This paper presents a geometric approach to the processing of two-dimensional geophysical data. The study has been carried out as an alternative to harmonic analysis, and it uses the properties of an image analysis method: mathematical morphology. Some examples illustrate the most interesting characteristics of the morphological approach which is then applied to the analysis of the gravity anomalies in the Indian Ocean. Two kinds of results have been obtained. From a methodological point of view, morphological analysis shows the interest of a method that does not need either a priori information on the spatial characteristics of the objects under study or global processings needing long computer times. From the geophysical point of view, the extraction and characterization of the undulations allow one to retrieve the geophysical phenomena recently discovered in this region and to reveal some features and structures that the harmonic analysis methods have not yet detected. ¿ American Geophysical Union 1989