Time-frequency analysis serves as a useful approach to solve different complex problems in seismic data processing. From a practical standpoint, the majority of time-frequency transform techniques frequently grapple with the trade-off between time and frequency localization adaptability, flexibility in sampling time and frequency, and the pursuit of computational efficiency. To address this, we tailor the streaming computation to implement a fast time-frequency transform, namely the streaming local time-frequency transform (SLTFT), which can significantly decrease the computational cost of adaptive time-frequency analysis. We add a localization scalar to the proceeding streaming algorithm to circumvent the need for taper functions, which provides rapid forward and inverse transforms and applicability in various scenarios.We demonstrate the adaptive time-frequency characteristics of the proposed method, which offers a nonstationary time-frequency representation with variable time-frequency localization. Numerical tests indicate that the proposed SLTFT is a more balanced method compared to previous time-frequency adaptive transforms. It proves suitable for a range of practical applications in nonstationary seismic data processing, including ground-roll attenuation, inverse-Q filtering, and multicomponent data registration.

Magnetotelluric (MT) natural signals are characterized by randomness, nonstationarity, and nonlinearity. At low frequencies, long-duration noise frequently reduces the signal-to-noise ratio (SNR). Especially around the dead band below 1 Hz, the data quality is poor due to the low energy of the natural MT field. This study presents a novel approach using adaptive multiscale sample entropy (AMSE) to identify noisy segments, mainly targeting highly predictable noise types such as square wave, impulse, and triangular-wave interference in low frequency. The primary method employs a robust empirical wavelet transform (REWT) for effective noise suppression. To enhance time–frequency resolution and improve the constraints of direct spectral segmentation in traditional empirical wavelet transform (EWT), the short-time Fourier transform (STFT) is applied to REWT components for enhanced signal-to-noise separation. In addition, Gaussian white noise is introduced to mitigate MT noise effects further. Results show that AMSE effectively identifies noisy segments, and the proposed REWT method successfully retains valuable low-frequency information while significantly suppressing square wave, triangular wave, and impulse noise. Field data show that this method enhances the quality of MT responses, resulting in smoother, more continuous apparent resistivity-phase curves with reduced errors, which improves the accuracy of inversion interpretation and provides a reliable dataset for subsequent calculation of inversion profiles.

Visco-acoustic full waveform inversion (FWI) is a widely-used high-resolution seismic inversion method. It aims to achieve a joint inversion of the velocity and quality factor (Q) models. The resolution of inversion results highly depends on the accuracy of the seismic wave simulation. In this paper, the symplectic stereo-modeling method (SSM) is used to solve the visco-acoustic wave equation. We compare a series of numerical properties between SSM and the traditional finite difference (FD) methods like Lax-Wendroff correction (LWC) method, including numerical dispersion, accuracy, efficiency, numerical errors, stability, etc. The results show that the maximum numerical dispersion error of SSM is about 9%, while that of LWC is about 24%. Meanwhile, SSM is closer to the analytical solution, computationally efficient and stable. We derive the velocity andQgradients for visco-acoustic FWI based on the adjoint-state method using the SSM method, namely SSM-based FWI. For the visco-acoustic Marmousi model, the results show that the proposed method has high inversion accuracy and minor numerical dispersion. Furthermore, for the field data, we implement a three-stage FWI for different frequency ranges and demonstrate the effectiveness of the proposed method.

Simulating seismic wave propagation by solving the wave equation is one of the most fundamental topics in applied geophysics. Considering the elastic nature of the Earth, it is important to simulate the elastic behavior of seismic waves. Compared with solving the acoustic wave equation, it often requires a larger computational cost to solve the elastic wave equation. For the finite-difference method, the computational cost for simulating elastic wavefields increases greatly to include multiple wavefield components. We propose to solve the scattered form of the frequency-domain elastic wave equation using a deep learning framework, called physics-informed neural networks (PINNs). PINNs use the physics principles (scattered elastic wave equations in our case) as the loss function. By inputting the spatial model coordinates and source locations into the network, we can evaluate the wavefield solutions of vertical and horizontal displacements in the domain of interest for arbitrary source locations. We demonstrate that this newly developed deep-learning-based method can simulate multicomponent elastic wavefields with reasonable accuracy.

Random noise is unavoidable in seismic exploration, especially under complex-surface conditions and in deep-exploration environments. The current problems in random noise attenuation include preserving the nonstationary characteristics of the signal and reducing computational cost of broadband, wide-azimuth, and high-density data acquisition. To obtain high-quality images, traditional prediction filters (PFs) have proved effective for random noise attenuation, but these methods typically assume that the signal is stationary. Most nonstationary PFs use an iterative strategy to calculate the coefficients, which leads to high computational costs. In this study, we extended the streaming prediction theory to the frequency domain and proposed the$f$-$x$-$y$streaming prediction filter (SPF) to attenuate random noise. Instead of using the iterative optimization algorithm, we formulated a constraint least-squares problem to calculate the SPF and derived an analytical solution to this problem. The multidimensional streaming constraints are used to increase the accuracy of the SPF. We also modified the recursive algorithm to update the SPF with the snaky processing path, which takes full advantage of the streaming structure to improve the effectiveness of the SPF in high dimensions. In comparison with 2-D$f$-$x$SPF and 3-D$f$-$x$-$y$regularized nonstationary autoregression (RNA), we tested the practicality of the proposed method in attenuating random noise. Numerical experiments show that the 3-D$f$-$x$-$y$SPF is suitable for large-scale seismic data with the advantages of low computational cost, reasonable nonstationary signal protection, and effective random noise attenuation.