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The pseudo-differential operator with symbol | k |α has been widely used in seismic modelling and imaging when involving attenuation, anisotropy and one-way wave equation, which is usually calculated using the pseudo-spectral method. For large-scale problems, applying high-dimensional Fourier transforms to solve the wave equation that includes pseudo-differential operators is much more expensive than finite-difference approaches, and it is not suitable for parallel computing with domain decomposition. To mitigate this difficulty, we present a truncated space-domain convolution method to efficiently compute the pseudo-differential operator |$\sqrt{-\nabla ^2}$|⁠ , and then apply it to viscoacoustic reverse-time migration. Although |$\sqrt{-\nabla ^2}$| is theoretically non-local in the space domain, we take the limited frequency band of seismic data into account, and constrain the approximated convolution stencil to a finite length. The convolution coefficients are computed by solving a least-squares inverse problem in the wavenumber domain. In addition, we exploit the symmetry of the resulting convolution stencil and develop a fast spatial convolution algorithm. The applications of the proposed method in Q -compensated reverse-time migration demonstrate that it is a good alternative to the pseudo-spectral method for computing the pseudo-differential operator |$\sqrt{-\nabla ^2}$|⁠ , with almost the same accuracy but much higher efficiency. [ABSTRACT FROM AUTHOR]

It remains challenging for elastic full waveform inversion (EFWI) to characterize the elastic properties of a target reservoir deep beneath complex overburden media. This can be attributed to two factors. (1) The complex wavefield distortions arising from the overburden obscure the target reflection properties, resulting in a target zone with limited energy illumination. (2) High-resolution EFWI for the whole inversion domain is computationally expensive. To overcome these challenges, instead of directly inverting for the subsurface model using surface seismic data, we develop a target-oriented elastic waveform inversion scheme. We first retrieve the elastic reflection response to the target zone of interest by projecting seismic data from the surface to the datum level. Then, we can apply high-resolution EFWI on the target zone by using the retrieved elastic reflection data. To better handle the complex overburden, which may include anisotropy and salt bodies, we make full use of the prior estimate of the overburden in the redatuming process to obtain a reliable reflection response to the target zone. In the numerical examples, we use the SEG Advanced Modeling (SEAM) model with an anisotropic overburden and a salt body model to demonstrate the feasibility and effectiveness of the proposed method and analyze the influence of anisotropy and high-contrast salt in the overburden on the redatuming and inversion results, respectively. [ABSTRACT FROM AUTHOR]

Effective diagnosis and understanding of the mechanism of intrapulmonary metastasis (IM) from multiple primary lung cancers (MPLC) aid clinical management. However, the actual detection panels used in the clinic are variable. Current research on tumor microenvironment (TME) of MPLC and IM is insufficient. Therefore, additional investigation into the differential diagnosis and discrepancies in TME between two conditions is crucial. Two hundred and fourteen non-small cell lung cancer patients with multiple tumors were enrolled and 507 samples were subjected to DNA sequencing (NGS 10). Then, DNA and RNA sequencing (master panel) were performed on the specimens from 32 patients, the TME profiles between tumors within each patient and across patients and the differentially expressed genes were compared. Four patients were regrouped with NGS 10 results. Master panel resolved the classifications of six undetermined patients. The TME in MPLC exhibited a high degree of infiltration by natural killer (NK) cells, CD56dim NK cells, endothelial cells, etc. P  < 0.05. Conversely, B cells, activated B cells, regulatory cells, immature dendritic cells, etc. P  < 0.001, were heavily infiltrated in the IM. NECTIN4 and LILRB4 mRNA were downregulated in the MPLC (P  < 0.0001). Additionally, NECTIN4 (P  < 0.05) and LILRB4 were linked to improved disease-free survival in the MPLC. In conclusion, IM is screened from MPLC by pathology joint NGS 10 detections, followed by a large NGS panel for indistinguishable patients. A superior prognosis of MPLC may be associated with an immune-activating TME and the downregulation of NECTIN4 and LILRB4 considered as potential drug therapeutic targets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The anisotropic characteristics of underground media play a crucial role in seismic wave propagation and should be accounted for during seismic imaging. The least-squares reverse time migration (LSRTM) method achieves ideal imaging results by suppressing migration artifacts and balancing amplitude. Therefore, pure quasi-P (P-qP) wave equations in tilted transversely isotropic (TTI) media have been widely used to implement LSRTM, owing to their ability to produce stable and noise-free wavefields. However, solving the anisotropic P-qP-wave equations typically necessitates the use of spectral-based methods, making them computationally inefficient, especially in 3D applications. In this study, we first develop a P-qP-wave equation in TTI media that can be efficiently computed through the finite-difference (FD) approach. Numerical tests show that, in comparison to the previous TTI P-qP-wave equation, the newly derived FD solvable TTI P-qP-wave equation yields reasonably accurate and highly efficient wavefield simulations. Then, building on our newly derived wave equation, we derive its adjoint migration and demigration operator to implement TTI LSRTM. Two synthetic examples suggest that the newly presented P-qP-wave TTI LSRTM approach effectively correct for the anisotropy effects, providing high-quality imaging results. Additionally, our approach has superior computational efficiency over the conventional P-qP-wave TTI LSRTM technique based on a hybrid FD pseudo-spectral (HFDPS) solver. [ABSTRACT FROM AUTHOR]

Seismic anisotropy exists in various types of strata and should be considered in seismic imaging schemes. Seismic imaging algorithms based on isotropic assumption neglect the effects of anisotropy on seismic data, which cause migration artifacts and waveform distortion. To correct the effects of anisotropy on seismic wave propagation, we propose an imaging algorithm that performs least-squares reverse time migration in vertical transversely isotropic acoustic media. We derive the following operators to implement this algorithm, the de-migration operator, its adjoint migration operator, and the corresponding gradient. However, an inaccurate estimated source wavelet will introduce error in the seismic simulation, and thus increase the mismatch between observed and synthetic data for least-squares reverse time migration. In addition, the noises, especially the noises with abnormal amplitudes in the seismic data, damage the inversion convergence and reduce the imaging resolution. To improve the image quality, we propose to use convolved wavefields between observed and synthetic data so that such a mismatch can be independent of the source wavelets. Also, we use the Student's t -distribution instead of L2 norm in our inversion scheme to better handle the seismic noise. Its implementation only modifies the gradient of the conventional least-square reverse time migration scheme. Our numerical tests show a clear improvement using our proposed imaging algorithm when compared with the conventional isotropic migration scheme for the anisotropic data. Also, the synthetic examples demonstrate the feasibility and effectiveness of our proposed source-independent algorithm using the Student's t -distribution. [ABSTRACT FROM AUTHOR]

The broadband finite-difference (FD) coefficients computed by a cost function have been widely applied to suppress of numerical dispersion. Under the same conditions, the FD coefficients with small low-wavenumber dispersion error will produce a more accurate numerical solution in the long-time seismic wave simulation. Thus, how to reduce the low-wavenumber dispersion error becomes a crucial problem. According to the research into the zero-point position at the dispersion curve for three types of cost function, we found that the more zero points concentrate on the low-wavenumber region, the less the dispersion error. Therefore, the concentration of zero points is a good way to reduce dispersion error, which can be implemented by modified wavenumbers of zero points. Then, we design a Lagrange dual problem with a restriction based on the modified wavenumbers. The requirements for constructing the Lagrange dual problem are the optimization function and restricted condition, where the former is based on the dispersion relation, and the latter comprises the modified wavenumbers. The solution of this optimization problem, calculated by the dual ascent method, affords a less low-wavenumber dispersion error than the solution yielded by the alternating direction method of multipliers (ADMM). The theoretical analysis and numerical modeling suggest that the proposed method is superior to the existing optimal FD coefficients in reducing numerical error accumulation in low-frequency simulation. [ABSTRACT FROM AUTHOR]

Anisotropic pseudo-acoustic forward modeling and migration imaging are critical for high-precision seismic exploration. However, the wavefields simulated by the traditional coupled anisotropic acoustic wave equation have the problems of shear wave noise and numerical simulation instability for epsilon that is less than delta. Furthermore, although the pure anisotropic acoustic wave equation expressed by the differential operators can solve the aforementioned noise interference and numerical simulation instability issues, its numerical simulation calculation is large, particularly in 3D industrial applications, because it has to be solved by the spectral-based method. In this paper, a pure anisotropic acoustic wave equation in a vertical transverse isotropic (VTI) medium that can be numerically computed using the efficient finite difference method is derived. This equation not only eliminates noise interference and numerical simulation instabilities, but also allows for an efficient wavefield simulation. We also implement reverse time migration (RTM) using the proposed VTI pure anisotropic acoustic wave equation. Two synthetic tests and one field data test are performed to evaluate the accuracy and robustness of the developed VTI RTM. The imaging results show that the proposed VTI RTM can correct the anisotropy effect on seismic wave propagation and improve migration imaging precision. [ABSTRACT FROM AUTHOR]

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

Anisotropy of subsurface media can affect the seismic wave travel time estimates, and then affect the imaging of target regions. To calibrate the effect of anisotropy, a VTI (transverse isotropy media with vertical symmetry axis) least-squares reverse-time migration (LSRTM) algorithm is used. However, if seismic data contains noise especially the outliers, the high-quality images cannot be produced by LSRTM based on an L2 norm. Considering that Student's t -distribution has better robustness than the L2 norm, this study derives a VTI-LSRTM algorithm based on Student's t-distribution (T-VTI-LSRTM) misfit function. The plane-wave encoding is introduced into the T-VTI-LSRTM to improve the computational efficiency. We conduct numerical tests using the complex models to illustrate the effectiveness and adaptability of the method. The sensitivity analysis of velocity and anisotropy parameters demonstrate that anisotropy and velocity parameters have a distinct effect on imaging results, in which velocity sensitivity is the strongest, then the epsilon and parameter delta sensitivity is the weakest. [ABSTRACT FROM AUTHOR]

Multi-scale full waveform inversion (FWI) in the time domain requires an accurate source signature estimation, which is difficult to obtain from the field data. As an alternative, we present a source-independent inversion algorithm that modifies Wiener filter calculations. A low-pass Wiener filter can be computed by using information from a reference trace rather than the true source wavelet. AWiener filter was designed to handle observed and modeled wave fields separately, with a misfit function consisting of the filtered wave field. The source wavelets for the observed and modeled wave fields are both eliminated in the misfit function, thus offsetting any adverse effects from a directly observed or adjoint source wavelet. As the filtered data can be expressed as a convolution of the reflection coefficient and the target source wavelet, it is straightforward to use a low to high frequency selection strategy. Although this new method uses the same forward-modeling and inversion schemes as conventional FWI, it differs in how it calculates the misfit function and corresponding adjoint source. In order to achieve more faithful inversion results and promote computational efficiency, multi-scale source-independent inversion and multi-source inversion strategies were also adopted. In particular, we realized that a weighted average of the zero-offset traces in the super gather constitutes a better choice for reference traces. Aside from this, the noise resistance capability of the proposed method was tested and synthetic data evaluations of both the source-independent and multi-source inversion strategies were undertaken to assess the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]