ABSTRACT Full 3D modeling of time-domain electromagnetic data requires tremendous computational resources. Consequently, simplified physics models prevail in geophysics, relying on a much faster but approximate 1D forward model. A method was introduced that combines the accuracy of a 1D simplified physics model with the flexibility of coarse grids to reduce modeling errors, thereby avoiding full 3D accurate simulations. The method was applied to time-domain airborne electromagnetics (AEM) data, generating data with a modeling error often smaller than the standard measurement noise level. The modeling error depends on the specific subsurface model (electrical conductivity values and angle representing the deviation of the 1D assumption) and the specific (temporal) discretization. Computation time can be decreased by a factor of 27. This modeling strategy may serve as an alternative to surrogate models or statistical relations derived from large 3D data sets.

ABSTRACT In this article, the Editor of Geophysics provides an overview of all technical articles in this issue of the journal.

ABSTRACT Due to limitations such as geographic, physical, or economic factors, collected seismic data often contain missing traces. Traditional reconstruction methods require extensive empirical parameter tuning and perform poorly on large contiguous sections of missing traces. Recent advances in deep learning have led to diffusion models with strong reconstruction capabilities. However, UNet-based diffusion models are computationally intensive and struggle to learn correlations between different traces. To address these challenges, we proposed SeisRDT — a latent diffusion transformer (DiT) based on representation learning for seismic data reconstruction. This uses a new architecture that we proposed, the representation diffusion transformer (RDT) architecture, which incorporates a relative positional bias that is added when calculating attention. It also uses a mask modeling scheme based on representation learning to enhance reconstructed data amplitude distribution consistency. The combination of these features enables the method to have global information awareness of the seismic data set, which is especially beneficial when there are large contiguous gaps in the data. Despite having these advantages that improve the quality of results, the proposed method has smaller computational resource requirements than most of the alternative approaches we compared it against. This is in part achieved due to its use of a pre-trained data compression model that compresses data into a latent space. Experiments on field and synthetic data sets show that our method achieves higher reconstruction accuracy than some existing methods and can handle various complex missing data scenarios. However, as the SeisRDT learns the probability distribution of the training data, it may not generalize well to data sets with significantly different distributions.

ABSTRACT Traveltime computation is an effective way to simulate seismic wave propagation in isotropic and anisotropic media. It often requires the phase and group velocities along a ray direction. The phase and group velocities are not functions of the ray direction, but functions of the slowness direction, which motivates the need for efficient numerical approaches for computing the slowness direction. A generalized method was proposed to achieve this goal in 3D tilted transverse isotropic media, which involves solving a nonlinear equation of two unknowns, the inclination and azimuthal angles of the slowness direction, and is computationally demanding. To overcome the difficulty, the equation was recast by projecting it onto the local coordinates that align with the axis of symmetry of the medium. Under the local coordinate system, the nonlinear equation reduces to an equation of one unknown, the inclination angle, with the azimuthal angle obtained from the given ray direction. Hence, the nonlinear equation can be solved efficiently and its solutions can be used to calculate the phase and group velocities. As an application, the proposed method was used to compute traveltimes in 3D vertical transverse isotropic (VTI) media. The calculated group velocities are incorporated into the fast sweeping method to solve the original anisotropic Eikonal equation directly on uniform meshes. The feasibility of the proposed group velocity calculation method is evaluated in three 3D homogeneous anisotropic models, and the application on traveltime computation is tested on a 3D homogeneous VTI model and the British Petroleum anisotropic VTI model.

ABSTRACT Space constraints in active surface wave surveys often lead to a limited aperture length and close source-to-receiver spacing, hindering mode separation and amplifying near-field effects. These factors distort the phase velocity estimates, reducing the accuracy of dispersion imaging and subsequent shear wave velocity estimation. Traditional wavefield transformation techniques, including ω-c transform, ω-k transform, τ-p transform, high-resolution linear Radon transform, and frequency-domain beamforming techniques, assume planar wavefronts and fail to account for near-field effects. On the other hand, the cylindrical frequency-domain beamforming method can only partially eliminate near-field effects. It struggles with mode separation, especially in cases where multiple modes are closely spaced due to shifts in energy peaks and finite-aperture limitations. Therefore, addressing near-field effects and mode separation is crucial for improving dispersion imaging. To overcome these challenges, a high-resolution Hankel function-based Radon transform (HRHRT) was proposed. The proposed method incorporates cylindrical weights to compensate for radiation damping and uses a tailored forward projection operator to address model incompatibility effects. Within a weighted preconditioned conjugate gradient least-squares framework, it effectively mitigates near-field effects while enhancing mode separation by reducing energy smearing and refining spectral power around modal peaks. The algorithm is rigorously tested on published synthetic and real-field data sets across diverse subsurface conditions. Synthetic results demonstrate the superiority of HRHRT over traditional wavefield transformation techniques by suppressing near-field effects at lower frequencies more effectively. Furthermore, inversion results show that HRHRT consistently yields the lowest mean absolute percentage error in shear wave velocity estimation compared to other methods. Application to real data sets confirms its ability to enhance the resolution of closely spaced modes. Consequently, HRHRT significantly improves the accuracy of predicted VS profiles from multichannel analysis of surface waves tests, making itself as a valuable advancement in surface wave dispersion imaging.

Abstract The focus of hydrocarbon reservoir exploration and development has increasingly shifted towards unconventional reservoirs, particularly tight formations. These reservoirs are distinguished by their low porosity and permeability, as well as a complex pore structure comprising numerous pores and fractures. Conventional poroelasticity-based rock physics models, which typically assume single-scale pore structures, are insufficient for characterizing acoustic wave responses. Consequently, establishing the relationship between acoustic waves and pore-scale heterogeneity remains a critical challenge. To address this problem, the present study focuses on acoustic logging in double-porosity formations described by Biot-Rayleigh theory. We propose a semi-analytical method for calculating the full-waveform acoustic responses in boreholes penetrating double-porosity formations and conduct numerical simulations to investigate the properties of acoustic logging response. To capture the frequency-dependent behavior of borehole waves, the dynamic permeability is incorporated into the double-porosity model. Synthetic signal analysis reveals distinct waveform characteristics in double-porosity medium compared to the results in the single-porosity medium. In high-permeability formations, the inclusions volume ratio has a frequency-dependent impact on wave behavior: (1) at low frequencies, Stoneley wave amplitude grows with inclusions volume ratio; (2) at high frequencies, pseudo-Rayleigh wave experiences both amplitude attenuation and velocity reduction as the inclusions volume ratio rises. In tight formations, changes in inclusions radius and volume ratio continue to influence acoustic fields, causing the shifts in arrival times and changes in wave amplitudes. The results highlight the essential role of incorporating pore-scale heterogeneity in effective reservoir characterization.

Abstract Over recent decades, acoustic single-well imaging technique has attracted increasing attention within the community of oil/gas exploration. Given the prevalence of cased boreholes in oil fields, it is of great significance to investigate the reflections under the condition of cased boreholes for far-field reflector detection. However, simulating wavefields for cased single-well imaging remains challenging. Instead of using the conventional finite-difference method which is considerably time-consuming, we proposed an efficient analytical method for simulating reflections by incorporating viscous linear-slip conditions, thus providing a reliable tool for characterizing the reflections in realistic scenarios involving imperfectly bonded interfaces. The efficiency and accuracy of the proposed method are validated through comparisons with reference solutions. Based on the proposed algorithm, we conduct numerical experiments to analyze the influence of the interface stiffness and viscosity on reflections. We find that the amplitudes of reflections initially increase and then decrease as the interface stiffness decreases for dipole sources, highlighting the advantage of using dipole sources in scenarios involving poor cement bonding quality. However, for monopole sources, the reflection amplitudes decrease nearly monotonically with decreasing stiffnesses. Additionally, for both dipole and monopole sources, the reflection characteristics are dominated by the interface stiffness rather than the viscosity in the case of large stiffness (i.e., good cement bonding). However, the reflections become highly sensitive to the interface viscosity when the stiffness is small (i.e., poor cement bonding). Consequently, the proposed method serves as a powerful tool for modeling and analyzing the reflections in cased single-well imaging with imperfectly bonded interfaces, providing a theoretical guidance for developing advanced logging equipment in oil/gas field exploration.

In transient electromagnetic (TEM) measurements, the resolution of shallow subsurface resistivity structures is largely determined by the early time responses. However the early times are disproportionately affected by system properties, such as the transmitter waveform, system filters and signal gating. In the time-domain, modelling these effects requires convolution operations, which can be computationally intensive. In this paper, convolution operations are cast as matrix products using natural splines and leveraging the fact that timing (i.e. waveform timing, gate times, model time discretization) is fixed. Matrices representing different effects, such as the waveform and gating, can then be combined via matrix multiplication. As such, once the matrix representation of the convolution(s) is constructed, all subsequent forward responses can be carried out convolution-free. Validation tests show that the matrix approach produces results that are largely within 2% of standard routines. The accuracy and flexibility of the approach make it a practical solution for TEM modelling, be it 1D, 2D or 3D applications.

Recent advancements in deep learning-based geophysical inversion have drawn considerable attention. Most of these inversions are supervised, which requires the creation of training models that capture as much prior geological information as is available in an area of interest. However, creating such geologically informed training models is challenging because some geological knowledge is difficult to be expressed in mathematical terms. Moreover, geological prior information is not always tied to specific spatial locations. To address these challenges, we propose a novel method based on alpha shapes, a concept from computational geometry, to generate training models that can easily integrate five key types of geological prior information, namely, (1) top boundaries, (2) dip angles, (3) surface outcrop contacts, (4) mineralization zones intersected by drillholes, and (5) measured physical property values on rock samples. We present three distinct scenarios to demonstrate how the proposed method can be employed to systematically generate geologically informed training models. We also show that deep generative models, such as the conditional variational autoencoder, trained on these geologically informed models, can not only output inversion results that align with prior geological knowledge but also quantify the associated uncertainties. To validate our approach, we apply it to a set of magnetic measurements collected in Qinghai Province, China, for the exploration of Cu-Mo critical mineral deposits. The resulting susceptibility models reveal a major dipping structure that is consistent with both surface geology and the magnetic data. The proposed method offers a flexible and unified framework for generating geologically informed training models for deep learning-based geophysical inversions.

Full-waveform inversion (FWI) is capable of handling various wave types, e.g., primary reflections, direct waves, diving waves, and multiple reflections. However, FWI often encounters high nonlinearity when the starting velocity model significantly deviates from the true velocity, and the existence of multiples can further worsen this situation. As a result, the objective function may be trapped in a local minimum, causing the inversion process to fail to converge to the global minimum. Constructing an objective function by decomposing multiples into different controlled orders and performing the FWI on multiples with consecutive orders can expedite convergence. However, conducting the FWI using multiples in an order-by-order way may result in high computational cost. In this study, we address this challenge by creating virtual sources and supergathers. These supergathers phase-encode many orders of multiples and integrate them into one for FWI, requiring only one FWI for all orders of multiples. By employing such a random phase-encoding scheme, crosstalk artifacts arising from interferences between mismatched multiple orders in the source and receiver wavefields can be largely mitigated. The proposed method is validated through numerical experiments with a synthetic dataset, as well as using marine field data from Madagascar. The results demonstrate that FWI employing phase-encoded multiples significantly improves convergence while maintaining computational efficiency.