This thesis presents the results of a multichannel reflection survey conducted off of the Western Isles of Scotland in 1981 in the Sea of the Hebrides region. Ten profiles were acquired to 12 seconds two-way time using an air-gun source and a 2.4 km 24 channel receiver, yielding 24 fold coverage with a gather spacing of 50 metres. The data have been processed at Durham using the reflection seismic processing software developed there over the past six years. The interpretation shows that the Mesozoic basins lie unconformably on up to 5 km thickness of Torridonian sediments, which in turn lie uncomformably on Lewisian crystalline basement. The presence of eastward dipping events in the basement are associated with thrust faults and are probably of Caledonian age. The later reactivation of these faults has controlled the formation of the Mesozoic basins. The thesis also contains details of the modifications made to both the computer hardware and the processing software of the Durham Seismic Processing System during the life-time of this project. The expansion of the facility has enabled a larger selection of faster algorithms to be written for the processing of multichannel reflection data. These include velocity filtering, autostatics and dip filtering routines. Particular attention has been given to the accurate determination of the velocity function used when processing the data and how this information may be used to help the geological interpretation.