Mechanical metamaterials capable of inducing local resonance effects can manipulate wave propagation at scales smaller than the wavelength, thereby offering an effective means of attenuating low-frequency vibrations. These materials offer a novel approach to mitigating railway-induced ground vibrations at lower frequencies. As a result, various locally resonant metamaterials on the order of meters in size have been designed either for embedding within the soil [33; 34; 35; 36] or atop the terrain [37; 38; 39; 40], aiming to mitigate elastic wave propagation and reduce vibration transmission through the ground. It has been demonstrated that forest trees function as natural metamaterials capable of mitigate wave propagation [41]. Forest trees can act as resonant elements whose longitudinal modes interact with Rayleigh-type surface waves, thereby diminishing ground vibrations [42]. Additional research shows that adjusting tree heights to form a continuous distribution of resonance frequencies enables the vegetation to behave like a graded wave-modulating structure, effectively broadening the attenuation bandwidth [43; 44]. Moreover, the role of tree canopy and branching in influencing attenuation performance was further analyzed through numerical simulations via the finite element method (FEM) [45; 46]. A systematic investigation has been conducted on the attenuation performance of forest trees situated on stratified soils [44]. Both analytical methods [47; 48] and the FEM [49] have also been employed to investigate the wave dispersion characteristics and associated stop bands of periodic trees. The aforementioned investigations regarding forest trees functioning as natural metamaterials for seismic or elastic wave attenuation have provided a novel approach to rail-transit-induced vibration reduction. Compared with the traditional mitigation measures of railway-induced ground vibrations [17; 18; 19; 20; 21; 22], forest trees are more effective at lower frequencies and offer advantages in terms of cost efficiency and environmental sustainability. In addition, existing studies generally adopt simplified two-dimensional models to investigate the attenuation of surface elastic waves by trees and the uncertainty in the attenuation efficiency of a tree row [44; 45], which overlook the discrete distribution of forest trees along the longitudinal direction. The influence of the longitudinal discreteness of forest trees on the performance of wave attenuation requires further investigation. The present work seeks to conduct an in-depth analysis of the attenuation behavior exhibited by forest trees arranged in a two-dimensional grid for mitigating railway-induced ground vibrations. The methodological innovation presented lies in these aspects. A three-dimensional semi-analytical method is used to calculate the responses of the coupled track-ground-tree grid system in the frequency domain. Trees are represented solely by their vertical trunks coupled to the ground surface. Complex factors such as branches, roots, and foliage are not included at this stage. The thin-layer method (TLM) is utilized in this study to derive the exact Green's function for harmonic point excitation applied to a stratified elastic half-space [50; 51; 52]. With the TLM, ground motions can be calculated directly in the frequency-spatial domain, avoiding the numerical inversion of Fourier transforms demanded by conventional methods [50; 51]. The variability in the vibration mitigation performance of forest trees--stemming from differences in their height, geometry, and spatial distribution--is evaluated through stochastic analysis. This work offers practical guidance for applying nearby vegetations as a viable solution to alleviate vibrations generated by rail transit activities. Subsequently, Section 2 outlines the modeling approach developed to assess the dynamic behavior of a multi-layered foundation with an arbitrary arrangement of trees.