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

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 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

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


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


RESULTSThe 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)

RESULTSThe variogram


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.


RESULTSBackfill bottom (m asl)


Comparison between the backfill bottom reconstruction by using standard lithostratigraphic correlation and that estimated by using OK-ED

RESULTSBackfill thickness (m)


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

RESULTSBackfill 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

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


THANK YOU FOR THE ATTENTION!!

Dr. Giancarlo Ciotoli, [email protected]

Dr. Francesco Stigliano, [email protected]


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.

Technology

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