The use of synthetic aperture radar (SAR) to investigate the ocean surface provides a wealth of useful information that is very seldom used to its full potential. Here we will discuss the application of multifractal techniques to detect oil spills and the dynamic state of the sea regarding turbulent diffusion. We present different techniques in order to relate the shape of the multifractal spectral functions and the maximum fractal dimension to the behaviour of the ocean surface. We compare eddy and sheared dominated flows with convective driven flows and discuss the different features and observation methods. We also compare the scaling of different oil spills detected by means of SAR images. Recent spills and weathered ones are selected and compared to investigate their behaviour in different spatial and temporal ranges. We calculate the partition function based on the grey intensity value of each SAR pixel deriving several types of multifractal spectra as a function of spill residence time estimated for each image. Image manipulations are seen to reduce the speckle noise and thus distinguish much better the texture of the oil spill images. The results are used to discuss how eddy diffusivity may be estimated and used in a description of the ocean surface using a simple turbulence kinematic simulation model to predict the shape of oil spills. Differences in the multifractal spectrum among SAR images may detect the slicks due to plankton and also provide information on the age of the oil spills, on the Lagrangian turbulent structure and on ocean surface diffusivity.