Conventional Reverse Time Migration Research Articles

One-step sparse-matrix method for full wave equation depth migration

By completely solving the second-order full-acoustic wave equation, two-way/full wave equation migration generates images up to arbitrary angles in inhomogeneous media. Full wave equation depth migration (FWDM) necessitates less wavefield storage during imaging, generates clearer imaging results, and has more computational flexibility compared with conventional reverse time migration. Conventionally, FWDM uses Runge-Kutta or two explicit one-way operators to extrapolate the data, which involves either a multirecursive process or complex square root computations of the Helmholtz operator, causing implementation complexities and inconveniences. To overcome these challenges, a novel algorithm called the one-step sparse-matrix method for FWDM (OSM-FWDM) is developed and executed. This method involves a straightforward calculation of the full wave equation propagator through a Taylor expansion and using the so-called precise integration method. The computational efficiency can be significantly improved by using sparse-matrix multiplication in the implementation of wavefield extrapolation. Building upon that, the method serves as a basic solution complemented by FWDM, offering straightforward, efficient, and easy coding characteristics. Our OSM-FWDM method is simpler and faster compared with conventional FWDM, all while maintaining imaging accuracy. In addition, a new solution that uses an extended velocity model to remove source-related artifacts in FWDM is developed and illustrated. These improvements are demonstrated through a series of numerical examples and a real data application.

Improving reverse time migration of ground-penetrating radar under zero-time imaging conditions using cross-correlation superposition projection

ABSTRACT Aiming to address the issue of significant artefact interference in conventional reverse time migration (RTM) imaging under zero-time imaging conditions of ground-penetrating radar (GPR), this study proposes an improvement of RTM using cross-correlation superposition projection (CSP) to enhance imaging quality. The method is based on the original RTM imaging framework, where all single-trace signals are individually processed using RTM. The individual imaging results are then multiplied pairwise and added together to create a CSP. After normalizing the CSP and properly setting the adaptive threshold, the CSP can focus RTM imaging on the GPR signal reflection interface area, effectively removing artefact interference. Synthetic data test confirms that the CSP-improved RTM, when compared to conventional RTM and Laplace filtering methods, not only preserves all effective information in imaging but also eliminates artefact interference. This improvement significantly enhances the quality and resolution of the imaging results. Furthermore, the practicality and effectiveness of the CSP-improved RTM method in engineering applications have been validated using a set of measured GPR data.

Elastic reverse time migration using an efficient and accurate adaptive variable grid discretization method

Abstract The conventional reverse time migration utilizes regularly sampled computational grids to simulate wave propagation. Selecting the appropriate grid sampling is important for computational accuracy and efficiency. In general, the uniform-size grid cannot represent the complexity of the geology well. The grid may appear sparse in the low-velocity zone, especially in shallow depths where dispersion may occur. Conversely, it may appear excessively dense in the high-velocity zone, such as at greater depths or within a salt body, which results in higher computational memory and time consumption. To overcome these issues, we developed an efficient and accurate adaptive variable grid discretization method that automatically selects the vertical grid size based on the velocity, depth, and dominant frequency of the wavelet in elastic medium. Then we reformulated the elastic equations based on the adaptive variable grid by introducing a mapping relationship. To test the effectiveness, accuracy, and efficiency of the equation, we implemented it to both the forward propagation and migration of elastic wavefield. Synthetic numerical examples demonstrate that our proposed method can achieve elastic wavefield separation and no significant dispersion phenomenon. The multi-component imaging accuracy of reverse time migration is nearly equivalent to the traditional method, while significantly improving computational efficiency and saving storage space.

Target-oriented image-domain elastic least-squares reverse time migration

Elastic least-squares reverse time migration (ELSRTM), as an imaging method, offers advantages over conventional elastic reverse time migration (ERTM), including higher resolution, better amplitude balancing, reduced crosstalk, and broader bandwidth. However, conventional ELSRTM involves iterative processes in the data domain, resulting in high computational costs. Moreover, since time is continuous during data domain extrapolation, it cannot solely focus on the target area within the subsurface medium. In contrast, image-domain ELSRTM (IDELSRTM) exhibits high computational efficiency and the ability to image target area. Currently, research on image-domain least-squares reverse time migration is predominantly focused on the acoustic wave assumption, despite elastic waves being closer to the actual subsurface medium and providing richer imaging information. In this study, within the framework of data domain ELSRTM, we derived the objective function for the IDELSRTM and introduced an L1 regularization term under the L2 norm to enhance inversion stability. We devised an inversion strategy employing the fast iterative shrinkage-thresholding algorithm (FISTA). Furthermore, drawing from the point spread functions theory in optics, we derived the mapping relationship between the elastic multi-parameter point spread functions (PSF) and the elastic multi-parameter Hessian matrix, and the relationship between the Hessian matrix and the ERTM images. We provided the computational method for the elastic multi-parameter Hessian matrix and utilized it as the linearized forward operator for IDELSRTM. Through numerical experiments, we further elucidated the relationship between the ERTM images and the Hessian matrix under the framework of IDELSRTM, along with the sources of crosstalk in ERTM. Applying our proposed target-oriented IDELSRTM method to layered models and the Marmousi2 model, we demonstrated its effectiveness in improving imaging resolution and quality with only a marginal increase in computational overhead compared to conventional ERTM.

Efficient Method for Enhancing Reverse-Time Migration Images Using Vertical Seismic Profiling Data

Vertical seismic profiling has garnered widespread attention in the industry as a supplement to seismic exploration due to its higher data quality compared to surface seismic data. However, its unique observation system in which geophones are only distributed within observation wells results in uneven coverage of subsurface structures. This can lead to significant noise when directly applying conventional reverse-time migration techniques used in surface seismic imaging. This study addresses the issue of noise suppression in reverse-time migration imaging associated with walk-away vertical seismic profiling and presents two main innovations. First, a common-receiver reverse-time migration imaging method is proposed, which uses the observation signals as excitation signals for the corresponding shots after reverse-time processing. Second, an excitation-time-constrained cross-correlation imaging condition is introduced to eliminate non-contributing portions of the wavefield, thereby modifying the traditional cross-correlation imaging condition to include an excitation time constraint. The combination of these methods enhances imaging quality by effectively suppressing noise, as demonstrated through theoretical analysis and numerical simulations with synthetic models.

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.

Nonlinear least-squares reverse time migration of prismatic waves for delineating steeply dipping structures

Prismatic reflections in seismic data carry abundant information about subsurface steeply dipping structures, such as salt flanks or near-vertical faults, playing an important role in delineating these structures when effectively used. Conventional linear least-squares reverse time migration (L-LSRTM) fails to use prismatic waves due to the first-order Born approximation, resulting in a blurry image of steep interfaces. We develop a nonlinear LSRTM (NL-LSRTM) method to take advantage of prismatic waves for the detailed characterization of subsurface steeply dipping structures. Compared with current least-squares migration methods of prismatic waves, our NL-LSRTM is nonlinear and thus avoids the challenging extraction of prismatic waves or the prior knowledge of L-LSRTM results. The gradient of NL-LSRTM consists of the primary and prismatic imaging terms, which can accurately project observed primary and prismatic waves into the image domain for the simultaneous depiction of near-horizontal and near-vertical structures. However, we find that the full Hessian-based Newton normal equation has two similar terms, which prompts us to make further comparison between the Newton normal equation and our NL-LSRTM. We determine that the Newton normal equation is problematic when applied to the migration problem because the primary reflections in the seismic records will be incorrectly projected into the image along the prismatic wavepath, resulting in an artifact-contaminated image. In contrast, the nonlinear data-fitting process included in the NL-LSRTM contributes to balancing the amplitudes of primary and prismatic imaging results, thus making NL-LSRTM produce superior images compared with the Newton normal equation. Several numerical tests validate the applicability and robustness of NL-LSRTM for the delineation of steeply dipping structures and illustrate that the imaging results are much better than the conventional L-LSRTM.

Viscoacoustic least squares reverse-time migration using L1-2 norm sparsity constraint

Abstract Least-squares reverse-time migration (LSRTM) has become an advanced technique for complex structures imaging of the subsurface, as it can provide a higher resolution and more balanced amplitude migrated image than conventional reverse-time migration (RTM). However, the intrinsic attenuation of subsurface introduces amplitude attenuation and phase dispersion of seismic wavefield, which leads to the inverted image kinematically and dynamically inexactitude. Moreover, the imperfect geometry, limited bandwidth of seismic data, and inappropriate modeling kernel etc., would inevitably introduce two side-effects in migrated image, resulting in degradation of LSRTM imaging potential. To alleviate above issues, we present a data-domain sparsity constraint viscoacoustic least-squares reverse-time migration algorithm in this paper. In particular, we utilize the decoupled constant Q fractional Laplacians (DFLs) viscoacoustic wave equation as the modeling kernel to describe the attenuation effects of the subsurface, while a model constraint constructed in the misfit function via L1-2 norm is carried out to clear the migrated artefacts and boost the imaging resolution. Thanks to the excellent performance in sparsity, the drawbacks of unconstraint LSRTM can be effectively mitigated by the L1-2 norm-based regularization. In this paper, we adopt the alternating direction of multipliers method (ADMM) to iteratively address the constrained L1-2 minimization problem by implementing a proximal operator, and three synthetic examples are hired to evaluate the effectiveness and practicability of the proposed strategy. Migration results prove that the proposed scheme can effectively compensate the attenuation effects, improve the resolution, and suppress the migration artifacts of inverted images even in the complex imaging situations.

Compact reverse time migration: A real-time approach for full waveform ultrasound imaging for breast.

We present compact reverse time migration (CRTM), a real-time ultrasound imaging method that can exploit the full waveform information of ultrasonic wave records for imaging breast tissue. Conventional reverse time migration (RTM) computes the gradient of the reflective ultrasound data with respect to the perturbation of the velocity model of the soft tissues and the gradient can indicate the interface between different types of body tissue. In contrast to conventional reflection ultrasound (B-mode), which is based on the high-frequency approximation to the wave equation, the RTM algorithm is based on the complete wave equation, and can thus exploit the full waveform (wide-spectrum) information of the data and provide an image with higher resolution. Unfortunately, the computational burden of RTM is noticeably higher than the ray-based B-mode. This precludes real-time applications, one of the most important features of ultrasound imaging. The proposed CRTM algorithm can significantly reduce the computational costs of RTM, such that it can be applied for real-time imaging. We demonstrate the performance of CRTM through a synthetic experiment of ultrasound breast imaging. CRTM can be potentially adapted to related signal-processing fields, such as seismic imaging, acoustic camera systems, and radar imaging.

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.

Multiparameter least‐squares reverse time migration using the viscoacoustic‐wave equation

AbstractIn viscoacoustic least‐squares reverse time migration methods, the reflectivity image associated with the Q factor is negligible, inverting only the velocity (v) parameter or v‐related variables such as squared slowness or bulk modulus. However, the Q factor influences the amplitude and phase of the seismic data, especially in basins containing gas reservoirs or storing . Therefore, the Q factor and its associated parameters must be considered in the context of viscoacoustic least‐squares reverse time migration. Thus, we propose a multiparameter viscoacoustic least‐squares reverse time migration procedure, which obtains the inverse of bulk modulus (κ) and the Q magnitude (τ) simultaneously. We derive and implement the multiparameter forward and adjoint pair Born operators and the gradient formulas concerning κ and τ parameters. Then, we apply these derivations in our proposed multiparameter approach, which can produce images with better balanced amplitudes and more resolution than conventional reverse time migration images.

Least Squares Reverse Time Migration of Ground Penetrating Radar Data Based on Modified Total Variation

As a fundamental part of ground penetrating radar (GPR) data processing, reverse time migration (RTM) can correctly position reflection waves and focusing diffraction waves on the proper spatial position. Least-squares reverse-time migration (LSRTM) is widely used in the seismic field for its ability to suppress artifacts and generate high-resolution images in comparison to conventional RTM. However, in the particular case of GPR detection methods, LSRTM is extremely susceptible to aliasing artifacts caused by under-sampling. In pursuit of enhanced precision in underground structure characterization, this paper presents the development of a new LSRTM based on modified total variation (MTV) regularization to improve imaging resolution. Initially, the objective function of LSRTM is derived by combining the Born approximation in 2-D transversal magnetic mode. Next, the adjoint equations and their gradients are solved using the Lagrange multiplier method. The objective function is then constrained by MTV regularization to ensure the precision and convergence of the LSRTM, which delivers a refined edge with reconstruction details. In the numerical experiments, in comparison to the conventional LSRTM method, the LSRTM-MTV algorithm demonstrated a 30.4% increase in computational speed and a 21.1% reduction in mean squared error (MSE). The outperformance of the proposed method is verified in detail through the image resolution and amplitude preservation in the test of synthetic data and laboratory data. Future research efforts will center on applying the proposed method to models featuring dispersive or anisotropic media that closely mimic real-world conditions and extending the application to various imaging techniques involving objective function minimization.

An improved reverse time migration for subsurface imaging over complex geological structures: A numerical study

In seismic exploration, it is a critical task to image and interpret different seismic signatures over complex geology due to strong lateral velocity contrast, steep reflectors, overburden strata and dipping flanks. To understand the behavior of these seismic signatures, nowadays Reverse Time Migration (RTM) technique is used extensively by the oil & gas industries. During the extrapolation phase of RTM, the source wavefield needs to be saved, which needs high storage memory and large computing time. These two are the main obstacles of RTM for production use. In order to overcome these disadvantages, in this study, a second-generation improved RTM technique is proposed. In this improved form, a shift operator is introduced at the time of imaging condition of RTM algorithm which is performed automatically both in space and time domain. This effort is made to produce a better-quality image by minimizing the computational time as well as numerical artefacts. The proposed method is applied over various benchmark models and validated by implementing over one field data set from the Jaisalmer Basin, India. From the analysis, it is observed that the method consumes a minimum of 45% less storage space and reduce the execution time by 20%, as compared to conventional RTM. The proposed RTM is found to work efficiently in comparison to the conventional RTM both in terms of imaging quality and minimization of numerical artefacts for all the benchmark models as well as field data.

Frequency-Domain Reverse-Time Migration with Analytic Green's Function for the Seismic Imaging of Shallow Water Column Structures in the Arctic Ocean.

Seismic oceanography can provide a two- or three-dimensional view of the water column thermocline structure at a vertical and horizontal resolution from the multi-channel seismic dataset. Several seismic imaging methods and techniques for seismic oceanography have been presented in previous research. In this study, we suggest a new formulation of the frequency-domain reverse-time migration method for seismic oceanography based on the analytic Green's function. For imaging thermocline structures in the water column from the seismic data, our proposed seismic reverse-time migration method uses the analytic Green's function for numerically calculating the forward- and backward-modeled wavefield rather than the wave propagation modeling in the conventional algorithm. The frequency-domain reverse-time migration with analytic Green's function does not require significant computational memory, resources, or a multifrontal direct solver to calculate the migration seismic images as like conventional reverse-time migration. The analytic Green's function in our reverse-time method makes it possible to provide a high-resolution seismic water column image with a meter-scale grid size, consisting of full-band frequency components for a modest cost and in a low-memory environment for computation. Our method was applied to multi-channel seismic data acquired in the Arctic Ocean and successfully constructed water column seismic images containing the oceanographic reflections caused by thermocline structures of the water mass. From the numerical test, we note that the oceanographic reflections of the migrated seismic images reflected the distribution of Arctic waters in a shallow depth and showed good correspondence with the anomalies of measured temperatures and calculated reflection coefficients from each XCDT profile. Our proposed method has been verified for field data application and accuracy of imaging performance.

Source-independent least-squares reverse time migration in vertical transversely isotropic media based on the Student’s t-distribution

Abstract Seismic anisotropy exists in various types of strata and should be considered in seismic imaging schemes. Seismic imaging algorithms based on isotropic assumption neglect the effects of anisotropy on seismic data, which cause migration artifacts and waveform distortion. To correct the effects of anisotropy on seismic wave propagation, we propose an imaging algorithm that performs least-squares reverse time migration in vertical transversely isotropic acoustic media. We derive the following operators to implement this algorithm, the de-migration operator, its adjoint migration operator, and the corresponding gradient. However, an inaccurate estimated source wavelet will introduce error in the seismic simulation, and thus increase the mismatch between observed and synthetic data for least-squares reverse time migration. In addition, the noises, especially the noises with abnormal amplitudes in the seismic data, damage the inversion convergence and reduce the imaging resolution. To improve the image quality, we propose to use convolved wavefields between observed and synthetic data so that such a mismatch can be independent of the source wavelets. Also, we use the Student’s t-distribution instead of L2 norm in our inversion scheme to better handle the seismic noise. Its implementation only modifies the gradient of the conventional least-square reverse time migration scheme. Our numerical tests show a clear improvement using our proposed imaging algorithm when compared with the conventional isotropic migration scheme for the anisotropic data. Also, the synthetic examples demonstrate the feasibility and effectiveness of our proposed source-independent algorithm using the Student’s t-distribution.

Atlantis — 20 years of seismic innovation finally removes the shroud of mystery

The Atlantis Field has gone through more than two decades of continuous seismic imaging efforts, during which time many innovative technologies were incubated, the most recent one being the successful application of full-waveform inversion (FWI) in salt environments. This technique led to a significant improvement in the subsalt image. However, imaging challenges remain for the Atlantis reservoirs, primarily due to the complex overburden salt geometries and the highly compartmentalized reservoir. Even with an improved velocity model from FWI, the conventional reverse time migration (RTM) images still suffer from illumination issues and contain strong migration swings that hinder the subsalt imaging and subsequent interpretations. Furthermore, early versions of FWI employed an acoustic assumption, leading to visible salt halos at the salt boundaries in the velocity model, which adversely impacted the reservoir imaging. In the last 12 months, elastic time-lag FWI (TLFWI) and FWI-derived reflectivity (FDR) imaging using long-offset ocean-bottom node data have minimized these imaging issues at Atlantis, providing another step change in subsalt understanding. Although the 3D RTM images using the elastic FWI velocity model are similar overall to their acoustic counterparts, the 4D time-lapse RTM images at Atlantis show noticeable improvements. Furthermore, FDR images derived from elastic FWI velocities show obvious benefits over the acoustic ones. With a more accurate modeling engine that allows for better match between synthetic and real data, FDR imaging shows improved illumination, higher signal-to-noise ratio, and better reservoir details over acoustic FDR imaging. This recent advancement in using elastic TLFWI has had immediate positive effects in facilitating the Atlantis Field's current and future development.

High Resolution Backscattering Acoustic Tomography Method Based on Reverse Time Migration for Arbitrary Wideband Sounding Signal

Backscattered wave acoustic tomography using wideband probing signals makes it possible to obtain three-dimensional (3D) images of scattering inhomogeneities. Signal processing based on the reverse time migration (RTM) method allows one to take into account the influence of background refractive obstacles of the medium to minimize distortions of reconstructed tomographic images. We propose a noniterative method of acoustic tomography in an immersion medium based on RTM approach supplemented with linear signal preprocessing to enhance resolution of reconstructing tomography images. The visualization of scattering objects is based on wave inversion from the measurement area considering the probing wave field specially distorted to perform regularized back convolution. The applicability of the proposed method for visualizing scattering objects in water is shown analytically, numerically and experimentally. The proposed method is resistant to noise according to regularization. The results obtained show the agreement between the numerical and analytical solution. Using the example of sounding with linear frequency modulation signals, it is demonstrated that the proposed method allows increasing the resolution of tomographic images in comparison with conventional RTM. The novelty of the proposed method is the preliminary filtration of the forward propagation wave in the course of solving the inverse problem. This approach improves the resolution of tomographic images and allows considering the influence of obstacles.

Least-Squares Full-Wavefield Reverse Time Migration Using a Modeling Engine With Vector Reflectivity

Conventional least-squares reverse time migration (LSRTM) generally involves a de-migration operator based on the first-order scattering approximation (Born modeling), which can only simulate the seismograms containing the primary reflected wave. When the input observed seismograms contain “redundant information” (especially multiples), crosstalk may occur in the imaging results. Therefore, we develop a least-squares full-wavefield reverse time migration (LSFWM), which is implemented based on a two-way modeling engine with vector reflectivity and the corresponding adjoint sensitive kernel. This modeling engine is modified from the variable density acoustic wave equation and can simulate the subsurface wavefield containing the primaries and multiples only by giving the accurate or estimated subsurface reflectivity and velocity. Theoretically, this LSFWM approach can eliminate the influence of “redundant information” on imaging and provide higher-quality imaging results compared to conventional LSRTM. In addition, since the modeling engine is based on vector reflectivity, the imaging results produced by the LSFWM are also vectorized, which can give more information about the subsurface structures, especially steep structures. And the imaging results produced by the LSFWM can accurately depict the subsurface reflectivity. These are helpful to obtain the information on subsurface structure and physical properties more clearly.

Joint elastic reverse time migration of towed streamer and sparse ocean-bottom seismic node hybrid data

Compared to 1C towed-streamer (TS) seismic exploration, 4C ocean-bottom seismic (OBS) node exploration has great advantages in complex structure imaging, lithology, and fluid identification using elastic waves. However, sparse spatial sampling of OBS node surveys highlights the problems of the imaging acquisition footprint, poor phase continuity, and low signal-to-noise ratio (S/N) with conventional elastic reverse time migration (ERTM) methods. Therefore, a solution of joint ERTM (J-ERTM) is proposed by combining sparse OBS node data with dense TS data. In the J-ERTM of the hybrid data, a novel weighted boundary condition combined with acoustic-elastic coupling equations and a vector-based crosscorrelation imaging condition are presented to perform PP and PS imaging by receiver-side tensorial extrapolation of TS and OBS node hybrid data. A synthetic example demonstrates that our method can effectively process TS and OBS node hybrid data and improve elastic imaging problems caused by OBS node sparse acquisition. J-ERTM techniques also are applied to an active-source OBS data set from the South China Sea. To improve the imaging quality with limited data, some preprocessing procedures for field TS and OBS node hybrid data sets are necessary, such as denoising, OBS node relocation, OBS node orientation correction, OBS node calibration, and others. After preprocessing, the pressure component and velocity components have a more physical energy relationship, more consistent frequency range and wavelet, and a higher S/N. Finally, the preprocessed hybrid data can be used for J-ERTM. The imaging results demonstrate that our method works well with field data.

Enhancing one-way wave equation-based migration with deep learning

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.