Non-Stationary Stochastic Media Modeling Based on FFT-MA and Ground Penetrating Radar Response

Ground penetrating radar (GPR) forward modeling serves as a fundamental basis for subsurface structure inversion and data interpretation. Conventional forward simulations are mostly established under the assumption of homogeneous or layered media. These methods fail to characterize the inherent heterogeneity of actual strata, leading to wave-field distortions and increased interpretation errors. To address this limitation, this study couples the Fast Fourier Transform-Moving Average (FFT-MA) non-stationary stochastic medium modeling approach with the Finite-Difference Time-Domain (FDTD) method, establishing a non-stationary stochastic medium GPR forward modeling framework that more accurately mimics real geological formations. First, the core principles of the FFT-MA method and the construction workflow for non-stationary stochastic media are elaborated. Subsequently, GPR electromagnetic wave-field forward simulations coupled with FFT-MA stochastic media are implemented via the FDTD method. Finally, a series of numerical experiments are conducted to investigate the influences of key parameters. The results demonstrate that the FFT-MA method can efficiently generate stochastic medium models with prescribed statistical properties. The proposed FDTD-coupled forward framework accurately reproduces the propagation and scattering of electromagnetic waves in random strata, significantly improving the authenticity and reliability of GPR forward modeling. It provides theoretical support and technical references for GPR data interpretation, inversion, and migration in complex heterogeneous formations.