Full waveform inversion (FWI) plays an important role in velocity modeling due to its high-resolution advantages. However, its highly non-linear characteristic leads to numerous local minimums, which is known as the cycle-skipping problem. Therefore, effectively addressing the cycle-skipping issue is crucial to the success of FWI. Well-log data contain rich information about subsurface medium parameters, providing inherent advantages for velocity modeling. Traditional well-log data interpolation methods to build velocity models have limited accuracy and poor adaptability to complex geological structures. We propose a well interpolation algorithm based on a generative diffusion model (GDM) to create initial models for FWI, trying to address the cycle-skipping problem. By integrating well-log data, migration images to encode physics-based geological priors in the velocity-model building process, our approach can provide much more detailed information of the faults and stratigraphic features. Numerical experiments demonstrate that the method produces accurate and reliable initial models. Compared to the conventional purely data-driven methods, our approach significantly enhances FWI performance and effectively mitigates the cycle-skipping issues.

Anisotropic reverse-time migration (RTM) yields more accurate images for subsurface medium than isotropic migration. However, conventional qP-wave (quasi-P-wave) RTM in transversely isotropic medium with vertical symmetry axis (VTI) suffers from the cross-talk which is caused by residual SV waves and the instabilities when ε is less than δ. To overcome these drawbacks, we present a new wave equation to characterize the propagation of seismic waves in the acoustic VTI medium. This new wave equation is described as the first-order velocity-stress vector wave equation that has specific physical meaning and is dynamically accurate. By decomposing the conventional qP-wave equation, we derive an elliptically anisotropic wave equation along with a non-elliptical operator. The latter is derived from an accurate phase velocity formulation using the acoustic approximation. Our solution is robust against S waves and remains numerically stable even for complex models, without the constraint of ε≥δ. Moreover, it exhibits high accuracy in both travel time and amplitude. The numerical tests demonstrate that our approach is attractive and promising when we perform qP-wave forward modeling and RTM. The comparison of images indicates the advantages of the proposed pure qP-wave on stability and accuracy.

Amplitude-preserving migration is very important for reservoir characterization, which can faithfully provide information on the strength of the reflectors. However, conventional migration algorithms do not compensate for variable illumination effects and can hardly obtain true amplitudes of medium parameter. Least-squares migration (LSM) is an effective method to address this issue. Unfortunately, there is a key problem with LSM methods: most LSM methods only consider illumination compensation but not consider the accuracy of migration velocity model. The accuracy of the migration velocity model directly affects the quality of migrated images. Moreover, changes in velocity are more indicative of reservoir properties than reflectivity. Therefore, it is necessary to incorporate velocity estimation into migration imaging to realize joint inversions. Based on these facts, we present an iterative reweighted LSM method by approximating the local Hessian using point spread functions. Then, we related the LSM results to the scattering potential, simultaneously achieving velocity update with illumination compensation. Based on the gradually changing characteristics of rock properties, we adopted a sparse derivative constraint rather than requiring the result to be sparse. Consequently, this processing caused the results to contain broader bandwidths, giving the image a more continuous and textured appearance. Next, we evaluated the proposed method using the Marmousi2 model. The results had a higher resolution and a more reliable amplitude than the initial migration images. Hence, we efficaciously completed the velocity model update, with our method achieving encouraging results under both relatively accurate migration velocity and highly smoothed migration velocity model tests.

Full-waveform inversion (FWI) serves as a useful tool to quantitatively investigate the properties of the subsurface. Presently, 3-D elastic FWI uses a finite-difference time-domain (FDTD) approach in numerical simulation. However, such an FDTD scheme often includes only second-order temporal approximations, causing errors in temporal dispersion in the case of a large time-stepping size. Such temporal dispersion will affect the inversion results and reduce the inversion quality. We introduce a unique 3-D elastic FWI using a temporal fourth-order finite-difference (FD) approximation. A new quasi-stress–velocity elastic equation is solved by the temporal fourth-order and spatial arbitrary even-order FDTD method, and a novel inversion procedure for the convolutional objective function based on this equation is derived. The multiscale strategy is used to enhance the robustness of our algorithm. The forward modeling and FWI examples presented here demonstrate that our method can achieve modeling and inversion with a high degree of accuracy.

Full waveform inversion (FWI) has been considered one of the most promising approaches to estimating the high-resolution subsurface parameters, which takes advantage of the kinematics and dynamics information of seismic data. However, FWI is greatly dependent on the accuracy of the initial model and vulnerable to the issue of local minimum. Moreover, the multi-source and multi-parameter crosstalk artifacts make multi-source elastic FWI (MS-EFWI) more likely to trap into a suboptimal inversion result. To remedy this defect, this study proposes an efficient elastic FWI (EFWI) paradigm that combines the crosstalk-free MS-EFWI method and a well-guided initial model-building algorithm. Specifically, we apply a harmonic wavelet encoding technology to MS-EFWI, by which the multi-source wavefields can be completely deblended without crosstalk noise. The well-guided structure-oriented interpolation, with the aid of the dip information derived from the initial migration images, is designed to build a satisfactory initial model and therefore reduce the risk of cycle skipping. Numerical examples based on the 2D Overthrust model and Marmousi model further demonstrate the feasibility and robustness of the proposed method with a relatively little number of iterations.

Viscous effects cause strong energy decay and waveform changes of seismic waves. These distortions can be corrected usingQ-compensated reverse time migration ($Q$-RTM) algorithms, and high-resolution migration images can be obtained. However, all$Q$-RTM methods require a relatively accurate$Q$model. The traditional wave-equation$Q$tomography can invert the$Q$model by eliminating the difference in peak frequency between the observed and synthetic early arrivals. However, this approach only can be used to invert the$Q$value only for large-scale applications or on the surface. Moreover, the reflected wave can also be applied in the extended domain, but its computational efficiency is low compared to that of the early arrivals. To overcome these problems, this work proposes a new wave-equation-based$Q$inversion methodology to evaluate more accurate underground$Q$values in local domain. The proposed approach is applicable both to the early arrivals and reflected waves. Accordingly, we first transform the seismic data into the local domain using a sliding Gaussian window to alleviate the crosstalk noise in nearby seismic waves. Then, we use an improved cross correlation algorithm between the amplitude spectra of the observed and synthetic data to calculate the peak frequency shift of each seismic event in local domain. Thus, the inversion accuracy of$Q$can be improved by using different kinds of waves. The numerical inversion examples demonstrate the ability of our proposed method to produce satisfactory inversion results, especially in high-attenuation and deep areas. The$Q$-RTM images further illustrate the accuracy of our proposed$Q$tomography method.

Elastic full waveform inversion (FWI) is more suitable to process multicomponent seismic data and can provide more subsurface medium information than acoustic FWI often with lower efficiency. Except for the parallel algorithms, source-encoding methods are usually adopted to improve the efficiency of FWI, but it often includes crosstalk noise. Besides, the additional source estimation process, critical for a successful FWI, would counteract the high-efficiency advantage of the source-encoding algorithm. We propose an elastic FWI with source-independent crosstalk-free encoding algorithm to solve the above problems. Arbitrary-phase harmonic sine functions are used as new source wavelets to perform the time-domain wavefield simulation regardless of the true wavelet. Treating the harmonic wavelet as the encoding operator and based on the orthogonality of trigonometric functions within integer periods, the amplitude and phase of each source are recovered from the blended source and adjoint wavefields so that the influence of crosstalk noise is avoided. With the deblended data, the proposed algorithm can be naturally applied to unfixed-spread acquisition systems. Moreover, we can conveniently perform the multiscale inversion by controlling the frequencies of simultaneous-source signals as conventional frequency-domain FWI does. Synthetic examples show that the proposed algorithm has high efficiency and accuracy with a strong robustness to the incorrect wavelets.

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.

Time-frequency analysis always plays a central role in the field of seismic processing due to the advantage in characterizing nonstationary signals. In this letter, we present a novel technique for seismic time-frequency analysis based on the high-order synchrosqueezing transform, which obtains more accurate instantaneous frequencies by using the higher order approximations for both amplitude and phase in order to achieve a highly energy-concentrated time-frequency representation. A synthetic example is employed to demonstrate the validity of the proposed method in sharpening time-frequency representation. Application on field data example further proves its potential in enhancing time-frequency resolution and delineating stratigraphic characteristics with higher precision and renders that this technique is promising for seismic data analysis.

The traditional high-order staggered-grid finite-difference (SGFD) method has high-order accuracy in space, but only the second-order accuracy in time, which makes the traditional SGFD method suffer from a large temporal dispersion error during long-distance wave propagation. This paper develops temporal fourth- and sixth-order and spatial arbitrary evenorder SGFD schemes to model isotropic elastic wave propagation. The temporal high-order SGFD schemes have smaller temporal dispersion than the traditional temporal second-order scheme, and thus allow larger time steps to attain a similar accuracy. The developed temporal high-order SGFD schemes are applied to simulate a quasi-stress–velocity wave equation (QWE) that is derived in the framework of a$k$-space approach. A split QWE (SQWE) is further developed, and numerical simulation of SQWE results in separated P (compressional)-wave and S (shear)-wave. Theoretical computational cost analysis verifies that the numerical simulation of QWE using the temporal fourthand sixth-order SGFD schemes is more efficient than the numerical simulation of the traditional stress–velocity wave equation using the traditional temporal second-order SGFD scheme in 2-D. In 3-D, the temporal fourth-order SGFD scheme still runs faster than the traditional temporal second-order scheme; however, the temporal sixth-order scheme is more efficient only when a longer stencil length than 12 is adopted. Numerical examples confirm the correctness of the developed elastic wave modeling schemes.