Frequency-domain Reverse-time Migration Research Articles

Adaptive Ultrasonic Full Matrix Capture Process for the Global Imaging of Complex Components with Curved Surfaces.

This work proposes a new global FD-RTM method to solve the problem of ultrasonic inspection of parts with complex geometric shapes. With this method, the frequency domain reverse time migration (FD-RTM) algorithm is used to adapt to the complex refraction of ultrasonic waves by the surface, while an interface solution algorithm based on tangent fitting is used to solve the interface position with high precision through the full matrix reception data. Based on high-precision interface information, a hybrid extrapolation algorithm and a situation-specific probe movement strategy are used to enable the probe to find the next sampling point according to the direction of the workpiece surface, allowing complex surface topography features to be identified without relying on the workpiece CAD drawing. This makes it possible to achieve the automated inspection of workpieces. To verify the proposed method's effectiveness, an aluminum alloy model with side-drilled holes (SDH) is used. The geometry of the model consists of multiple convex and concave surfaces. By comparing the local FD-RTM imaging with images synthesized using the entire scan path, it is shown that gFD-RTM improved the imaging performance. Compared with FD-RTM, the average signal-to-noise ratio of gFD-RTM was increased by 20%, and the array performance index (API) was reduced by 70%, indicating effective detection coverage.

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.

Frequency-Domain Reverse-Time Migration With Attenuation Compensation

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

Ultrasonic full-matrix imaging of curved-surface components

Curved-surface components (CSC) are ubiquitous in engineering practice such as automobiles, aerospace and pipelines. However, they are prone to void and crack defects which greatly degenerate mechanical properties and are badly in need of effective detection. Ultrasonic full-matrix imaging is a conspicuous method in nondestructive testing. However, the research on high-quality imaging of CSC is still limited. In this paper, an ultrasonic imaging method based on frequency-domain reverse-time migration (FD-RTM) is developed for CSC at the first attempt, unrestricted to the surface shape of components. Through discretization of the acoustic wave equation in the frequency domain, the wavefields of all excitations are extrapolated together to obtain the source and received wavefields at each frequency. After implementation of the imaging conditions, the high-quality image of the defects is obtained. The efficaciousness of the method was examined with the numerical simulation and laboratory experiment, in both of which the void and V-shaped crack defects in copper and aluminum CSCs were imaged in high quality. Results have proven that FD-RTM has obvious advantages over the existing imaging methods for CSC. Therefore, the proposed method shows great potential in defect detection for CSC in various fields.

Ultrasound Imaging of Bottom Opening Crack Based on Frequency-Domain Reverse Time Migration

In 2-dimension (2D), a frequency-domain reverse time migration (FRTM) based on the optimal 9-point finite difference method (FDM) is introduced into the field of ultrasonic non-destructive testing (NDT). This study solves the challenge that conventional ultrasound imaging methods are difficult to image defects completely. In numerical investigations, the use of multiple reflection waves and the necessity of bottom identification are explained. In actual inspection, the method of bottom identification is given, and then the bottom opening crack (BOC) of different lengths in the aluminum block can be completely imaged. Furthermore, the conventional total focusing method (TFM) cannot image the sides of the BOCs using the same data as FRTM. Therefore, the quantitative analysis of BOC based on the complete imaging results of FRTM is more convincing. On this basis, the optimization methods for the number of grid points placed at each wavelength and the frequency calculation range are also given. On the premise of ensuring high image quality, the imaging computation time is reduced to 1/18 of the original, which improves the computing efficiency of the FRTM.

Review of the Applicability of 4D Time-Lapse Seismic Monitoring System Based on Frequency-Domain Reverse-Time Migration to Pohang CCS Demonstration

Review of the Applicability of 4D Time-Lapse Seismic Monitoring System Based on Frequency-Domain Reverse-Time Migration to Pohang CCS Demonstration

Hybrid Reconstruction of Subsurface 3-D Objects Using FRTM and VBIM Enhanced by Monte Carlo Method

A hybrid method is proposed to reconstruct the subsurface 3-D objects with electromagnetic fields. The frequency-domain reverse time migration (FRTM) is first used to determine the approximate locations and sizes of the objects. Then, based on these results, the full-wave inversion, the variational Born iteration method (VBIM) is used to reconstruct both the shapes and dielectric parameters of the objects. The Monte Carlo method (MCM) is adopted to further refine the reconstructed shapes. Numerical simulations show that the proposed hybrid method can be effectively used for the subsurface imaging and detection.

Subsurface Reconstruction From GPR Data by 1-D DBIM and RTM in Frequency Domain

This letter presents the joint reconstruction of unknown subsurface structures by the full-wave inversion (FWI) and reverse time migration (RTM) imaging. In the FWI, the 1-D distorted Born iteration method (DBIM) is employed to retrieve the dielectric parameters of the layered subsurface medium by minimizing the difference between measured fields and calculated fields via Frechet derivatives. Based on the inversion results, the RTM is directly performed in the frequency domain to image the buried objects using the ground-penetrating radar (GPR) data. Numerical and laboratory experiments show that the proposed joint method can be used to reconstruct the subsurface structures reliably and efficiently.

Frequency-domain reverse-time migration with accelerated wave simulation via generalized multiscale finite element

Reverse time migration (RTM) is widely used due to its ability to recover complex geological structures that might not be imaged correctly with methods based on ray theory. However, RTM incurs a considerable computational cost. For this reason, we applied a model reduction technique that solves local spectral problems on a fine grid to simulate wave propagation rapidly on a coarser grid. We can also greatly reduce the computational cost by applying a frequency-domain implementation that requires only one matrix inversion for wave simulation. The multiscale model reduction, a fundamental aspect of the generalized multiscale finite element method, is obtained by utilizing a set of basis functions determined from a local spectral problem. We can tune the accuracy and computational speed by varying the number of basis functions. Applying RTM with fewer basis functions provides results more rapidly, though the usable results are restricted to lower frequencies. However, we can still clearly interpret large-scale structures from the multiscale RTM result. Tuning accuracy and speed of the imaging algorithm is especially useful when the velocity model needs to be actively updated, as it allows faster generation of trial images. In addition, multiscale RTM with a larger number of basis functions can provide faster imaging than the reference case, which uses the continuous-Galerkin finite element approach, without sacrificing accuracy.

Frequency-Domain Reverse-Time Migration of Ground Penetrating Radar Based on Layered Medium Green's Functions

A frequency-domain reverse-time migration (RTM) algorithm based on the layered medium dyadic Green's function (DGF) is proposed for high-resolution and efficient subsurface imaging using ground penetrating radar (GPR). Different from the conventional RTM, which is performed by the finite-difference time domain (FDTD) method, both the forward and backward extrapolation wavefields in this frequency-domain RTM are computed by the multiplication between the frequency spectra of the excitation source or the recorded GPR data and the layered medium DGFs. The final image is reconstructed by the direct summation of all the wavefields for all the sampling frequencies in the frequency domain, instead of transforming them back to the time domain and processing them. Two-dimensional (2-D) or 3-D numerical and laboratory experiments show that the proposed frequency-domain RTM algorithm can yield almost the same imaging results as the conventional time domain RTM algorithm but requires less than two orders of magnitude in computational costs. The proposed GPR imaging method is verified to be competent for the fast 3-D imaging of potential larva rocks under the lunar surface, which can provide critical information for the regolith-drilling task of the Chang-E 5 lunar exploration mission of China. Real-time subsurface imaging by RTM could be fulfilled and be widely applied to engineering geophysics, such as urban utility detection, through-wall imaging, and ice monitoring by ground-coupled or air-borne GPR.

Reverse time migration Lamb wave imaging based on mode separation

Frequency domain reverse time migration method is used to reconstruct damages in isotropic and anisotropic plates. Considering multimode overlapping, the Lamb wave signals scattered by the defects may result in artifacts in defect imaging. The scattering signals are thus pre-processed by using a mode separation method based on the vibration symmetry difference between the fundamental guided modes. Based on the multi-element array ultrasonic technique, a numerical study is carried out for defect imaging of aluminum and composite plates by using the frequency reverse time migration method. This paper is organized as follows. Firstly, in order to capture multi-directional information about damages, scattering Lamb wave signals caused by the defects are numerically collected by an annular array of transducers through using the finite element simulation. Secondly, after the pre-processing of mode separation, the separated scattering signals are time-reversed and used to stimulate the corresponding receivers. The Green's function is utilized to back-propagate the scattering Lamb signals in frequency domain, so that the back-propagated acoustic field information of monitored area can be obtained. Finally, the defect images are reconstructed by the cross-correlation between the incident acoustic field and the back-propagated acoustic field. To illustrate the influence of mode separation, the numerical experiments are carried out on an aluminum plate with single defect and on another composite plate with two adjacent identical defects. The reconstructed results from frequency domain reverse time migration method with and without mode separation are compared. The comparison indicates the importance of mode separation. Furthermore, the method is extended to detecting the double adjacent defects with different depths in the composite plate. The imaging result illustrates that the presupposed two adjacent defects with different depths are successfully identified. Numerical results demonstrate that the pre-processing of mode separation helps to effectively remove the artifacts resulting from the multimode interference in the imaging process. The proposed frequency reverse time migration method presents a strong potential for detecting and imaging defects in isotropic and anisotropic plates, which is capable of accurately measuring multi-site defects with information about geometry, size and depth.

Least-squares reverse time migration in frequency domain using the adjoint-state method

A new scheme is presented to implement a least-squares frequency domain reverse time migration (LS-FRTM). This scheme expresses the gradient of the misfit function with respect to the model as the product of the conjugated Green’s functions and the data residuals in the frequency domain based on the adjoint state method. In the 2D case, for each frequency all the Green’s functions from the shots to the reflectors and from the reflectors to the receivers which depend on the background velocity can be calculated once using the lower/upper decomposition. The pseudo-Hessian matrix which is also expressed as a function of the Green’s function is used as a substitute for the approximate Hessian to amplitude compensation for the gradient. Since the linearized inversion does not update the background velocity, the Green’s function needs to be calculated only once. An iteration based LS-FRTM can be implemented with high efficiency. As examples supporting our assertion, we present the results obtained by applying our method to the 2D Marmousi model.

Frequency-domain reverse-time migration with source estimation

Although artificially generated seismic sources such as dynamite, vibroseis, and air guns are used in seismic exploration, it is not easy to exactly recover the source wavelet in field recording or in data processing. For this reason, seismic data processing often assumes that an explosive-source wavelet can be described by a well-known function (e.g., a Ricker wavelet), a near-offset trace, or a deconvolved wavelet. In frequency-domain waveform inversion, it has been proven that a source wavelet can be estimated by an optimization method, and incorporating the source wavelet estimation into an inversion algorithm yields better inversion results. We have developed source wavelet estimation into 2D two-way frequency-domain reverse-time migration. The source wavelet is first estimated independently of reverse-time migration by an optimization method such as the full Newton method. It is then used in reverse-time migration. This source-wavelet-incorporated reverse-time migration algorithm is applied to three model data sets: a simple anticline model, the Institut Français du Petrole (IFP) Marmousi model, and the BP 2004 EAGE model. Numerical examples were used to show that better migration images can be obtained by using an estimated source wavelet than those obtained by using a designatured wavelet without source estimation. To enhance the migrated images, the Laplacian filter is applied and migrated images are scaled using the diagonal of the pseudo-Hessian matrix. It is expected that the source wavelet estimation method can be directly applied to 2D or 3D time-domain two-way reverse-time migration.

Implementation of prestack reverse time migration using frequency-domain extrapolation

We implement prestack reverse time migration (RTM) using frequency-domain extrapolation. We assume the observed data are the scattered field from the seismic experiment; then we time reverse them and derive the corresponding multipoint virtual sources to place along the receiver line rather than treat them as boundary conditions, which are common in time-domain reverse time migration (TRTM). Because the number of virtual sources is equal to the number of independent true sources in prestack frequency-domain reverse-time migration (FRTM), wavefield extrapolation is efficient in the frequency domain using a direct lower/upper (LU) triangular solver for 2D solutions and is still feasible using a parallel iterative or hybrid direct/iterative solver for 3D solutions. Each frequency implicitly contains information for all times, so we can implement the excitation-time and crosscorrelation imaging conditions straightforwardly without disk storage or input/output (I/O). Comparing costs, prestack shot-record FRTM is competitive with prestack shot-record TRTM. In our tests, prestack acoustic-wave FRTM accurately recovers the correct images of subsurface reflectors using 2D synthetic data.