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. Document Type: Original article Cited as: Xu, S., Liu, Y., Zou, Z., Liu, Y. Borehole full-waveform inversion of monopole logging in slow formations: Insights for shear-wave velocity profiling. Advances in Geo-Energy Research, 2025, 17(1): 82-90. https://doi.org/10.46690/ager.2025.07.07

Recent advances in theory and technology of oil and gas geophysics

The present study interprets the subsurface structure of the Rajian area using seismic sections and the identification of hydrocarbon-bearing zones using petrophysical analysis. The Rajian area lies within the Upper Indus Basin in the southeast (SE) of the Salt Range Potwar Foreland Basin. The marked horizons are identified using formation tops from two vertical wells. Seismic interpretation of the given 2D seismic data reveals that the study area has undergone severe distortion illustrated by thrusts and back thrusts, forming a triangular zone within the subsurface. The final trend of those structures is northwest–southeast (NW–SE), indicating that the area is part of the compressional regime. The zones interpreted by the study of hydrocarbon potential include Sakessar limestone and Khewra sandstone. Due to the unavailability of a petrophysics log within the desired investigation depths, lithology cross-plots were used for the identification of two potential hydrocarbon-bearing zones in one well at depths of 3740–3835 m (zone 1) and 4015–4100 m (zone 2). The results show that zone 2 is almost devoid of hydrocarbons, while zone 1 has an average hydrocarbon saturation of about 11%.

In complex near-surface geologic settings, first-arrival traveltime tomography suffers from strong data noise and uneven raypath coverage. To reduce the inversion non-uniqueness, model smoothing is necessary but often without incorporating structural constraints based on seismic images. The reasons include lack of shallow reflections, strong noise, and gradient velocity field with strong lateral variation. We propose to estimate the near-surface structural trend from the velocity solution of deformable-layer tomography (DLT), that inverts for velocity contours directly. Then the structural dips derived from the DLT solution are taken as the structural regularization in the subsequent traveltime tomographic inversion. Tests for the 2011 SAGEEP workshop model illustrate that this DLT-guided structural regularization steers the tomographic inversion toward more accurate near-surface models. The application of the DLT-guided structural regularization to a field data reveals the near-surface geology of a beach area in Qingdao, China. The DLT solution could complement seismic images or other structural information in regularizing tomographic inversion.