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Mapping the anthropic backfill of the historical center of Rome (Italy) by using Intrinsic Random Functions of order k (IRF-k)
 

Mapping the anthropic backfill of the historical center of Rome (Italy) by using Intrinsic Random Functions of order k (IRF-k)

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Mapping the anthropic backfill of the historical center of Rome (Italy) by using Intrinsic Random Functions of order k (IRF-k) ...

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

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    Mapping the anthropic backfill of the historical center of Rome (Italy) by using Intrinsic Random Functions of order k (IRF-k) Mapping the anthropic backfill of the historical center of Rome (Italy) by using Intrinsic Random Functions of order k (IRF-k) Presentation Transcript

    • Mapping the Anthropic Backfill of the Historical Center of Rome (Italy) by Using Intrinsic Random Functions of Order k (IRF-k)
      • GIANCARLO CIOTOLI , FRANCESCO STIGLIANO, FABRIZIO MARCONI , MASSIMILIANO MOSCATELLI , MARCO MANCINI , GIAN PAOLO CAVINATO
      CNR-IGAG, National Research Council , Institute of Environmental Geology and Geoengineering
      • The research has been developed in the framework of the UrbiSIT Project realised by CNR-IGAG for the Department of the Italian Civil Protection. (www.urbisit.it)
      • The UrbiSIT Project is aimed to provide tools for the evaluation of geological hazards in urban areas by using integrated geological and geotechnical models.
      • In this work the reconstruction from borehole data of the backfill bottom surface in the historical center of Rome by using and compare different interpolation techniques is presented.
      OBJECTIVES
    • 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
      • The variety of available deterministic and probabilistic interpolation methods has led to question about which is the most appropriate in different contexts.
      • deterministic methods (IDW, Splines, NN, RBF, etc.) use mathematical functions to estimate values at unknown locations on the degree of similarity with respect to the known neighboring points
      • geostatistical methods use both mathematical and statistical methods to predict unknown values based on the spatial auto-correlation among data points defined by the variogram model.
      INTERPOLATION METHODS
    • METHODS
    • STUDY AREA Location of the boreholes used in this study (about 1400). Digital Terrain Model (DTM) of Rome Province. Tiber river Colosseum
    • 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
      • Ordinary kriging (OK) and ordinary kriging with external drift (OK-ED) have been compared with the Intrinsic Kriging (IRF-k approach).
      • OK-ED has been used in exploiting the ability of regression to relate the target variable to other spatially distributed variables (i.e. Digital Terrain Model).
      • IRF- k was introduced to extend the scope of kriging to non stationary cases. The advantage of this method is that the estimation is performed by using an automatic procedure avoiding the time-consuming modeling of the variogram..
      RESULTS Geostatistical Interpolation
    • WHY THE USE OF EXTERNAL DRIFT?
      • The ED helps in the prediction of a variable Z, known only at discrete points (i.e. boreholes) in the study area, through another variable S, exhaustively known in the same area.
      • In the presence of a trend the variable Z(x) is not stationary, but the auxiliary variable, S(x), represents the local mean and could be considered locally stationary.
      • In the present study Z(x) is the backfill depth (in meters a.s.l.), obtained from the borehole database, and the covariable S(x) is the DTM at the spatial resolution of 20x20 m.
    • 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
    • RESULTS The variogram The presence of a trend at large distance suggests the application of a non stationary method, i.e. IRF-k.
    • 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
    • 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
    • RESULTS Backfill bottom (m asl)
    • Comparison between the backfill bottom reconstruction by using standard lithostratigraphic correlation and that estimated by using OK-ED RESULTS Backfill thickness (m)
    • Comparison between the backfill thickness reconstructed by using litostratigraphic correlation (line filled polygons) (Funiciello, 1995) and by using OK-ED RESULTS Backfill thickness (m)
    • CONCLUSIONS
      • Results confirm that topographic information improves the estimation of the backfill bottom.
      • OK with ED and IRF-k with ED seems to provide both the best estimation and coherent results in accordance with the validation statistics.
      • Considering the similar RSME (respectively 0.14 and 0.13) between the two methods and considering that backfill data show a structured variogram, the OK-ED is the most appropriate interpolator.
    • FUTURE WORK
      • OK-ED results could be improved by using:
      • further topographic information, i.e. DTM from historical cartography and present DTM with high resolution (i.e., 5x5m).
      • geophysical data (i.e., georadar and electrical resistivity tomography)
      • archeological data
    • THANK YOU FOR THE ATTENTION!! Dr. Giancarlo Ciotoli, PhD [email_address] Dr. Francesco Stigliano, technologist [email_address]
    • 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.