Acquisition and processing requirements for high quality 3D by xlt14877

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									         Acquisition and processing requirements for high quality 3D
                   reconstructions from GPR investigations
                        Maurizio Lualdi, Luigi Zanzi, Luigia Binda

                                Politecnico di Milano, Italy


                                         Abstract
         In the last few years, the GPR technology has been improved to meet the
requirements needed for radar investigations on building elements. Many manufacturers have
developed new high frequency shielded antennas to ensure very high resolution images. 3D
GPR reconstructions are particularly useful for the diagnostic investigation of historic
buildings. They can be applied to find details or inclusions inside a structural element (wall,
pillar, roof or floor) when the complex geometry cannot be understood by standard 2D GPR
investigations. The detection of voids, metal or timber elements, the location of timber beams
and the detail of their connection to the bearing wall, are examples of problems that can find
a reliable answer provided that the GPR technique is applied in 3D mode.
         In order to carry out a successful 3D GPR survey it is necessary to acquire a dense
grid of GPR traces. Accuracy in antenna position and orientation is very important for a
successful application of a 3D migration software to produce images that can be directly
interpreted by the end-users. An array of antennas helps to ensure a regular spacing in the
cross-line direction of the survey but the array is heavy and large so that it might be
inappropriate to investigate vertical elements like walls, pillars and columns and difficult to
adapt to the shape of the surface decorations especially in historical buildings.
         For these reasons, an important objective of the ONSITEFORMASONRY project
(EESD project EVK4-2001-00091) is the development of a new positioning system for 3D
GPR acquisitions executed with a small high frequency antenna. The requirements to reach
the goal are discussed referring to examples that demonstrate the feasibility and cost-
effectiveness of 3D experiments when a proper positioning system is available. Position
accuracy and spatial sampling requirements are closely related and the acquisition time can
be significantly reduced when the positioning system ensures a high level of accuracy (i.e.,
few mm). Accurate acquisitions are an essential pre-condition for a reliable application of a
3D data focusing program. A dedicated focusing program is discussed with special attention
to some important aspects related with the antenna configuration and the near-field condition
of the radar experiments on building elements.




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                                        Introduction
        The diffusion of 3D radar investigations is still limited by the slow development of
dedicated equipment and acquisition tools. The technology available on the market is not
advanced enough to make 3D experiments fast, accurate and cost effective.
        The most serious problems concern the acquisition technique, specifically the system
for monitoring the antenna position, and the processing software. Antenna positioning is a
critical issue because a 3D effective reconstruction needs data collected with a position
accuracy of about λ/20, i.e., about half a centimeter when a 1GHz antenna is used. The
solutions available on the market for monitoring the antenna position along a profile (1D
positioning) are effective and easy-to-use. On the contrary, no effective solutions exist for
monitoring the antenna position when a flat surface is surveyed (2D positioning). At present,
the suppliers of high frequency antennas do only propose the use of thin plastic pads marked
with the lines of the planned parallel profiles. Accuracy in preserving the correct position and
orientation of the antenna strongly depends on the skill and care of the operator. As a result,
the quality in positioning is not ensured and the acquisition time is normally inversely
proportional to the spatial accuracy of the collected data. A correct antenna orientation is as
much important as a correct antenna position since radar antennas are polarized and directive
so that the energy reflected or diffracted by the targets depends on the respective antenna-
target orientation. When the correct orientation is not ensured the data suffer from
fluctuations of the signal intensity that might reduce the reliability of the final data
interpretation (Reppert et al., 2002). A few examples of feasibility studies for the design of
new positioning systems are documented in the scientific literature. One of the most
advanced is discussed by Doerksen (2002) and consists of an optical mouse mounted on one
side of the antenna. It is an interesting and applicable technique but it still suffers from the
problem that it cannot ensure a regular spatial distribution of the collected data and it does not
control the antenna orientation unless two mouse are used.
        Another important issue is the 3D processing software; in fact the benefits of a good
migration program and of a good 3D graphic software can be very much appreciated by the
end users. Commercial software for radar processing is evolving but only in the last few years
the suppliers have been distributing products for 3D processing and the quality of these
products has not reached the required level yet. Specifically, some software products present
good performances in terms of 3D graphics but they are not advanced enough concerning the
migration operation. The migration is a specific processing operation aimed to represent the
scattering targets honoring their position and geometry, within the resolution limits given by
the signal frequency. It is a computationally expensive operation and in the same time it is a
delicate task since the quality of the final result strongly depends on a balanced selection of
some critical parameters. As a result, a good 3D software program must be computationally
efficient but also flexible enough to offer the operator the necessary options for optimizing
the most critical parameters.


                              Potential of 3D experiments
        The 3D reconstructions of the investigated element are especially useful when the
issue is a morphological problem such as the detection of targets that consist of a single or a
number of scattering objects.
        For instance, the existence of timber, metal or concrete beams or the existence of
metal chains or tie rods, i.e., the existence of linear elements that are observed as diffraction
hyperbolas in the plane of the radar profiles orthogonal to the direction of these elements, can


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be effectively documented by a 3D reconstruction from which the end-user can easily extract
quantitative results such as position, depth and also dimensions provided that the wavelength
is short enough compared to the target size.
        Example N.1. – One of the most puzzling problems is the detection of the supporting
structure in timber floors when it is hidden on the extrados by a pavement and on the intrados
by a ceiling. Fig.1 shows the 3D reconstruction of the secondary timber elements supported
by the principal beam in a timber floor. The investigation was carried out with a 1GHz
antenna by surveying the area with parallel profiles orthogonal to the beam direction.
        Example N.2. – Another case that proves the effectiveness of 3D investigations is
shown in fig.2 and 3. The application was aimed to validate the assumption supposed by the
expert about the origin of the fresco shown in the picture. According to the experts, this
fresco is older than the 16th century church where it is now located. The wall supporting the
fresco was cut out and completely moved to its present position after the preparation of an
appropriate niche. At those times, this was a quite diffused habit. In order to preserve its
integrity during the transportation, the cut wall with the fresco was confined by a timber
frame that was removed later before fixing the perimeter of the fresco with a new plaster.
Sometimes, the timber frame or some elements of it were left in the niche and hidden behind
the plaster. The result of the 3D reconstruction (fig.3), obtained by combining the radar data
collected along orthogonal profiles as indicated in fig.2, shows an image parallel to the fresco
surface but taken at a depth of about 10cm. A red, i.e., scattering, target can be detected at the
base of the fresco. With high probability, it is the base of the timber frame that was left into
the niche. On the other 3 sides such an intense radar signal is not observed but only a weak
energy return that can be associated with the discontinuity between the older fresco wall and
the masonry wall of the church. It is possible to conclude that the assumption of the art
experts was very reliable and that only the base of the timber frame was not removed before
replacing the plaster.




Fig. 1. 3D reconstruction of some small    Fig. 2. Fresco assumed to belong      Fig. 3. Vertical section extracted
beams belonging to the beam structure of   to an older church. The arrows        from the volume of the migrated
a timber floor.                            indicate the direction of the radar   radar data at a distance of 10cm
                                           profile collected with a 1GHz         from the surface.
                                           antenna.

       Example N.3. – One of the most difficult problem for the engineer who has to study
the safety of existing timber floors, is the knowledge of the type and dimension of the
connection beam-wall. Only in the case of some internal partition walls which do not
continue up to the last floor, the beam-wall connection can be studied from the top by
surveying the upper floor. In all the other cases this information can usually be collected only


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through destructive investigation inside the wall or by using the georadar from the external
side of the bearing wall. This is another example of a problem that is difficult to solve with
2D radar surveys whereas it can be brilliantly solved with a 3D reconstruction as presented in
fig.4 and fig.5. Fig.4 shows a laboratory specimen that was built to simulate this situation.
The timber beam penetrates into the brick wall down to a distance from the opposite side of
about 15cm. The radar experiment was performed on the side opposite to the beam by
executing a dense set of vertical parallel profiles. Fig.5 shows 6 sections extracted at
increasing distances measured from the investigation side. Around a distance of 15cm we
observe the highest intensity of the radar signal reflected by the extremity of the timber beam
inserted into the masonry specimen. According to this experiment, the accuracy in measuring
the beam position with a 1GHz antenna is in the order of two centimeters.
        All the above examples relate to images produced from radar data collected with high
accuracy and processed with software programs specifically designed for 3D reconstructions.
The quality of the reconstructions demonstrates the potential of this methodology.
Nevertheless, the success of a method is not only associated with the quality of the results but
also with the cost-benefit ratio compared to those offered by the most conventional methods.
This is the motivation for technological improvements in the direction of facilitating the
acquisition of accurate 3D data (problem of the positioning system) and in the direction of
improving the quality of the 3D software programs.




Fig. 4. Laboratory specimen used to validate the     Fig. 5. Radar sections parallel to the investigation surface
applicability of radar inspections to measure the    extracted at increasing depths. The highest intensity of the
penetration of the timber beam, into the masonry     reflection produced by the extremity of the beam is
wall. The data were collected on the side opposite   observed around 15cm which corresponds to the correct
to the beam.                                         estimate.



                               Requirements for 3D acquisitions

        The main requirement that must be fulfilled to collect a dataset that can be
successfully transformed into a realistic 3D reconstruction is expressed by the Nyquist
Theorem. According to Nyquist, the area must be surveyed with a density of the measuring
points sufficient to prevent spatial aliasing problems. When this requirement is not satisfied



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we can expect a severe degradation of the migration results and a decrease of resolution. In
principle, the Nyquist requirement is

                                           λ
                                    ∆x ≤                   (1)
                                           4

where ∆x is the maximum distance between two measuring points and λ is the wavelength
of the highest frequency in the antenna band.
        As an example, equation (1) requires that the trace spacing for a medium with a
velocity of 7.5 cm/ns surveyed with a frequency band extending from 500 MHz to 1500 MHz
is lower than 1.25 cm. As a result, a good positioning system for a high frequency antenna
should be able to ensure a trace spacing in the order of 1 cm and with a relative accuracy that
must be a small fraction of this spacing. If we accept a relative accuracy of 1%, the absolute
accuracy of the positioning system in a 1 m2 area is about 1 cm.
        To validate experimentally the spatial sampling requirement, we planned a 3D
experiment with a 1GHz antenna over a reinforced concrete floor. The acquisition was
performed manually being extremely careful in preserving the position accuracy and the
correct antenna orientation. The data were collected with a very dense spatial sampling and
then were progressively decimated to explore the spacing that should not be exceeded to
preserve the quality of the final result.
        In fig.6, a vertical section of the collected data volume after progressive decimation
can be observed. The corresponding sections obtained after the application of the processing
sequence, including migration, is shown in fig.7. The example shows that the spatial
sampling can be drastically reduced without affecting the quality of the result. This is true up
to a spacing of about 2.76 cm that is an interval much longer than the interval required by the
Nyquist theorem as discussed above. Actually, this result is not in contradiction with the
Nyquist theory since the requirement expressed by equation (1) is the most restrictive
requirement corresponding to the most unfavourable situation that occurs when a very near-
surface target is illuminated laterally with a surface wave. In such a case the diffraction curve
that appears in the radar section, under the assumption of a constant velocity medium and a
monostatic system, consists of two symmetric dip lines departing from the surface in the
position of the target (fig.8). Instead, the diffraction curves for deeper targets are hyperbolas
that asymptotically tend to the lines of the surface target. The Nyquist theory requires that the
delay of the reflection time between two subsequent measuring points is lower than half a
period of the wave. By applying this condition to a generic point belonging to a diffraction
hyperbola we get the following equation (fig.8)

                                               1
                                    ∆x ≤                   (2)
                                              dt
                                           2f
                                              dx

where f is the wave frequency. Of course, equation (2) degenerates into equation (1) when the
target depth is zero. In real experiments the diffraction hyperbolas are observed with a limited
aperture because of absorption and antenna directivity. Thus, we understand from fig.8 that
when we observe buried targets, condition (1) can be relaxed into a less restrictive condition
given by equation (2) to be applied where the diffraction dip is higher, i.e., at the limit of the
diffraction aperture.
        By applying equation (2) to the data of fig.6 we come to a maximum trace spacing of
about 2.5cm that basically corresponds to the experimental conclusions documented by fig.7



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where we start to observe some degradations only when we move from a spacing of 2.76 cm
to a spacing of 3.68 cm. The degradation consists of a minor decrease of resolution although
all the rebars are still clearly visible. To observe more severe degradations of the final image
we have to increase the interval up to 5.52 cm. If we look at the subsampled raw data that
produced these results (fig.6), it is amazing to see how the quality of the final image is stable
in comparison with the apparent severe degradations observed on the raw data. This is a very
interesting conclusion that comes from the discussed example: provided that the data are
collected with a high position and orientation accuracy, there is no need to oversample the
data, i.e., the spatial sampling in both X and Y directions can be set up according to the
nominal values required by the Nyquist theorem. This means that a 3D 1GHz survey over a 1
square meter concrete slab can be successfully executed with only 40 parallel profiles (80 if
both X and Y directions must be surveyed). Moreover, the test has demonstrated that 25
profiles for each direction, i.e., a spacing of 4 cm, although a little beyond the theoretical
limit, are enough to preserve a quality and a resolution sufficient to solve most of the
practical applications so that the acquisition time can be further reduced. This tolerance
regarding the Nyquist limit is a consequence of the fact that the final image is often
insensitive to the highest frequency components of the nominal antenna spectrum since these
components are usually received with very low energy because of absorption and because of
the downloading effect induced by antenna-ground coupling.




Fig. 6. Raw data belonging to a radar profile orthogonal to the concrete rebars after
progressive spatial decimation.




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             Fig. 7. Migrated sections obtained from the decimated data of fig.6.

        Actually, to extend the conclusions derived from fig.7 to the orthogonal direction, i.e.,
to the distance between parallel profiles, we should consider a more general situation where
the rebars are not orthogonal to the profiles. Thus, the experiment was repeated by rotating
45o the profile direction with respect to the rebar orientation. The final result validates the
above conclusions (fig.9).
        Summarizing, the result from the laboratory experiment discussed above is that the
setup of a 3D acquisition performed with a good positioning system, i.e., a positioning system
that can ensure an accuracy of 1 cm in a 1 m2 area and can preserve the correct orientation of
the antenna, can be designed according to the lowest spatial sampling intervals required by
the theory. As an example, a 1GHz antenna survey can be designed on a grid size ranging
from 2.5 to 5 cm depending on the medium velocity and absorption. This means that half an
hour can be enough to survey a 1 m2 area, provided that the positioning tool does not require
a complex and long installation. If these requirements are satisfied, 3D surveys are successful
and cost effective. On the contrary, if the accuracy of the data position and the correct
orientation of the antenna are not ensured, 3D surveys are not going to be rewarding and the
benefit of the 3D migration of the data will be lost due to traveltime and amplitude effects
induced by position and orientation errors respectively (Groenenboom et al., 2001; Reppert et
al., 2002).




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Fig. 8. Diffraction curves expected on a radar profile executed with a monostatic system for
scattering targets buried at different depths. To prevent spatial aliasing, the Nyquist condition
must be applied considering the maximum slope of the diffraction curve as actually observed
in the real experiment where the diffraction aperture is limited by absorption and antenna
directivity.




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Fig. 9. Horizontal section extracted from the migrated volumes produced from data collected
along profiles oriented 45o with respect to the reinforcement mesh. With a spacing of 3.98 cm
between parallel profiles the resolution of the experiment is still preserved and only minor
degradations are observed.

        According to the above results, data density can be reduced to the minimum if the
positioning systems is accurate. But an additional problem must be solved: how to ensure a
regular distribution of the measurement points. In other words, there are probably more than
one good solutions that can fulfill the accuracy requirement but that practically does not
allow a reduction of data density during acquisition since they do not force the antenna to
follow a regular path. As an example, an optical mouse system (Doerksen, 2002) or any other
system where the movement of the antenna is monitored but is totally free, is not a good
candidate to solve simultaneously all the problems. The antenna must be triggered during the
survey. Now, if triggering is time-controlled, the data volume will tend to be oversized to
ensure that the spatial sampling requirement is satisfied even when the antenna is running
faster. On the contrary, if triggering is space-controlled by the positioning system itself, in
principle, the data volume can be kept to a minimum. Anyway, in both cases, a practical
solution must be found to drive the operator in order to visit all the grid points of the survey
area.
        In conclusions, the optimal solution is a system that can ensure simultaneously
position accuracy, constant antenna orientation and full coverage of a regular grid of
measurement points. With such a system, the final quality is preserved and acquisition time,
memory allocation and processing time are minimized.

                    Hints for improving the 3D reconstructions

        In principle, 3D reconstructions can be produced by assembling radar profiles
processed with a 2D processing software. Nevertheless, there are some processing steps that
are more rewarding when they are applied in 3D mode.
        An example is the subtraction of the background noise that is usually performed by
subtracting the average trace. By implementing the algorithm in 3D mode, the estimate of the
background signal is statistically more reliable and the final result is more effective.
        Another important operation that can take benefit from a 3D approach is the focusing
algorithm. A good solution to produce a 3D focusing code efficient and sufficiently flexible


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consists of the 2D-2step method originally proposed by Gibson et al. (1983) to process
seismic data for geophysical exploration. This algorithm is based on two subsequent
bidimensional migrations executed along orthogonal directions and is quite attractive because
it dramatically reduces the computation time. Gibson et al. demonstrated that in a
homogeneous medium this approach is exactly equivalent to a real 3D migration. In a non
homogeneous medium the focusing operator is approximated but the deviation from the real
3D operator is of a negligible order compared to the inaccuracy in the definition of the
operator resulting from the poor resolution normally experienced in velocity estimation.
        The algorithm, as proposed by Gibson et al., is applicable to monostatic radar system.
Anyway, it can be extended to GPR bistatic systems (Valle et al., 2000), provided that the
acquisitions are executed with a constant azimuth of the TX-RX axis and that the first 2D
migration step is performed in this direction. Assuming that this direction is the y direction
and that a scattering target is located in x=0, y=0, z=Z, as shown in fig.10, then the
diffraction surface observed by the bistatic system will have equation

                                x 2 ( y − a)                   x 2 ( y + a)
                           2                  2           2                   2
                      T0                             T0
                t=             + 2 +         +                + 2 +                        (3)
                      2         v       v2           2         v       v2

where To=2Z/v, v being the velocity of the homogeneous medium. This diffraction surface
can be migrated in the target position by migrating first in the y direction, according to

                                         a 2 (y − a)                     a 2 (y + a)
                                    2                2              2                  2
                               t0                              t0
                     t=                 − 2 +        +                  − 2 +
                               2         v      v2             2         v      v2

where t is the time in the original data volume and t0 the time in the partially migrated
volume, and then in the x direction, according to

                                            2
                                           t0 v 2
                                                  = Z 2 + a2 + x2 .
                                             4

        Whatever the focusing operator is, an approximate description of the antenna footprint
should be always included to limit the migration aperture. This helps to reduce the clutter and
to prevent migration artifacts especially for near-surface targets. A practical and convenient
approach is to calibrate the operator aperture directly on the data by analyzing the lateral
extension of the target diffractions. The option of defining a different aperture for the in-line
and for the cross-line directions can be very useful for focusing linear targets (beams, tie-
rods, etc.) and near-surface targets since the diffractions produced by these objects do not
present a circular symmetry. This is quite obvious for linear targets that can be efficiently
migrated by drastically reducing the aperture in the direction parallel to the target.




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                          y          Tx
                                             scanner in (x,y,0)
                                 a
                                     Rx
                                                                x
                       target in (0,0,Z)
           Fig. 10. Map view of a 3D bistatic experiment over a scattering target.

        As a consequence, a good practice for producing optimal reconstructions of linear
targets distributed along orthogonal directions (crossing beams, reinforcement mesh, etc.)
consists of separately focusing the 3D data collected along the orthogonal directions using an
unbalanced operator. The sum of the resulting volumes will produce a 3D reconstruction of
the targets much more effective than the result achievable by summing the data before the 3D
migration.
        Fig.11 shows a result obtained with this procedure: the target was again a
reinforcement mesh in a concrete floor. The reconstruction is quite effective, although the
dimension of the rebars is overestimated for obvious resolution limits that can be removed
only by using higher radar frequencies.




Fig. 11. 3D reconstructions of a reinforcement mesh in a concrete floor. The image on the left
was obtained by sectioning the 3D focused volume while the image on the right is an iso-
intensity picture of the same volume. Of course, the dimension of the rebars is overestimated
because of resolution limits that can be removed only by using higher radar frequencies.

        For near-surface targets, including scattering points, the asymmetric shape of the
diffraction depends on the antenna separation, on the finite dimensions of the antennas and on
their polarization. As an example, fig.12 compares the XT section with the YT section
intersecting the diffraction produced by a cylindrical target embedded in a homogeneous
medium at about 10 cm from the surface.




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        The comparison demonstrates the asymmetry of the diffraction surface in the
orthogonal directions. The diffraction curve predicted by equation (3) is also overimposed to
show the deviation of the analytical description from the real diffraction surface as a result of
antenna dimension and polarization. This suggests that an advanced software for focusing
targets observed in the near-field should also include an appropriate correction of the
diffraction equation to reduce these deviations.




Fig. 12. Radar sections intersecting the diffraction produced by a cylindrical target embedded
in a homogeneous medium at about 10 cm from the surface. Note the asymmetry of the XT
(left) and YT (right) sections. The black line is the analytical description of the diffraction
according to equation (3). The deviation from the real diffraction is a result of antenna
dimension and polarization.



                                        Conclusions

        The application of 3D reconstruction to some typical cases found in the preservation
of Cultural Heritage, shows the importance of 3D for the solution of difficult problems,
which sometimes were up to now approached only by destructive investigation.
        The GPR 3D investigation seems to be successful particularly in the detection of the
hidden structure of timber floors or roofs.
        To cut the costs of 3D acquisitions and to ensure the quality of the results, new
solutions are needed for the problem of antenna positioning. The positioning system should
ensure simultaneously position accuracy (within 1 cm in a 1 m2 area), constant antenna
orientation and full coverage of a regular grid of measurement points. With such a system,
the final quality is preserved and acquisition time, memory allocation and processing time
can be minimized.




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        An advanced software for 3D data focusing is also an essential tool to make 3D
reconstructions effective and rewarding. The software should be based on an efficient scheme such
as the 2D-2step algorithm to reduce the computation time. It must be flexible enough to accept a
different aperture for the in-line and for the cross-line directions. Finally, the focusing operator
should also include an appropriate correction of the diffraction equation to take into account the
near-field effects associated with the antenna dimension and polarization.




                                           References
Doerksen, K., 2002, Improved optical positioning for GPR based structure mapping, Proceedings
    9th Int. Conf. on Ground Penetrating Radar GPR2002, April 29 - May 2, Santa Barbara,
    California.
Gibson, B., Larner, K., Levin, S., 1983, Efficient 3-D migration in two steps, Geophysical
    Prospecting, 31, pp.1-33.
Groenenboom, J., Van Der Kruk, J., Zeeman, J.H., 2001, 3D GPR data and the influence of
    positioning errors on image quality, Extended Abstracts of the 63rd Meeting of the European
    Association of Geoscientists and Engineers, June 11–15, Amsterdam.
Reppert, P.M., Roffman, R.A., Dale Morgan, F., 2002, The effects of antenna orientation on GPR
    data quality, Proceedings of the Symposium on the Application of Geophysics to
    Environmental & Engineering Problems SAGEEP 2002, February 10-14, Las Vegas.
Valle, S., Zanzi, L., Lentz, H., Braun, H.M., 2000, Very high resolution radar imaging with a
    stepped frequency system, Proceedings 8th Int. Conf. on Ground Penetrating Radar GPR2000,
    May 23-26, Gold Coast, Australia, pp.464-470.




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