Cross-correlation Imaging Condition Research Articles

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

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

An Application of 3D Cross-Well Elastic Reverse Time Migration Imaging Based on the Multi-Wave and Multi-Component Technique in Coastal Engineering Exploration

Precise surveys are indispensable in coastal engineering projects. The extensive presence of sand in the coastal area leads to significant attenuation of seismic waves within unsaturated loose sediments. As a result, it becomes challenging for seismic waves to penetrate the weathered zone and reach the desired depth with significant amount of energy. In this study, the application of three-dimensional (3D) cross-well elastic reverse time migration (RTM) imaging based on multi-wave and multi-component techniques in coastal engineering exploration is explored. Accurate decomposition of vector compressional (P) and shear (S) waves is achieved through two wavefield decoupling algorithms without any amplitude and phase distortion. Additionally, compressional wave pressure components are obtained, which facilitates subsequent independent imaging. This study discusses and analyzes the imaging results of four imaging strategies under cross-correlation imaging conditions in RTM imaging. The analysis leads to the conclusion that scalarizing vector wavefields imaging yields superior imaging of P- and S-waves. Furthermore, the imaging results obtained through this approach are of great physical significance. In order to validate the efficacy of this method in 3D geological structure imaging in coastal areas, RTM imaging experiments were performed on two representative models. The results indicate that the proposed 3D elastic wave imaging method effectively generates accurate 3D cross-well imaging of P- and S-waves. This method utilizes the multi-wave and multi-component elastic wave RTM imaging technique to effectively leverage the Earth’s elastic medium without increasing costs. It provides valuable information about the distribution of subsurface rock layers, interfaces, and other structures in coastal engineering projects. Importantly, this can be achieved without resorting to extensive excavation or drilling operations. This method addresses the limitations of current cross-well imaging techniques, thereby providing abundant and accurate geological and geophysical information for the analysis and interpretation of 3D geological structures in coastal engineering projects. It has important theoretical and practical significance in real-world production, as well as for the study of geological structures in coastal engineering.

A simple image correlation technique for imaging subsurface damage from low-velocity impacts in composite structures

A robust computer vision system is proposed to visualize subsurface barely visible impact damage (BVID) in composite structures through a simple image correlation technique together with a damage imaging condition. This system uses a digital camera to record a video of the surface motion, capturing micron-scale dynamic movement from guided waves propagating on the surface of the structure generated via a sweeping frequency excitation (chirp) up to the ultrasonic frequency range. As the excitation frequency changes during the chirp, waves become trapped within this damaged region, forming standing waves to generate local resonance at specific frequencies. This localized resonance accumulates high wave energy in the region, generating a higher transverse displacement at the damage site compared to the remaining part of the structure. In this work, a simple image correlation technique is proposed to correlate each filtered video frame with the temporal mean of the filtered wavefield video to highlight standing waves at localized damage. The proposed image correlation technique is distinct from digital image correlation (DIC) since it does not use correlation for subset matching to track the movement of surface patterns between two images (video frames). Instead, it uses correlation to directly quantify similarities between corresponding image pixels (windows). Utilizing a single camera greatly simplifies system complexity and hence enhances the practicality and potential for real-time performance over a recently developed technique that utilized 3D DIC with a stereo camera for vision-based BVID detection. To realize the aim, work was conducted in two sequential steps: (1) off-axis 2D DIC was employed rather than 3D DIC to examine the potential of employing a single camera to capture images and extract not only in-plane displacement but also a fraction of transverse displacement in which local resonance is dominant and (2) image correlation was then employed, supplanting the off-axis 2D DIC image processing involved in the first step, to highlight the damage with significantly less processing complexity. This proposed technique using a zero-mean normalized cross-correlation imaging condition, rather than the total wave energy used for DIC-based approaches, is efficient and effective for identifying regions of minute surface movement from local resonance within the damage region without the use of the computationally intensive interpolation to get the sub-pixel gray level information followed by subset matching employed in DIC-based image processing. Two geometrically identical CFRP composite honeycomb panels that had been subjected to low-velocity impacts were used for verification and validation, and two excitation location configurations were tested for each panel. Damaged images produced with correlation for a 100 mm × 100 mm field of view using a single 3-s video, or a total of 19,200 video frames, show accurate damage imaging capabilities regardless of excitation location that exceed that of DIC techniques and is comparable to benchmark damage images obtained from laser Doppler vibrometry, ultrasonic C-scans, and X-ray CT scans. This success of correlation-based imaging of subsurface BVID demonstrates substantial improvements in efficiency and practicality and shows high potential for in situ and real-time computer vision-based nondestructive inspection or structural health monitoring of subsurface BVID in composite aircraft and other critical structures.

Consistency of the inverse scattering imaging condition, the energy norm imaging condition and the impedance kernel in acoustic and elastic reverse-time migration

Abstract In this work, we draw connections between the imaging conditions using the impedance kernel, the inverse scattering imaging condition, and the energy norm imaging condition in acoustic and elastic reverse-time migration (RTM). Traditional RTM often introduces large low-wavenumber artifacts that degrade image quality in intricate geological structures with large velocity variations. In practice, the Laplacian filter is commonly used to remove these low-wavenumber artifacts, but it changes the image wavenumber spectrum. The advanced imaging conditions of the inverse scattering, the energy norm, and the impedance kernel can effectively remove the low-wavenumber artifacts while not changing the wavenumber spectrum. This study aims to build a connection between these three types of imaging conditions by conducting detailed analysis in the wavenumber domain for acoustic and elastic RTMs. We find that they are exactly the same except for the varying weights of the source-receiver wavefield cross-correlation. All three imaging conditions can generate clear RTM images that are not affected by low-wavenumber artifacts. Numerical examples for a simple model, Sigsbee 2a, and BP models verify the consistency of these three imaging conditions and show their advantage over conventional simple zero-lag cross-correlation imaging conditions. This is important for improving the quality and reliability of seismic imaging technology.

Excitation time imaging condition reverse time migration based on physics-informed neural network traveltime calculation with wavefield decomposition using optical flow vector

Abstract Although the excitation-time imaging condition offers a lower memory consumption and higher computational efficiency compared to cross-correlation imaging condition, it has not been widely used in industrial applications because of the accuracy problem of traveltime calculation and the influence of low-wave-number noise. In this paper, we introduce the physics-informed neural network (PINN) algorithm to achieve a high-precision traveltime calculation of the source forward wavefield. Subsequently, we introduce a technique for high-precision wavefield decomposition of the reverse-time wavefield via the optical flow vector, enabling us to realize a correlation-weighted stacking imaging of each wavefield. Model experiments and real data processing show that the proposed traveltime calculation algorithm based on PINN offers high accuracy and good applicability in the excitation time reverse-time migration imaging of complex models, and correlation-weighted stacking imaging based on optical flow vector-based wavefield separation can significantly suppress the noise with low wavenumber and achieve high-precision imaging of complex models.

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.

Q-Compensated Gaussian Beam Migration under the Condition of Irregular Surface

The viscosity of actual underground media can cause amplitude attenuation and phase distortion of seismic waves. When seismic images are processed assuming elastic media, the imaging accuracy for the deep reflective layer is often reduced. If this attenuation effect is compensated, the imaging quality of the seismic data can be significantly improved. Q-compensated Gaussian beam migration (Q-GBM) is an effective seismic imaging method for viscous media, and it has the advantages of both wave equation and ray-based Q-compensated imaging methods. This study develops a Q-GBM method in visco-acoustic media with an irregular surface. Initially, the basic principles of Gaussian beam in visco-acoustic media are introduced. Then, by correcting the complex-value time of the Gaussian beam in visco-acoustic media, energy compensation and phase correction are carried out for the forward continuation wavefield at the seismic source of the irregular surface and the reverse continuation wavefield at the beam center, which effectively compensates the absorption and attenuation effects of visco-acoustic media on the seismic wavefield. Further, a Q-GBM method under the irregular surface is proposed using cross-correlation imaging conditions. Through migration tests for three numerical models of visco-acoustic media with irregular surfaces, it is verified that our method is an effective depth domain imaging technique for seismic data in visco-acoustic media under the condition of irregular surfaces.

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.

Gaussian-weighted crosscorrelation imaging condition for microseismic source localization

Time-reversal imaging is a powerful method for the localization of microseismic events. Conventional time-reversal imaging methods such as autocorrelation imaging or grouped crosscorrelation imaging may suffer from imaging artifacts, e.g., caused by less refined velocity models, noise-contaminated data, and data acquired from sparse receiver networks. These artifacts typically reduce imaging quality and may cause subsequent misinterpretations leading to false positives. To address these issues, we develop a new imaging condition that comprises three steps for each time step. First, we divide the back-propagated wavefield into parts according to their maximum absolute amplitudes. Second, the amplitudes of the back-propagated wavefield are weighted by a Gaussian function with the spatial extent of the prevailing wavelength of the event, centered at the absolute maximum of that part of the wavefield. Finally, we zero-lag crosscorrelate these weighted wavefields at each space point to obtain an image for this time step. The final image is gained by summing the images for each time step. This process collects all energy concentrations along the back projection process, and the energy on the wavefront overlaps and collapses at the hypocenter leading to high-resolution images displaying little to no imaging artifacts. Numerical examples using the Marmousi-II and the 3D SEG overthrust models and a 3D field data example indicate the performance of our method. High-resolution low-noise source images allow unique identification of sources even for source clusters, noisy data, and sparse acquisitions. The source localization errors are smaller than the dominant wavelength of the signal, where a smooth model with a mean velocity error of approximately 5% was considered in the synthetic examples, and a homogeneous model was used in the field data example.

Crosscorrelation-based Marchenko imaging with an optimal aperture

The Marchenko method can retrieve Green’s functions among virtual sources in the subsurface and receivers at the surface from single-sided reflection data. This process, called Marchenko redatuming, allows the estimation of the full-wavefield information in the inhomogeneous subsurface. The retrieved Green’s functions form the input for creating the subsurface image free of artifacts caused by internal multiples. However, when using the crosscorrelation imaging condition in Marchenko imaging, the shallower regions of the obtained image suffer from reduced resolution due to unwanted interference, which occurs in the crosscorrelation gathers at far offsets. With a simple model, we have found that the image resolution obtained using the crosscorrelation Marchenko imaging (CCMI) method is influenced by image position and the integral range of the crosscorrelation function. To overcome this problem, we develop an optimal aperture-bounded crosscorrelation imaging condition using only the constructive wavefields during integration. The optimal aperture is defined as an intercept at which the time difference between the first arrivals of up- and downgoing Green’s functions equals one wavelet period. The integration of the crosscorrelation function is then performed over the determined optimal range that varies with the image position rather than a fixed aperture. As a result, we exclude the unwanted destructive interference from the crosscorrelation gather, resulting in a high-resolution image. The effectiveness of our method has been validated with its applications to synthetic and field data tests.

Correction to: Efficient least-squares reverse time migration using local cross-correlation imaging condition

Correction to: Efficient least-squares reverse time migration using local cross-correlation imaging condition

Generating Azimuth–Reflection Angle Gathers From Reverse Time Migration Using the High-Dimensional Local Phase Space Approximation of Seismic Wavefields

Amplitude-preserving angle gathers are ideal inputs for seismic prestack inversion. However, due to the limitation of computational efficiency, generating subsurface azimuth–reflection angle gathers from 3-D seismic imaging is still a very difficult task. In this article, we propose a new method to generate azimuth–reflection angle gathers from 3-D reverse time migration (RTM). The proposed method approximately reconstructs the source wavefield using high-dimensional wavelets and the excitation information. After using directional vectors to calculate the subsurface observation angles and applying the cross correlation imaging condition, we can generate azimuth–reflection angle gathers by angle binning. Without storing source wavefields or reconstructing source wavefields using boundary conditions, the proposed method has high computational efficiency. Numerical experiments on a synthetic model and a real marine seismic dataset demonstrate that compared with the excitation amplitude imaging condition, the proposed method can generate azimuth–reflection angle gathers with continuous complete events and high signal-to-noise ratio. The image quality and resolution of angle gathers are significantly improved. At the same time, the computational complexity does not increase much.

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.

Time-lapse seismic imaging using shot gathers with nonrepeatable source wavelets

In time-lapse seismic applications, the signal produced by changes in the properties of subsurface rocks is generally obscured by noise associated with imperfect repeatability between surveys. A particularly important obstacle in the formation of time-lapse difference images is variation in the effective source wavelet between baseline and monitoring data sets. However, the partially separable influence of the wavelet within Green’s function model of seismic data permits two frequency-domain matching filters to be designed, which act to reduce source wavelet nonrepeatability. One is based on the spectral ratio of the baseline and monitoring wavelets and can be applied when prior estimates of the wavelets are available; the other is the average spectral ratio of the baseline and monitoring traces and can be applied when prior estimates are unavailable. After balancing the data sets with either of these filters, we further prepare for the imaging step with time-shift corrections, using a published fast local crosscorrelations algorithm, preparing the difference data for use in an imaging algorithm. Reverse time migration is engaged for the imaging task, but we observe that residual repeatability errors tend to be magnified at this stage when source-normalized crosscorrelation imaging conditions are used. Testing indicates that replacing this with a Poynting vector imaging condition strongly suppresses remaining errors in a robust manner. This includes stability within simulated data environments to noise-free data and data with random noise, up to signal-to-noise ratios of roughly one. Furthermore, our method illustrates better performance when compared with the conventional least-squares matching filter and common-depth-point-domain warping. At present, there is no common workflow for seismic imaging directly using time-lapse shot gathers. Our research contribution lies not only in the two matching filters but also in a novel workflow for time-lapse seismic imaging.

On the estimation of reflectivity in reverse time migration: Implementational forms of the inverse-scattering imaging condition

The inverse-scattering imaging condition (ISIC) for reverse time migration (RTM) aims at recovering amplitudes proportional to seismic reflectivity. It has been derived as the high-frequency asymptotic inverse of Born modeling, which justifies its being called a true-amplitude imaging condition. It involves the temporal and spatial derivatives of the up- and downgoing wavefields, in this way generalizing the conventional crosscorrelation imaging condition. The temporal derivations can be redistributed between different wavefield contributions, in this way deriving a set of different implementational forms of the ISIC. By making use of the wave equation for the up- and downgoing wavefields, one can substitute the time derivatives by the Laplacian operator. This provides a theoretical foundation for a popular filter for reducing the backscattering artifacts in RTM. Using Born data from a simple three-layer model and the Marmousi II model as well as the Sigsbee2b data, we have determined that the theoretical equivalence of the equations leads to similar but not identical images. Our numerical tests indicate that the ISIC versions using spatial derivatives are the most economical approach, and that the images obtained with the second time derivative of the source wavefield indicate slightly improved resolution over the other implementations, making the combination of these two characteristics the best choice.

Frequency-Domain Q-Compensated Reverse Time Migration Using a Stabilization Scheme

Seismic attenuation occurs during seismic wave propagation in a viscous medium, which will result in a poor image of subsurface structures. The attenuation compensation by directly amplifying the extrapolated wavefields may suffer from numerical instability because of the exponential compensation for seismic wavefields. To alleviate this issue, we have developed a stabilized frequency-domain Q-compensated reverse time migration (FQ-RTM). In the algorithm, we use a stabilized attenuation compensation operator, which includes both the stabilized amplitude compensation operator and the dispersion correction operator, for the seismic wavefield extrapolation. The dispersion correction operator is calculated based on the frequency-domain dispersion-only viscoacoustic wave equation, while the amplitude compensation operator is derived via a stabilized division of two propagation wavefields (the dispersion-only wavefield and the viscoacoustic wavefield). Benefiting from the stabilization scheme in the amplitude compensation, the amplification of the seismic noises is suppressed. The frequency-domain cross-correlation imaging condition is exploited to obtain the compensated image. The layered model experiments demonstrate the effectiveness and great compensation performance of our method. The BP gas model examples further verify its feasibility and stability. The field data applications indicate the practicability of the proposed method. The comparison between the acoustic and compensated results confirms that the proposed method is able to compensate for the seismic attenuation while suppressing the amplification of the high-frequency seismic noise.

High-Precision Depth Domain Migration Method in Imaging of 3D Seismic Data in Coalfield

Fault structures developed in coal seams, which are often associated with roof collapse, water inrush, gas outburst, and other accidents, are common geological hazards in coal exploration and development. The accurate detection of micro-structures such as small faults has always been a research focus to ensure safety in coalfields. Three-dimensional (3D) seismic research is one of the most efficient methods for obtaining the structural characteristics of coal areas and identify small faults in coal seams, but it is difficult for traditional seismic data imaging technologies to meet the high-precision demand of current coal exploration. Aiming at the characteristics of 3D seismic data in coalfields, we calculated the difference coefficients based on the optimized inversion algorithm and proposed a variable-density acoustic equation optimized with a temporal–spatial staggered-grid finite difference forward algorithm. On this basis, by combining normalized cross-correlation imaging conditions and GPU/CPU collaborative parallel processing technology, we developed an efficient and high-precision 3D reverse time migration method suitable for 3D seismic data in coalfields. Numerical tests verified the accuracy and efficiency of the proposed migration method for the imaging of coal-measure strata with small fault structures and could effectively identify 5 m small faults in the coal seam. The migration test of 3D seismic data in real coalfields showed that our 3D reverse time migration method has good practicability for high-precision imaging of 3D seismic data in coalfields and is an effective method for the precise imaging of small faults in coal measures.

Efficient least-squares reverse time migration using local cross-correlation imaging condition

Abstract The data-domain least-squares reverse time migration (LSRTM), a promising imaging method for obtaining a high-resolution reflectivity image, can be implemented by matching the de-migrated data to the observed one. However, LSRTM requires expensive computational costs in its implementation due to tremendous memory usage (direct storage on disk/memory) for saving source wavefields and repeatable forward/backward wavefield simulations with iterations compared to conventional RTM. Although the source wavefield reconstruction technique can be used to reduce the memory usage, additional computational cost is inevitable because it is implemented during backward wavefield simulation. To alleviate the computational burden, we have developed an efficient LSRTM scheme with local cross-correlation imaging condition (LSRTM-LC), which can use pre-saved source wavefields according to the window size. Because the window size is much shorter than the total recording time for wavefield extrapolation, storing source wavefields into computer memory can be feasible. In addition, the procedure for storing source wavefields is implemented only at the first iteration because the background velocity is fixed during iterations of LSRTM. To validate the feasibility of the LSRTM-LC scheme, we have carried out several numerical tests with synthetic datasets. Numerical tests demonstrated that LSRTM-LC can provide us with equivalent de-migrated data from saved source wavefields and the gradient vector obtained from LSRTM-LC compared to those obtained from the conventional LSRTM. As a result, LSRTM-LC can generate the same quality of reflectivity models as conventional LSRTM, however, it requires less computational costs compared to conventional LSRTM.

Reverse time migration of GPR data based on accurate velocity estimation and artifacts removal using total variation de-noising

Reverse time migration (RTM) is the important intermediate step for focusing the radar diffracted energy of the targets in ground penetrating radar imaging. The conventional RTM algorithm demands a large number of iterative trial experiments and depends on the experts' decision on the estimation of the velocity or relative permittivity of the subsurface medium. Meanwhile, the RTM profile is vulnerable to artifacts, which are composed of noise interference, multiple interferences, arc-shaped clutter, and crosstalk, so it is difficult to inspect visually. Therefore, we propose a RTM method based on accurate velocity estimation and total variation (TV) de-noising to improve the accuracy of the RTM imaging. Firstly, the appropriate migration velocity is obtained automatically by autofocusing metrics to reduce the number of visual inspection times and corrections in the migration processing. Secondly, the TV de-noising strategy based on split Bregman iterative is applied to the RTM profile with the cross-correlation imaging condition, so that the edge of the target can be obvious and the position can be accurate. Then, we apply the proposed method to the simulation data of the pipeline model and the tunnel lining model. All results show that the selected three different autofocusing metrics have unimodality and unbiasedness, which can focus on a single relative permittivity to obtain appropriate migration velocity. Furthermore, the TV de-noising strategy successfully eliminates artifacts, reconstructs contours, enhances the edge sharpness, and improves the quality and accuracy of the radar profile. Finally, we take the field data of the LiuYang River tunnel to verify the applicability of our method, we choose 2–30 as a wider range of relative permittivity based on prior information. Considering the different lateral velocity of the field data, we adopt lateral segmentation processing to improve the quality of the GPR profile. The tests of simulation data and the field data indicate that the proposed method can provide a scientific and effective way for accurate interpretation of GPR data.

Source-Free P-SV Converted-Wave Reverse-Time Migration Using First-Order Velocity-Dilatation-Rotation Equations

The cross-correlation imaging condition between source- and receiver-wavefields is often used in the elastic wave reverse-time migration (RTM) to utilize P- and S-waves. However, it cannot be applied in the absence of source information (e.g., source location, and source wavelet), which is quite common in passive source exploration. We employ a source-free P-SV converted-wave imaging condition, which only requires the back-propagating receiver-wavefield to utilize the P-SV converted waves in imaging the subsurface structures. The imaging condition is independent of source information, which can avoid the extrapolation and reconstruction of the source-wavefield. As a result, the computational cost is decreased to about one-third of conventional RTM that uses source-wavefield reconstruction strategies, e.g., random boundaries. The memory requirement could be also reduced by avoiding the calculation of source-wavefield. Because our imaging condition uses the vector P-wavefield and vector S-wavefield to utilize the P-SV waves, it is necessary to decouple P-wavefield and S-wavefield during the reverse-time extrapolation of receiver-wavefield. We use the first-order velocity-dilatation-rotation elastic wave equations to realize the reverse-time propagation of vector receiver-wavefield, where the vector P-wavefield and vector S-wavefield can be obtained directly. Based on the above methods, a source-free P-SV converted-wave RTM of multi-component seismic data is realized. The model tests show that this method can generate promising subsurface images and can be complementarily used when conventional cross-correlation imaging conditions are not suitable.