Xiao-Hui Yang

Shear-wave velocity is a key parameter for subsurface material characterization, and Rayleigh wave inversion is widely used to retrieve S-wave velocity profiles in near-surface imaging and ambient noise tomography. While the fundamental mode is typically observable, higher modes are often absent or limited due to field conditions, complicating the inversion process. Existing frameworks require prior identification of mode numbers, which traditionally relies on either manual supervision or repeated inversions. Manual identification is susceptible to subjective errors and inefficiency, whereas repeated inversions depend heavily on the accuracy of the initial model, reducing robustness. To address these limitations, this study proposes a novel automatic method for higher-mode identification in Rayleigh wave dispersion curves using a broad learning network. The proposed method directly models the relationship between higher-mode dispersion curves and their corresponding mode numbers, leveraging the known mode number of the fundamental mode. Validation through numerical simulations and field data applications demonstrates its effectiveness in accurately identifying higher-mode numbers. Furthermore, inversion tests incorporating the identified mode numbers confirm that the proposed method enhances inversion reliability, mitigating the adverse effects of mode misidentification on S-wave velocity estimation. Although the method identifies only one mode number at a time and requires retraining when applied to new field data, the high training efficiency of the BL network enables rapid adaptation to different dataset. By providing a scalable and computationally efficient solution for multimodal dispersion curve inversion, this study advances subsurface exploration in geophysical applications.

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.

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.

Gravity data inversion is of critical importance in geophysics, encompassing a range of applications, such as the exploration of geological resources, the identification of geological structures, and the detection of groundwater resources. This study proposes a three-dimensional (3D) machine learning approach to enhance the efficiency of the aforementioned exploration tasks by leveraging gravity data. The mapping relationship between gravity data and subsurface density structures is modeled by the broad learning network, distinguished by its high training efficiency and robust modeling capability. Notably, the proposed inversion method obviates the constraints on the number of anomalies prior to the inversion process. This is achieved by setting one anomaly with varied locations for different training samples. Numerical and field data applications demonstrate the efficiency of the proposed 3D machine learning gravity data inversion method, especially in automatically determining the number of anomalies. In particular, the proposed method produced accurate density inversion results in the field application, aiding in the identification of potential oil and gas reservoirs in the target region and offering the potential for broader application in other resource exploration. The proposed inversion method can promote the construction of density structures of subsurfaces based on gravity data.

The electrical resistivity method is widely used in near-surface mineral exploration. At present, the deterministic algorithm is commonly employed in three-dimensional (3-D) electrical resistivity inversion to obtain subsurface electrical structures. However, the accuracy and efficiency of deterministic inversion rely on the initial model. In practice, obtaining an initial model that approximates the true subsurface electrical structures remains challenging. To address this issue, we introduce a broad learning (BL) network to determine the initial model and utilize the limited memory quasi-Newton (L-BFGS) algorithm to conduct the 3-D electrical resistivity inversion task. The powerful mapping capability of the BL network enables one to find the model that elucidates the actual observed data. The single-layer BL network makes it efficient and easy to realize, leading to much faster network training compared to that using the deep learning network. Both the synthetic and field experiments suggest that the BL framework could effectively obtain the initial model based on observed data. Furthermore, in comparison to using a homogeneous medium as the initial model, the L-BFGS inversion with the BL framework-designed initial model improves the inversion accuracy of subsurface electrical structures and expedites the convergence speed of the iteration. This study provides an effective approach for fast initial model design in a data-driven manner when the prior information is unavailable. The proposed method can be useful in high-precision imaging of near-surface mineral electrical structures.

Rayleigh wave inversion is a reliable method for inverting the S-wave velocities to reflect the stiffness status of the soil and rock masses of the subsurface. The optimization potential of neural networks in the inversion task is gaining recognition among researchers. Regarding neural-network-based Rayleigh wave inversion, a closer functional relationship between the training samples and the unknown function to be modeled indicates improved inversion performance. The traditional sampling method involves randomly generating samples within a predefined search space, which can result in some samples deviating from the actual functional relationship, thus reducing the accuracy and stability of the inversion. However, few studies consider the sample selection issue in the inversion process based on neural networks. This study proposes a sample selection method for selecting more appropriate training samples to overcome the neglect of sample selection, enhancing the functional modeling of neural networks for Rayleigh wave inversion. The implementation of the proposed sample selection method involves two procedures. First, the random samples are generated within a predefined search space to create a pool of samples. Afterward, the mean moving correlation coefficients of the samples inside the pool are calculated to select more suitable samples for network training based on the moving correlation calculation. Numerical simulations and field data applications demonstrate the necessity and effectiveness of the proposed sample selection method for neural-network-based Rayleigh wave inversion. It is concluded that the proposed method effectively enhances the performance of S-wave velocity estimation through Rayleigh wave inversion using neural networks.

Shear-wave (S-wave) velocity is considered an essential parameter for the study of the earth, and Rayleigh wave inversion has been widely accepted and used to determine it. Given high-quality measured dispersion curves, the inversion performance depends on the applied optimization algorithm inside the inversion process. We propose a novel inversion framework to promote efficient and accurate inversion, i.e., a two-stage broad learning inversion framework (TS-BL). The proposed TS-BL not only inherits the powerful mapping capability and simple configured structure of broad learning (BL) network but also makes two significant improvements to better acclimatize itself to Rayleigh wave inversion. First, TS-BL adopts a two-stage inversion strategy to perform optimizing two times. It does not yield the same search space in the two inversion stages. In the first stage, because the inversion aims to find an approximation rather than the accurate value of model parameters, the difficulty in constructing the mapping model is reduced by sacrificing accuracy. Then, an effective BL network can be established using smaller sample sizes. In the second stage, the search space becomes much narrower, commencing with the approximation results obtained in the prior stage. This helps the final BL network to easily and quickly model the actual relationship between measured dispersion curves and unknown model parameters. After that, the forward modeling of measurements rather than the validation data set is exploited for tuning the network’s hyperparameters. The physical model is superior to the validation data set for selecting a suitable network complexity to adapt to the measured dispersion curves because the latter only describes an overall relationship. As a result, accurate S-wave velocities can be efficiently acquired by using the proposed TS-BL with a low cost of training samples. The efficiency and reliability of TS-BL have been demonstrated in numerical and field data examples.