Correlation-based Modeling of Seismic Newtonian Noise in Half-Space and Full-Space Media

Seismic Newtonian noise, arising from fluctuating gravitational forces on detector test masses due to ambient seismic activity, represents a fundamental sensitivity limit for low-frequency gravitational-wave observatories such as the Einstein Telescope. Effective mitigation of Newtonian noise requires detailed knowledge of the statistical correlations between the Newtonian acceleration perturbation at the test mass and the seismic displacement field measured by surrounding sensor arrays. In this work, the gravitoelastic correlation tensors (the cross-correlations between the Newtonian acceleration perturbation and the seismic displacement field) are derived and numerically validated for Rayleigh waves and body waves in half-space and full-space media, considering test masses located above and below ground, with and without a spherical cavity. The analytical solutions provide exact and asymptotic benchmarks for validating a Cartesian numerical integration framework, which reproduces the corresponding gravitoelastic tensors across Rayleigh-wave and body-wave models, establishing a unified tool for Newtonian-noise modeling and sensor-array design in future gravitational-wave detectors.