Excitation Amplitude Imaging Condition Research Articles

Efficient extended least-squares reverse time migration based on an excitation amplitude imaging condition

In least-squares reverse time migration (LSRTM), which is typically an overdetermined linear inverse problem, the kinematic traveltime error from an inaccurate migration velocity leads to migration image degradation and slow convergence speed. Extended LSRTM (ELSRTM), with an extended imaging condition along the subsurface offset in LSRTM, can effectively mitigate sensitivity to the migration velocity accuracy by adding an extra dimension to the model space. However, for assembling migration images, large imaging condition operations that are proportional to the number of subsurface-offset bins hinder the practical application of ELSRTM. To address this computational problem in ELSRTM, we develop an efficient ELSRTM method based on a modified excitation amplitude (ExA) imaging condition. Furthermore, our ELSRTM method can correctly represent the forward source wavefield by convolving the source wavelet with the ExA. With the forward source wavefield represented this way, Born-modeled data can be simulated efficiently. Thus, wavefield simulation for generating the forward source wavefield is implemented only once at the first iteration. Based on these computational advantages, our ELSRTM method becomes highly efficient. Synthetic data examples on a modified Marmousi2 velocity model demonstrate that our ELSRTM method produces an accurate migration image efficiently even if an inaccurate migration velocity is used. Field data acquired from the Chukchi Sea of the Arctic Ocean also are used to verify the practicality of our ELSRTM method.

Least‐squares reverse time migration using the most energetic source wavefields based on excitation amplitude imaging condition

AbstractLeast‐squares reverse time migration, a linearized inversion problem, can provide high‐quality migration image by minimizing the misfit function, which is defined by predicted and observed data. According to the theory of data‐domain least‐squares reverse time migration, a forward source wavefield that is simulated with a fixed background velocity does not change during iterations. However, storing the forward source wavefield directly into computer memory involves substantial memory consumption. Although a source wavefield reconstruction technique can be applied during least‐squares reverse time migration iterations, this approach can increase the computational cost because of the need for additional wavefield simulations. To alleviate this computational issue in storing the forward source wavefield, we propose an efficient least‐squares reverse time migration scheme based on an excitation amplitude method. Unlike conventional excitation amplitude imaging conditions, the proposed least‐squares reverse time migration scheme enables one to reconstruct the forward source wavefield by convolving a source wavelet with the excitation amplitude of Green's function at the excitation time. With this excitation amplitude method, the forward source wavefield can be efficiently stored in the computer memory because the sizes of the excitation amplitude and excitation time maps are equal to the size of one snapshot. To validate the feasibility of our least‐squares reverse time migration scheme, we perform dot‐product tests and compare forward source wavefields, demigrated data and gradient vectors obtained by conventional least‐squares reverse time migration and our proposed least‐squares reverse time migration. Using numerical tests on synthetic data, we confirm that our least‐squares reverse time migration can produce high‐quality migration results with a significant improvement in computational efficiency with respect to performance time and memory consumption.

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.

An efficient low-frequency artifact suppression method at excitation time for excitation amplitude imaging condition

An efficient low-frequency artifact suppression method at excitation time for excitation amplitude imaging condition

2-D and 3-D Image-Domain Least-Squares Reverse Time Migration Through Point Spread Functions and Excitation-Amplitude Imaging Condition

The enormous computational overheads and excessive storage requirements are two obstacles to the data-domain least-squares reverse time migration (RTM) approach for the application of large-scale 3-D seismic data. To alleviate this problem, we have developed an image-domain least-squares RTM (IDLSRTM) approach through point spread functions (PSFs) and excitation-amplitude (EA) imaging condition, denoted as EA-IDLSRTM. The key point is that the EA imaging condition, as a cost-effective and practical imaging condition, is used to reconstruct the RTM image and localized PSFs. There are two benefits to this combination. One is that the EA imaging condition can effectively reconstruct the RTM image and localized PSFs with less computational overhead and storage requirement, relative to the zero-lag cross correlation (CC) imaging condition. Another important benefit is that the redundant source wavelets in both the RTM and PSF images computed by the CC imaging condition can be removed by the EA imaging condition, prior to the image-domain inversion. As a result, the proposed approach can explicitly reduce the condition number of the Hessian matrix used in the conventional IDLSRTM approach, which will produce a less ill-conditioned inverse problem. In addition, we introduce an angle-dependent filter for the attenuation of low-wavenumber artifacts to accelerate the convergence. Several experiments with synthetic and field data demonstrate that the proposed EA-IDLSRTM approach can efficiently and effectively recover the high-resolution and high-fidelity reflectivity image. Meanwhile, EA-IDLSRTM can provide better imaging quality than the conventional IDLSRTM approach in the case of relatively smoothed velocity.

Reverse-Time Migration Using Local Nyquist Cross-Correlation Imaging Condition

Reverse-time migration (RTM) has the particular capacity for complex geological structure imaging. However, massive storage and high computational costs caused by conventional cross-correlation imaging conditions restrict the large-scale application of RTM. The excitation amplitude imaging condition (EAIC) has the cheapest imaging cost, but inadequate wavefield information causes less tolerance for noise. To alleviate these limitations, we introduce a local Nyquist cross-correlation imaging condition, which serves as a transition between the conventional cross-correlation imaging conditions and the EAIC. Instead of using the full wavefields or only the excitation amplitude to construct imaging, the local cross-correlation imaging condition (LCIC) utilizes the wavefields around the corresponding time of the maximum amplitude at each grid during the source wavefield simulation. Moreover, considering the possible oversampling situations in the LCIC, the Nyquist sampling theorem is flexibly embedded into the local cross-correlation scheme to further reduce the storage costs and improve the efficiency of RTM. Compared with the cross-correlation imaging conditions, the proposed strategy can obtain the similar results and reduce the storage requirement and time costs significantly. In the meantime, it maintains better adaptability to the complex imaging environments than the EAIC. Migration tests of synthetic and field datasets demonstrate that the local Nyquist cross-correlation scheme features good feasibility, efficiency, and practicability in RTM. As a consequence, the proposed local Nyquist cross-correlation imaging condition can effectively save storage and time costs and provide a reliable migrated image even from noisy observed data.

A Stable Q Compensated Reverse Time Migration Method Based on Excitation Amplitude Imaging Condition

A Stable Q Compensated Reverse Time Migration Method Based on Excitation Amplitude Imaging Condition

Optimizing the wavefield storage strategy in reflection-acoustic logging reverse-time migration

In this paper, wavefield storage optimization strategies are discussed with respect to reverse-time migration (RTM) imaging in reflection-acoustic logging, considering the problem of massive wavefield data storage in RTM itself. In doing so, two optimization methods are proposed and implemented to avoid wavefield storage. Firstly, the RTM based on the excitation-amplitude imaging condition uses the excitation time to judge the imaging time, and accordingly, we only need to store a small part of wavefield, such as the wavefield data of dozens of time points, the instances prove that they can even be imaged by only two time points. The traditional RTM usually needs to store the wavefield data of thousands of time points, compared with which the data storage can be reduced by tens or even thousands of times. Secondly, the RTM based on the random boundary uses the idea that the wavefield scatters rather than reflects in a random medium to reconstruct the wavefield source and thereby directly avoid storing the forward wavefield data. Numerical examples show that compared with other migration algorithms and the traditional RTM, both methods can effectively reduce wavefield data storage as well as improve data-processing efficiency while ensuring imaging accuracy, thereby providing the means for high-efficiency and high-precision imaging of fractures and caves by boreholes.

Attenuating Crosstalk Noise of Simultaneous-Source Least-Squares Reverse Time Migration With GPU-Based Excitation Amplitude Imaging Condition

Least-squares reverse time migration (LSRTM) can provide higher quality images than conventional reverse time migration, which is helpful to image simultaneous-source data. However, it still faces the problems of the crosstalk noise, great computation time, and storage requirement. We propose a new LSRTM approach by using the excitation amplitude (EA) imaging condition to suppress the crosstalk noise. Since only the maximum amplitude or limited local maximum amplitudes at each imaging point and the corresponding travel time step(s) need to be saved, the great storage problem can be naturally solved. Consequently, the proposed algorithm can avoid the frequent memory transfer and is suitable for the graphics processing unit (GPU) parallelization. Besides, the shared memory with high bandwidth is used to optimize the GPU-based algorithm. In order to further improve the image quality of EA imaging condition, we adopt the shaping regularization as a constraint. The single-source tests with Marmousi and salt models show the feasibility of our algorithm to image the complex and subsalt structures, among which a wrong background velocity is used to test its sensitivity to the velocity error. The noise-free and noise-included simultaneous-source examples demonstrate the ability of EA imaging condition to suppress the crosstalk noise. During the implementation of the GPU parallelization, we find that the shared memory cannot always optimize the GPU parallel algorithm and just works well for the eighth- or higher order spatial finite difference scheme.

A stable approach for Q-compensated viscoelastic reverse time migration using excitation amplitude imaging condition

The earth [Formula: see text] filtering causes poor illumination of the subsurface. Compensating for the attenuated amplitude and distorted phase is crucial during elastic reverse time migration (ERTM) to improve the imaging quality. Conventional [Formula: see text]-compensated ERTM ([Formula: see text]-ERTM) methods tend to boost the attenuated energy to inverse the [Formula: see text] effects. These methods usually suffer from severe numerical instability because of the unlimited amplification of the high-frequency noise. Low-pass filtering is generally used to stabilize the process, however, at the expense of precision. We have developed a stable compensation approach in this paper. Based on the decoupled fractional Laplacians viscoelastic wave equation, two compensation operators are obtained by extrapolating wavefield in the dispersion-only and viscoelastic media. Because no explicit amplification is included, these two operators are absolutely stable for implementation. To improve the division morbidity for calculating the compensation operators, we use the excitation amplitude criterion and embed the operators into a vector-based [Formula: see text]-compensated excitation amplitude imaging condition. With the derived imaging condition, we could compensate for the absorption accurately without needing to concern the stability issue. The [Formula: see text]-ERTM results for noise-free data are carried out over a simple layered model and a more realistic Marmousi model with an attenuating area to verify the feasibility of the proposed approach. The migration results for noisy data from the Marmousi model further prove that the proposed method performs better fidelity, adaptability, and antinoise performance compared with conventional compensation method with low-pass filtering.

Vector-based excitation amplitude imaging condition for elastic RTM

In recent years, many studies have focused on elastic reverse time migration (RTM). In response to the problems associated with elastic RTM, we propose a new procedure for 2D elastic multicomponent RTM. In this new method, decomposed P- and S-wave components are obtained from the decoupled propagation of the source and receiver wavefields, which allows the expedient calculation of the Poynting vectors and the incident and reflection angles of the P- and S-waves. In addition, we deduce the vector-based excitation amplitude imaging condition. This process automatically accounts for the particle vibration directions when determining the angle-dependent signed reflection coefficients, and does not require the sign to be determined apart from the value of the reflection coefficients. This concept was further extended to the source-normalized crosscorrelation imaging condition. The reflection coefficient of the layered model test was in agreement with the Zoeppritz theory, the PP and PS wave images of the Marmousi II model were clear, and the PS wave images had higher resolution and richer details. In addition, since the calculated reflection coefficients are angle-dependent, they can be easily used for the extraction of angle-domain common-image gathers. Moreover, the imaging condition avoids the polarization reversal in PS wave images and does not require all of the source wavefield data. Consequently, the computation and storage requirements are significantly reduced, which will facilitate the use of the elastic RTM in practice.

Common-image gathers using the excitation amplitude imaging condition

Common-image gathers (CIGs) are extensively used in migration velocity analysis. Any defocused events in the subsurface offset domain or equivalently nonflat events in angle-domain CIGs are accounted for revising the migration velocities. However, CIGs from wave-equation methods such as reverse time migration are often expensive to compute, especially in 3D. Using the excitation amplitude imaging condition that simplifies the forward-propagated source wavefield, we have managed to extract extended images for space and time lags in conjunction with prestack reverse time migration. The extended images tend to be cleaner, and the memory cost/disk storage is extensively reduced because we do not need to store the source wavefield. In addition, by avoiding the crosscorrelation calculation, we reduce the computational cost. These features are demonstrated on a linear [Formula: see text] model, a two-layer velocity model, and the Marmousi model.

A modified excitation amplitude imaging condition for prestack reverse time migration

In wave-equation-based migration, the imaging condition is an important factor that impacts migration accuracy and efficiency. Among the commonly used imaging conditions, the excitation amplitude imaging condition has high resolution, accuracy and low storage and input/output burden when compared with others. However, the excitation amplitude extracted by this imaging condition in its current form will produce a distorted migration image for certain scenarios. In this paper, a modified excitation amplitude imaging condition is proposed that addresses the above problem and produces migrated images free from distortion for complicated geologic models. In this paper, we propose a method to effectively use the modified shortest path method (MSPM) for extracting the maximum amplitude around the first-arrival events. Then, the excitation amplitude imaging condition is applied to obtain a continuous and clear migration image. This process can, to some extent, improve the distorted migration image produced by the traditional excitation amplitude imaging condition. Some numerical tests with synthetic data of Sigsbee2a and Marmousi-II models show that the improvement is feasible and effective in complex-structure media.

Polarity-consistent excitation amplitude imaging condition for elastic reverse time migration

Imaging conditions can not only affect the computational efficiency and storage cost of reverse time migration (RTM) but determine the quality of the final migrated images. This paper extends the idea of the well amplitude-preserved and highly-efficient excitation amplitude imaging condition from acoustic RTM to elastic RTM. For elastic RTM, the maximum amplitude of the separated P-wave and the corresponding image time of each grid point are saved during the forward modeling of the source wavefield and then PP and PS images are obtained by dividing the separated P- and S-waves of the backward-propagated receiver wavefield by the precomputed P-waves at each grid point that satisfies the image time. However, polarity reversals of the PS image will cause destructive interference when the stacked image is needed. In order to solve this problem, we propose the polarity-consistent excitation amplitude imaging condition by combining the excitation amplitude imaging condition with a shot-domain polarity reversal correction method. Then we provide the detailed realization process of this imaging condition in elastic RTM. By utilizing the relatively stable and well amplitude-preserved source-normalized cross-correlation imaging condition as a comparison, we testify to the feasibility and validity of the proposed imaging condition in the aspects of amplitude preservation property, imaging capability of complex structures, storage cost and computational efficiency. Considering the balance between the efficiency and image quality, the polarity-consistent excitation amplitude imaging condition can be a good choice for elastic RTM.

Stretch-free migration imaging condition

Prestack migration has angle-dependent wavelet stretch effects, which lowers the image resolution at large reflection angles. Most current stretch correction methods operate on the migrated images. We develop a new stretch-free imaging condition, which does a shrink-and-shift operation on the extracted propagation wavelet after extrapolation, but before the imaging condition is applied. The algorithm is illustrated with the excitation amplitude imaging condition; the new images show successful stretch corrections over wide angle apertures, and preserve amplitude and phase.

Excitation amplitude imaging condition for prestack reverse-time migration

An implicitly stable ratio imaging condition for prestack reverse-time migration (RTM) was defined using excitation criteria. Amplitude maxima and their corresponding occurrence times were saved at each grid point during forward source wavefield extrapolation. Application of the imaging condition involves dividing the amplitudes of the back-propagated receiver wavefield by the precomputed maximum source wavefield amplitude only at the grid points that satisfy the image time at each time step. The division normalizes by the source amplitude, so only the highest signal-to-noise ratio portion of the data is used. Provided that the source and receiver wavefield amplitudes are accurate at the reflection points, the peak wavelet amplitudes in the migrated image are the angle-dependent reflection coefficients and low wavenumber artifacts are significantly reduced compared to those in images calculated by crosscorrelation. Using excitation information and time-binning for the imaging condition improves computational and storage efficiency by three or more orders of magnitude when compared to crosscorrelation with the full source wavefield. Numerical tests with synthetic data for the Marmousi2 model have shown this method to be a cost-effective and practical imaging condition for use in prestack RTM.