Reverse Time Migration Method Research Articles

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.

Shallow crustal structure of the northern Longmen Shan fault zone revealed by a dense seismic array with ambient noise analysis

The Longmen Shan (LMS) fault zone located in the southwest of China is not only the boundary tectonic zone of the Tibetan Plateau and South China block, but also an important part of the north–south seismic belt of China. To investigate the detailed crustal structure of the LMS fault zone, we deployed a dense seismic array of 151 short-period temporary stations in its northern section from March 16 to April 6, 2023. Continuous vertical component ambient noise waveforms recorded by these stations were cross-correlated for all station pairs, enabling the extraction of Rayleigh wave phase velocity dispersion curves across periods ranging from 0.5 s to 6 s. We then inverted these data to derive the crustal shear wave velocity using direct surface wave tomography. Meanwhile, a linear sub-array consisting of 54 stations and crossing the surface rupture of the 2008 Wenchuan earthquake was used to image the fault structure by applying the Transmitted Surface Wave Reverse Time Migration method (TSW-RTM). The ambient noise tomography results show that strong lateral heterogeneity exists in the shallow crust in the study area, with a high shear velocity in the northwest and a low shear velocity in the southeast. The low shear velocity is generally distributed between the Yingxiu-Beichuan fault (YBF) and the Guanxian-Jiangyou fault (GJF). The results of TSW-RTM indicate that the Wenchuan-Maoxian fault (WMF) and the YBF are both characterized with a steep dip to the northwest. Our results could serve as the important basis for the study of segmentation characteristics of the LMS fault and seismic hazard preparation and mitigation.

An efficient illumination compensation method for reverse time migration

AbstractBy directly solving the full two‐way wave equation, reverse time migration has superiority over other imaging algorithms in handling steeply dipping structures and other complicated geological models. Moreover, by incorporating the asymptotic inversion operator into reverse time migration imaging condition, the imaging algorithm is able to give a quantitative estimation of parameter perturbation in high‐frequency approximation sense. However, because conventional asymptotic inversion only accounts for geometrical spreading, uneven illumination due to irregular acquisition geometry and inhomogeneous subsurface at each image point is neglected. The omit of illumination compensation significantly affects the imaging quality. Wave‐equation‐based illumination compensation methods have been extensively studied in the past. However, the traditional wave‐equation‐based illumination compensation methods usually require high computational cost and huge storage. In this paper, we propose an efficient wave‐equation‐based illumination compensation method. Under high‐frequency approximation, we first define a Jacobian determinant to measure the regularity of subsurface illumination, and then illumination compensation operators are proposed based on the Jacobian. Through boundary integration, we further express the illumination compensation operators through extrapolated wavefields; the explicit computation of asymptotic Green's functions is thus avoided, and an efficient illumination compensation implementation for reverse time migration is achieved. Numerical results with both synthetic and field data validate the effectiveness and efficiency of the presented method.

2D acoustic equation prestack reverse-time migration based on an optimized combined compact difference scheme

Abstract Reverse-time migration (RTM) is widely regarded as one of the most accurate migration methods available today. A crucial step in RTM involves extending seismic wavefields forward and backward. Compared to the conventional central finite-difference (CFD) scheme, the combined compact difference (CCD) scheme offers several advantages, including a shorter difference operator and the suppression of numerical dispersion under coarse grids. These attributes conserve memory and enhance effectiveness while maintaining the same level of differential precision. In this article, we begin with the five-point eighth-order CCD scheme and utilize the least squares method and Lagrange multiplier method to optimize the difference coefficients. This optimization is guided by the concept of dispersion-relation-preserving (DRP). The result is the acquisition of an optimized combined compact difference (OCCD) scheme, further enhancing the ability to suppress numerical dispersion. We thoroughly compare and analyze dispersion relationships and stability conditions. In addition, we examine several crucial steps in the RTM of the second-order acoustic wave equation. These steps include absorption boundary conditions, boundary storage strategy, and Poynting vector imaging conditions. Finally, we apply both the CCD and OCCD schemes in the RTM of the layered model, graben model, and SEG/EAGE salt model. We compare these results with those obtained from CFD's RTM. Numerical findings demonstrate that, in contrast to the CFD scheme, the CCD scheme effectively suppresses numerical dispersion and enhances imaging accuracy. Moreover, the optimized OCCD scheme further improves the ability to suppress numerical dispersion and can obtain better imaging results, which is an effective RTM method suitable for coarse grid conditions.

Research on the differential coefficient least-squares optimization method of reverse time migration in acoustic-reflected S-wave imaging logging

Research on the differential coefficient least-squares optimization method of reverse time migration in acoustic-reflected S-wave imaging logging

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.

A New Method of Plane-Wave Ultrasound Imaging Based on Reverse Time Migration.

Coherent plane-wave compounding technique enables rapid ultrasound imaging with comparable image quality to traditional B-mode imaging that relies on focused beam transmission. However, existing methods assume homogeneity in the imaged medium, neglecting the heterogeneity in sound velocities and densities present in real tissues, resulting in noise reverberation. This study introduces the Reverse Time Migration (RTM) method for ultrasound plane-wave imaging to overcome this limitation, which is combined with a method for estimating the speed of sound in layered media. Simulation results in a homogeneous background demonstrate that RTM reduces side lobes and grating lobes by approximately 30 dB, enhancing the contrast-to-noise ratio by 20% compared to conventional delay and sum (DAS) beamforming. Moreover, RTM achieves superior imaging outcomes with fewer compounding angles. The lateral resolution of the RTM with 5-9 angle compounding is able to achieve the effectiveness of the DAS method with 15-19 angle compounding, and the CNR of the RTM with 11-angle compounding is almost the same as that of the DAS with 21-angle compounding. In a heterogeneous background, experimental simulations and in vitro wire phantom experiments confirm RTM's capability to correct depth imaging, focusing reflected waves on point targets. In vitro porcine tissue experiments enable accurate imaging of layer interfaces by estimating the velocities of multiple layers containing muscle and fat. The proposed imaging procedure optimizes velocity estimation in complex media, compensates for the impact of velocity differences, provides more reliable imaging results.

Three‐Dimensional Teleseismic Elastic Reverse‐Time Migration With Deconvolution Imaging Condition and Its Application to Southwest Japan

AbstractWe have developed a novel deconvolution‐based reverse time migration method to image lithospheric structures using teleseismic data recorded by dense seismic arrays. Unlike traditional approaches that rely on the retrieval of Green's functions (or receiver functions), the new method directly utilizes the recorded three‐component (3‐C) seismic waveforms to reconstruct subsurface wavefields, which has the advantage of avoiding the estimation and removal of source time function. Importantly, it enables the asymptotic estimation of P‐to‐S transmission conversion coefficients at the elastic discontinuities and enhances resolving power for the fine‐scale heterogeneities. Taking these improvements, we have obtained a full three‐dimensional (3‐D) high‐resolution image of the subduction zone beneath southwest Japan. This image provides a comprehensive configuration of the severely deformed subducting plate beneath the Kii Channel and Kinki Peninsula.

Viscoacoustic VTI media reverse time migration method in the complex-domain based on the staining algorithm

Underground media exhibit characteristics of viscosity and anisotropy, with vertical transversely isotropic (VTI) media being a common example of anisotropic media. Consequently, it is crucial to address the viscoacoustic VTI wave equation during forward modeling and migration imaging processes to attain highly precise imaging outcomes. However, conventional subsalt imaging techniques yield low accuracy and suffer from a low signal-to-noise ratio. To overcome this challenge, this study proposes a staining algorithm-based viscoacoustic vertical transversely isotropic reverse time migration (VTI RTM) in the complex-domain method by deriving the complex-domain viscoacoustic VTI equation. This method requires both the traditional real velocity field and the imaginary velocity field as inputs. The imaginary velocity field contains stained geological bodies and significant areas without data. Seismic waves propagate normally in the real wavefield, while in the imaginary wavefield, reflections occur only when the wavefront encounters stained geological bodies. The proposed method is assessed through testing on both a horizontally layered model and a salt model. Through comparative analysis, it has been verified that the method fully incorporates reflected waves with distinct structural features into the imaginary wavefield. Numerical experiments demonstrate that this method can accurately image subsalt structures.

Efficient reverse time migration method in tilted transversely isotropic media based on a pure pseudoacoustic wave equation

In general, velocity anisotropy in shale media has been widely observed in laboratory and field work, which means that disregarding this characteristic can lead to inaccurate imaging locations when data are imaged with reverse time migration (RTM). Wavefields simulated with the conventional coupled pseudoacoustic wave equation may introduce S-wave noise and this equation is only valid in transversely isotropic media ([Formula: see text]). Certain decoupled qP-wave equations require the use of the pseudospectral method, which makes them computationally inefficient. To address these issues, we develop a new pure qP acoustic wave equation based on the acoustic assumption, which can be solved more efficiently using the finite-difference (FD) method. This equation can also be used in the forward-modeling process of RTM in tilted transversely isotropic (TTI) media. First, we perform a Taylor expansion of the root term in the pure qP-wave dispersion relation. This leads to an anisotropic dispersion relation that is decomposed into an elliptical anisotropic background factor and a circular correction factor. Second, we obtain the pure qP-wave equation in TTI media without a pseudodifferential operator. The new equation can be efficiently solved using FD methods and can be applied to RTM in TTI media with strong anisotropy. Our method indicates greater tolerance to numerical errors and is better suited for strong anisotropy, as compared with previously published methods. Numerical examples indicate the high kinematic and phase accuracy of our pure qP-wave equation along with its stability in TTI media characterized by ([Formula: see text]). By using a sag model and an overthrust TTI model, we determine the efficiency and accuracy of our TTI RTM.

Efficient least-squares reverse time migration in TTI media using a finite-difference solvable pure qP-wave equation

Abstract The anisotropic characteristics of underground media play a crucial role in seismic wave propagation and should be accounted for during seismic imaging. The least-squares reverse time migration (LSRTM) method achieves ideal imaging results by suppressing migration artifacts and balancing amplitude. Therefore, pure quasi-P (P-qP) wave equations in tilted transversely isotropic (TTI) media have been widely used to implement LSRTM, owing to their ability to produce stable and noise-free wavefields. However, solving the anisotropic P-qP-wave equations typically necessitates the use of spectral-based methods, making them computationally inefficient, especially in 3D applications. In this study, we first develop a P-qP-wave equation in TTI media that can be efficiently computed through the finite-difference (FD) approach. Numerical tests show that, in comparison to the previous TTI P-qP-wave equation, the newly derived FD solvable TTI P-qP-wave equation yields reasonably accurate and highly efficient wavefield simulations. Then, building on our newly derived wave equation, we derive its adjoint migration and demigration operator to implement TTI LSRTM. Two synthetic examples suggest that the newly presented P-qP-wave TTI LSRTM approach effectively correct for the anisotropy effects, providing high-quality imaging results. Additionally, our approach has superior computational efficiency over the conventional P-qP-wave TTI LSRTM technique based on a hybrid FD pseudo-spectral (HFDPS) solver.

Imaging of cylindrical inhomogeneites in a parallel plate waveguide with reverse time migration method

Abstract While reverse time migration (RTM) algorithm is commonly used in geophysical explorations, this paper addresses the RTM imaging procedure for reconstructing of lossy dielectric discontinuities in a planar waveguide using electromagnetic waves at a single frequency. The direct problem of the related configuration is solved via method of moments (MoM) to produce the synthetic scattered data to be used in RTM. The achievements of the method are examined and verified by including different numerical examples. It is shown that the RTM approach can be used as an alternative imaging methodology in parallel plate waveguide problems.

Ultrasonic imaging of delamination in thick CFRP laminates using an energy-compensation reverse time migration method

In ultrasonic reflection method, the precision of defect detection in thick carbon fiber reinforced plastics (CFRP) is compromised by acoustic energy attenuation. An energy-compensation reverse time migration (ECRTM) method is proposed to identify multiple defects accurately. Forward and backward wavefields are formed using the finite element method within an anisotropic acoustic model based on the Christoffel equation and Bond transformation. To enhance the imaging quality of CFRP laminates, a novel cross-correlation imaging condition is introduced to compensate for energy dissipation caused by geometric diffusion and variations of the far-field radiation intensity at the emitter with the propagation direction. Employing ultrasonic detection technology with a multi-element array, numerical and experimental research on defect imaging was conducted, considering delamination with various sizes and positions in a multidirectional CFRP laminate. In comparison to other ultrasonic imaging methods, the near-surface artifacts in RTM images are mitigated by the far-field radiation directivity factor, while the deep information is enhanced by the geometric diffusion compensation factor in the ECRTM images. As a result, the precise position of delamination in CFRP laminates is achievable, demonstrating superior imaging capabilities, especially for deep delamination.

Определение границ геологических слоёв методом миграции в обратном времени

The article is devoted to solving an important practical problem - determining the structure of the subsurface space of the geological environment based on surface seismic data. Thanks to the registration of seismic waves reflected from the boundaries of geological layers, it is possible to delineate hydrocarbon deposits, which makes it possible to effectively plan a field development scheme. Optimizing the production process makes it possible to make it profitable, including when developing unconventional hydrocarbon deposits. The paper discusses the technology of constructing a migration image using the reverse time migration method. In the general case, an analytical derivation of the calculation formulas was carried out. For the practically significant case of an acoustic environment, simplified calculation formulas are explicitly written out and implemented in the form of a software algorithm. The issue of improving the quality of the migration image without significantly increasing the computational complexity of the problem is discussed separately. The authors demonstrated the performance of this approach using the widely used Marmousi geological model.

A stable Q-compensated reverse-time migration method using a modified fractional viscoacoustic wave equation

Seismic wave propagation inside the earth is usually accompanied by amplitude dissipation and velocity dispersion. It is essential to accurately characterize these effects and make the corresponding compensations in seismic reverse-time migration (RTM) and the following interpretation. Due to the approximation of [Formula: see text] in the derivation, the conventional fractional viscoacoustic wave equation in strongly attenuative media is unsatisfactory. This paper develops a modified viscoacoustic wave equation by combining the relationship between angular frequency and complex wavenumber. The numerical simulation demonstrates its advantage of high accuracy in describing constant- Q effects, especially in strongly attenuative media with small Q values. A truncated Taylor-series expansion algorithm and a pseudospectral method are developed to solve this equation during wave propagation. To address the issue of numerical instability in Q-compensated RTM ( Q-RTM), a stabilized technology with regularization is further developed. Unlike the conventional filtering method implemented in the wavenumber domain, our approach only adds an explicit regularization term, which can be directly computed in the space domain. Furthermore, this regularization depends on velocities and quality factors, significantly improving its applicability in complicated structures. Noise-free data tests demonstrate that our Q-RTM method can effectively correct phase distortion, compensate for amplitude attenuation, and produce high-resolution migrated images without any cutoff-frequency artifacts caused by filtering. Noisy data experiments further verify the antinoise performance and robustness of our method.

Reverse time migration and genetic algorithms Combined for Reconstruction in Transluminal Shear Wave Elastography: An In Silico Case Study

A new reconstruction approach that combines Reverse Time Migration (RTM) and Genetic Algorithms (GAs) is proposed for solving the inverse problem associated with transluminal shear wave elastography. The transurethral identification of the first thermal lesion generated by transrectal High Intensity Focused Ultrasound (HIFU) for the treatment of prostate cancer, was used to preliminarily test in silico the combined reconstruction method. The RTM method was optimised by comparing reconstruction images from several cross-correlation techniques, including a new proposed one, and different device configurations in terms of the number and arrangement of emitters and receivers of the conceptual transurethral probe. The best results were obtained for the new proposed cross-correlation method and a device configuration with 3 emitters and 32 receivers. The RTM reconstructions did not completely contour the shape of the HIFU lesion, however, as planned for the combined approach, the areas in the RTM images with high level of correlation were used to narrow down the search space in the GA-based technique. The GA-based technique was set to find the location of the HIFU lesion and the increment in stiffness and viscosity due to thermal damage. Overall, the combined approach achieves lower level of error in the reconstructed values, and in a shorter computational time, compared to the GA-based technique alone. The lowest errors were accomplished for the location of HIFU lesion, followed by the contrast ratio of stiffness between thermally treated tissue and non-treated normal tissue. The homologous ratio of viscosity obtained higher level of error. Further investigation considering diverse scenarios to be reconstructed and with experimental data is required to fully evaluate the feasibility of the combined approach.

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.

Viscoacoustic reverse time migration with stable and effective two-way attenuation compensation

Intrinsic attenuation in seismic wave propagation leads to amplitude dissipation and phase dispersion in seismic data. The attenuation (∼1/ Q) effect is a common cause for inaccurate image locations and dimmed image energy in reverse time migration (RTM). Conventional viscoacoustic or viscoelastic RTM methods implement attenuation compensation by reversing the sign of the amplitude loss term and keeping the dispersion term unchanged for forward and backward wavefield extrapolation, which requires the decoupled viscoacoustic wave equation and gives rise to the numerical instability issue. To address these problems, we develop a stable and effective two-way attenuation-compensated viscoacoustic RTM method. Our method uses a new two-way normalized crosscorrelation imaging condition to compensate the attenuation effect. In the new imaging condition, only the attenuated forward wavefield of sources and the viscoacoustic Green’s functions of receivers are required, which eliminates the instability source arising from the operation of reversing the sign of the dissipation term in the viscoacoustic wave equation. Because no modifications are made to the viscoacoustic wave equation, the new imaging condition can be calculated without any additional computational cost and can be applied to decoupled and coupled viscoacoustic wave equation-based RTMs, which is more flexible than other attenuation compensation strategies. Two synthetic tests and one field data example are presented to demonstrate the stability and effectiveness of our method.

Wide‐spectrum reconstruction of a velocity model based on the wave equation reflection inversion method and its application

AbstractMost seismic data used for conventional exploration lack far‐offset signals and effective low‐frequency components. This makes it difficult for conventional full waveform inversion methods to recover the low‐wavenumber components of mid‐ and deep‐layer models. To resolve the bottleneck of ray‐theoretical reflection traveltime tomography, wave equations, such as reflection inversion methods, are receiving increasing attention. We reconstructed a wide‐spectrum velocity model based on the multiscale wave‐equation reflection inversion method for model decomposition. First, using the dynamic image warping method to obtain reflection traveltime residuals, the wave‐equation reflection traveltime inversion was used to recover the low‐wavenumber components of the background model, which also solved the cycle‐skipping problem. Second, the medium‐wavenumber component of the model is then supplemented by the reflection waveform inversion, while the reflectivity model is obtained relying on the least‐squares reverse time migration method. Based on this method, the background and perturbation models are updated alternately and iteratively. At the same time, the stratum structural tensor information was extracted using the perturbed model image to construct a preconditioned operator for the stratum structural constraint, suppress unreasonably high‐wavenumber components in the generalized gradient and improve the geological consistency of the inversion results. Testing of the model using the Sigsbee2b model and seismic field data from the East China Sea showed that, compared with the conventional reflection traveltime tomography method based on prestack depth migration, the wave‐equation reflection inversion strategy with well‐matched information from traveltimes to waveforms significantly improved the accuracy of the middle and deep velocity modelling and enhanced the imaging quality of the whole body.

Steeply dipping structural target oriented viscoacoustic prismatic reverse time migration in frequency domain and its application

AbstractSteeply dipping structural imaging is a great challenge due to its poor illumination. Conventional migration methods are unable to produce an accurate image of complex steeply dipping structures. The prismatic wave can improve the illumination of steeply dipping structures and is often used to improve the imaging results of such structures. Traditional elastic wave theory assumes that seismic waves do not attenuate when propagating through subsurface media. However, during seismic wave propagation, the wave energy decays exponentially due to the absorption and attenuation of the ground layer. Subsurface attenuation leads to amplitude loss and phase distortion of seismic waves, resulting in blurring of migration amplitudes when this attenuation is not taken into account during imaging. To address this issue, a frequency‐domain Q‐compensated prismatic reverse time migration method is proposed, which derives Q‐compensated prismatic wavefield propagation operators. In the proposed frequency‐domain Q‐compensated prismatic reverse time migration, Q attenuation is fully compensated along three propagation paths and two propagation types of prismatic waves. The optimized four‐order mixed 25‐point difference format and LU decomposition method are used to solve the Q‐compensated prismatic wavefield propagation equations with high computational efficiency. Numerical and field data examples demonstrate that the proposed frequency‐domain Q‐compensated prismatic reverse time migration method can compensate for deep attenuation energy and improve the imaging resolution of steeply dipping structures.