Existing context-based offline meta-reinforcement learning (COMRL) methods primarily focus on task representation learning and given-context adaptation performance. They often assume that the adaptation context is collected using task-specific behavior policies or through multiple rounds of collection. However, in real applications, the context should be collected by a policy in a one-shot manner to ensure efficiency and safety. We find that intrinsic context ambiguity across multiple tasks and out-of-distribution (OOD) issues due to distribution shift significantly affect the performance of one-shot adaptation, which has been largely overlooked in most COMRL research. To address this problem, we propose using heteroscedastic uncertainty in representation learning to identify ambiguous and OOD contexts, and train an uncertainty-aware context collecting policy for effective one-shot online adaptation. The proposed method can be integrated into various COMRL frameworks, including classifier-based, reconstrution-based and contrastive learning-based approaches. Empirical evaluations on benchmark tasks show that our method can improve one-shot adaptation performance by up to 36% and zero-shot adaptation performance by up to 34% compared to existing baseline COMRL methods.

f–k filtering and Radon transform (RT) are classical methods for processing 2-D seismic signals. They assume that target signal events exhibit specific trajectories in the time–offset domain (linear, parabolic, and hyperbolic) and process them accordingly. In fact, seismic signals are nonstationary, with geometric and dynamic characteristics changing pointwise. This makes that these methods suboptimal for processing such signals. The 2-D nonstationary convolution filtering conducted in the time–space domain allows filter variations point-by-point, adapting to the nonstationarity of seismic signals. However, obtaining the filter factors involves complex calculations, making it not widely applicable. This article proposes an efficient method based on a two-dimensional nonstationary convolution model (TNCM) and termed two-dimensional nonstationary filtering by operator scaling (TNFOS). Leveraging the resemblance among filters, specific filter factors can be easily acquired by extracting and scaling the reference filter factors. Through the cascading of filters, TNFOS effectively fulfills nearly all design requirements for 2-D velocity or dip filtering, enabling the broad implementation of 2-D nonstationary filtering. Using synthetic and field experiments, we tested the efficiency of TNFOS and provided four successful applications in suppressing seismic interference.

Extracting a reliable model of quality factor$Q$from the spectral information of seismic signals is a significantly important step for seismic imaging and reservoir characterization. However, the conventional$Q$estimation approach based on the frequency domain is susceptible to the high oscillative spectrum created by the unavoidable random and coherent noise in the observed signal. To address this issue, we introduce an absorption-constrained wavelet power spectrum inversion (AWPSI) method. The inversion involves absorption constraint (AC) and spectrum constraint (SC), where the AC term is a novel constraint for estimating the wavelet’s amplitude spectrum or power spectrum. By treating medium absorption as a physical prior and utilizing information from all waveforms rather than individual ones, AWPSI can yield high-quality wavelet power spectra and ensure stable$Q$estimation results. In addition, the proposed method has no limitations on the type of wavelet. Since its inversion target is wavelet power spectra, AWPSI is broadly applicable to various frequency-based$Q$estimation approaches. We validate the effectiveness of the proposed method using both synthetic and actual vertical seismic profile (VSP) data.

High-dimensional time-frequency (TF) transforms are essential tools in seismic data processing. However, commonly used transforms such as Ridgelet, Curvelet, and Contourlet exhibit limitations in time-shifting invariance and basis function selection, which impacts on their effectiveness in seismic data analysis. To address these limitations, this study introduces optimal basic wavelet (OBW)-Ridgelet, a novel approach integrating the OBW with the Ridgelet transform. By combining OBW with Ridgelet, this method aims to enhance the TF localization for seismic structural analysis and time-shifting invariance property. We also present a workflow for seismic discontinuity detection, employing the C3 algorithm to the decomposed seismic data to get multiscale coherence and introduce the similarity coefficient for scale selection of the multiscale coherence. Synthetic and field data examples demonstrate the effectiveness and robustness of the proposed method, yielding promising results for seismic signal interpretation. The integration of OBW-Ridgelet enriches the toolkit for seismic signal analysis and holds the potential for refining seismic feature detection and interpretation in practical applications.

Improving the resolution of nonstationary reflection seismic data without well data is challenging, as it requires prior estimation of the$Q$-value. The coupling of reflectivity sequence and wavelet introduces spectral fluctuations, rendering the extraction of$Q$highly unstable. While some statistical wavelet amplitude estimation methods, such as spectral shaping (SS) and contraction operator mapping (COM), can yield smooth wavelet amplitude spectra, they do not contribute to$Q$analysis as they lack a physical mechanism for absorption attenuation. Therefore, we propose an absorption-constrained wavelet power spectrum inversion (AWPSI) method based on the segmented stationary convolution model (SSCM). The absorption constraint (AC) term incorporates prior knowledge of the medium’s$Q$-effect and enables simultaneous inversion of wavelet amplitude spectra for all windows. Incorporating AWPSI into COM and SS methods leads to AWPSI-COM and AWPSI-SS methods, which yield higher precision wavelet power spectra and remove the spectral fluctuations caused by reflectivity sequences. We demonstrate that AWPSI enables COM to extract wavelet amplitude spectra more accurately while preserving the attenuation characteristics caused by$Q$-effect. Using the equivalent$Q$field obtained by the AWPSI-COM method, an inverse$Q$-filter can be performed to generate accurate high-resolution seismic profiles. Synthetic and actual stacked seismic data verify the effectiveness of the proposed method.

Random noise attenuation is a critical step in seismic data processing. Since the distribution of field noise is complex and unknown, this poses a challenge to noise attenuation methods where the default noise distribution is known, such as a Gaussian distribution. To address this issue, we propose a method called Seismic Random Noise Gaussianization Framework (SRNGF) to attenuate random noise with unknown distribution. Specifically, SRNGF couples the Gaussianization subproblem and Gaussian denoising subproblem based on the Plug-and-Play (PaP) framework. The Gaussianization submodule with learnable parameters maps seismic data with the noise of unknown distribution to the one corrupted by Gaussian noise. The learnable parameters can be updated through unsupervised online training according to the noise of the unknown distribution on a single field data. The gaussian denoising submodule, which can be replaced by seismic denoiser, aims only for Gaussian noise removal, making SRNGF incorporate the denoiser prior for seismic data. Thus, we incorporate different kinds of seismic (non-deep/deep learning (DL)) denoisers into SRNGF and give their corresponding implementations of SRNGF. Experiments on noise with unknown distribution qualitatively and quantitatively validate the superiority of SRNGF. SRNGF improves the results of non-DL/DL seismic denoiser by a large margin.

In the zero-offset vertical seismic profile (VSP), if the data noise is weak, the spectral ratio method (SRM) is considered to be the most reliable and commonly used method for estimating the medium$Q$factor. However, due to the possible picking error in the first-arrival time of the downgoing waveform, the estimated$Q$value fluctuates, which affects the subsequent attenuation compensation and lithology analysis. In order to overcome this fluctuation, we present an iterative maximum posterior probability (IMAP) method that uses zero-offset VSP data to invert the medium$Q$factor. Based on SRM, this method gives the maximum posterior probability (MAP) method for inverting the quality factor$Q$, establishes the update formulas of quality factor$Q$and travel time difference$\Delta t$, and performs alternate iterations on them. Since the prior information of the formation is introduced and$\Delta t$is corrected in each iteration, the inversion result can eliminate the fluctuations in the$Q$value and velocity caused by the$\Delta t$error. Two synthetic experimental examples and one field experiment verify the effectiveness and superiority of the proposed method.