Zero-lag Cross-correlation Imaging Condition Research Articles

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

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

A reverse time migration-based multistep angular spectrum approach for ultrasonic imaging of specimens with irregular surfaces

We develop a new ultrasonic imaging framework for non-destructive testing of an immersed specimen featuring an irregular top surface and demonstrate its capability of accurately depicting the lower surfaces of multiple damages hidden in the specimen. Central to the framework is a multistep angular spectrum approach (ASA), via which the forward propagation wavefields of wave sources and backward propagation wavefields of the received wave signals are calculated. Upon applying a zero-lag cross-correlation imaging condition of reverse time migration (RTM) to the obtained forward and backward wavefields, the image of the specimen with an irregular surface can be reconstructed, in which hidden damages, if any and regardless of quantity, are visualized. The effectiveness and accuracy of the framework are examined using numerical simulation, followed with experiment, in both of which multiple side-drilled holes, at different locations in aluminum blocks with various irregular surfaces, are characterized. Results have proven that multiple damages in a specimen with an irregular surface can be individually localized, and the lower surface of each damage can further be imaged accurately, thanks to the RTM-based algorithm in which multiple wave reflections from the specimen bottom are taken into wavefield extrapolation. The proposed imaging approach presents higher computational efficiency, compared to conventional RTM, and enhanced imaging contrast over prevailing total focusing methods.

Elastic Least-Squares Imaging in Tilted Transversely Isotropic Media for Multicomponent Land and Pressure Marine Data

Traditional elastic reverse-time migration (RTM) involves P-/S-wave separation for the source and receiver wavefields, followed by applying the zero-lag cross-correlation imaging condition to produce PP and PS images. In anisotropic media, P-/S-wave decomposition requires a higher memory and computational cost than that in isotropic media. In addition, finite acquisition apertures and band-limited source functions result in unsatisfactory resolutions and amplitudes. To mitigate these problems, we present an elastic least-squares imaging method for tilted transversely isotropic media and apply it to land multicomponent and marine pressure data. Unlike traditional RTM, we use the relative perturbations to the product of density and squared axial (compressional/shear) velocities as reflectivity models ($$\Delta \ln{C}_{33}$$ and $$\Delta \ln{C}_{55}$$), and estimate them by solving a linear inverse problem. Numerical experiments illustrate that subsurface reflectors can be well resolved in adjoint images for land multicomponent data, because of the presence of both P- and S-waves in seismograms. Least-squares migration helps to further improve spatial resolution and image amplitudes. Since there are no direct S-waves in marine streamer data, adjoint RTM images of $$\Delta \ln{C}_{55}$$ are mainly resolved with the converted S-waves and are not as good as those in $$\Delta \ln{C}_{33}$$ images. By approximating the Hessian inverse, least-squares migration allows us to take advantage of the weak converted P–S–P-waves and improve the $$\Delta \ln{C}_{55}$$ image quality. Numerical experiments for synthetic and field data demonstrate the feasibility and advantage of the proposed least-squares TTI RTM compared with wave-mode separation-based elastic RTM. In field data experiments, we observe that since there are no strong P–S–P converted waves in streamer pressure records from the marine survey, the reflectors in $$\Delta \ln{C}_{55}$$ image might be mainly imaged from P-waves due to the amplitude versus offset (AVO) effects.

Reverse Time Migration of Seismic Forward-Prospecting Data in Tunnels Based on Beamforming Methods

For tunneling in complex geological conditions, effective and accurate advanced prospecting techniques are required to detect unexpected geological heterogeneities in front of the tunnel face. Reverse time migration (RTM) method is a promising method to image the geological changes based on seismic forward-prospecting data acquired in tunnels. However, conventional tunnel-based RTM images suffer interference of “trailing” artifacts. Beamforming method can obtain a focused wave front through the stack of wavefield, resulting in improved data quality and RTM results. In this study, we incorporate the beamforming method in RTM imaging procedure, and propose a “sweep and stack” mode RTM method as well as its calculation scheme. Three tunnel-based models with different kinds of geological interfaces are designed to generate synthetic seismic records. Wavefield extrapolation is achieved by an acoustic staggered-grid finite-difference algorithm and zero-lag cross-correlation imaging condition is applied to present RTM results. Analysis and comparison of conventional RTM results and “sweep and stack” mode record-side beamforming RTM results illustrate that, both methods can successfully identify the geological interface ahead of the tunnel face, while record-side beamforming RTM images present more concentrated energy arcs with higher amplitude, which is preferred for geology interpretations. Moreover, the synthetic test in a noisy environment demonstrates that record-side beamforming RTM has better anti-noise capability than the conventional RTM approach. A field test in a highway tunnel construction site is performed to show the good application effects of “sweep and stack” mode RTM in practical seismic detections.

Impact damage visualization in a honeycomb composite panel through laser inspection using zero-lag cross-correlation imaging condition

A fully non-contact laser-based nondestructive inspection (NDI) system is developed to detect and visualize damage in structures. The study focuses on the size quantification and characterization of a barely visible impact damage (BVID) in a honeycomb composite panel. The hardware consists of a Q-switched Nd:YAG pulse laser that probes the panel by generating broadband guided waves via thermo-elastic expansion. The laser, in combination with a set of galvano-mirrors is used to raster scan over a two-dimensional surface covering the damaged region of an impacted quasi-isotropic [60/0/−60]s honeycomb composite panel. The out-of-plane velocities are measured at a fixed location normal to the surface by a laser Doppler vibrometer (LDV). An ultrasonic full wavefield assembled from the three-dimensional space-time data matrix in the interrogated area is first acquired and then processed for imaging the impacted damage area. A wavenumber filtering technique in terms of wave vectors is applied to distinguish the forward and backward wavefields in the wavenumber-frequency domain. A zero-lag cross correlation (ZLCC) imaging condition is then employed in the space-frequency domain for damage imaging. The ZLCC imaging condition consists of cross correlating the incident and reflected wavefields in the entire scanned region. The condition not only images the damage boundary between incident and reflected waves outside the damage region but also, for longer time windows, enables to capture the momentary standing waves formed within the damaged region. The ZLCC imaging condition imaged two delaminated region: a main delamination, which was a skewed elliptic with major and minor axis lengths roughly 17 mm and 10 mm respectively, and a secondary delamination region approximately 6 mm by 4 mm, however, which can only be shown at higher frequency range around 80–95 kHz. To conclude, the ZLCC results were in very good agreement with ultrasonic C-scan and X-ray computed tomographic (X-ray CT) scan results. Since the imaging condition is performed in the space-frequency domain, the imaging from ZLCC can also reveal resonance modes which are shown in the main delaminated area by windowing a narrow frequency band sequentially.

Converted-wave guided imaging condition for elastic reverse time migration with wavefield separation

Elastic reverse time migration (ERTM), which is capable of using multicomponent seismic data, provides not only an improvement of the P-P image compared to the one derived from acoustic RTM, but also more opportunities to understand the subsurface through converted wave images (P-S, S-P, and S-S images). However, the polarity reversals in P-S and S-P images and cross-talk noises generated in S-P and S-S images degrade the converted wave images of ERTM. To overcome these problems, we derive a new P-S converted wave imaging condition for 2D ERTM based on wavefield separation techniques. The proposed imaging condition, called converted-wave guided (CWG) imaging condition, incorporates an extra term that represents the sign and wavelength of S-waves converted from source wavefields into the zero-lag cross-correlation imaging condition for P-S imaging. The extra term compensates for the polarity reversal of separated S-waves from receiver wavefields because the converted S-waves from source wavefields also have the change in polarity. In addition, since this CWG imaging condition produces images where P- and S-waves from source wavefields and S-waves from receiver wavefields coincide, image resolution is enhanced without generating spurious events. Our approach is motivated by the specific feature of ERTM that generates converted waves at the reflection points (conventional imaging points) when proper elastic models are used. Through a numerical experiment with a simple elastic model, we demonstrate that the proposed CWG imaging condition successfully corrects the polarity reversal and provides higher image resolution. We also test our migration algorithm on a synthetic ocean bottom cable (OBC) dataset created using the Marmousi-II model. The P-S image obtained from CWG imaging condition shows continuous events and improved image resolution.

Barely visible impact damage imaging using non-contact air-coupled transducer/laser Doppler vibrometer system

The aim of this study is to investigate the capability of the zero-lag cross-correlation imaging condition of an A0 Lamb wave mode in imaging a barely visible impact damage in a carbon fiber–reinforced polymer composite using a fully non-contact-guided wave-based non-destructive inspection system. A 16-ply (45/0/-45/90)2s carbon fiber–reinforced polymer laminate was impacted at three different locations with different impact energies using a drop ball at three drop heights causing three barely visible impact damages with different sizes. The A0 Lamb wave mode is generated inside the laminate using a circular air-coupled transducer and detected along the damaged region using a laser Doppler vibrometer. The measured wavefield is then decomposed into a forward and backward propagating wavefields by applying a frequency–wavenumber filtering post-processing technique. The decomposed wavefields are then cross-correlated in the frequency domain using zero-lag cross-correlation imaging condition producing a detailed cumulative damage image. The images obtained in frequency domain highlight the three damaged areas with higher zero-lag cross-correlation values compared to other parts of the inspected areas. The experimental investigation has shown a good correlation between the zero-lag cross-correlation imaging condition and C-scan images, which demonstrate a strong capability of guided wave zero-lag cross-correlation imaging condition technique in approximating the location and size of relatively small barely visible impact damages in thin composite structures.

Lamb-wave-based two-dimensional areal scan damage imaging using reverse-time migration with a normalized zero-lag cross-correlation imaging condition

This article presents a two-dimensional, non-contact, areal scanning system to image and quantify multiple sites of damage in isotropic plates using reverse-time migration with a normalized zero-lag cross-correlation imaging condition. The hybrid system composed of a single piezoelectric actuator mounted onto the structure and a laser Doppler vibrometer for two-dimensional scan. The laser Doppler vibrometer scanned a region in the vicinity of the lead zirconate titanate actuator to capture the scattered wavefield introduced by the damage. The proposed damage imaging technique takes into account the amplitude, phase, and all the frequency content of the single-mode Lamb waves propagating in the plate; thus, the size of multiple sites of damage can be imaged without bias, regardless of the damage locations. Damage image quality was used as a metric to compare two-dimensional areal scans and linear scans as well as to compare the proposed method with existing imaging conditions. The experimental results show that the two-dimensional reverse-time migration/normalized zero-lag cross-correlation technique is capable of imaging and quantification of multiple damage sites in an aluminum plate using a single lead zirconate titanate actuator and a nearby, areal laser Doppler vibrometer scan.

Imaging of local porosity/voids using a fully non-contact air-coupled transducer and laser Doppler vibrometer system

This study exploits the feasibility of imaging zones of local porosity/voids simulated by introducing microspheres during layup of a unidirectional carbon fiber–reinforced polymer composite panel. A fully non-contact hybrid system primarily composed of an air-coupled transducer and a laser Doppler vibrometer was used for imaging the local porosity/void zones from the guided wave response. To improve image resolution, several preprocessing techniques are performed. The wavefield reconstructed from the laser Doppler vibrometer measurements was first “denoised” using a one-dimensional wavelet transform in the time domain followed by a two-dimensional wavelet transform in the spatial domain. From the total wavefield, the much weaker backscattered waves were separated from the stronger incident wave by frequency–wavenumber domain filtering. In order to further enhance the signal-to-noise ratio and sharpen the image, the attenuation of incident wave propagation to the damage site was compensated through two proposed weight functions. Finally, a zero-lag cross-correlation was performed for imaging the zone where the compensated incident and backscattered waves were in phase. This improved imaging condition, the “denoised” weighted zero-lag cross-correlation, was proposed and tested for defect imaging in the composite panel with eight intentionally introduced zones of high porosity/voids of varying diameters (1.59–6.35 mm) and depths (0.36–1.08 mm). As expected, the sensitivity of the non-contact air-coupled transducer/laser Doppler vibrometer hybrid system was limited by the wavelength of the excitation signal. The system incorporated with the denoised weighted zero-lag cross-correlation imaging condition for guided wave interrogation gave similar image quality in comparison with that by the immersion C-scan.

Damage imaging using non-contact air-coupled transducer/laser Doppler vibrometer system

In this work, a rapid imaging technique is proposed for imaging damage in metallic plates using a zero-lag cross-correlation imaging condition in the frequency domain. A fully non-contact, single-side access, hybrid inspection system employing air-coupled transducer (ACT) for the generation of anti-symmetric Lamb wave mode and laser Doppler vibrometer (LDV) for dynamic visualization of the Lamb wavefield is used to experimentally verify the proposed technique on three identical aluminum plates with same notch geometry but with various orientations at different locations. The notches (10 mm × 5 mm) are grooved in the aluminum plates using electric discharge machining with a maximum depth of 40% of plate’s thickness and with the following orientations 90°, 60°, and 45° with respect to the horizontal axis. A damage image is constructed by cross-correlating the forward and backward propagating wavefields in the aluminum plates which are separated by analyzing the actual laser Doppler vibrometer measured wavefield using a frequency–wavenumber filtering post-processing technique. The experimental results demonstrate a strong capability of guided wave zero-lag cross-correlation imaging condition technique in localizing, sizing, and detecting the orientation of relatively small defects in the isotopic material.

Damage identification for composite structures using a cross-correlation reverse-time migration technique

This article presents a reverse-time migration technique to image damage by cross-correlating forward and backward propagating wavefields in composite structures using flexural wave signals. First, theory and procedures are presented for damage imaging for composite plates using a zero-lag cross-correlation imaging condition for reverse-time migration, briefly called cross-correlation-based reverse-time migration. The zero-lag cross-correlation was calculated between the forward wavefield and the backward wavefield. The forward wavefield is formed by the excitation from the actuator using a finite difference method, and the backward wavefield is generated by back-propagating the time-reversed scattered wavefield using the same finite difference method. Simulation studies were first examined to verify the capability of using the proposed zero-lag cross-correlation imaging condition to image single and multiple sites of damage. Two experiments were conducted where either the surface-mounted piezoelectric wafers or non-contact laser Doppler vibrometer was used for receiving the scattered wave signals along a linear array. The scattered wave signals were extrapolated in reverse-time to generate backward propagating wavefields. The experimental studies demonstrated that the cross-correlation-based reverse-time migration can accurately locate and image multiple sites of damage with improved resolution and higher efficiency in comparison with classical pre-stack reverse-time migration.