We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. This paper presents a 3-D regionalized model of the European crust and mantle velocity structure down to depths of approximately 400 km. The model is entirely based upon the existing geological and geophysical literature and it incorporates topographic and bathimetric features. The resulting model is denominated I-data set. About 6400 vertical structures at nodes with an average separation of about 100 km are used to define the model.
Linear interpolation is used to define the model between the nodes.
The I-data set of Europe is compared quantitatively with some of the recent models obtained from body and surface wave tomographic studies. To test the I-data set, surface wave dispersion analysis is performed along some selected great circle paths. Broadband waveform synthetics are also calculated along some paths and compared with the observed time series. The first digital version of this structure database is available for public use. ICTP Preprint No.