The fractality of marine measurement networks and of the Earth's sampled magnetic field

We highlight the fractal behaviour of marine measurement networks when determining the Earth's total magnetic field and the spatial trend of the field itself. This approach is a convenient alternative method of assessing the coverage of an area by a set of measurements whenever the environmental situations do not permit a regular distribution of the measurement points. The Earth's magnetic field is sampled in marine areas when the measuring apparatus is moving, even at low speeds, whilst attempts are made to respect the spatial planning which has been pre-determined on the basis of the resolution sought after. However, the real distribution of the measurements presents numerous disturbances which are mainly due to environmental factors. In the case of distributions containing vast areas with no measurement points it is no longer possible to apply Shannon's theorem in 1-D and 2-D. In our paper we apply the fractal theory to certain 1-D and 2-D measurement distributions order to obtain a coverage estimate of the area and the capacity of reconstructing the field. We also examine the trend of the power spectra S of numerous magnetic profiles noting that almost all of them illustrate the dependency with the frequency f in the form S » f-b which is characteristic (necessary condition) of self-similar or self affine fractals.