Reverse Time Migration Method Research Articles

Converted-wave reverse time migration imaging in subduction zone settings

SUMMARYWe use a newly developed 2-D elastic reverse time migration (RTM) imaging algorithm based on the Helmholtz decomposition to test approaches for imaging the descending slab in subduction zone regions using local earthquake sources. Our elastic RTM method is designed to reconstruct incident and scattered wavefields at depth, isolate constituent P- and S-wave components via Helmholtz decomposition, and evaluate normalized imaging functions that leverage dominant P and S signals. This method allows us to target particular converted-wave scattering geometries, for example incident S to scattered P, which may be expected to have dominant signals in any given data set. The method is intended to be applied to dense seismic array observations that adequately capture both incident and converted wavefields. We draw a direct connection between our imaging functions and the first-order contrasts in shear wave material properties across seismic discontinuities. Through tests on synthetic data using either S → P or P → S conversions, we find that our technique can successfully recover the structure of a subducting slab using data from a dense wide-angle array of surface stations. We also calculate images with a small-aperture array to test the impact of array geometry on image resolution and interpretability. Our results show that our imaging technique is capable of imaging multiple seismic discontinuities at depth, even with a small number of earthquakes, but that limitations arise when a small aperture array is considered. In this case, the presence of artefacts makes it more difficult to determine the location of seismic discontinuities.

Reverse time migration for imaging periodic obstacles with electromagnetic plane wave

Abstract We propose novel reverse time migration (RTM) methods for the imaging of periodic obstacles using only measurements from the lower or upper side of the obstacle arrays at a fixed frequency. We analyze the resolution of the lower side and upper side RTM methods in terms of propagating modes of the Rayleigh expansion, Helmholtz–Kirchhoff equation and the distance of the measurement surface to the obstacle arrays, where the periodic structure leads to novel analysis. We give some numerical experiments to justify the competitive efficiency of our imaging functionals and the robustness against noises. Further, numerical experiments show sharp images especially for the vertical part of the periodic obstacle in the lower-RTM case, which is not shared by results for imaging bounded compactly supported obstacles.

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.

Three-Dimensional Ultrasonic Reverse-Time Migration Imaging of Submarine Pipeline Nondestructive Testing in Cylindrical Coordinates

Submarine pipelines are a safe and energy-efficient mode of gas transport. However, due to the complex manufacturing process and harsh operating environment, submarine pipelines are subject to fatigue cracks under long-term cyclic loading. A comprehensive and high-precision characterization strategy for submarine pipelines can effectively prevent potential safety hazards and have significant economic and social repercussions. As a matter of fact, pipeline defects cannot be reliably detected with current traditional 2D methods. On the other hand, in ultrasonic testing, cylindrical geometry increases the complexity of the 3D wave field in the submarine pipeline space and significantly influences the accuracy of the detection results. In this paper, we put forward a novel method for 3D ultrasonic image testing that is suitable for cylindrical coordinates. In order to accurately simulate the ultrasonic signal received from pipelines, we generalize the 3D staggered-grid finite-difference method from Cartesian coordinates to cylindrical ones and simulate the full wave field in the 3D pipeline space. Then, signal processing is performed on the ultrasound simulation records, and 3D reverse-time migration imaging of submarine pipeline defects can be effectively achieved using the reverse-time migration method and cross-correlation imaging conditions. The results obtained from simulations and real field data show that the proposed method provides high-quality 3D imaging of defects in pipelines, taking into account multiple scattering and mode conversion information at the bottom of the defects.

Reverse time migration imaging method for tunnel seismic forward‐prospecting in viscoacoustic media

AbstractThe imaging of geological structure in front of a tunnel face is conducive to the safe construction of tunnels. The reverse time migration (RTM) method is popular for its high imaging accuracy. However, most of the current tunnel seismic RTM methods assume complete elasticity, ignoring the nature of wave propagation attenuation, resulting in a poor imaging outcome, especially when tunnelling in the shallow subsurface. Thus, it is necessary to study tunnel RTM suitable for attenuating strata. First, considering the frequency of tunnel seismic forward‐prospecting is usually higher than that of ground surface seismic exploration, we established a corresponding tunnel viscous media model to enable viscoacoustic forward modelling of seismic wavefield. Then, a simultaneous compensation approach for its amplitude and phase velocity is proposed based on the combination of the real and imaginary parts of the complex modulus. After the compensation of seismic wavefields, the tunnel Q‐RTM imaging method in viscoacoustic media is formed, and its effectiveness is verified by numerical examples. Compared with RTM without attenuation compensation, tunnel Q‐RTM effectively enhances the imaging energy and has higher positioning accuracy, improving the imaging effect of complex structures (especially at larger distances from the tunnel face). In the end, a detailed case study is presented to demonstrat the potential of the proposed method for field application.

Ultrasonic imaging of different shaped cracks in an isotropic plate by synthesizing time reversal and reverse time migration methods

The accuracy of reverse time migration (RTM) image of a crack is greatly affected by the position and excitation waveform of PZT transducer as the transmitter. The position of the transmitter is obtained by processing the direct-arrival flexural waves recorded at the receivers using the time reversal method. The excitation waveform generated by the transmitter is represented by the direct-arrival wave recorded at the closest receiver and their position relation, modifying the deconvolution imaging condition of RTM. Three types of cracks with different shapes located on the back of aluminum plates are investigated by employing two linear arrays composed of PZT transducer and laser vibrometer, and their high-resolution images are reconstructed using the modified RTM method. The results show that the obtained positions and shapes of the cracks are consistent with those of the actual cracks, the MRE and RMSE between them are less than 2.06% and 2.82 mm, respectively.

Plane-wave least-squares diffraction imaging using short-time singular spectrum analysis

Abstract Diffractions are seismic waves generated by small-scale heterogeneities in the subsurface. These are often superimposed by strong reflections so that they are not visible on the image, leading to misinterpretation and incorrect localization of the scatterers. Therefore, the separation of diffracted and reflected waves is a crucial step in identifying these small-scale diffractors. To realize the separation of diffraction and imaging, a least-squares reverse time migration method of plane waves (PLSRTM) optimized with short-time singular spectrum analysis (STSSA) was developed in this work. The proposed STSSA algorithm exploits the properties of singular spectral analysis (SSA) to separate linear signals. By establishing the Hanning window and the energy compensation function, it also compensates for the shortcomings of SSA in local dip processing and convergence of linear signals. As there is no clear boundary between reflected and diffracted waves, the energy loss during separation leads to a slow convergence rate of the diffraction wave imaging technique. We use STSSA as a constraint for PLSRTM, which greatly improves the imaging quality for diffraction waves. The tests with the Sigsbee2A model and noisy seismic data have shown that our method can effectively improve the resolution of diffraction wave imaging and that the constraint of STSSA increases the robustness to noisy data.

Deep crustal structures with reverse time migration applied to offshore wide-angle seismic data: Equatorial and North-West Brazilian margins

We image the Moho discontinuity and deep crustal layers by applying the Reverse Time Migration (RTM) method to wide-angle seismic (WAS) data that were acquired along two different profiles in NW and SE offshore Brazil, where the spacing between OBS is 12.5 km and 150 m between shots. The application of this method is quite uncommon to ocean bottom seismometers (OBS) data due to the OBS wide spacing deployment and low folds. We analyze the effectiveness of the RTM method when applied to the reflectivity of the WAS data. We imaged the structures by cross-correlating the forward and backward wavefields given by the acoustic seismic equation. This allowed us to use each interface crossed by a ray as both a source and a receiver. The velocity models used to perform RTM were previously obtained by applying a procedure of two-dimensional forward ray-tracing followed by a damped least-squares travel time inversion. The results obtained have an unexpected large contribution from the wavefield traveling as refractions within the Earth and, because of that, we can talk about recovering refractors from the RTM results. We obtained strong and continuous refractors for depths of 7–15 km that correspond to the basement and the Moho discontinuity. As we move landwards, the refractors that correspond to the Moho discontinuity disappear due to the deepening of the surface. Finally, we investigate how the slight change on the velocity model influences the result of the RTM method. The obtained results are promising for a wide range of applications at a crustal scale seismic exploration, with wide-angle seismic data.

In-Wall Imaging for the Reconstruction of Obstacles by Reverse Time Migration.

In this paper, the reverse time migration (RTM) method is applied to the single-frequency reconstruction of embedded obstacles in a wall to perform an introductory study for in-wall imaging. The aim is to determine the geometrical properties of an object embedded in a wall by the use of an information function provided via the RTM method. The method is based on the computation of that information function separately at each point on a reconstruction domain. It is defined as the correlation levels between the incident fields emitted from sources and the back-propagation of the scattered field. The problem is taken from a broader perspective in order to show and confirm the effectiveness of the method. For this purpose, numerical experiments within a fundamental scenario are determined in a particular order to perform an essential Monte Carlo simulation. The paper uses a comparative study to make an objective evaluation of the achievement level of the method in in-wall imaging. The results reveal that the method is at the applicable level of achievement.

A fast and accurate elastic reverse-time migration method based on decoupled elastic wave equations

The extrapolation and decomposition of different mode waves are very important to efficiently obtain multi-wave depth images for elastic reverse-time migration (ERTM). To achieve this goal successfully, we firstly develop an efficient and accurate staggered-grid finite-difference method (SFDM) based on decoupled elastic wave equations. This developed SFDM uses two sets of difference operator lengths for decoupled elastic wave equations to respectively perform the extrapolation of decoupled P- and S-wavefields and employs the least squares (LS) to minimize the objective functions respectively constructed from the time-space dispersion equations of P- and S-waves to generate their corresponding difference coefficients. This developed method can theoretically be regarded as the optimal SFDM based on least squares (LSSFDM), and it can provide the high-precision separated wavefields of different mode waves simultaneously and reduce the computing time effectively for elastic wave modeling under the given accuracy requirements. The modeling results of different models illustrate that our developed LSSFDM based on decoupled elastic wave equations can generate the decomposed P- and S-wavefields and suppress their numerical dispersions effectively. Secondly, we present a fast and accurate ERTM method based on this developed LSSFDM to successfully achieve the multi-wave imaging results, including PP, PS, SP and SS images. The ERTM examples of different models demonstrate that our ERTM based on this developed LSSFDM can accurately obtain the high-precision depth images of multimode waves and effectively reduce the computing time of wavefield extrapolation.

Least‐squares reverse time migration with flux‐corrected transport technique

AbstractDue to high computational costs and memory requirements, it is necessary to use coarse grids for least‐squares reverse time migration when processing large‐scale field data. According to the dispersion relation, strong numerical dispersion will occur in least‐squares reverse time migration images when the migration velocity of the shallow strata is low, reducing the resolution of the migration results. To overcome this shortcoming, we propose new least‐squares reverse time migration implementation method with a modified flux‐corrected transport technique. This algorithm involves two main steps: obtain an appropriate calibration parameter for flux‐corrected transport through forward modelling and perform least‐squares reverse time migration using flux‐corrected transport. We remove the non‐linear processing from conventional flux‐corrected transport algorithm often used in computational fluid dynamics based on the assumption that the seismic wavefield is relatively continuous and smooth without strong ripples, which makes it possible to apply flux‐corrected transport to least‐squares reverse time migration without increasing too much computation complexity. To suppress the numerical dispersion more effectively, the diffusion fluxes along the diagonal direction are added to flux‐corrected transport. Numerical tests on synthetic data and field data illustrate that compared to the conventional least‐squares reverse time migration method, the proposed method produces images with fewer migration artefacts, more accurate amplitudes and faster convergence speed on the coarse grids.

High resolution acoustic tomography based on backpropagation of waves

A method of high-resolution acoustic tomography of scattering inhomogeneities based on the method of reverse time migration is proposed. An inhomogeneous background medium with a known distribution of refractive inhomogeneities is considered, where it is necessary to detect scattering inhomogeneities. Probing is carried out by broadband arbitrary waveforms. The method of reverse time migration is supplemented with linear filtering of the direct propagation field, which makes it possible to increase the resolution of reconstructed images. The results of numerical modeling and experiment are presented. Sounding was carried out in water at frequencies from 20 to 350 kHz using a signal with linear frequency modulation. The source of the ultrasonic signal was fixed and irradiated the objects under study in the water. The scattered signal was measured in a plane near the surface in water on a rectangular area with a step of less than 2 mm. Signal processing by the proposed method made it possible to reconstruct a three-dimensional image of scattering inhomogeneities with a resolution of about 7 mm. Comparison of the proposed method and the reverse time migration method showed that the proposed method allows obtaining a higher resolution.

Steeply dipping structure imaging with prismatic waves incorporating wavefield decomposition

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

Free-surface elastic wave injection and wavefield reconstruction with applications to elastic reverse time migration

Accurately injecting and extrapolating multicomponent seismic data is a major step in elastic reverse time migration (RTM) and full-waveform inversion. The theoretical basis of this process is the seismic representation theorem. We propose a numerical approach based on the collocated-grid MacCormack finite-difference (FD) scheme to implement the injection and extrapolation. The MacCormack FD scheme defines wavefield parameters on the same grid. When dealing with the boundary condition in the representation theorem, it is more advantageous than the commonly used staggered-grid FD scheme which defines the stress and velocity on offset grids; thus, interpolations are required to link the boundary values to nearby nodes. In contrast, with the MacCormack scheme, the traction and particle velocity data can be directly injected into the boundary nodes as equivalent concentrated forces, force dipoles, and double couples. The accuracy of this approach is validated by comparing the regenerated wavefield with the original wavefield. Our primary purpose is to develop an injection method for elastic RTM, but this approach also can be used to numerically investigate other interesting issues in the elastic wave injection, including errors and artifacts caused by injection from unclosed boundaries, incomplete boundary values, and uncertain velocity models. In particular, seismic data are usually acquired on the ground surface where the traction-free condition is naturally maintained. We simulate a land acquisition scenario by generating a synthetic multicomponent data set on a traction-free surface. The reconstructed wavefields from velocity data are compared with the original forward-propagated waves to evaluate the accuracy of the boundary treatments. Two multicomponent elastic RTM examples are presented to demonstrate the applications of the proposed injection method. By combining the regenerated receiver-side wavefield and the vectorized imaging condition, the PP, PS, SP, and SS images are calculated.

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.

Seismic migration in viscoacoustic vertical transversely isotropic media using a pure qP wave equation

AbstractSeismic anisotropic attenuation and anisotropic velocity exist widely in the earth's interior and have a great influence on the propagation of seismic waves. Ignoring the effects of attenuation anisotropy may lead to amplitude imbalance or noise in reflection seismic imaging, thus reducing the quality of the imaging results. In order to incorporate attenuation anisotropy into imaging methods and explore its effect on imaging, based on a novel two‐way pure qP wave equation in viscoacoustic vertical transversely isotropy media, we propose the corresponding reverse time migration and least‐squares reverse time migration method. Both imaging methods can accurately obtain subsurface structure information, especially the least‐squares reverse time migration has the potential to compute accurate subsurface reflectivity. In this paper, we first introduce the pure qP wave equation in viscoacoustic vertical transversely isotropy media. As the equation is derived from the complex dispersion relation of P wave, wave propagation can be simulated without interference of SV wave and limitation of anisotropic parameters. Then, we derive the corresponding linearized wave equation and adjoint gradient for updating the imaging result. Finally, using two synthetic models, we demonstrate the effectiveness of the imaging method and discuss the effect of attenuation anisotropy on seismic imaging.

Least‐squares reverse time migration based on an efficient pure qP‐wave equation

AbstractSeismic waves propagating in anisotropic earth media suffer from waveform distortion, which leads to degraded resolution in seismic data imaging if this adverse effect is not corrected. Additionally, the wavefields simulated by the traditional coupled pseudo‐acoustic wave equations contain undesired shear wave artefacts and are unstable when Thomsen's anisotropy parameter ε is less than δ. To address these issues, many pure qP‐wave equations are proposed to describe wave propagation in anisotropic media. However, these equations are either low precision or high accuracy but computationally expensive. Considering the trade‐off between the computation efficiency and simulation accuracy, we derive a pure qP‐wave equation from the exact dispersion formula in tilted transverse isotropic media. The newly derived equation has only two higher order partial derivatives, which can better balance the accuracy and efficiency than the previous pure qP‐wave equations. The least‐squares reverse time migration method can balance amplitudes, suppress migration artefacts and improve imaging resolution. Then, based on the newly derived pure qP‐wave equation, we derive the Born modelling operator and adjoint migration operator and develop an anisotropic least‐squares reverse time migration method. To achieve the accelerated convergence, we introduce a generalized minimum residual algorithm to implement the anisotropic least‐squares reverse time migration method. Numerical simulation results show that the proposed pure qP‐wave equation outperforms the previous equations in balancing the trade‐off between accuracy and efficiency. In addition, synthetic examples demonstrate the effectiveness and robustness of our proposed anisotropic least‐squares reverse time migration method in correcting the deviations due to anisotropic effects.

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.

Elastic Reverse Time Migration Method for Single-Well Imaging and Elimination of Azimuthal Ambiguity With a Combined Receiver System

Elastic Reverse Time Migration Method for Single-Well Imaging and Elimination of Azimuthal Ambiguity With a Combined Receiver System

Research on noise suppression of imaging data by optimized least squares reverse time migration method

Least squares reverse time migration imaging is an imaging theory based on the accurate description of geological structures by seismic waves, which can greatly improve the detection accuracy. In the complex environment of deep region, the influence of noise on the imaging resolution of reverse time migration is particularly significant. In this paper, an optimized least squares reverse time migration imaging method with better amplitude fidelity and higher imaging accuracy is proposed. This method suppresses the noise interference by reducing the residual value between the inversion data and the actual data. The experimental results in the paper show that the optimized least squares reverse time migration can achieve high accuracy and high resolution imaging, especially in the deep region. This method is effective and feasible.