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Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and
                 Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                      Vol. 2, Issue 4, July-August 2012, pp.1036-1039
   The Use of Ground Penetrating Radar for the Detection and
Study of a Buried Marble and in Situ Location of Possible Cracks
                               Ahmed Faize*, Abdellah Driouach*
                        *Department of Electromagnetism, University of Tetouan Morocco



 ABSTRACT                                                  data processing must be performed. Forward
This work described the use of two methods to              modeling allows us to experiment with and predict
detect possible abnormalities, debris and cracks           the way in which variations in subsurface material
inside block of marble. The first method was               properties (and the related variation in dielectric
based on the direct detection of block of marble           properties) are captured in GPR data.
buried at depth of 0.2 m using Ground                          GPR is used for the exploration of the subsoil in
Penetrating Radar (GPR). The second method                 several research fields such as the detection of
was based on the use of simulation software                landmines [5], geology [6], civil engineering [7],
named GprMax2D for the same block but at                   glaciology [8, 9] and archeology [10]. It was also
depth of 0.5 m. Our results showed that GPR                successfully applied to 2D imaging of cracks and
technology combined with adequate simulation               fractures in resistive soils such as gneiss [11].
software may be used in the field of exploitation              Elsewhere, the use of GPR has been suggested
of marble in specialized careers. Indeed, they             for the exploration of some careers of granite [12].
allow in situ distinguishing between usable                GPR has been previously used to map fractures in
blocks of marble with higher quality and blocks            non buried marble quarry [13, 14]. However, to our
with fractures or leftover debris in their interior.       knowledge, such work has never been done on
                                                           buried marble.
Keywords    - Ground          Penetrating     Radar;           In this work we extend the use of GPR for the
Simulation; Marble                                         detection a buried blocks of marble. In fact, the
                                                           marble may present some defects such as cracks
I. INTRODUCTION                                            and non desired internal breaks, resulting in debris
    Ground penetrating radar (GPR) is a similar            of marble or plaque of lower quality.
technique to the seismic imagery reflection [1]. It            The objective of this work is i) to try to detect a
uses electromagnetic waves that propagate and              bloc of marble that was buried by extrapolating
refract in heterogeneous medium in order to scan, to       structural data obtained from the surface of bloc of
localize and to identify quantitative variations           marble, and ii) to detect the depth and the
within electric and magnetic proprieties of the soil.      continuity of cracks within this bloc. To do so, we,
GPR frequencies usually range from 10 MHz to 2.6           first, carried out a GPR survey on buried real bloc
GHz. When using lower frequency antenna                    of marble, followed by a simulation of GPR signals
(between 10 and 100 MHz) investigated depth will           on the some bloc buried inside a dielectric medium,
be higher (more than 10 m), however resolution             which is a simulated soil (𝜀 𝑟 = 3, 𝜎 =
remains lower [2].                                         0.0001 𝑆/𝑚 ). The simulation is performed using
    The treatment of geophysical data is based on          GprMax software, whose calculations are based on
numeric modeling of signals captured by the radar.         the finite difference time domain (FDTD) [15].
Within electromagnetic field numeric modeling
appeared at the beginning of the seventies [3] and         II. OPERATING PRINCIPLE OF THE
coincided with the introduction of powerful and            GPR
accessible microprocessors that allow realization of           GPR is a nondestructive method that has been
personal calculation within a short time [4]. It is        proved for internal imaging of several types of
possible to model the physical proprieties                 geological materials such as granite and engineered
implicated in any geophysical technique by using           materials such as concrete construction and other
either forward modeling or inverse modeling.               buried structures (pipes, cables ...). The signal can
Forward modeling takes as model subsoil that               penetrate into the soil and into material buried
includes all of its appropriate physical proprieties       within the soil, allowing its detection as well as its
and uses theoretical equations in order to simulate        depth below the ground surface.
the response of the receiver. This, in turn, will              The operating principles of various existing
determine a given technique to measure through the         GPR radar are based on the same principle: a
model. However, reverse modeling uses data                 transmitting antenna is placed in contact with the
collected from the field in order to create a model        ground, emitting short pulses towards the ground
of subsoil that will fit better with the original data.    (Figure 1 (b) Tx). The electromagnetic wave
To obtain reliable data, a number of measures and          generated propagates inside the ground that is


                                                                                                 1036 | P a g e
Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and
                 Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                      Vol. 2, Issue 4, July-August 2012, pp.1036-1039
considered as a dielectric medium. If an obstacle      III. RESULT
(Marble in our case) is encountered, a part of the       A. Experimental part
signal emitted by the antenna of GPR returns to the      The blocks of marble used, has for dimension: 1.3
soil surface (reflected wave) and then detected by     m length and 1 m width (Fig. 2). This block is
the receiving antenna (Figure 1 (b) Rx). This          buried at a depth of 0.2 m. For measurements, 24
recovered wave reflects a trace of subsoil at a        profiles of 1 m of length (in the x direction), 30
specific point and at given time. As the user moves    profiles of 1.4 m of length (y direction) and 0.2 m
the GPR radar above the studied field, new signals     spacing between two profiles, were taken. Each
are transmitted and reflected signals are again        emission and reflection signal is recorded during a
recovered at the receiving antenna. This process       period of 32 ns.
(sending and receiving generated signals) leads to       The position of the block of the marble is
the acquisition of a set of traces of soil, as         revealed, with a precision, by the radargram
numerical data, following a straight prospecting       obtained by the GPR (Fig. 3).A radargram (Fig.3
direction thereby establishing what it is called a     and Fig.4) is typically carried out using the
radargram or a B-scan (Figure 1 (c)) of the studied    displacement of a 2.3 GHz antenna. Arrows
medium. The treatment of the data set is provided      numbered 1, in Figure 2, indicate the position of
by specialized software that allows the obtaining of   cracks in the studied marble block. The pseudo-
hyperbola (Figure 1 (c)). Note that the hyperbola      horizontal events seen in figure 3 indicate the
observed in this figure, is an extremely important     positions of upper and lower edges of the block
index, since it gives, suitable information about      (The arrows number 2). We observed a difference
localization of buried objects.                        of signal amplitudes, given by the GPR. This
                                                       difference is due to the variation of relative
                                                       permittivity values. The hyperbolas indicated by
                                                       arrow 3 in Figure 4 show the diffraction of the
                                                       incident waves on the corners of blocks of marble.
                                                       These waves were diffracted by constructive
                                                       interference, giving rise to two diffraction
                                                       hyperbolas (commented on above) in each of the
                                                       horizontal edges of the rectangular surface. The
                                                       discontinuity observed in the upper of block,
                                                       indicates the presence of breaks at this level (Fig. 4,
                                                       arrow 4).




Fig.1: Schematic explanation of the principle of
                   the GPR.

     Before interpretation, GPR processing filters
were used in order to reduce clutter or any
unwanted noise in the raw-data, to enhance
extraction of information from received signals and
to produce an image of the subsurface with all the
features and/or targets of interest, which makes          Fig.2: Photo of block of marble that will be
GPR data interpretation easier. Each radargram was              buried and studied by the GPR
filtered using Reflexw V4.5.0 software [16] by
applying the processing sequences described below.

    1. Dewow filtering (1.2 ns)
    2. Bandpass frequency (380/700/4600/5200)
    3. Energy decay (0.45)
    4. Background removal based on all traces




                                                                                            1037 | P a g e
Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and
                   Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                        Vol. 2, Issue 4, July-August 2012, pp.1036-1039




 Fig.3: Radargram of block of marble in line 10
                along the x axis                          Fig.5: B scan of GPR signals obtained using
                                                          GprMax2D for model composed of Marble
                                                                 (𝜺 𝒓 = 𝟓. 𝟓, 𝝈 = 𝟎. 𝟎𝟐𝟓𝟓 𝑺/𝒎 )

                                                        IV. CONCLUSION
                                                            Using GPR technology combined with adequate
                                                        simulation software is very useful in the field of
                                                        exploitation of marble in specialized careers.
                                                        Indeed, it allows obtaining a detailed picture of the
                                                        subsoil, allowing to distinguish, in a quick, cheap
                                                        and effective manner, the blocks of marble with
                                                        higher quality and without defects (therefore
                                                        usable) from blocks which fractures or rests of
                                                        fragments in their inside.

                                                                         REFERENCES
                                                        [1]   Jan C. Francké., 2003. Applications of GPR
  Fig.4: Radargram of block of marble in line 2               For Surface Mining. 2nd International
                along the y axis                              Workshop on Advanced GPR, 14-16 May,
                                                              Dellft, The Netherlands.
  A. Treatment by GprMax
    Figure 5 (a) shows a geometric model of marble      [2]   Noon, D., A., Stickley G., F., and Longstaff,
used for simulation of radar signals reflected by a           D.,    1998.    A     frequency-independent
simulator (GprMax). This block, with dielectric               characterization of GPR penetration and
characteristic (𝜀 𝑟 = 5.5, 𝜎 = 0.0255 𝑆/𝑚 ), is               resolution performance, Journal of Applied
buried, this time at 0.5 m depth. The emission and            Geophysics, 40, 127- 137.
reflection of the simulated signal is recorded for
period of time of 35 ns using an excitation source of   [3]   Chen, H.W., and Tai-Min H., 1998. “Finite
Ricker type for a central frequency of 2.3 GHz.               Difference Time Domain Simulation of GPR
This frequency corresponds to wave length directed            Data”. Journal of Applied Geophysics, 40,
                                                c
in the simulated medium [15]: λ =                  =          139-163.
                                              3f εr
  3.10 8                                                [4]   Ceruzzi Paule E., 1998 A History of Modern
               = 0.025 m. The spatial increment: ∆x =         Computing History of Computing. MIT
6.9.10 9 . 3
                 λ                                            Press, Cambridge, Massachusetts.
∆y = ∆l = = 0.0025 m. The total simulated
            10
                                                        [5]   M, Sato, Y, Hamada, X, Feng, F. Kong, Z.
length is 2.0 m x 1.6 m, which corresponds to 800 x
                                                              Zeng and G. Fang. 2004. GPR using an array
640 cells ((2.0/∆x) x (1.6/∆x)).
                                                              antenna for landmine detection. Near Surface
    Figure 5 (b) shows the simulation result of this
                                                              Geophysics. 3-9.
model. In this figure different hyperbolas can be
                                                        [6]   Gu, Z.W., 1994. The Application of Ground
distinguished: those noted 1, denote the depth
                                                              Penetrating     Radar     to     Geological
position of the upper edge of the block, those
                                                              Investigation on Ground in Cold Regions,
numbered 2, indicate the position of cracks. Figure
                                                              Journal of Glaciology and Geocryology, 16,
5 (b) shows a sub horizontal crack numbered 3.
                                                              283-289.




                                                                                            1038 | P a g e
Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and
                   Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                        Vol. 2, Issue 4, July-August 2012, pp.1036-1039
[7]    Ulriksen, C.P.F., 1982, Application of
       impulse radar to civil engineering. PhD
       Thesis, Lund University of Technology,
       Lund, Sweden.
[8]    Navarro, F. J., Lapazaran, J. J., Machio, F.
       Martin C., and Otero, J., 2009. On the Use of
       GPR Energetic Reflection coefficients in
       Glaciological Applications, Geophysical
       Research, 11 EGU2009-9804, EGU General
       Assembly.
[9]    Woodward, J., and Burke, M.J. 2007.
       Applications of Ground-Penetrating Radar to
       Glacial and Frozen Materials, Journal of
       environmental and engineering geophysics,
       12, 69-85, March 2007.
[10]   Leckebusch, J. 2003. Ground-Penetrating
       Radar: A Modern Three-dimensional
       Prospection      Method.       Archaeological
       Prospection, 10, 213-240.
[11]    Grasmueck, M. 1996.           3-D Ground-
       penetrating radar applied to fracture imaging
       in gneiss: Geophysics, 61, 1050-1064.
[12]   Xiaojian, Y., and Haizhong, Y., 1997. The
       Applications of GPR to Civil Engineering in
       China, Shenzhen Dasheng Advanced Science
       & Technique Engineering Co., Ltd.
[13]    Sambuelli, L., and Calzoni, C., 2010.
       Estimation of thin fracture aperture in a
       marble block by GPR sounding. Bollettino di
       Geophysica Teorica e Applicata, 51, 239-
       252.
[14]   Capizzi, P., and Cosentino, P.L., 2011.
       Electromagnetic         and         ultrasonic
       investigations on a roman marble block.
       Journal of Geophysics and Engineering. 8,
       S117, doi: 10.1088/1742-2132/8/3S11.
[15]   Giannopoulos A, “GprMax2D3D, User’s
       Guide”                    2005:HYPERLINK
       http://www.gprmax.org"http://www.gprmax.
       org
[16]   K.J. Sandmeier, Reflexw Version 4.5.
       Licence number 597 Licenced to centro
       tecnologico del Marmol y la Piedra Spain.




                                                                                 1039 | P a g e

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Ground Penetrating Radar
 

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  • 1. Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1036-1039 The Use of Ground Penetrating Radar for the Detection and Study of a Buried Marble and in Situ Location of Possible Cracks Ahmed Faize*, Abdellah Driouach* *Department of Electromagnetism, University of Tetouan Morocco ABSTRACT data processing must be performed. Forward This work described the use of two methods to modeling allows us to experiment with and predict detect possible abnormalities, debris and cracks the way in which variations in subsurface material inside block of marble. The first method was properties (and the related variation in dielectric based on the direct detection of block of marble properties) are captured in GPR data. buried at depth of 0.2 m using Ground GPR is used for the exploration of the subsoil in Penetrating Radar (GPR). The second method several research fields such as the detection of was based on the use of simulation software landmines [5], geology [6], civil engineering [7], named GprMax2D for the same block but at glaciology [8, 9] and archeology [10]. It was also depth of 0.5 m. Our results showed that GPR successfully applied to 2D imaging of cracks and technology combined with adequate simulation fractures in resistive soils such as gneiss [11]. software may be used in the field of exploitation Elsewhere, the use of GPR has been suggested of marble in specialized careers. Indeed, they for the exploration of some careers of granite [12]. allow in situ distinguishing between usable GPR has been previously used to map fractures in blocks of marble with higher quality and blocks non buried marble quarry [13, 14]. However, to our with fractures or leftover debris in their interior. knowledge, such work has never been done on buried marble. Keywords - Ground Penetrating Radar; In this work we extend the use of GPR for the Simulation; Marble detection a buried blocks of marble. In fact, the marble may present some defects such as cracks I. INTRODUCTION and non desired internal breaks, resulting in debris Ground penetrating radar (GPR) is a similar of marble or plaque of lower quality. technique to the seismic imagery reflection [1]. It The objective of this work is i) to try to detect a uses electromagnetic waves that propagate and bloc of marble that was buried by extrapolating refract in heterogeneous medium in order to scan, to structural data obtained from the surface of bloc of localize and to identify quantitative variations marble, and ii) to detect the depth and the within electric and magnetic proprieties of the soil. continuity of cracks within this bloc. To do so, we, GPR frequencies usually range from 10 MHz to 2.6 first, carried out a GPR survey on buried real bloc GHz. When using lower frequency antenna of marble, followed by a simulation of GPR signals (between 10 and 100 MHz) investigated depth will on the some bloc buried inside a dielectric medium, be higher (more than 10 m), however resolution which is a simulated soil (𝜀 𝑟 = 3, 𝜎 = remains lower [2]. 0.0001 𝑆/𝑚 ). The simulation is performed using The treatment of geophysical data is based on GprMax software, whose calculations are based on numeric modeling of signals captured by the radar. the finite difference time domain (FDTD) [15]. Within electromagnetic field numeric modeling appeared at the beginning of the seventies [3] and II. OPERATING PRINCIPLE OF THE coincided with the introduction of powerful and GPR accessible microprocessors that allow realization of GPR is a nondestructive method that has been personal calculation within a short time [4]. It is proved for internal imaging of several types of possible to model the physical proprieties geological materials such as granite and engineered implicated in any geophysical technique by using materials such as concrete construction and other either forward modeling or inverse modeling. buried structures (pipes, cables ...). The signal can Forward modeling takes as model subsoil that penetrate into the soil and into material buried includes all of its appropriate physical proprieties within the soil, allowing its detection as well as its and uses theoretical equations in order to simulate depth below the ground surface. the response of the receiver. This, in turn, will The operating principles of various existing determine a given technique to measure through the GPR radar are based on the same principle: a model. However, reverse modeling uses data transmitting antenna is placed in contact with the collected from the field in order to create a model ground, emitting short pulses towards the ground of subsoil that will fit better with the original data. (Figure 1 (b) Tx). The electromagnetic wave To obtain reliable data, a number of measures and generated propagates inside the ground that is 1036 | P a g e
  • 2. Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1036-1039 considered as a dielectric medium. If an obstacle III. RESULT (Marble in our case) is encountered, a part of the A. Experimental part signal emitted by the antenna of GPR returns to the The blocks of marble used, has for dimension: 1.3 soil surface (reflected wave) and then detected by m length and 1 m width (Fig. 2). This block is the receiving antenna (Figure 1 (b) Rx). This buried at a depth of 0.2 m. For measurements, 24 recovered wave reflects a trace of subsoil at a profiles of 1 m of length (in the x direction), 30 specific point and at given time. As the user moves profiles of 1.4 m of length (y direction) and 0.2 m the GPR radar above the studied field, new signals spacing between two profiles, were taken. Each are transmitted and reflected signals are again emission and reflection signal is recorded during a recovered at the receiving antenna. This process period of 32 ns. (sending and receiving generated signals) leads to The position of the block of the marble is the acquisition of a set of traces of soil, as revealed, with a precision, by the radargram numerical data, following a straight prospecting obtained by the GPR (Fig. 3).A radargram (Fig.3 direction thereby establishing what it is called a and Fig.4) is typically carried out using the radargram or a B-scan (Figure 1 (c)) of the studied displacement of a 2.3 GHz antenna. Arrows medium. The treatment of the data set is provided numbered 1, in Figure 2, indicate the position of by specialized software that allows the obtaining of cracks in the studied marble block. The pseudo- hyperbola (Figure 1 (c)). Note that the hyperbola horizontal events seen in figure 3 indicate the observed in this figure, is an extremely important positions of upper and lower edges of the block index, since it gives, suitable information about (The arrows number 2). We observed a difference localization of buried objects. of signal amplitudes, given by the GPR. This difference is due to the variation of relative permittivity values. The hyperbolas indicated by arrow 3 in Figure 4 show the diffraction of the incident waves on the corners of blocks of marble. These waves were diffracted by constructive interference, giving rise to two diffraction hyperbolas (commented on above) in each of the horizontal edges of the rectangular surface. The discontinuity observed in the upper of block, indicates the presence of breaks at this level (Fig. 4, arrow 4). Fig.1: Schematic explanation of the principle of the GPR. Before interpretation, GPR processing filters were used in order to reduce clutter or any unwanted noise in the raw-data, to enhance extraction of information from received signals and to produce an image of the subsurface with all the features and/or targets of interest, which makes Fig.2: Photo of block of marble that will be GPR data interpretation easier. Each radargram was buried and studied by the GPR filtered using Reflexw V4.5.0 software [16] by applying the processing sequences described below. 1. Dewow filtering (1.2 ns) 2. Bandpass frequency (380/700/4600/5200) 3. Energy decay (0.45) 4. Background removal based on all traces 1037 | P a g e
  • 3. Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1036-1039 Fig.3: Radargram of block of marble in line 10 along the x axis Fig.5: B scan of GPR signals obtained using GprMax2D for model composed of Marble (𝜺 𝒓 = 𝟓. 𝟓, 𝝈 = 𝟎. 𝟎𝟐𝟓𝟓 𝑺/𝒎 ) IV. CONCLUSION Using GPR technology combined with adequate simulation software is very useful in the field of exploitation of marble in specialized careers. Indeed, it allows obtaining a detailed picture of the subsoil, allowing to distinguish, in a quick, cheap and effective manner, the blocks of marble with higher quality and without defects (therefore usable) from blocks which fractures or rests of fragments in their inside. REFERENCES [1] Jan C. Francké., 2003. Applications of GPR Fig.4: Radargram of block of marble in line 2 For Surface Mining. 2nd International along the y axis Workshop on Advanced GPR, 14-16 May, Dellft, The Netherlands. A. Treatment by GprMax Figure 5 (a) shows a geometric model of marble [2] Noon, D., A., Stickley G., F., and Longstaff, used for simulation of radar signals reflected by a D., 1998. A frequency-independent simulator (GprMax). This block, with dielectric characterization of GPR penetration and characteristic (𝜀 𝑟 = 5.5, 𝜎 = 0.0255 𝑆/𝑚 ), is resolution performance, Journal of Applied buried, this time at 0.5 m depth. The emission and Geophysics, 40, 127- 137. reflection of the simulated signal is recorded for period of time of 35 ns using an excitation source of [3] Chen, H.W., and Tai-Min H., 1998. “Finite Ricker type for a central frequency of 2.3 GHz. Difference Time Domain Simulation of GPR This frequency corresponds to wave length directed Data”. Journal of Applied Geophysics, 40, c in the simulated medium [15]: λ = = 139-163. 3f εr 3.10 8 [4] Ceruzzi Paule E., 1998 A History of Modern = 0.025 m. The spatial increment: ∆x = Computing History of Computing. MIT 6.9.10 9 . 3 λ Press, Cambridge, Massachusetts. ∆y = ∆l = = 0.0025 m. The total simulated 10 [5] M, Sato, Y, Hamada, X, Feng, F. Kong, Z. length is 2.0 m x 1.6 m, which corresponds to 800 x Zeng and G. Fang. 2004. GPR using an array 640 cells ((2.0/∆x) x (1.6/∆x)). antenna for landmine detection. Near Surface Figure 5 (b) shows the simulation result of this Geophysics. 3-9. model. In this figure different hyperbolas can be [6] Gu, Z.W., 1994. The Application of Ground distinguished: those noted 1, denote the depth Penetrating Radar to Geological position of the upper edge of the block, those Investigation on Ground in Cold Regions, numbered 2, indicate the position of cracks. Figure Journal of Glaciology and Geocryology, 16, 5 (b) shows a sub horizontal crack numbered 3. 283-289. 1038 | P a g e
  • 4. Ahmed Faize*, Abdellah Driouach / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1036-1039 [7] Ulriksen, C.P.F., 1982, Application of impulse radar to civil engineering. PhD Thesis, Lund University of Technology, Lund, Sweden. [8] Navarro, F. J., Lapazaran, J. J., Machio, F. Martin C., and Otero, J., 2009. On the Use of GPR Energetic Reflection coefficients in Glaciological Applications, Geophysical Research, 11 EGU2009-9804, EGU General Assembly. [9] Woodward, J., and Burke, M.J. 2007. Applications of Ground-Penetrating Radar to Glacial and Frozen Materials, Journal of environmental and engineering geophysics, 12, 69-85, March 2007. [10] Leckebusch, J. 2003. Ground-Penetrating Radar: A Modern Three-dimensional Prospection Method. Archaeological Prospection, 10, 213-240. [11] Grasmueck, M. 1996. 3-D Ground- penetrating radar applied to fracture imaging in gneiss: Geophysics, 61, 1050-1064. [12] Xiaojian, Y., and Haizhong, Y., 1997. The Applications of GPR to Civil Engineering in China, Shenzhen Dasheng Advanced Science & Technique Engineering Co., Ltd. [13] Sambuelli, L., and Calzoni, C., 2010. Estimation of thin fracture aperture in a marble block by GPR sounding. Bollettino di Geophysica Teorica e Applicata, 51, 239- 252. [14] Capizzi, P., and Cosentino, P.L., 2011. Electromagnetic and ultrasonic investigations on a roman marble block. Journal of Geophysics and Engineering. 8, S117, doi: 10.1088/1742-2132/8/3S11. [15] Giannopoulos A, “GprMax2D3D, User’s Guide” 2005:HYPERLINK http://www.gprmax.org"http://www.gprmax. org [16] K.J. Sandmeier, Reflexw Version 4.5. Licence number 597 Licenced to centro tecnologico del Marmol y la Piedra Spain. 1039 | P a g e