Wiener filter transformations of gravity and magnetic fields and a regional interpretation of the midland valley of Scotland and northern Ireland

Abstract

The spectral representation of gravity and magnetic fields shows that the mathematical expressions describing these fields are the result of the convolution of factors which depend on the geometry of the causative body, the physical properties of the body and the type of field being observed. If a field is known then it is possible to remove or alter these factors to map other fields or physical parameters which are linearly related to the observed field. The transformations possible are: continuation, reduction to the pole, converting between gravity and magnetic fields, converting between components of measurement, calculation of derivatives and mapping magnetization and density distributions and relief on interfaces. Digital Wiener filters, designed using a least squares error criterion, provide an accurate method for effecting these transformations If the field to be transformed is contaminated by noise anomalies, Whose average autocorrelation function can be estimated, then the Wiener filter can be optimized to suppress this noise. The British Isles resulted, in Lower Palaeozoic times, from the collision of two continental masses. Consideration of published geological, aeromagnetic, gravity and crustal seismic data suggests that the Midland Valley of Scotland and Northern Ireland overlies the suture of this ocean closing process. Ophiolite zones on either side of the Midland Valley suggest the location of ancient diverging sub duction zones and the Midland Valley graben appears to be down faulted as a result of compression between the two converging continents It is possible to relate the tectonic, stratigraphic and igneous features of the area to this model and to use the model to predict and to use the geophysics to locate, previously unknown features The post Carboniferous features in the area appear to be related to continental drifting of Europe from America.