Although reverse time migration (RTM) is a powerful imaging method, it uses only the adjoint of the wave-propagation operator and produces only a blurred image. Through linearized inversion, least-squares RTM (LSRTM) reduces migration artifacts, balances the amplitudes, and improves the resolution of the imaging results. Compared to data-domain LSRTM, image-domain LSRTM (ID-LSRTM) is a more practical choice because it typically requires one round of RTM and subsequently solves the deblurring problem of the conventional RTM image involving the Hessian matrix. The Hessian matrix can be effectively replaced by a set of point-spread functions (PSFs). PSFs are traditionally obtained through one round of demigration-migration; hence, the traditional PSF estimation has a computational cost that is twice that of the RTM. We have deduced an analytic expression of the Hessian/PSF by using an asymptotic Green’s function and derived an efficient estimation strategy for the Hessian/PSF. The proposed method significantly reduces the computational cost and allows more flexible spatial sampling of PSFs without interference. Based on the explicitly calculated PSFs, ID-LSRTM can be achieved by solving an optimization problem with combined total-variation and curvelet-domain L1 regularizations. The total computational cost of the proposed LSRTM is approximately the same as that of the conventional RTM. Numerical examples of synthetic and field data find that the proposed LSRTM significantly improves image quality while being highly efficient.

Picking the first arrival is an important step in seismic processing. The large volume of the seismic data calls for automatic and objective picking. In this paper, we formulate first-arrival picking as an intelligent Markov decision process in the multi-dimensional feature attribute space. By designing a reasonable model, the global optimization is carried out in the reward function space to obtain the path with the largest cumulative reward value, to achieve the purpose of automatically picking up the first arrival. The state-value function contains a distance-related discount factor γ, which enables the Markov decision process to pick up the first-arrival continuity to consider the lateral continuity of the seismic data and avoid the bad trace information in the seismic data. On this basis, the method of this paper further introduces the optimized model that is a fuzzy clustering-based multi-dimensional attribute reward function and structure-based Gaussian stochastic policy, thereby reducing the difficulty of model design, and making the seismic data pick up more accurately and automatically. Testing this approach in the field seismic data reveals its properties and shows it can automatically pick up more reasonable first arrivals and has a certain quality control ability, especially the first-arrival energy is weak (the signal-to-noise ratio is low) or there are adjacent complex waveforms in the shallow layer.

SUMMARY: In the case of long-range propagation of forward scattering, due to the accumulation of phase changes caused by the velocity perturbations, the validity of the Born approximation will be violated. In contrast, the phase-change accumulation can be handled by the Rytov approximation, which has been widely used for long-distance propagation with only forward scattering or small-angle scattering involved. However, the weak scattering assumption (i.e. small velocity perturbation) in the Rytov approximation limits its scope of application. To address this problem, we analyse the integral kernel of the Rytov transform using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation and we demonstrate that the integral kernel is a function of velocity perturbation and scattering angle. By applying a small scattering angle approximation, we show that the phase variation has a linear relationship with the slowness perturbation, no matter how strong the magnitude of perturbation is. Therefore, the new integral equation is then referred to as the generalized Rytov approximation (GRA) because it overcomes the weak scattering assumption of the Rytov approximation. To show the limitations of the Rytov approximation and the advantages of the proposed GRA method, first we design a two-layer model and we analytically calculate the errors introduced by the small scattering angle assumption using plane wave incidence. We show that the phase (traveltime) variations predicted by the GRA are always more accurate than the Rytov approximation. Particularly, the GRA produces accurate phase variations for the normal incident plane wave regardless of the magnitude of velocity perturbation. Numerical examples using Gaussian anomaly models demonstrate that the scattering angle has a crucial impact on the accuracy of the GRA. If the small scattering angle assumption holds, the GRA can produce an accurate phase approximation even if the velocity perturbation is very strong. On the contrary, both the first-order Rytov approximation and the GRA fail to get satisfying results when the scattering angle is large enough. The proposed GRA method has the potential to be used for traveltime modelling and inversion for large-scale strong perturbation media.

High-resolution and high-fidelity seismic inversion imaging is one of the core issues of lithologic reservoir exploration. As a linearization subproblem of full-waveform inversion, least-squares migration (LSM) can obtain inversion results with more reliable amplitude, better resolution, and fewer artifacts that can be solved in either the data domain or image domain. For data-domain LSM, the calculation of the data-domain iteration can be very computationally intensive. In practical situations, the convexity of the cost function of LSM could be poor, resulting in slow or even nonconvergence iteration, so the ideal inversion imaging results cannot be reached. The image-domain LSM (ID-LSM) follows the logic of image deblurring, which realizes the effects of LSM in another way. The key problem of ID-LSM is to calculate a reliable Hessian matrix that can be effectively replaced by a set of point-spread functions (PSFs). Affected by the unknown source wavelet, the accuracy of the background velocity, and the accuracy of the forward/migration operator, the calculation results of the Hessian/PSF cannot be accurate. We first illustrate the impact of incorrect Hessian/PSF on ID-LSM through numerical experiments. To eliminate the influence of the inaccuracy of PSF, we develop the ID-LSM problem as a high-dimensional image deconvolution problem. An alternate update strategy of PSF and imaging results is given under the framework of the expectation-maximization algorithm by additionally introducing prior information about PSF and the inversion result. Numerical examples of synthetic data and field data verify that our method significantly improves image quality.

Accurate time–frequency representation (TFR) is essential for resolving spectral components in seismic signal analysis and enhancing geological interpretation. In this study, we present an enhanced (a new) Generalized S-Transform (GST) that integrates a chirp-modulated window, improving time–frequency localization, reducing spectral smearing, and increasing resolution. Furthermore, a multi-objective optimization strategy is employed to tune the GST parameters, effectively distinguishing transient and harmonic components within the signal. These advancements enhance the adaptive characteristics of GST, optimizing the frequency-dependent windowing function for more effective feature extraction. To validate its effectiveness, the proposed method is applied to both synthetic and real seismic data, employing a frequency-weighted RGB mapping approach based on raised cosine basis functions for visualization. Comparative analysis with conventional TFR methods—standard S-Transform (ST), General Linear Chirplet Transform (GLCT), and Adaptive Generalized S-Transform (AGST)—demonstrates that our approach achieves higher resolution and clearer geological feature delineation.