Hammond, GilesLacaille, GrégoireAlkharashi, Abdulelah2026-05-032025https://hdl.handle.net/20.500.14154/78839This report develops a computational model to predict low-frequency displacement noise in interferometric gravitational wave detectors due to seismic motion transmitted through the suspension and suspension thermal noise from dissipation in fused-silica fibres. The seismic contribution is obtained by propagation to the test mass using quadruple suspension transfer functions, and suspension thermal noise is modelled for the pendulum, vertical, and violin modes using effective mechanical loss angles and thermoelastic nulling the fused-silica fibres. The model is applied to Advanced LIGO to reproduce the expected modes and displacement level requirements, after the validation is complete, the same model is then extended to the A♯ upgrade configuration. Results from A♯ thermoelastic nulling give a mid-fibre diameter of 1300.12 µm (stress 1.61 GPa), and a predicted suspension thermal displacement of 4.34×10⁻²⁰ m/√Hz. The combined total of both noises shows A♯ achieving a lower displacement noise level than aLIGO across the observation band, with suspension features shifted away from the most sensitive frequencies.46enGravitational wave detectorsAdvanced LIGOSeismic noiseQuadruple pendulum suspensionThermal NoiseA-sharp (A♯)Fused-silica fibresThermoelastic nullingFluctuation-dissipation theoremThesis