pair of cross-correlations using source and receiver wavefields. Results show that the cross-correlation information belonging to the same propagation contributes most to the crosswell image, and the other information always generates migration noises. Moreover, we apply the proposed method to a real-field dataset. Processing results validate the effectiveness of the proposed means for eliminating false events in the crosswell models and improving image quality.

Proper orthogonal decomposition based seismic source wavefield reconstruction for finite element reverse time migration

The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration (RTM), because it requires the operation of the source and receiver wavefields at the same time. The boundary value method (BVM), based on the finite difference method (FDM), can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield, which can reduce the storage burden of the RTM data. Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces, we develop a source wavefield reconstruction strategy based on the finite element method (FEM), using proper orthogonal decomposition (POD) to enhance computational efficiency. In this method, we divide the whole time period into several segments, and construct the POD basis functions to get a reduced order model (ROM) for the source wavefield reconstruction in each segment. We show the corresponding quantitative analysis of the storage requirement of the POD-FEM. Numerical tests on the homogeneous model show the effectiveness of the proposed method, while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method (FSM) and the BVM, and can be effectively applied in imaging.

Frequency-Domain Reverse-Time Migration With Attenuation Compensation

Seismic wave suffers from amplitude attenuation and phase distortion when propagating in the attenuating media, thus reverse time migration (RTM) for viscous media should take the attenuation effects into consideration. Compensating for the attenuation effects in RTM may occur numerical instability because of the exponential amplification of the extrapolated wavefields. To obtain stable imaging results, we have developed a stabilized Q-compensated reverse time migration in the frequency domain. This algorithm is implemented by the following steps: first, we use the Kolsky-Futterman model to derive a frequency-domain viscoacoustic wave equation, which can simulate the amplitude loss and phase dispersion effects separately. Then, we calculate the source wavefields in the viscoacoustic media. Next, treating the recorded (viscoacoustic) data as the receiver sources, we can obtain the phase-dispersion-only and viscoacoustic receiver wavefields, which can be used to construct the stabilized Q-compensated receiver wavefields. Finally, we apply the deconvolution imaging condition for obtaining a Q-compensated image. A simple anticline model and gas chimney model are used to verify the effectiveness of the proposed approach. The Q-compensated images for the noise-free data indicate the algorithmic stability and compensation accuracy of the proposed scheme. The noisy data tests for the gas chimney model demonstrate the good anti-noise property of our method. The field data applications further prove its feasibility and practicability.

Improving the memory efficiency of RTM using both Nyquist sampling and DCT based on GPU

Abstract Reverse time migration (RTM) is used to obtain complex structural images of subsurface media. The RTM can be expressed as a zero-lag cross-correlation between the source and receiver wave fields. As imaging conditions can be calculated based on the pre-stored source wavefield and the received wavefield generated during backward modelling, only the source wavefield must be stored in the memory (or disc). Therefore, reducing source-wavefield storage requirements can improve memory efficiency. High-performance computing based on graphic processing units (GPUs) is being developed to reduce the computational time in wave-propagation modelling. Accordingly, GPU-based RTM technology has the potential to improve the computational efficiency of RTM. Storage of the source wavefield wholly in GPU video random-access memory (VRAM) may further improve computational efficiency. In this paper, we present a new algorithm for a three-dimensional (3D) GPU-based RTM that can enable efficient storage of the source wavefield in VRAM using both Nyquist sampling and discrete cosine transform (DCT) compression. A numerical example employing a modified SEG/EAGE 3D overthrust model presented in this study verifies that the proposed algorithm requires only 2% of the memory usage of conventional RTM while producing similar results.

Elastic geometric-mean reverse time migration for source imaging

Passive source location is a fundamental problem in earthquake seismology and reservoir characterization with fluid injection. It has been shown that geometric-mean reverse time migration (GmRTM) can produce source images with improved resolution and fewer migration artifacts than conventional time-reversal imaging in acoustic media. However, the acoustic assumption often requires data windowing and polarity correction when we apply it to the elastic data, which involves manual efforts and introduces uncertainties. Therefore, we have extended this crosscorrelation-based GmRTM imaging method to elastic media. Back-propagation and Helmholtz decomposition are conducted individually for each receiver wavefield, after which we apply zero-lag crosscorrelations over the decoupled P or/and S wavefields to obtain the corresponding P-, S-, and PS-source images. Considering the influences of random noise, anisotropy, and interferences from multiple sources, we test the proposed elastic GmRTM method on a synthetic example with a layered model and determine its advantages over other imaging conditions (e.g., time-reversal imaging). The method is further validated using another synthetic test based on the elastic Marmousi model and a field-data example from Oklahoma.

Wave-equation diffraction imaging using pseudo dip-angle gather

Diffraction images can directly indicate local heterogeneities, such as faults, fracture zones, and erosional surfaces, that are of high interest in seismic interpretation and unconventional reservoir development. We have adopted a new tool called pseudo dip-angle gather (PDAG) for imaging diffractors using the wave equation. PDAG has significantly lower computational cost compared to the classic dip-angle gather (DAG) due to the use of plane-wave gathers, a fast local Radon transform algorithm, and a one-side decomposition assumption. Pseudo dip angle is measured from the vertical axis to the bisector of the plane-wave surface incident angle and scattered wave-propagation angle. PDAG is generated by choosing the zero lag of the correlation of the plane-wave source wavefields and the decomposed receiver wavefields. It reveals diffraction and reflection patterns similar to DAG, that is, diffractions spreading as a flat event and reflections focused on a specular angle, whereas they may have dissimilar coverage for diffraction and different focused locations for reflection compared to that of DAG. A windowed median filter is then applied to each PDAG for extracting the diffraction energy and suppressing the focused reflection energy. In addition, the stacked PDAG can be used to evaluate the migration accuracy by measuring the flatness of the image gathers. Numerical tests on synthetic and field data sets demonstrate that our method can efficiently produce accurate results for diffraction images.

Deep Learning for Enhancing Multisource Reverse Time Migration

Reverse time migration (RTM) is a technique used to obtain high-resolution images of underground reflectors; however, this method is computationally intensive when dealing with large amounts of seismic data. Multi-source RTM can significantly reduce the computational cost by processing multiple shots simultaneously. However, multi-source-based methods frequently result in crosstalk artifacts in the migrated images, causing serious interference in the imaging signals. Plane-wave migration, as a mainstream multi-source method, can yield migrated images with plane waves in different angles by implementing phase encoding of the source and receiver wavefields; however, this method frequently requires a trade-off between computational efficiency and imaging quality. We propose a method based on deep learning for removing crosstalk artifacts and enhancing the image quality of plane-wave migration images. We designed a convolutional neural network that accepts an input of seven plane-wave images at different angles and outputs a clear and enhanced image. We built over 500 1024×256 velocity models, and employed each of them using plane-wave migration to produce raw images at 0°, ±10°, ±20°, and ±30° as input of the network. Labels are high-resolution images computed from the corresponding reflectivity models by convolving with a Ricker wavelet. Random sub-images with a size of 512×128 were used for training the network. Numerical examples demonstrated the effectiveness of the trained network in crosstalk removal and imaging enhancement. The proposed method is superior to both the conventional RTM and plane-wave RTM (PWRTM) in imaging resolution. Moreover, the proposed method requires only seven migrations, significantly improving the computational efficiency. In the numerical examples, the processing time required by our method was approximately 1.6% and 10% of that required by RTM and PWRTM, respectively.

First-order multiples imaging aided by water bottom

Surface-related multiples frequently propagate into the subsurface and contain abundant information on small reflection angles. Compared with the conventional migration of primaries, migration of multiples offers complementary illumination and a higher vertical resolution. However, crosstalk artifacts caused by unrelated multiples during reverse time migration (RTM) using multiples severely degrade the reliability and interpretation of the final migration images. Therefore, we proposed RTM using first-order receiver-side water-bottom-related multiples for eliminating crosstalk artifacts and enhancing vertical resolution. We first backward propagate the first-order receiver-side water-bottom-related multiples using a water-layer model, followed by saving the upper boundary wavefield. Then we produce the source wavefield using a seismic wavelet and the receiver wavefield by back-extrapolating the saved boundary. Finally, the cross-correlation imaging condition is applied to generate the final image. This method transforms the receiver-side multiples into primaries, followed by the conventional migration processing procedures. Numerical examples using synthetic datasets demonstrate that our method significantly enhances the imaging quality by eliminating crosstalk artifacts and improving the resolution.

Memory-efficient source wavefield reconstruction and its application to 3D reverse time migration

Reverse time migration (RTM) generally uses the zero-lag crosscorrelation imaging condition, requiring the source and receiver wavefields to be known at the same time step. However, the receiver wavefield is calculated in time-reversed order, opposite to the order of the forward-propagated source wavefield. The inconvenience can be resolved by storing the source wavefield on a computer memory/disk or by reconstructing the source wavefield on the fly for multiplication with the receiver wavefield. The storage requirements for the former approach can be very large. Hence, we have followed the latter route and developed an efficient source wavefield reconstruction method. During forward propagation, the boundary wavefields at N layers of the spatial grid points and a linear combination of wavefields at [Formula: see text] layers of the spatial grid points are stored. During backward propagation, it reconstructs the source wavefield using the saved wavefields based on a new finite-difference stencil ( M is the operator length parameter, and [Formula: see text]). Unlike existing methods, our method allows a trade-off between accuracy and storage by adjusting N. A maximum-norm-based objective function is constructed to optimize the reconstruction coefficients based on the minimax approximation using the Remez exchange algorithm. Dispersion and stability analyses reveal that our method is more accurate and marginally less stable than the method that requires storage of a combination of boundary wavefields. Our method has been applied to 3D RTM on synthetic and field data. Numerical examples indicate that our method with [Formula: see text] can produce images that are close to those obtained using a conventional method of storing M layers of boundary wavefields. The memory usage of our method is [Formula: see text] times that of the conventional method.

Angle-Weighted Reverse Time Migration With Wavefield Decomposition Based on the Optical Flow Vector

Reverse time migration (RTM) is based on the two-way wave equation, so its imaging results obtained by conventional zero-lag cross-correlation imaging conditions contain a lot of low-wavenumber noises. So far, the wavefield decomposition method based on the Poynting vector has been developed to suppress these noises; however, this method also has some problems, such as unstable calculation of the Poynting vector, low accuracy of wavefield decomposition, and poor effect of large-angle migration artifacts suppression. This article introduces the optical flow vector method to RTM to realize high-precision wavefield decomposition for both the source and receiver wavefields and obtains four directions of wavefields: up-, down-, left-, and right-going. Then, the cross-correlation imaging sections of one-way propagation components of forward- and back-propagated wavefields are optimized and stacked. On this basis, the reflection angle of each imaging point is calculated based on the optical flow vector, and an attenuation factor related to the reflection angle is introduced as the weight to generate the optimal stack images. The tests of theoretical model and field marine seismic data illustrate that compared with the conventional RTM with wavefield decomposition based on the Poynting vector, the angle-weighted RTM with wavefield decomposition based on the optical flow vector proposed in this article can achieve wavefield decomposition for both the source and receiver wavefields and calculate the reflection angle of each imaging point more accurately and stably. Moreover, the proposed method adopts angle weighting processing, which can further eliminate large-angle migration artifacts and effectively improve the imaging accuracy of RTM.

Research note: Inverse propagation in 1.5‐dimensional amplitude‐versus‐offset joint migration inversion

ABSTRACTThe state‐of‐the‐art joint migration inversion faces the so‐called amplitude‐versus‐offset challenge, due to adopting over‐simplified one‐way propagation, reflection and transmission operators to avoid over‐parameterization in the inversion process. To overcome this challenge, we apply joint migration inversion to horizontally layered media (or 1.5‐dimensional media) and parameterize the solution space via density and velocity models. In this scenario, one‐way propagation, reflection and transmission operators required by the joint migration inversion process can be analytically and correctly derived from the subsurface models, so the amplitude‐versus‐offset challenge is successfully overcome. We introduce a new concept, which is named ‘inverse propagation’, into our 1.5‐dimensional amplitude‐versus‐offset joint migration inversion. It can correctly reconstruct subsurface wavefields by using a surface‐recorded receiver wavefield with all the influence of transmission, reflection and multiples accounted for. A synthetic example is used to demonstrate the correctness of the inverse propagation. This work is the foundation to further develop the 1.5‐dimensional amplitude‐versus‐offset joint migration inversion technology.

Addressing the crosstalk issue in imaging using seismic multiple wavefields

Surface-related-multiple wavefields constitute redundant information in conventional migration and can often be difficult to attenuate. However, when used for migration, multiple wavefields can improve subsurface illumination. Unfortunately, the process of imaging using multiples involves the management of crosstalk, which largely restricts its application. Crosstalk causes phantom images formed by spurious correlation of unrelated events in a migration process. These events can be unrelated orders of multiples in the source and receiver wavefields; they can also be one event associated with a reflector in the source wavefield and another event generated by a different reflector in the receiver wavefield. We have first examined crosstalk by explicitly investigating its generation mechanisms in a migration process and classifying it into different categories based on causality. Following this analysis, crosstalk can be predicted in a migration process and subtracted in the image domain; however, this method is usually difficult to apply due to the complexity of wavefield separation and adaptive subtraction. Furthermore, we develop different algorithms to attenuate the crosstalk, including a deconvolution imaging condition, a least-squares migration (LSM) method, and an advanced algorithm combining LSM with a deconvolution imaging condition. We evaluate these different strategies with synthetic examples. A deconvolution imaging condition can attenuate some crosstalk, but it is less effective at suppressing strong coherent crosstalk events. However, the LSM method can fundamentally address the crosstalk issue, and this approach is further optimized when combined with a deconvolution imaging condition.

Low-rank representation of omnidirectional subsurface extended image volumes

Subsurface-offset gathers play an increasingly important role in seismic imaging. These gathers are used during velocity model building and inversion of rock properties from amplitude variations. Although powerful, these gathers come with high computational and storage demands to form and manipulate these high-dimensional objects. This explains why only limited numbers of image gathers are computed over a limited offset range. We avoid these high costs by working with highly compressed low-rank factorizations. These factorizations are obtained via a combination of probings with the double two-way wave equation and randomized singular-value decompositions. In turn, the resulting factorizations give us access to all subsurface offsets without having to form the full extended image volumes (EIVs) that are at best quadratic in image size. As a result, we can easily handle situations in which conventional horizontal offset gathers are no longer focused. More importantly, the factorization also provides a mechanism to use the invariance relation of EIVs for velocity continuation. With this technique, EIVs for one background velocity model can be directly mapped to those of another background velocity model. Our low-rank factorization inherits this invariance property, so that factorization costs arise only once when examining different imaging scenarios. Because all imaging experiments only involve the factors, they are computationally efficient with costs that scale with the rank of the factorization. Examples using 2D synthetics, including a challenging imaging example with salt, validate the methodology. Instead of brute-force explicit crosscorrelations between shifted source and receiver wavefields, our approach relies on the underlying linear-algebra structure that enables us to work with these objects without incurring unfeasible demands on computation and storage.