This paper presents a new methodological framework to assess the conformity of multivariate high-resolution SAR data in terms of asymptotic statistics. Three important statistical properties are studied by applying statistical hypotheses testing, successively: circularity, sphericity and spherical symmetry. Starting from the classical tests designed for the multivariate Gaussian case, these tests are extended to the Spherically Invariant Random Vector (SIRV) stochastic model. A zero-mean test is proposed for both Gaussian and SIRV stochastic processes. The link between the spherical symmetry property and the conformity to the SIRV model is established asymptotically by the specific structure of the quadricovariance matrix. Two high and very high resolution datasets are used to illustrate departures from the standard model assumptions: TerraSAR-X multi-pass InSAR and ONERA RAMSES POLSAR images. As well, the derived tests are applied on the appropriate synthetic dataset. The detection results are qualitatively and quantitatively analysed and some important inferences are drawn regarding these two datasets.