Mapping the anthropic backfill of the historical center of Rome (Italy) by using Intrinsic Random Functions of order k (IRF-k) Ciotoli Giancarlo, Francesco Stigliano, Fabrizio Marconi, Massimiliano Moscatelli, Marco Mancini, Gian Paolo Cavinato - Institute of Environmental Geology and Geo-engineering (I.G.A.G.), National Research Council, Italy

3. WHY THE ANTHROPIC BACKFILL IN URBAN AREAS ? In ancient town the anthropic backfill can be considered as a “geological unit” due to its high thickness. Their poor geotechnical characteristics could cause: differential settlements damage flooding phenomena in buried creeks seismic amplification shallow collapses

5. METHODS

6. STUDY AREA Location of the boreholes used in this study (about 1400). Digital Terrain Model (DTM) of Rome Province. Tiber river Colosseum

7. RESULTS Deterministic Interpolation *IDW = Inverse Distance Weighting **RBF = Radial Basis Function Method Parameter Min (m) Max (m) RMSE (m) R 2 IDW* Power=2 0.70 21.96 4.033 0.335 IDW Power=3 0.53 22.70 4.151 0.335 IDW Power=4 0.51 23.70 4.307 0.326 IDW Power=5 0.50 23.93 4.429 0.317 IDW Power=6 0.50 23.99 4.518 0.310 IDW Power=7 0.48 24.00 4.584 0.305 RBF** Multiquadric -0.40 21.96 4.296 0.301 RBF Completely Regularised Spline 1.96 17.98 3.956 0.315 RBF Spline with Tension 1.97 17.81 3.958 0.314

10. The choice of the DTM as deterministic covariable is due to the fact that the backfill bottom generally follows the original morphology of the area. THE EXTERNAL DRIFT

11. RESULTS The variogram The presence of a trend at large distance suggests the application of a non stationary method, i.e. IRF-k.

12. In the case of OK and OK-ED the experimental variogram has been constructed up to a distance at which  (h) reaches a sill . Direction 335 Direction 65  (h) = 40*Nugget+200*Spherical(2400,1200,335.0) RESULTS The variogram

13. RESULTS Validation b c Estimated data have been validated by using a subset of boreholes. algorithm R 2 RMSE (m) a OK 0.792 0.31 b KED 0.919 0.14 c IRF-k ED 0.928 0.13

14. RESULTS Backfill bottom (m asl)

15. Comparison between the backfill bottom reconstruction by using standard lithostratigraphic correlation and that estimated by using OK-ED RESULTS Backfill thickness (m)

16. Comparison between the backfill thickness reconstructed by using litostratigraphic correlation (line filled polygons) (Funiciello, 1995) and by using OK-ED RESULTS Backfill thickness (m)

19. THANK YOU FOR THE ATTENTION!! Dr. Giancarlo Ciotoli, PhD [email_address] Dr. Francesco Stigliano, technologist [email_address]

20. FUTURE WORK Inverse Distance Weighted . Is an exact local deterministic interpolation technique. It provides a weight to all the surrounding points. The weight of each point is inversely proportional to its distance from that point. Therefore according to this method the further away the point is from the unsampled point the lesser its weight in defining the value at the unsampled location. So points closer to the unknown point will have a greater influence in determining its value. RBF . a series of deterministic interpolation techniques that fit a mathematical function to a specified number of nearest points. The unknown points are estimated by plotting their position on the spline. The main function of the spline is to minimize the curvature of the overall surface. In this kind of interpolator redundant values are often ignored. Kriging . This method predicts the values at unsampled points based on the regression trends. It uses semivaroigram and covariance for trend analysis . This method provides an estimate of the accuracy of the predictions. After the construction of the empirical semivariogram, a model is fitted to the plotted values using a defined function.