The high resolution in synthetic aperture radar (SAR) systems is reduced by the speckle appearing in the images. This speckle noise is generated by the coherent processing of radar signals and exists in all types of coherent imaging systems. We study the statistical properties of speckle noise in a four-look SEAS AT SAR image to show evidence of correlation between underlying looks resulting in correlated values for adjacent pixels in the final image. Concentrating on homogeneous areas of the image, experimental determination of the SNR and of the probability density of the recorded intensity is performed. It is shown that the intensity fluctuations due to speckle noise in homogeneous areas are not gamma distributed. A model incorporating the empirical correlation coefficient is extracted from experimental data.