Validity of the Quasi-Static Approximation in Low-Field NMR Signal Modeling for Petroleum-Bearing Porous Media

Low-field nuclear magnetic resonance (NMR) is widely used for nondestructive characterization of petroleum-related porous media, including pore-structure evaluation, fluid identification, relaxation analysis, wettability assessment, and displacement monitoring. Conventional NMR signal models usually rely on the quasi-static approximation, in which the detected magnetic field is assumed to respond instantaneously to Bloch-governed nuclear magnetization. However, classical electrodynamics requires electromagnetic fields generated by time-dependent magnetization sources to depend on the source state at a retarded time. In this study, a retarded magnetic-dipole formulation is developed to evaluate finite-propagation-time effects in low-field NMR signal modeling. The analysis shows that the correction appears mainly as a phase shift governed by the dimensionless parameter ϵ=ω0L/v, where ω0 is the Larmor angular frequency, L is the characteristic source–receiver distance, and v is the effective electromagnetic propagation velocity, with v=c in free space. Relaxation-induced amplitude corrections are generally smaller. Numerical examples demonstrate that the quasi-static approximation is well justified when ϵ≪1, as typically satisfied in laboratory core NMR. For extended-scale configurations, including unilateral, borehole, underground, and surface NMR, larger propagation paths and medium-dependent electromagnetic properties may increase ε and produce systematic phase deviations. This work provides a theoretical criterion for assessing the validity range of the quasi-static approximation in low-field NMR applications for petroleum-related porous media.