A new approach for reconstructing seismic data based on affine fractal interpolation functions is presented. Specifically, the required vertical scaling factors are determined by using analytical methods such as bounding rectangles or error minimisation. Our method is applied to real data of the seismic activity occurring in the Ionian Sea for the years 1970–2016 (with magnitude \(M_s \ge 4.5\) ). By analysing the real and the reconstructed seismograms, our results indicate that the fractal interpolation method is promising. A comparison with previous techniques is also provided.