Subaqueous mass-movements are a significant marine geohazard, with the potential to cause large-scale tsunami and damage seafloor infrastructure. Their sedimentary deposits (mass-transport deposits, or MTDs) can show complex but well-defined internal structure across many scales in outcrop examples. In seismic images, however, the internal character of MTDs often appears chaotic, disordered or lacking coherent internal reflectors. Conversely, cores sampled from MTDs with such seismic response can show little evidence of deformation. As a consequence, previous studies have struggled to integrate core-, outcrop- and seismic-scale observations of MTDs, preventing the full use of geophysical data for geohazard assessment. This thesis examines the major controls on the seismic response of MTDs. Chapter 1 develops a geostatistical method to characterise MTDs lacking in coherent internal seismic reflections. The method provides probabilistic estimates of the lateral and vertical dominant scale lengths and Hurst number (roughness) from a seismic image and co-incident borehole log. Chapter 2 applies diffraction imaging to two seismic profiles acquired in the Gulf of Cadiz to characterise the heterogeneous internal structure of MTDs. The resulting images are able to image internal structure and are better able to identify small and thin deposits compared to conventional full-wavefield imaging. Chapter 3 introduces a series of conceptual models for the geophysical properties of shallow sediments to explore the mechanisms that could generate an apparently chaotic-to-transparent response, common to sub-bottom profiler images of MTDs. Full-wavefield seismic modelling experiments show that stratal disruption alone can generate a reduction in seismic amplitudes, without reducing the magnitude of internal impedance contrasts. This discrepancy may explain the frequent contradiction between core-scale and seismic-scale observations of the internal structure of MTDs. Chapter 4 models the seismic response of a fossil MTD outcropping at Vernasso Quarry, north east Italy. A workflow is developed to efficiently model seismic experiments with different source bandwidths and streamer lengths. The results of these experiments indicate that the resolution of the image depends strongly on the source bandwidth, and less strongly on the length of the streamer, likely due to the large proportion of diffracted energy in the seismic response.