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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) 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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The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
METHODS
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
STUDY AREA
Location of the boreholes used in this study (about 1400).
Digital Terrain Model (DTM) of Rome Province.
Tiber river
Colosseum
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
RESULTS Deterministic Interpolation
Method Parameter Min
(m)Max (m)
RMSE (m)
R2
IDW* Power=2 0.70 21.96 4.033 0.335IDW Power=3 0.53 22.70 4.151 0.335IDW Power=4 0.51 23.70 4.307 0.326IDW Power=5 0.50 23.93 4.429 0.317IDW Power=6 0.50 23.99 4.518 0.310IDW Power=7 0.48 24.00 4.584 0.305RBF** Multiquadric -0.40 21.96 4.296 0.301RBF Completely
Regularised Spline1.96 17.98 3.956 0.315
RBF Spline with Tension 1.97 17.81 3.958 0.314
*IDW = Inverse Distance Weighting**RBF = Radial Basis Function
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
RESULTSThe variogram
The presence of a trend at large distance suggests
the application of a non stationary method, i.e. IRF-k.
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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)
RESULTSThe variogram
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
RESULTSValidation
algorithm R2 RMSE (m)
a OK 0.792 0.31
b KED 0.919 0.14
c IRF-k ED 0.928 0.13
b c
Estimated data have
been validated by using a
subset of boreholes.
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
RESULTSBackfill bottom (m asl)
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
Comparison between the backfill bottom reconstruction by using standard lithostratigraphic correlation and that estimated by using OK-ED
RESULTSBackfill thickness (m)
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
Comparison between the backfill thickness reconstructed by using litostratigraphic correlation (line filled polygons) (Funiciello, 1995) and by using OK-ED
RESULTSBackfill thickness (m)
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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.
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
FUTURE WORK
1. 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
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
THANK YOU FOR THE ATTENTION!!
Dr. Giancarlo Ciotoli, [email protected]
Dr. Francesco Stigliano, [email protected]
The 11th International Conference on Computational Science and Applications (ICCSA 2011) June 20-23, 2011, University of Cantabria, Santander, Spain
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.