Understanding the spatial and temporal evolution of melt distribution in the crust is crucial in providing insight into the development of sub-volcanic crustal stratigraphy and composition. A quantitative model of heat and mass transport through a compacting, highly crystalline crustal mush created through repetitive intrusions of is presented. In contrast with previous static models of heat transfer in the crust, it is found that realistic, intermediate emplacement rates are capable of forming persistent high melt fractions in the shallow crust. The structure of the high melt fraction volumes consists of crystal-poor lenses within a crystalline matrix, where the lenses accumulate through segregation at the top of the system, bounded by the solidus isotherm. Melt distributions predicted by thermo-mechanical modelling provide evidence for the emerging concept of mushmatism and its dominant role in the lifecycle of shallow crustal magma reservoirs. Results of the thermo-mechanical model are benchmarked against those of static models and used to estimate velocities across sub-volcanic systems. Velocity anomalies are estimated using a combination of Karato's method and Berryman's self-consistent approach. Comparison between the velocity profiles estimated from the thermo-mechanical model and those developed using a static model to match recorded data from the SEA-CALIPSO seismic experiment show that lower emplacement rates of only 10 mmpa, compared with 750 mmpa in the static model, are required to produce the same velocity signature when melt segregation is accounted for. Resulting velocity models are used to generate synthetic seismic data for a full waveform inversion (FWI) using a starting model recovered from a synthetic travel-time inversion produced with the software package tomo2d. The resulting velocity model recovered using FWI investigates its potential use in recovering the fine-scale structure of sub-volcanic plumbing systems and the maximum inversion frequency at which a full-scale 3D FWI at active volcanic centres could be implemented.