This work is an investigation of the anelastic structure of the Derbyshire Dome and adjacent areas from the analysis of high frequency, 0.6 - 4.2 Hz, fundamental mode Rayleigh waves observed from quarry blasts within the study area. Seismic field experiments, designed and implemented to record Rayleigh waves accurately, are discussed together with the data preparation sequence. The effects of possible errors on timing and amplitude measurements are investigated and reduced. Time domain measurements indicate the Carboniferous Limestone district of the Derbyshire Dome consists of smaller provinces the boundaries of which are marked by sudden changes in group velocity and co-incide with geological surface features. Similar provinces are not found in the adjacent Millstone Grit district. Approximate estimates of group velocity are higher over the limestone than over the Millstone Grit district. Transformation into the frequency domain facilitates the determination of group arrival times and amplitude spectrum of each Rayleigh wave recorded. Least squares interstation analyses provide estimates of group slowness dispersion for the districts and component provinces and the Rayleigh wave specific attenuation factor, Qy-1(v), as a function of frequency for certain districts and provinces. Group slowness which ranges from 0.33 - 1.1 s km 1, increasing generally with frequency, is higher in the Millstone Grit district. Qy-1 (v) ranges between 0.01'and 0.08 showing no marked correlation with surface lithology. Models of shear wave velocity, ß(z), and intrinsic specific 11 attenuation factor for shear waves, Qßl(z), with depth, z, are obtained for the upper 1.5 km of the crust in each district and province from the inversion of the observed dispersion and Q-1(v)Y data using linearised and Hedgehog techniques for ß(z) and similar methods for Qßl(z). The deep geology of the area is inferred from the ß(z) models. The limestone district is divided by a major basement fault, to which surface features may be related. The Carboniferous Limestone of different provinces is underlain directly by Ordovician mudstones or Devonian sandstones. A sedimentary basin, of 1.5 km thickness, displaying rhythmic sedimentation is postulated within the Millstone Grit district. Fluid saturation conditions are inferred from the Qß1(2) models. On comparison with previous laboratory work values of Q1-ß which exhibit a possible frequency dependence imply partial saturation of the upper layers of the limestone district whilst field estimates of Qß-1 not exhibiting any frequency dependence imply the Millstone Grit district to be fully saturated at all levels. Two mechanisms of dissipation based on the petrographic character of the rock and fluid flow are believed to operate jointly.