As field seismic data sizes are dramatically increasing toward exabytes, automating the labeling of ``structural monads'' --- corresponding to geological patterns and yielding subsurface interpretation --- in a huge amount of available information would drastically reduce interpretation time. Since customary designed features may not account for gradual deformations observable in seismic data, we propose to adapt the wavelet-based scattering network methodology with a tessellation of geophysical images. Its invariances are expected to be able to thwart the effect of the tectonics. The sparse structure of extracted feature vectors suggest to resort to dimension reduction methods before classification. The most promising one is based on a tessellated version of scattering decompositions, combined with a standard affine PCA classifier. Extensive comparative results on a four-class seismic database show the effectiveness of the proposed method in terms of seismic data labeling and object retrieval, in affordable computational time.