Spatial interpolation of surface point velocity using an adaptive neuro-fuzzy inference system model: a comparative study

Surface displacement measurements of the earth’s crust using GNSS observations are a discrete form and occur at the location of stations. Therefore, it is not possible to study crustal deformation as a continuous field. To overcome this problem, we propose the idea of using an adaptive neuro-fuzzy inference system (ANFIS) model. In the new method, the geodetic coordinates of GPS stations are input vectors, and the components of the displacement field in two-dimensions ( V e , V n ) are used as an output. The new method is analyzed using the observations of 25 GPS stations located in the northwest of Iran. Due to ample GPS stations and a tectonically active area, this region has been selected for study. The results of the new model are compared with the GPS-observed results, and with results produced by three alternative interpolation processes, namely artificial neural network (ANN), Ordinary Kriging (OK) and polynomial velocity field. The root-mean-square error (RMSE), correlation coefficient and relative error are calculated for all four interpolation processes. In the testing step, the averaged RMSE of the ANN, ANFIS, OK, and polynomial models is 2.0, 1.6, 2.7 and 3.2 mm year. The estimated velocity field by the ANFIS has been converted to a strain field and compared to the strain obtained from GPS measurements. Comparing the modeled strains with the ANFIS and GPS output for two control stations shows a correlation coefficient of 0.94 between the new model and GPS. The results reveal the capability and efficiency of ANFIS in comparison with ANN, OK and polynomial models.