Slow formations, characterized by shear-wave velocities lower than those of the borehole fluid, present significant challenges for shear-wave velocity estimation using monopole acoustic logging, primarily due to the absence of critically refracted shear waves. To address this limitation, a borehole full-waveform inversion framework is proposed in this paper, which employs low-frequency monopole excitation to exploit the sensitivity of Stoneley waves to shear velocity. The elastic wave equation is reformulated in cylindrical coordinates as a recurrent neural network structure within a deep learning framework, allowing automatic differentiation for efficient gradient computation without adjoint-state methods. Numerical experiments reveal that while high-frequency monopole data can accurately recover compressional-wave velocities, they fail to resolve shear-wave velocities due to weak Stoneley energy in the high-frequency data. In contrast, strong low-frequency Stoneley waves enable robust and reliable shear-wave inversion. An inversion workflow is further proposed, in which an initial shear-wave velocity model is derived by applying a velocity ratio to the inverted compressional-wave model and subsequently refined through inversion of low-frequency monopole data. The proposed approach yields high-accuracy shear velocity profiles in the near-wellbore region and remains effective under complex geological conditions, including small-scale anomalies and ultra-slow formations. These results highlight the critical role of Stoneley waves in monopole-based inversion and offer a practical solution for estimating the shear-wave velocities of slow and unconsolidated formations.

Oil and gas are important energy resources and industry materials. They are stored in pores and fractures of subsurface rocks over thousands of meters in depth, making the finding and distinguishing them to be a significant challenge. The geophysical methods, especially the seismic and well-logging methods, are the effective ways to identify the oil and gas reservoirs and are widely used in industry. Due to the complexity of near surface and subsurface structures of new exploration targets, the geophysical methods based on advanced computation methods and physical principles are continuously proposed to cope with the emerging challenges. Thus, some new advances in theory and technology of oil and gas geophysics are summarized in this editorial material, especially focusing on the geophysical data processing, numerical simulation technology, rock physics modeling, and reservoir characterization.