High signal-to-noise ratio (SNR) seismic waveform data are conductive to various studies in seismology. Seismic denoising aims to enhance SNR by eliminating additive noise through signal processing while preserving important features of the seismic signal. Conventional parametric seismic denoising methods often require selecting appropriate parameters to achieve optimal results, which may be limiting when dealing with various types and scales of seismic data. Here, we develop an adaptive parameter-free denoising method by combining general cross-validation (GCV) thresholding and pixel connectivity in synchrosqueezed (SS) domain. In this denoising framework, the synchrosqueezed continuous wavelet transform (SS-CWT) is first applied to obtain a high-resolution time–frequency representation. Then, the GCV approach, which allows for choosing the (nearly) optimal threshold without relying on any prior knowledge about the noise level, is employed to attenuate most of the low-energy noise. After that, the relatively isolated high-energy residual noise remaining in the SS-CWT spectrum is removed using pixel connectivity thresholding. Finally, the inverse SS-CWT is applied to the thresholded spectrum to obtain the denoised seismic record. As the thresholds for GCV and pixel connectivity are derived from the spectrum characteristics of the data being analyzed, the proposed denoising approach is highly adaptive and parameter-free. We demonstrate the effectiveness and versatility of the proposed denoising framework using synthetic data and real seismic data from diverse monitoring scenarios, including land, ocean, and emerging distributed acoustic sensing (DAS). The results indicate that the method is a stable and efficient tool for seismic data denoising. Graphical Abstract

Earthquake forecast and risk assessment are of key importance in reducing casualties and property losses. However, they have not been fully achieved due to the complexity of earthquakes. Numerous studies have explored the correspondence of the b-value with changes in effective stress, leveraging temporal and spatial variations to identify precursor characteristics of destructive events in both natural and induced seismic activities. However, robust interpretation of predictive b-values hinges on rigorous estimation, as biased results can mislead conclusions. This paper provides a comprehensive review of spatiotemporal b-value estimation methods alongside statistical significance tests. A pilot b-value analysis of natural earthquakes and induced seismicity manifested the valid impression. The expansion of monitoring datasets with the development of acquisition technology or dense array and advanced estimation methodology will augment the utility of b-value analysis in seismic research and hazard assessment.

Reduction to the pole (RTP) is a fundamental method for interpreting magnetic anomaly data. It faces challenges at low magnetic latitudes and uneven observation surfaces, potentially leading to inaccurate localization of magnetic sources. To address these issues, we develop a novel approach under the machine-learning framework for achieving stable and rapid magnetic RTP in arbitrary regions. First, a single magnetic dipole with random size, position, and magnetization magnitude is used in the forward model to generate samples of the original total magnetic intensity (TMI) anomaly data and the corresponding vertical TMI, which simplifies the establishment of training data. Second, the broad learning system (BLS) is used to establish a mapping relationship between the original and vertical TMI data, as the BLS exhibits a fast network training process due to its concise network structure and strong mapping ability. The combination of the sample generation strategy and BLS allows for rapid network construction and RTP completion. The feasibility of our method is validated by synthetic models and field applications. Synthetic data tests suggest that the BLS approach can be effectively applied to magnetic RTP across various regions, such as the magnetic equator and undulating surfaces. It demonstrates superior accuracy and noise robustness compared to the wavenumber-domain method. Field applications indicate that BLS prediction results facilitate further exploration of mining areas and save over 91% of the time compared with the equivalent source and deep-learning methods. This study is useful for the rapid and accurate localization of magnetic sources and for providing horizontal positional constraints for 3D magnetic inversion.

Microseismic events play a crucial role in mapping fault and fracture distributions in natural and induced earthquakes. Detecting and localizing microseismic events is challenging due to low signal-to-noise ratios. Waveform stacking imaging location is a practical approach for automatically detecting and localizing microseismic events, assuming that the traveltime-corrected seismic waveforms will stack and enhance coherently. However, coherent stack enhancement is susceptible to polarity reversal caused by the nonexplosive components of the source mechanism, which can lead to an unfocused source image, making it difficult to retrieve the optimal location accurately. In this study, we develop a new polarity correction method to address this issue based on the fact that the instantaneous phase difference between two seismic signals with opposite polarity is ±π. First, the Hilbert transform is applied to the original seismic record to obtain the instantaneous amplitude A(t) and phase φ(t). Then, a new signal is constructed by multiplying A(t) with cos[2φ(t)]. The constructed signals for different receivers have the same polarity; therefore, they can be used to refocus the source image. Furthermore, they preserve positive and negative amplitudes, which contributes to noise suppression. Synthetic tests show that our method can effectively achieve polarity correction and noise suppression, enabling a high-resolution source image. Application to real hydraulic fracturing data demonstrates that our method can detect and locate more microseismic events at the fracturing depths, suggesting its effectiveness and potential advantage in microseismic data processing. Because the polarity correction is performed in the data domain without relying on specific receiver layouts, the method is computationally efficient and could be applied to real-time microseismic monitoring across various sites, such as hydraulic fracturing and volcano monitoring.

Microseismic event locations provide critical insights into fracture locations and stress conditions within rock formations, which are essential for seismic hazard monitoring. In practice, pick-based location methods are widely utilized due to their high computational efficiency. However, the accuracy of picking is compromised when the signal-to-noise ratio (SNR) is low. Source location utilizing equal differential time (EDT) surfaces between station pairs represents an effective strategy for mitigating picking errors. Typically, EDT surfaces are constructed using either a fixed width or a fixed probability density function (PDF), which presents challenges in simultaneously achieving high resolution and accuracy. To address this issue, we propose an adaptive probabilistic imaging location method that constructs EDT surfaces by incorporating an adaptive PDF linked to the SNR of arrival picking data. The location probability imaging function is defined as the product of the independent EDT surfaces used for locating sources. For high-SNR data, where picking errors are typically small, the adaptive PDF converges more rapidly than the Gaussian distribution, yielding higher resolution by assigning lower probabilities to locations distant from true positions. For low-SNR data, where picking errors are typically large, the adaptive PDF exhibits heavy-tailed characteristics with a slower rate of decrease, enhancing accuracy by assigning higher probabilities to likely true locations. The effectiveness and stability of the method are validated through theoretical analyses and synthetic data tests. Application to mine microseismic data indicate that the proposed method improves the accuracy and resolution of microseismic event locations relative to other methods.

Three-dimensional (3-D) magnetic inversion is an essential technique for revealing the distribution of subsurface magnetization structures. Conventional methods are often time-consuming and suffer from ambiguity due to limited observations and non-uniqueness. To address these limitations, we propose a novel inversion method under the machine learning framework. First, we design a training sample generation space by extracting the horizontal positions of magnetic sources from the analytic signal amplitude and the reduced-to-the-pole anomalies of magnetic field data. We then employ coordinate transformation to achieve data augmentation within the designed space. Subsequently, we utilize a broad learning network to map the magnetic anomalies to 3-D magnetization structures, reducing the magnetic inversion time. The efficiency of the proposed method is validated through both synthetic and field data. Synthetic examples indicate that compared to the traditional inversion method, the proposed method approximates the true model more closely. It also outperforms traditional and deep learning methods in terms of computational efficiency. In the field example of the Danzhukeng Pb-Zn-Ag deposit in South China, the inversion result is consistent with drilling and controlled-source audio frequency magnetotelluric survey data, providing valuable insights for subsequent exploration. This study provides a new practical tool for processing and interpreting magnetic anomaly data.