The seismic reflection exploration technique has long been established in the oil industry as one of its most successful geophysical exploration tools. It has evolved from a very simple technique (2-D line profiling) to become the most advanced geophysical exploration technique of all (the 3-D reflection technique). Besides its successful use in the oil industry, seismic reflection can also be used to investigate shallow targets. To date, most shallow seismic investigation practitioners have only used the 2-D line profiling technique, as it is easy and cheap to carry out. Depending on the target, some geophysical investigation techniques can provide an answer to archaeological needs, since they are fast, reliable and above all nondestructive. However, this is not the case for the 2-D seismic reflection method, as it is generally considered to be an unsuitable technique. One of the aims of this dissertation is to test the 2-D line profiling technique with a spatially highly condensed geometry to detect the now-buried vallum (defensive ditch) of a Roman fort at Inveresk, Edinburgh, Scotland. The results are compared with the results of two previously obtained resistivity profiles. An excavation programme around the site had established the existence of only one ditch fort, although this is unusual for a Roman fort, as most of them had at least two ditches enclosing them. The qualitative resistivity results revealed four low apparent resistivity anomalies, with two of them being possible ditch-related anomalies in the area where the ditch (or ditches) was predicted. The 2-D seismic reflection profile acquired a very condensed dataset using a CDP jump-roll geometry. The geophones with a hammer source were spaced at 0.25 m interval along a 50 m long line, yielding a total of 2992 traces. The result of this seismic reflection profile confirms the presence of two ditch-like structures about 3 m and 1 m deep, as inferred from the resistivity profiles. Since one of them is too shallow to be a Roman ditch, the seismic results appear to confirm the existence of only one ditch at this fort. The condensed 2-D method is thus capable of imaging very shallow buried structures such as ditches only one or two metres deep. The use of current 3-D seismic reflection oil industry technology technique in shallow investigation work is still in an early phase. The limiting factor of transferring this technology is primarily the cost. There is also a problem in scaling down the survey to suit a shallow target. The primary aim of this dissertation is to describe a case history of an attempt to map out the underground tunnels of an abandoned coal mine using 3-D seismic reflection methods, suitably adapted from the 3-D seismic reflection technology used in the oil exploration industry. The site selected for the survey is located in a brownfield site, part of West of Scotland Science Park, Glasgow, Scotland. The 3-D survey was designed to acquire a highly condensed dataset with a full range of source- receiver azimuths, very high fold of coverage, and in the fastest acquisition time possible. For that, a combination of a full and random 3-D survey geometry methods was applied. The data were recorded using a 144-channel, 24-bit recording system. A 100-700 Hz sweep of the mini-vibroseis source was used to try to obtain high frequency broad-band data. To randomise the common mid-points, each source was placed pseudo-randomly within a 4 m2 area at every 4 m interval. The single element geophones formed a rectangular swath of 8 by 18 on a 2 m grid. The data were processed using industry standard 3-D processing software, using three different approaches successively. The results reveal an undulating top bedrock surface 3-7 m below ground surface. Although convincing images of underground voids or coal seams were not successfully obtained, the results reveal a general pattern of possible mineworks (or a thick coal seam), showing that such 3-D work is feasible and cost- effective. In retrospect, both the geology and the abandoned workings at the chosen site were probably too complex as a test target. A by-product of the 3-D reflection study is the development of a new simple and robust mapping technique. This new technique is named 'surface tomography' as it utilises the tomography concept in a simplified form. The aim is to develop a semi-automated method which may pinpoint areally small velocity anomalies on the top bedrock velocity map (say a 2 m diameter anomaly due, for example, to a buried mineshaft). Only the first breaks from all the source-receiver pairs corresponding to the refracted arrival from the top bedrock surface are used. Any propagation through a low velocity zone within the bedrock will experience a time lag (an increase in travel time) and vice- versa for a high-velocity zone. The first arrival times are reduced to a representative average velocity. Any reduced time that is higher than the average reduced time is considered to have experienced a time lag and vice-versa. To ensure that only raypaths propagating along the bedrock surface were used, the first arrivals from a distance less than the crossover distance of the bedrock arrival and the direct arrival (from the layer above) are deleted. Colour-coded maps of some 80,000 reduced times from the 3-D first breaks were produced to display the anomalies. The results show a systematic pattern of colours striking in the same direction as the general strike of the area. The combined information from this study, the 3-D reflection work and borehole information has been used to revise the geological model of the area.