Localized water-rich areas in aquifers can cause severe accidents during coal mining, including property damage and casualties. Traditional ground-based geophysical methods often struggle in the mountainous terrains where coal mines are typically located. To address this, we applied a high-resolution exploration and interpretation strategy based on advancements in semi-airborne transient electromagnetic (SATEM) technology, integrating drilling and logging to detect water-rich areas in the Huangling coal mine. Our approach involved acquiring high signal-to-noise ratio electromagnetic (EM) data near the transmitting line source, using unstructured tetrahedral meshes to simulate complex topography, and employing a quasi-Newton optimization algorithm for detailed 3-D inversion. Synthetic tests demonstrate the accuracy of this method in resolving underground conductivity structures, even in challenging terrains. Field data inversion showed a good fit with observed data and good agreement with resistivity logging, confirming the reliability of the results. This study not only addresses the critical need for efficient water hazard detection in coal mining but also offers significant potential for mineral exploration, geological surveying, and disaster prevention.

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.

Seismic modeling is crucial for tackling waveform-based inverse problems in geophysics. Physics-informed neural networks (PINNs) have become a popular tool for simulating seismic waves. Their ability to incorporate partial differential equations (PDEs), initial conditions (ICs), and boundary conditions directly into the loss function allows for physically accurate modeling. The prevalent approach in the current literature treats the wave equation as a parametric PDE. However, the majority of the existing studies simulate wavefields for a specific velocity model, necessitating network retraining for different models, thereby diminishing modeling efficiency. In response, we present a velocity-encoded (VE) PINN (VE-PINN) that introduces feature parameters to represent various layered velocity models, integrating them into the network. Drawing inspiration from supervised learning, our approach employs a VE method to compute initial wavefields for variable layered models. Remarkably, our proposed VE-PINN demonstrates the ability to generalize across different ICs within the dataset. This eliminates the need to retrain the network for each new solution, offering significant efficiency gains. Numerical results show that the VE-PINN significantly enhances efficiency in solving the acoustic wave equation for various layered velocity models compared with finite-difference methods (FDMs). Subsequently, we extend the application of our method to time-domain simulation for variable source locations, demonstrating that the VE-PINN yields the results that are consistent with numerical wavefields.

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.

Solving the wave equation is an essential step in the simulation of seismic wavefields. Physics-informed neural networks (PINNs) have been widely applied in geophysics. However, there are still some challenges in solving the time-domain wave equation due to the complexity of seismic wavefields and the point source singularity. Numerical solutions can be used as initial conditions to constrain the network training. However, numerical solver-assisted methods have their own accuracy and stability limitations. We propose to use the analytical solutions of the wave equation as prior knowledge. This method does not rely on numerical solvers of the wave equation. It avoids the point source singularity by using analytical wavefields as initial conditions. In addition, we tackle the issue of balancing different terms in the loss function by proposing task-decomposed PINNs (TD-PINNs). TD-PINNs divide the network training into three steps, including pre-training, full-learning, and the physics-enhanced training. The performance of TD-PINNs to solve the wave equation has been tested in different models, and the results show that it can simulate seismic wave propagation with reasonable accuracy.